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(* Title: Provers/blast.ML 
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ID: $Id$ 
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory 
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Copyright 1997 University of Cambridge 
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Generic tableau prover with proof reconstruction 

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SKOLEMIZES ReplaceI WRONGLY: allow new vars in prems, or forbid such rules?? 
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Needs explicit instantiation of assumptions? 
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Given the typeargs system, constructor Const could be eliminated, with 
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TConst replaced by a constructor that takes the typargs list as an argument. 

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However, Const is heavily used for logical connectives. 

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Blast_tac is often more powerful than fast_tac, but has some limitations. 
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Blast_tac... 
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* ignores wrappers (addss, addbefore, addafter, addWrapper, ...); 
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this restriction is intrinsic 
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* ignores elimination rules that don't have the correct format 
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(conclusion must be a formula variable) 
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* rules must not require higherorder unification, e.g. apply_type in ZF 
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+ message "Function Var's argument not a bound variable" relates to this 
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* its proof strategy is more general but can actually be slower 
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Known problems: 

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"Recursive" chains of rules can sometimes exclude other unsafe formulae 
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from expansion. This happens because newlycreated formulae always 
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have priority over existing ones. But obviously recursive rules 
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such as transitivity are treated specially to prevent this. Sometimes 
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the formulae get into the wrong order (see WRONG below). 
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Loop detection: before expanding a haz formula, see whether it is a duplicate
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With substition for equalities (hyp_subst_tac): 
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When substitution affects a haz formula or literal, it is moved 
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back to the list of safe formulae. 
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But there's no way of putting it in the right place. A "moved" or 
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"no DETERM" flag would prevent proofs failing here. 
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*) 
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(*Should be a type abbreviation?*) 

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type netpair = (int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net; 

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signature BLAST_DATA = 

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sig 

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type claset 

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val equality_name: string 
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val not_name: string 
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val notE : thm (* [ ~P; P ] ==> R *) 
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val ccontr : thm 
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val contr_tac : int > tactic 
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val dup_intr : thm > thm 
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val hyp_subst_tac : bool ref > int > tactic 
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val claset : unit > claset 
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val rep_cs : (* dependent on classical.ML *) 
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claset > {safeIs: thm list, safeEs: thm list, 
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hazIs: thm list, hazEs: thm list, 
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swrappers: (string * wrapper) list, 
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uwrappers: (string * wrapper) list, 
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safe0_netpair: netpair, safep_netpair: netpair, 
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haz_netpair: netpair, dup_netpair: netpair, xtra_netpair: ContextRules.netpair} 
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val cla_modifiers: (Args.T list > (Method.modifier * Args.T list)) list 
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val cla_meth': (claset > int > tactic) > thm list > Proof.context > Proof.method 
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end; 
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signature BLAST = 

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sig 

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type claset 
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exception TRANS of string (*reports translation errors*) 
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datatype term = 
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Const of string * term list 
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 Skolem of string * term option ref list 
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 Free of string 
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 Var of term option ref 
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 Bound of int 
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 Abs of string*term 
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 $ of term*term; 
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type branch 
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val depth_tac : claset > int > int > tactic 
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val depth_limit : int ref 
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val blast_tac : claset > int > tactic 
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val Blast_tac : int > tactic 
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val setup : theory > theory 
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(*debugging tools*) 
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val stats : bool ref 
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val trace : bool ref 
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val fullTrace : branch list list ref 
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val fromType : (indexname * term) list ref > Term.typ > term 
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val fromTerm : Term.term > term 
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val fromSubgoal : Term.term > term 
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val instVars : term > (unit > unit) 

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val toTerm : int > term > Term.term 
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val readGoal : theory > string > term 
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val tryInThy : theory > int > string > 
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(int>tactic) list * branch list list * (int*int*exn) list 
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val trygl : claset > int > int > 
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(int>tactic) list * branch list list * (int*int*exn) list 
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val Trygl : int > int > 
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(int>tactic) list * branch list list * (int*int*exn) list 
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val normBr : branch > branch 
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end; 
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functor BlastFun(Data: BLAST_DATA) : BLAST = 
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struct 
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type claset = Data.claset; 

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val trace = ref false 
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and stats = ref false; (*for runtime and search statistics*) 
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datatype term = 
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Const of string * term list (*typargs constantas a terms!*) 
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 Skolem of string * term option ref list 
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 Free of string 
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 Var of term option ref 
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 Bound of int 
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 Abs of string*term 
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 op $ of term*term; 
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(** Basic syntactic operations **) 

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fun is_Var (Var _) = true 

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 is_Var _ = false; 

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fun dest_Var (Var x) = x; 

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fun rand (f$x) = x; 

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(* maps (f, [t1,...,tn]) to f(t1,...,tn) *) 

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val list_comb : term * term list > term = Library.foldl (op $); 
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(* maps f(t1,...,tn) to (f, [t1,...,tn]) ; naturally tailrecursive*) 

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fun strip_comb u : term * term list = 
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let fun stripc (f$t, ts) = stripc (f, t::ts) 
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 stripc x = x 
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in stripc(u,[]) end; 
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(* maps f(t1,...,tn) to f , which is never a combination *) 

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fun head_of (f$t) = head_of f 

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 head_of u = u; 

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(** Particular constants **) 

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fun negate P = Const (Data.not_name, []) $ P; 
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fun isNot (Const (c, _) $ _) = c = Data.not_name 
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 isNot _ = false; 
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fun mkGoal P = Const ("*Goal*", []) $ P; 
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fun isGoal (Const ("*Goal*", _) $ _) = true 
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 isGoal _ = false; 
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val TruepropC = ObjectLogic.judgment_name (the_context ()); 
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val TruepropT = Sign.the_const_type (the_context ()) TruepropC; 

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fun mk_Trueprop t = Term.$ (Term.Const (TruepropC, TruepropT), t); 
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fun strip_Trueprop (tm as Const (c, _) $ t) = if c = TruepropC then t else tm 
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 strip_Trueprop tm = tm; 

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(*** Dealing with overloaded constants ***) 
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(*alist is a map from TVar names to Vars. We need to unify the TVars 
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faithfully in order to track overloading*) 

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fun fromType alist (Term.Type(a,Ts)) = list_comb (Const (a, []), map (fromType alist) Ts) 
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 fromType alist (Term.TFree(a,_)) = Free a 
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 fromType alist (Term.TVar (ixn,_)) = 

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(case (AList.lookup (op =) (!alist) ixn) of 
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NONE => let val t' = Var(ref NONE) 
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in alist := (ixn, t') :: !alist; t' 
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end 
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 SOME v => v) 
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(*refer to the theory in which blast is initialized*) 
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val typargs = ref (fn ((_, T): string * typ) => [T]); 
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fun fromConst alist (a, T) = 
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Const (a, map (fromType alist) (! typargs (a, T))); 

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(*Tests whether 2 terms are alphaconvertible; chases instantiations*) 

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fun (Const (a, ts)) aconv (Const (b, us)) = a=b andalso aconvs (ts, us) 
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 (Skolem (a,_)) aconv (Skolem (b,_)) = a=b (*arglists must then be equal*) 
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 (Free a) aconv (Free b) = a=b 

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 (Var(ref(SOME t))) aconv u = t aconv u 
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 t aconv (Var(ref(SOME u))) = t aconv u 

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 (Var v) aconv (Var w) = v=w (*both Vars are unassigned*) 
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 (Bound i) aconv (Bound j) = i=j 
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 (Abs(_,t)) aconv (Abs(_,u)) = t aconv u 

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 (f$t) aconv (g$u) = (f aconv g) andalso (t aconv u) 

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 _ aconv _ = false 
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and aconvs ([], []) = true 

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 aconvs (t :: ts, u :: us) = t aconv u andalso aconvs (ts, us) 

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 aconvs _ = false; 

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fun mem_term (_, []) = false 

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 mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts); 

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fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts; 

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fun mem_var (v: term option ref, []) = false 

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 mem_var (v, v'::vs) = v=v' orelse mem_var(v,vs); 

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fun ins_var(v,vs) = if mem_var(v,vs) then vs else v :: vs; 

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(** Vars **) 

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(*Accumulates the Vars in the term, suppressing duplicates*) 

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fun add_term_vars (Skolem(a,args), vars) = add_vars_vars(args,vars) 
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 add_term_vars (Var (v as ref NONE), vars) = ins_var (v, vars) 
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 add_term_vars (Var (ref (SOME u)), vars) = add_term_vars(u,vars) 
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 add_term_vars (Const (_,ts), vars) = add_terms_vars(ts,vars) 
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 add_term_vars (Abs (_,body), vars) = add_term_vars(body,vars) 
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 add_term_vars (f$t, vars) = add_term_vars (f, add_term_vars(t, vars)) 
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 add_term_vars (_, vars) = vars 
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(*Term list version. [The fold functionals are slow]*) 
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and add_terms_vars ([], vars) = vars 

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 add_terms_vars (t::ts, vars) = add_terms_vars (ts, add_term_vars(t,vars)) 

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(*Var list version.*) 

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and add_vars_vars ([], vars) = vars 

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 add_vars_vars (ref (SOME u) :: vs, vars) = 
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add_vars_vars (vs, add_term_vars(u,vars)) 
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 add_vars_vars (v::vs, vars) = (*v must be a ref NONE*) 
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add_vars_vars (vs, ins_var (v, vars)); 
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233 

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(*Chase assignments in "vars"; return a list of unassigned variables*) 

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fun vars_in_vars vars = add_vars_vars(vars,[]); 

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237 

238 

239 
(*increment a term's nonlocal bound variables 

240 
inc is increment for bound variables 

241 
lev is level at which a bound variable is considered 'loose'*) 

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fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u 
2854  243 
 incr_bv (inc, lev, Abs(a,body)) = Abs(a, incr_bv(inc,lev+1,body)) 
244 
 incr_bv (inc, lev, f$t) = incr_bv(inc,lev,f) $ incr_bv(inc,lev,t) 

245 
 incr_bv (inc, lev, u) = u; 

246 

247 
fun incr_boundvars 0 t = t 

248 
 incr_boundvars inc t = incr_bv(inc,0,t); 

249 

250 

251 
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond. 

252 
(Bound 0) is loose at level 0 *) 

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fun add_loose_bnos (Bound i, lev, js) = if i<lev then js 
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else (ilev) ins_int js 
2854  255 
 add_loose_bnos (Abs (_,t), lev, js) = add_loose_bnos (t, lev+1, js) 
256 
 add_loose_bnos (f$t, lev, js) = 

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add_loose_bnos (f, lev, add_loose_bnos (t, lev, js)) 
2854  258 
 add_loose_bnos (_, _, js) = js; 
259 

260 
fun loose_bnos t = add_loose_bnos (t, 0, []); 

261 

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fun subst_bound (arg, t) : term = 
2854  263 
let fun subst (t as Bound i, lev) = 
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if i<lev then t (*var is locally bound*) 
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else if i=lev then incr_boundvars lev arg 
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else Bound(i1) (*loose: change it*) 
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 subst (Abs(a,body), lev) = Abs(a, subst(body,lev+1)) 
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 subst (f$t, lev) = subst(f,lev) $ subst(t,lev) 
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 subst (t,lev) = t 
2854  270 
in subst (t,0) end; 
271 

272 

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(*Normalize...but not the bodies of ABSTRACTIONS*) 
2854  274 
fun norm t = case t of 
2952  275 
Skolem (a,args) => Skolem(a, vars_in_vars args) 
18177  276 
 Const(a,ts) => Const(a, map norm ts) 
15531  277 
 (Var (ref NONE)) => t 
278 
 (Var (ref (SOME u))) => norm u 

2854  279 
 (f $ u) => (case norm f of 
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Abs(_,body) => norm (subst_bound (u, body)) 
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 nf => nf $ norm u) 
2854  282 
 _ => t; 
283 

284 

285 
(*Weak (onelevel) normalize for use in unification*) 

286 
fun wkNormAux t = case t of 

287 
(Var v) => (case !v of 

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SOME u => wkNorm u 
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 NONE => t) 
2854  290 
 (f $ u) => (case wkNormAux f of 
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Abs(_,body) => wkNorm (subst_bound (u, body)) 
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 nf => nf $ u) 
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 Abs (a,body) => (*etacontract if possible*) 
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(case wkNormAux body of 
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nb as (f $ t) => 
20664  296 
if member (op =) (loose_bnos f) 0 orelse wkNorm t <> Bound 0 
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then Abs(a,nb) 
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298 
else wkNorm (incr_boundvars ~1 f) 
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 nb => Abs (a,nb)) 
2854  300 
 _ => t 
301 
and wkNorm t = case head_of t of 

302 
Const _ => t 

303 
 Skolem(a,args) => t 

304 
 Free _ => t 

305 
 _ => wkNormAux t; 

306 

307 

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(*Does variable v occur in u? For unification. 
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Dangling bound vars are also forbidden.*) 
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fun varOccur v = 
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let fun occL lev [] = false (*same as (exists occ), but faster*) 
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 occL lev (u::us) = occ lev u orelse occL lev us 
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and occ lev (Var w) = 
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v=w orelse 
15531  315 
(case !w of NONE => false 
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 SOME u => occ lev u) 
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 occ lev (Skolem(_,args)) = occL lev (map Var args) 
18177  318 
(*ignore Const, since term variables can't occur in types (?) *) 
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 occ lev (Bound i) = lev <= i 
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 occ lev (Abs(_,u)) = occ (lev+1) u 
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 occ lev (f$u) = occ lev u orelse occ lev f 
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 occ lev _ = false; 
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323 
in occ 0 end; 
2854  324 

325 
exception UNIFY; 

326 

327 
val trail = ref [] : term option ref list ref; 

328 
val ntrail = ref 0; 

329 

330 

331 
(*Restore the trail to some previous state: for backtracking*) 

332 
fun clearTo n = 

3083  333 
while !ntrail<>n do 
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(hd(!trail) := NONE; 
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trail := tl (!trail); 
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ntrail := !ntrail  1); 
2854  337 

338 

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(*Firstorder unification with bound variables. 
2854  340 
"vars" is a list of variables local to the rule and NOT to be put 
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on the trail (no point in doing so) 
2854  342 
*) 
4065  343 
fun unify(vars,t,u) = 
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let val n = !ntrail 
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fun update (t as Var v, u) = 
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if t aconv u then () 
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else if varOccur v u then raise UNIFY 
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else if mem_var(v, vars) then v := SOME u 
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else (*avoid updating Vars in the branch if possible!*) 
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if is_Var u andalso mem_var(dest_Var u, vars) 
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then dest_Var u := SOME t 
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352 
else (v := SOME u; 
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trail := v :: !trail; ntrail := !ntrail + 1) 
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354 
fun unifyAux (t,u) = 
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355 
case (wkNorm t, wkNorm u) of 
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356 
(nt as Var v, nu) => update(nt,nu) 
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357 
 (nu, nt as Var v) => update(nt,nu) 
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358 
 (Const(a,ats), Const(b,bts)) => if a=b then unifysAux(ats,bts) 
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359 
else raise UNIFY 
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360 
 (Abs(_,t'), Abs(_,u')) => unifyAux(t',u') 
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361 
(*NB: can yield unifiers having dangling Bound vars!*) 
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362 
 (f$t', g$u') => (unifyAux(f,g); unifyAux(t',u')) 
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363 
 (nt, nu) => if nt aconv nu then () else raise UNIFY 
18177  364 
and unifysAux ([], []) = () 
365 
 unifysAux (t :: ts, u :: us) = (unifyAux (t, u); unifysAux (ts, us)) 

366 
 unifysAux _ = raise UNIFY; 

3083  367 
in (unifyAux(t,u); true) handle UNIFY => (clearTo n; false) 
2854  368 
end; 
369 

370 

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371 
(*Convert from "real" terms to prototerms; etacontract. 
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372 
Code is similar to fromSubgoal.*) 
4065  373 
fun fromTerm t = 
374 
let val alistVar = ref [] 

375 
and alistTVar = ref [] 

376 
fun from (Term.Const aT) = fromConst alistTVar aT 

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377 
 from (Term.Free (a,_)) = Free a 
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378 
 from (Term.Bound i) = Bound i 
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379 
 from (Term.Var (ixn,T)) = 
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380 
(case (AList.lookup (op =) (!alistVar) ixn) of 
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381 
NONE => let val t' = Var(ref NONE) 
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382 
in alistVar := (ixn, t') :: !alistVar; t' 
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383 
end 
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384 
 SOME v => v) 
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385 
 from (Term.Abs (a,_,u)) = 
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386 
(case from u of 
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387 
u' as (f $ Bound 0) => 
20664  388 
if member (op =) (loose_bnos f) 0 then Abs(a,u') 
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389 
else incr_boundvars ~1 f 
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390 
 u' => Abs(a,u')) 
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391 
 from (Term.$ (f,u)) = from f $ from u 
2854  392 
in from t end; 
393 

4065  394 
(*A debugging function: replaces all Vars by dummy Frees for visual inspection 
395 
of whether they are distinct. Function revert undoes the assignments.*) 

396 
fun instVars t = 

12902  397 
let val name = ref "a" 
4065  398 
val updated = ref [] 
18177  399 
fun inst (Const(a,ts)) = List.app inst ts 
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400 
 inst (Var(v as ref NONE)) = (updated := v :: (!updated); 
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401 
v := SOME (Free ("?" ^ !name)); 
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402 
name := Symbol.bump_string (!name)) 
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403 
 inst (Abs(a,t)) = inst t 
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404 
 inst (f $ u) = (inst f; inst u) 
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405 
 inst _ = () 
15570  406 
fun revert() = List.app (fn v => v:=NONE) (!updated) 
4065  407 
in inst t; revert end; 
408 

409 

2854  410 
(* A1==>...An==>B goes to [A1,...,An], where B is not an implication *) 
18177  411 
fun strip_imp_prems (Const ("==>", _) $ A $ B) = strip_Trueprop A :: strip_imp_prems B 
2854  412 
 strip_imp_prems _ = []; 
413 

414 
(* A1==>...An==>B goes to B, where B is not an implication *) 

18177  415 
fun strip_imp_concl (Const ("==>", _) $ A $ B) = strip_imp_concl B 
416 
 strip_imp_concl A = strip_Trueprop A; 

417 

2854  418 

419 

420 
(*** Conversion of Elimination Rules to Tableau Operations ***) 

421 

9170  422 
exception ElimBadConcl and ElimBadPrem; 
423 

424 
(*The conclusion becomes the goal/negated assumption *False*: delete it! 

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425 
If we don't find it then the premise is illformed and could cause 
9170  426 
PROOF FAILED*) 
427 
fun delete_concl [] = raise ElimBadPrem 

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428 
 delete_concl (P :: Ps) = 
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429 
(case P of 
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430 
Const (c, _) $ Var (ref (SOME (Const ("*False*", _)))) => 
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431 
if c = "*Goal*" orelse c = Data.not_name then Ps 
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432 
else P :: delete_concl Ps 
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433 
 _ => P :: delete_concl Ps); 
2854  434 

18177  435 
fun skoPrem vars (Const ("all", _) $ Abs (_, P)) = 
2854  436 
skoPrem vars (subst_bound (Skolem (gensym "S_", vars), P)) 
437 
 skoPrem vars P = P; 

438 

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439 
fun convertPrem t = 
9170  440 
delete_concl (mkGoal (strip_imp_concl t) :: strip_imp_prems t); 
2854  441 

442 
(*Expects elimination rules to have a formula variable as conclusion*) 

443 
fun convertRule vars t = 

444 
let val (P::Ps) = strip_imp_prems t 

445 
val Var v = strip_imp_concl t 

18177  446 
in v := SOME (Const ("*False*", [])); 
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447 
(P, map (convertPrem o skoPrem vars) Ps) 
9170  448 
end 
449 
handle Bind => raise ElimBadConcl; 

2854  450 

451 

452 
(*Like dup_elim, but puts the duplicated major premise FIRST*) 

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0ab67cb765da
introduced binding priority 1 for linear combinators etc.
haftmann
parents:
16976
diff
changeset

453 
fun rev_dup_elim th = (th RSN (2, revcut_rl)) > assumption 2 > Seq.hd; 
2854  454 

455 

4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

456 
(*Rotate the assumptions in all new subgoals for the LIFO discipline*) 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

457 
local 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

458 
(*Count new hyps so that they can be rotated*) 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

459 
fun nNewHyps [] = 0 
18177  460 
 nNewHyps (Const ("*Goal*", _) $ _ :: Ps) = nNewHyps Ps 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

461 
 nNewHyps (P::Ps) = 1 + nNewHyps Ps; 
2854  462 

5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

463 
fun rot_tac [] i st = Seq.single st 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

464 
 rot_tac (0::ks) i st = rot_tac ks (i+1) st 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

465 
 rot_tac (k::ks) i st = rot_tac ks (i+1) (rotate_rule (~k) i st); 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

466 
in 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

467 
fun rot_subgoals_tac (rot, rl) = 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

468 
rot_tac (if rot then map nNewHyps rl else []) 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

469 
end; 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

470 

2854  471 

2999
fad7cc426242
Penalty for branching instantiations reduced from log3 to log4.
paulson
parents:
2952
diff
changeset

472 
fun TRACE rl tac st i = if !trace then (prth rl; tac st i) else tac st i; 
2854  473 

5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

474 
(*Resolution/matching tactics: if upd then the proof state may be updated. 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

475 
Matching makes the tactics more deterministic in the presence of Vars.*) 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

476 
fun emtac upd rl = TRACE rl (if upd then etac rl else ematch_tac [rl]); 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

477 
fun rmtac upd rl = TRACE rl (if upd then rtac rl else match_tac [rl]); 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

478 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

479 
(*Tableau rule from elimination rule. 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

480 
Flag "upd" says that the inference updated the branch. 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

481 
Flag "dup" requests duplication of the affected formula.*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

482 
fun fromRule vars rl = 
4065  483 
let val trl = rl > rep_thm > #prop > fromTerm > convertRule vars 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

484 
fun tac (upd, dup,rot) i = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

485 
emtac upd (if dup then rev_dup_elim rl else rl) i 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

486 
THEN 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

487 
rot_subgoals_tac (rot, #2 trl) i 
3244
71b760618f30
Basis library version of type "option" now resides in its own structure Option
paulson
parents:
3101
diff
changeset

488 
in Option.SOME (trl, tac) end 
9170  489 
handle ElimBadPrem => (*reject: prems don't preserve conclusion*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

490 
(warning("Ignoring weak elimination rule\n" ^ string_of_thm rl); 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

491 
Option.NONE) 
9170  492 
 ElimBadConcl => (*ignore: conclusion is not just a variable*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

493 
(if !trace then (warning("Ignoring illformed elimination rule:\n" ^ 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

494 
"conclusion should be a variable\n" ^ string_of_thm rl)) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

495 
else (); 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

496 
Option.NONE); 
2854  497 

498 

3101
e8a92f497295
Again "norm" DOES NOT normalize bodies of abstractions
paulson
parents:
3092
diff
changeset

499 
(*** Conversion of Introduction Rules ***) 
2854  500 

501 
fun convertIntrPrem t = mkGoal (strip_imp_concl t) :: strip_imp_prems t; 

502 

503 
fun convertIntrRule vars t = 

504 
let val Ps = strip_imp_prems t 

505 
val P = strip_imp_concl t 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

506 
in (mkGoal P, map (convertIntrPrem o skoPrem vars) Ps) 
2854  507 
end; 
508 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

509 
(*Tableau rule from introduction rule. 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

510 
Flag "upd" says that the inference updated the branch. 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

511 
Flag "dup" requests duplication of the affected formula. 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

512 
Since haz rules are now delayed, "dup" is always FALSE for 
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

513 
introduction rules.*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

514 
fun fromIntrRule vars rl = 
4065  515 
let val trl = rl > rep_thm > #prop > fromTerm > convertIntrRule vars 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

516 
fun tac (upd,dup,rot) i = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

517 
rmtac upd (if dup then Data.dup_intr rl else rl) i 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

518 
THEN 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

519 
rot_subgoals_tac (rot, #2 trl) i 
2854  520 
in (trl, tac) end; 
521 

522 

3030  523 
val dummyVar = Term.Var (("etc",0), dummyT); 
2854  524 

525 
(*Convert from prototerms to ordinary terms with dummy types 

2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

526 
Ignore abstractions; identify all Vars; STOP at given depth*) 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

527 
fun toTerm 0 _ = dummyVar 
18177  528 
 toTerm d (Const(a,_)) = Term.Const (a,dummyT) (*no need to convert typargs*) 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

529 
 toTerm d (Skolem(a,_)) = Term.Const (a,dummyT) 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

530 
 toTerm d (Free a) = Term.Free (a,dummyT) 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

531 
 toTerm d (Bound i) = Term.Bound i 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

532 
 toTerm d (Var _) = dummyVar 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

533 
 toTerm d (Abs(a,_)) = dummyVar 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

534 
 toTerm d (f $ u) = Term.$ (toTerm d f, toTerm (d1) u); 
2854  535 

536 

537 
fun netMkRules P vars (nps: netpair list) = 

538 
case P of 

18177  539 
(Const ("*Goal*", _) $ G) => 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

540 
let val pG = mk_Trueprop (toTerm 2 G) 
19482
9f11af8f7ef9
tuned basic list operators (flat, maps, map_filter);
wenzelm
parents:
19037
diff
changeset

541 
val intrs = maps (fn (inet,_) => Net.unify_term inet pG) nps 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

542 
in map (fromIntrRule vars o #2) (Tactic.orderlist intrs) end 
2854  543 
 _ => 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

544 
let val pP = mk_Trueprop (toTerm 3 P) 
19482
9f11af8f7ef9
tuned basic list operators (flat, maps, map_filter);
wenzelm
parents:
19037
diff
changeset

545 
val elims = maps (fn (_,enet) => Net.unify_term enet pP) nps 
9f11af8f7ef9
tuned basic list operators (flat, maps, map_filter);
wenzelm
parents:
19037
diff
changeset

546 
in map_filter (fromRule vars o #2) (Tactic.orderlist elims) end; 
2854  547 

3092  548 

549 
(*Pending formulae carry md (may duplicate) flags*) 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

550 
type branch = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

551 
{pairs: ((term*bool) list * (*safe formulae on this level*) 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

552 
(term*bool) list) list, (*haz formulae on this level*) 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

553 
lits: term list, (*literals: irreducible formulae*) 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

554 
vars: term option ref list, (*variables occurring in branch*) 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

555 
lim: int}; (*resource limit*) 
3092  556 

557 
val fullTrace = ref[] : branch list list ref; 

558 

559 
(*Normalize a branchfor tracing*) 

560 
fun norm2 (G,md) = (norm G, md); 

561 

562 
fun normLev (Gs,Hs) = (map norm2 Gs, map norm2 Hs); 

563 

5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

564 
fun normBr {pairs, lits, vars, lim} = 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

565 
{pairs = map normLev pairs, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

566 
lits = map norm lits, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

567 
vars = vars, 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

568 
lim = lim}; 
3092  569 

570 

4065  571 
val dummyTVar = Term.TVar(("a",0), []); 
3092  572 
val dummyVar2 = Term.Var(("var",0), dummyT); 
573 

4065  574 
(*convert Blast_tac's type representation to real types for tracing*) 
575 
fun showType (Free a) = Term.TFree (a,[]) 

576 
 showType (Var _) = dummyTVar 

577 
 showType t = 

578 
(case strip_comb t of 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

579 
(Const (a, _), us) => Term.Type(a, map showType us) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

580 
 _ => dummyT); 
4065  581 

582 
(*Display toplevel overloading if any*) 

18177  583 
fun topType thy (Const (c, ts)) = SOME (Sign.const_instance thy (c, map showType ts)) 
584 
 topType thy (Abs(a,t)) = topType thy t 

585 
 topType thy (f $ u) = (case topType thy f of NONE => topType thy u  some => some) 

586 
 topType _ _ = NONE; 

4065  587 

588 

3092  589 
(*Convert from prototerms to ordinary terms with dummy types for tracing*) 
18177  590 
fun showTerm d (Const (a,_)) = Term.Const (a,dummyT) 
3092  591 
 showTerm d (Skolem(a,_)) = Term.Const (a,dummyT) 
592 
 showTerm d (Free a) = Term.Free (a,dummyT) 

593 
 showTerm d (Bound i) = Term.Bound i 

15531  594 
 showTerm d (Var(ref(SOME u))) = showTerm d u 
595 
 showTerm d (Var(ref NONE)) = dummyVar2 

3092  596 
 showTerm d (Abs(a,t)) = if d=0 then dummyVar 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

597 
else Term.Abs(a, dummyT, showTerm (d1) t) 
3092  598 
 showTerm d (f $ u) = if d=0 then dummyVar 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

599 
else Term.$ (showTerm d f, showTerm (d1) u); 
3092  600 

4065  601 
fun string_of sign d t = Sign.string_of_term sign (showTerm d t); 
3092  602 

19037  603 
(*Convert a Goal to an ordinary Not. Used also in dup_intr, where a goal like 
604 
Ex(P) is duplicated as the assumption ~Ex(P). *) 

605 
fun negOfGoal (Const ("*Goal*", _) $ G) = negate G 

606 
 negOfGoal G = G; 

607 

608 
fun negOfGoal2 (G,md) = (negOfGoal G, md); 

609 

610 
(*Converts all Goals to Nots in the safe parts of a branch. They could 

611 
have been moved there from the literals list after substitution (equalSubst). 

612 
There can be at most onethis function could be made more efficient.*) 

613 
fun negOfGoals pairs = map (fn (Gs,haz) => (map negOfGoal2 Gs, haz)) pairs; 

614 

615 
(*Tactic. Convert *Goal* to negated assumption in FIRST position*) 

616 
fun negOfGoal_tac i = TRACE Data.ccontr (rtac Data.ccontr) i THEN 

617 
rotate_tac ~1 i; 

618 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

619 
fun traceTerm sign t = 
19037  620 
let val t' = norm (negOfGoal t) 
4065  621 
val stm = string_of sign 8 t' 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

622 
in 
18177  623 
case topType sign t' of 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

624 
NONE => stm (*no type to attach*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

625 
 SOME T => stm ^ "\t:: " ^ Sign.string_of_typ sign T 
4065  626 
end; 
3092  627 

628 

629 
(*Print tracing information at each iteration of prover*) 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

630 
fun tracing sign brs = 
14984  631 
let fun printPairs (((G,_)::_,_)::_) = immediate_output(traceTerm sign G) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

632 
 printPairs (([],(H,_)::_)::_) = immediate_output(traceTerm sign H ^ "\t (Unsafe)") 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

633 
 printPairs _ = () 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

634 
fun printBrs (brs0 as {pairs, lits, lim, ...} :: brs) = 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

635 
(fullTrace := brs0 :: !fullTrace; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

636 
List.app (fn _ => immediate_output "+") brs; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

637 
immediate_output (" [" ^ Int.toString lim ^ "] "); 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

638 
printPairs pairs; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

639 
writeln"") 
3092  640 
in if !trace then printBrs (map normBr brs) else () 
641 
end; 

642 

5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

643 
fun traceMsg s = if !trace then writeln s else (); 
4065  644 

3092  645 
(*Tracing: variables updated in the last branch operation?*) 
4065  646 
fun traceVars sign ntrl = 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

647 
if !trace then 
4065  648 
(case !ntrailntrl of 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

649 
0 => () 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

650 
 1 => immediate_output"\t1 variable UPDATED:" 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

651 
 n => immediate_output("\t" ^ Int.toString n ^ " variables UPDATED:"); 
4065  652 
(*display the instantiations themselves, though no variable names*) 
19502  653 
List.app (fn v => immediate_output(" " ^ string_of sign 4 (the (!v)))) 
4065  654 
(List.take(!trail, !ntrailntrl)); 
655 
writeln"") 

3092  656 
else (); 
657 

658 
(*Tracing: how many new branches are created?*) 

659 
fun traceNew prems = 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

660 
if !trace then 
3092  661 
case length prems of 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

662 
0 => immediate_output"branch closed by rule" 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

663 
 1 => immediate_output"branch extended (1 new subgoal)" 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

664 
 n => immediate_output("branch split: "^ Int.toString n ^ " new subgoals") 
3092  665 
else (); 
666 

667 

668 

2854  669 
(*** Code for handling equality: naive substitution, like hyp_subst_tac ***) 
670 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

671 
(*Replace the ATOMIC term "old" by "new" in t*) 
2854  672 
fun subst_atomic (old,new) t = 
15531  673 
let fun subst (Var(ref(SOME u))) = subst u 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

674 
 subst (Abs(a,body)) = Abs(a, subst body) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

675 
 subst (f$t) = subst f $ subst t 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

676 
 subst t = if t aconv old then new else t 
2854  677 
in subst t end; 
678 

679 
(*Etacontract a term from outside: just enough to reduce it to an atom*) 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

680 
fun eta_contract_atom (t0 as Abs(a, body)) = 
2854  681 
(case eta_contract2 body of 
20664  682 
f $ Bound 0 => if member (op =) (loose_bnos f) 0 then t0 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

683 
else eta_contract_atom (incr_boundvars ~1 f) 
2854  684 
 _ => t0) 
685 
 eta_contract_atom t = t 

686 
and eta_contract2 (f$t) = f $ eta_contract_atom t 

687 
 eta_contract2 t = eta_contract_atom t; 

688 

689 

690 
(*When can we safely delete the equality? 

691 
Not if it equates two constants; consider 0=1. 

692 
Not if it resembles x=t[x], since substitution does not eliminate x. 

693 
Not if it resembles ?x=0; another goal could instantiate ?x to Suc(i) 

694 
Prefer to eliminate Bound variables if possible. 

695 
Result: true = use as is, false = reorient first *) 

696 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

697 
(*Can t occur in u? For substitution. 
4354
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

698 
Does NOT examine the args of Skolem terms: substitution does not affect them. 
4196
9953c0995b79
Now applies "map negOfGoal" to lits when expanding haz rules.
paulson
parents:
4149
diff
changeset

699 
REFLEXIVE because hyp_subst_tac fails on x=x.*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

700 
fun substOccur t = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

701 
let (*NO vars are permitted in u except the arguments of t, if it is 
4354
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

702 
a Skolem term. This ensures that no equations are deleted that could 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

703 
be instantiated to a cycle. For example, x=?a is rejected because ?a 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

704 
could be instantiated to Suc(x).*) 
4354
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

705 
val vars = case t of 
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

706 
Skolem(_,vars) => vars 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

707 
 _ => [] 
4354
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

708 
fun occEq u = (t aconv u) orelse occ u 
15531  709 
and occ (Var(ref(SOME u))) = occEq u 
4354
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset

710 
 occ (Var v) = not (mem_var (v, vars)) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

711 
 occ (Abs(_,u)) = occEq u 
2854  712 
 occ (f$u) = occEq u orelse occEq f 
713 
 occ (_) = false; 

714 
in occEq end; 

715 

3092  716 
exception DEST_EQ; 
717 

18177  718 
(*Take apart an equality. NO constant Trueprop*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

719 
fun dest_eq (Const (c, _) $ t $ u) = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

720 
if c = Data.equality_name then (eta_contract_atom t, eta_contract_atom u) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

721 
else raise DEST_EQ 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

722 
 dest_eq _ = raise DEST_EQ; 
3092  723 

4196
9953c0995b79
Now applies "map negOfGoal" to lits when expanding haz rules.
paulson
parents:
4149
diff
changeset

724 
(*Reject the equality if u occurs in (or equals!) t*) 
2854  725 
fun check (t,u,v) = if substOccur t u then raise DEST_EQ else v; 
726 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

727 
(*IF the goal is an equality with a substitutable variable 
2854  728 
THEN orient that equality ELSE raise exception DEST_EQ*) 
3092  729 
fun orientGoal (t,u) = case (t,u) of 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

730 
(Skolem _, _) => check(t,u,(t,u)) (*eliminates t*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

731 
 (_, Skolem _) => check(u,t,(u,t)) (*eliminates u*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

732 
 (Free _, _) => check(t,u,(t,u)) (*eliminates t*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

733 
 (_, Free _) => check(u,t,(u,t)) (*eliminates u*) 
2854  734 
 _ => raise DEST_EQ; 
735 

2894  736 
(*Substitute through the branch if an equality goal (else raise DEST_EQ). 
737 
Moves affected literals back into the branch, but it is not clear where 

4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

738 
they should go: this could make proofs fail.*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

739 
fun equalSubst sign (G, {pairs, lits, vars, lim}) = 
3092  740 
let val (t,u) = orientGoal(dest_eq G) 
741 
val subst = subst_atomic (t,u) 

2854  742 
fun subst2(G,md) = (subst G, md) 
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

743 
(*substitute throughout list; extract affected formulae*) 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

744 
fun subForm ((G,md), (changed, pairs)) = 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

745 
let val nG = subst G 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

746 
in if nG aconv G then (changed, (G,md)::pairs) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

747 
else ((nG,md)::changed, pairs) 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

748 
end 
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

749 
(*substitute throughout "stack frame"; extract affected formulae*) 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

750 
fun subFrame ((Gs,Hs), (changed, frames)) = 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

751 
let val (changed', Gs') = foldr subForm (changed, []) Gs 
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset

752 
val (changed'', Hs') = foldr subForm (changed', []) Hs 
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

753 
in (changed'', (Gs',Hs')::frames) end 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

754 
(*substitute throughout literals; extract affected ones*) 
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset

755 
fun subLit (lit, (changed, nlits)) = 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

756 
let val nlit = subst lit 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

757 
in if nlit aconv lit then (changed, nlit::nlits) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

758 
else ((nlit,true)::changed, nlits) 
2854  759 
end 
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset

760 
val (changed, lits') = foldr subLit ([], []) lits 
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset

761 
val (changed', pairs') = foldr subFrame (changed, []) pairs 
3092  762 
in if !trace then writeln ("Substituting " ^ traceTerm sign u ^ 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

763 
" for " ^ traceTerm sign t ^ " in branch" ) 
3092  764 
else (); 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

765 
{pairs = (changed',[])::pairs', (*affected formulas, and others*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

766 
lits = lits', (*unaffected literals*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

767 
vars = vars, 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

768 
lim = lim} 
2854  769 
end; 
770 

771 

772 
exception NEWBRANCHES and CLOSEF; 

773 

774 
exception PROVE; 

775 

4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

776 
(*Trying eq_contr_tac first INCREASES the effort, slowing reconstruction*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

777 
val contr_tac = ematch_tac [Data.notE] THEN' 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

778 
(eq_assume_tac ORELSE' assume_tac); 
2854  779 

4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

780 
val eContr_tac = TRACE Data.notE contr_tac; 
2854  781 
val eAssume_tac = TRACE asm_rl (eq_assume_tac ORELSE' assume_tac); 
782 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

783 
(*Try to unify complementary literals and return the corresponding tactic. *) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

784 
fun tryClose (G, L) = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

785 
let 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

786 
fun close t u tac = if unify ([], t, u) then SOME tac else NONE; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

787 
fun arg (_ $ t) = t; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

788 
in 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

789 
if isGoal G then close (arg G) L eAssume_tac 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

790 
else if isGoal L then close G (arg L) eAssume_tac 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

791 
else if isNot G then close (arg G) L eContr_tac 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

792 
else if isNot L then close G (arg L) eContr_tac 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

793 
else NONE 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

794 
end; 
2854  795 

796 
(*Were there Skolem terms in the premise? Must NOT chase Vars*) 

797 
fun hasSkolem (Skolem _) = true 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

798 
 hasSkolem (Abs (_,body)) = hasSkolem body 
2854  799 
 hasSkolem (f$t) = hasSkolem f orelse hasSkolem t 
800 
 hasSkolem _ = false; 

801 

802 
(*Attach the right "may duplicate" flag to new formulae: if they contain 

803 
Skolem terms then allow duplication.*) 

804 
fun joinMd md [] = [] 

805 
 joinMd md (G::Gs) = (G, hasSkolem G orelse md) :: joinMd md Gs; 

806 

807 

808 
(** Backtracking and Pruning **) 

809 

810 
(*clashVar vars (n,trail) determines whether any of the last n elements 

811 
of "trail" occur in "vars" OR in their instantiations*) 

812 
fun clashVar [] = (fn _ => false) 

813 
 clashVar vars = 

814 
let fun clash (0, _) = false 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

815 
 clash (_, []) = false 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

816 
 clash (n, v::vs) = exists (varOccur v) vars orelse clash(n1,vs) 
2854  817 
in clash end; 
818 

819 

820 
(*nbrs = # of branches just prior to closing this one. Delete choice points 

821 
for goals proved by the latest inference, provided NO variables in the 

822 
next branch have been updated.*) 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

823 
fun prune (1, nxtVars, choices) = choices (*DON'T prune at very end: allow 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

824 
backtracking over bad proofs*) 
17795  825 
 prune (nbrs: int, nxtVars, choices) = 
2854  826 
let fun traceIt last = 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

827 
let val ll = length last 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

828 
and lc = length choices 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

829 
in if !trace andalso ll<lc then 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

830 
(writeln("Pruning " ^ Int.toString(lcll) ^ " levels"); 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

831 
last) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

832 
else last 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

833 
end 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

834 
fun pruneAux (last, _, _, []) = last 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

835 
 pruneAux (last, ntrl, trl, (ntrl',nbrs',exn) :: choices) = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

836 
if nbrs' < nbrs 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

837 
then last (*don't backtrack beyond first solution of goal*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

838 
else if nbrs' > nbrs then pruneAux (last, ntrl, trl, choices) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

839 
else (* nbrs'=nbrs *) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

840 
if clashVar nxtVars (ntrlntrl', trl) then last 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

841 
else (*no clashes: can go back at least this far!*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

842 
pruneAux(choices, ntrl', List.drop(trl, ntrlntrl'), 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

843 
choices) 
2854  844 
in traceIt (pruneAux (choices, !ntrail, !trail, choices)) end; 
845 

5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

846 
fun nextVars ({pairs, lits, vars, lim} :: _) = map Var vars 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

847 
 nextVars [] = []; 
2854  848 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

849 
fun backtrack (choices as (ntrl, nbrs, exn)::_) = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

850 
(if !trace then (writeln ("Backtracking; now there are " ^ 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

851 
Int.toString nbrs ^ " branches")) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

852 
else (); 
3083  853 
raise exn) 
854 
 backtrack _ = raise PROVE; 

2854  855 

2894  856 
(*Add the literal G, handling *Goal* and detecting duplicates.*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

857 
fun addLit (Const ("*Goal*", _) $ G, lits) = 
2894  858 
(*New literal is a *Goal*, so change all other Goals to Nots*) 
18177  859 
let fun bad (Const ("*Goal*", _) $ _) = true 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

860 
 bad (Const (c, _) $ G') = c = Data.not_name andalso G aconv G' 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

861 
 bad _ = false; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

862 
fun change [] = [] 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

863 
 change (lit :: lits) = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

864 
(case lit of 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

865 
Const (c, _) $ G' => 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

866 
if c = "*Goal*" orelse c = Data.not_name then 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

867 
if G aconv G' then change lits 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

868 
else negate G' :: change lits 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

869 
else lit :: change lits 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

870 
 _ => lit :: change lits) 
2854  871 
in 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

872 
Const ("*Goal*", []) $ G :: (if exists bad lits then change lits else lits) 
2854  873 
end 
874 
 addLit (G,lits) = ins_term(G, lits) 

875 

876 

2952  877 
(*For calculating the "penalty" to assess on a branching factor of n 
878 
log2 seems a little too severe*) 

3083  879 
fun log n = if n<4 then 0 else 1 + log(n div 4); 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

880 

af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

881 

3021
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset

882 
(*match(t,u) says whether the term u might be an instance of the pattern t 
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset

883 
Used to detect "recursive" rules such as transitivity*) 
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset

884 
fun match (Var _) u = true 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

885 
 match (Const (a,tas)) (Const (b,tbs)) = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

886 
a = "*Goal*" andalso b = Data.not_name orelse 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

887 
a = Data.not_name andalso b = "*Goal*" orelse 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

888 
a = b andalso matchs tas tbs 
4065  889 
 match (Free a) (Free b) = (a=b) 
890 
 match (Bound i) (Bound j) = (i=j) 

891 
 match (Abs(_,t)) (Abs(_,u)) = match t u 

892 
 match (f$t) (g$u) = match f g andalso match t u 

18177  893 
 match t u = false 
894 
and matchs [] [] = true 

895 
 matchs (t :: ts) (u :: us) = match t u andalso matchs ts us; 

3021
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset

896 

39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset

897 

4300  898 
(*Branches closed: number of branches closed during the search 
899 
Branches tried: number of branches created by splitting (counting from 1)*) 

900 
val nclosed = ref 0 

901 
and ntried = ref 1; 

902 

4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

903 
fun printStats (b, start, tacs) = 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

904 
if b then 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

905 
writeln (endTiming start ^ " for search. Closed: " 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

906 
^ Int.toString (!nclosed) ^ 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

907 
" tried: " ^ Int.toString (!ntried) ^ 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

908 
" tactics: " ^ Int.toString (length tacs)) 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

909 
else (); 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

910 

561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

911 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

912 
(*Tableau prover based on leanTaP. Argument is a list of branches. Each 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

913 
branch contains a list of unexpanded formulae, a list of literals, and a 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

914 
bound on unsafe expansions. 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

915 
"start" is CPU time at start, for printing search time 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

916 
*) 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

917 
fun prove (sign, start, cs, brs, cont) = 
4653  918 
let val {safe0_netpair, safep_netpair, haz_netpair, ...} = Data.rep_cs cs 
2854  919 
val safeList = [safe0_netpair, safep_netpair] 
920 
and hazList = [haz_netpair] 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

921 
fun prv (tacs, trs, choices, []) = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

922 
(printStats (!trace orelse !stats, start, tacs); 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

923 
cont (tacs, trs, choices)) (*all branches closed!*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

924 
 prv (tacs, trs, choices, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

925 
brs0 as {pairs = ((G,md)::br, haz)::pairs, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

926 
lits, vars, lim} :: brs) = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

927 
(*apply a safe rule only (possibly allowing instantiation); 
3917  928 
defer any haz formulae*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

929 
let exception PRV (*backtrack to precisely this recursion!*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

930 
val ntrl = !ntrail 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

931 
val nbrs = length brs0 
2854  932 
val nxtVars = nextVars brs 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

933 
val G = norm G 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

934 
val rules = netMkRules G vars safeList 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

935 
(*Make a new branch, decrementing "lim" if instantiations occur*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

936 
fun newBr (vars',lim') prems = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

937 
map (fn prem => 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

938 
if (exists isGoal prem) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

939 
then {pairs = ((joinMd md prem, []) :: 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

940 
negOfGoals ((br, haz)::pairs)), 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

941 
lits = map negOfGoal lits, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

942 
vars = vars', 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

943 
lim = lim'} 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

944 
else {pairs = ((joinMd md prem, []) :: 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

945 
(br, haz) :: pairs), 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

946 
lits = lits, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

947 
vars = vars', 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

948 
lim = lim'}) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

949 
prems @ 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

950 
brs 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

951 
(*Seek a matching rule. If unifiable then add new premises 
2854  952 
to branch.*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

953 
fun deeper [] = raise NEWBRANCHES 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

954 
 deeper (((P,prems),tac)::grls) = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

955 
if unify(add_term_vars(P,[]), P, G) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

956 
then (*P comes from the rule; G comes from the branch.*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

957 
let val updated = ntrl < !ntrail (*branch updated*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

958 
val lim' = if updated 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

959 
then lim  (1+log(length rules)) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

960 
else lim (*discourage branching updates*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

961 
val vars = vars_in_vars vars 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

962 
val vars' = foldr add_terms_vars vars prems 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

963 
val choices' = (ntrl, nbrs, PRV) :: choices 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

964 
val tacs' = (tac(updated,false,true)) 
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset

965 
:: tacs (*no duplication; rotate*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

966 
in 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

967 
traceNew prems; traceVars sign ntrl; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

968 
(if null prems then (*closed the branch: prune!*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

969 
(nclosed := !nclosed + 1; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

970 
prv(tacs', brs0::trs, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

971 
prune (nbrs, nxtVars, choices'), 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

972 
brs)) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

973 
else (*prems nonnull*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

974 
if lim'<0 (*faster to kill ALL the alternatives*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

975 
then (traceMsg"Excessive branching: KILLED"; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

976 
clearTo ntrl; raise NEWBRANCHES) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

977 
else 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

978 
(ntried := !ntried + length prems  1; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

979 
prv(tacs', brs0::trs, choices', 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

980 
newBr (vars',lim') prems))) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

981 
handle PRV => 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

982 
if updated then 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

983 
(*Backtrack at this level. 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

984 
Reset Vars and try another rule*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

985 
(clearTo ntrl; deeper grls) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

986 
else (*backtrack to previous level*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

987 
backtrack choices 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

988 
end 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

989 
else deeper grls 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

990 
(*Try to close branch by unifying with head goal*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

991 
fun closeF [] = raise CLOSEF 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

992 
 closeF (L::Ls) = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

993 
case tryClose(G,L) of 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

994 
NONE => closeF Ls 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

995 
 SOME tac => 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

996 
let val choices' = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

997 
(if !trace then (immediate_output"branch closed"; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

998 
traceVars sign ntrl) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

999 
else (); 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1000 
prune (nbrs, nxtVars, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1001 
(ntrl, nbrs, PRV) :: choices)) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1002 
in nclosed := !nclosed + 1; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1003 
prv (tac::tacs, brs0::trs, choices', brs) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1004 
handle PRV => 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1005 
(*reset Vars and try another literal 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1006 
[this handler is pruned if possible!]*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1007 
(clearTo ntrl; closeF Ls) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1008 
end 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1009 
(*Try to unify a queued formula (safe or haz) with head goal*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1010 
fun closeFl [] = raise CLOSEF 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1011 
 closeFl ((br, haz)::pairs) = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1012 
closeF (map fst br) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1013 
handle CLOSEF => closeF (map fst haz) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1014 
handle CLOSEF => closeFl pairs 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1015 
in tracing sign brs0; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1016 
if lim<0 then (traceMsg "Limit reached. "; backtrack choices) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1017 
else 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1018 
prv (Data.hyp_subst_tac trace :: tacs, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1019 
brs0::trs, choices, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1020 
equalSubst sign 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1021 
(G, {pairs = (br,haz)::pairs, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1022 
lits = lits, vars = vars, lim = lim}) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1023 
:: brs) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1024 
handle DEST_EQ => closeF lits 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1025 
handle CLOSEF => closeFl ((br,haz)::pairs) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1026 
handle CLOSEF => deeper rules 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1027 
handle NEWBRANCHES => 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1028 
(case netMkRules G vars hazList of 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1029 
[] => (*there are no plausible haz rules*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1030 
(traceMsg "moving formula to literals"; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1031 
prv (tacs, brs0::trs, choices, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1032 
{pairs = (br,haz)::pairs, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1033 
lits = addLit(G,lits), 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1034 
vars = vars, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1035 
lim = lim} :: brs)) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1036 
 _ => (*G admits some haz rules: try later*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1037 
(traceMsg "moving formula to haz list"; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1038 
prv (if isGoal G then negOfGoal_tac :: tacs 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1039 
else tacs, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1040 
brs0::trs, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1041 
choices, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1042 
{pairs = (br, haz@[(negOfGoal G, md)])::pairs, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1043 
lits = lits, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1044 
vars = vars, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1045 
lim = lim} :: brs))) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1046 
end 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1047 
 prv (tacs, trs, choices, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1048 
{pairs = ([],haz)::(Gs,haz')::pairs, lits, vars, lim} :: brs) = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1049 
(*no more "safe" formulae: transfer haz down a level*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1050 
prv (tacs, trs, choices, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1051 
{pairs = (Gs,haz@haz')::pairs, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1052 
lits = lits, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1053 
vars = vars, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1054 
lim = lim} :: brs) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1055 
 prv (tacs, trs, choices, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1056 
brs0 as {pairs = [([], (H,md)::Hs)], 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1057 
lits, vars, lim} :: brs) = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1058 
(*no safe steps possible at any level: apply a haz rule*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1059 
let exception PRV (*backtrack to precisely this recursion!*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1060 
val H = norm H 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1061 
val ntrl = !ntrail 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1062 
val rules = netMkRules H vars hazList 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1063 
(*new premises of haz rules may NOT be duplicated*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1064 
fun newPrem (vars,P,dup,lim') prem = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1065 
let val Gs' = map (fn Q => (Q,false)) prem 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1066 
and Hs' = if dup then Hs @ [(negOfGoal H, md)] else Hs 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1067 
and lits' = if (exists isGoal prem) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1068 
then map negOfGoal lits 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1069 
else lits 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1070 
in {pairs = if exists (match P) prem then [(Gs',Hs')] 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1071 
(*Recursive in this premise. Don't make new 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1072 
"stack frame". New haz premises will end up 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1073 
at the BACK of the queue, preventing 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1074 
exclusion of others*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1075 
else [(Gs',[]), ([],Hs')], 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1076 
lits = lits', 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1077 
vars = vars, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1078 
lim = lim'} 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1079 
end 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1080 
fun newBr x prems = map (newPrem x) prems @ brs 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1081 
(*Seek a matching rule. If unifiable then add new premises 
2854  1082 
to branch.*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1083 
fun deeper [] = raise NEWBRANCHES 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1084 
 deeper (((P,prems),tac)::grls) = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1085 
if unify(add_term_vars(P,[]), P, H) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1086 
then 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1087 
let val updated = ntrl < !ntrail (*branch updated*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1088 
val vars = vars_in_vars vars 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1089 
val vars' = foldr add_terms_vars vars prems 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1090 
(*duplicate H if md permits*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1091 
val dup = md (*earlier had "andalso vars' <> vars": 
11152
32d002362005
Blast bug fix: now always duplicates when applying a haz rule,
paulson
parents:
11119
diff
changeset

1092 
duplicate only if the subgoal has new vars*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1093 
(*any instances of P in the subgoals? 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1094 
NB: boolean "recur" affects tracing only!*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1095 
and recur = exists (exists (match P)) prems 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1096 
val lim' = (*Decrement "lim" extra if updates occur*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1097 
if updated then lim  (1+log(length rules)) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1098 
else lim1 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1099 
(*It is tempting to leave "lim" UNCHANGED if 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1100 
both dup and recur are false. Proofs are 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1101 
found at shallower depths, but looping 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1102 
occurs too often...*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1103 
val mayUndo = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1104 
(*Allowing backtracking from a rule application 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1105 
if other matching rules exist, if the rule 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1106 
updated variables, or if the rule did not 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1107 
introduce new variables. This latter condition 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1108 
means it is not a standard "gammarule" but 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1109 
some other form of unsafe rule. Aim is to 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1110 
emulate Fast_tac, which allows all unsafe steps 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1111 
to be undone.*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1112 
not(null grls) (*other rules to try?*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1113 
orelse updated 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1114 
orelse vars=vars' (*no new Vars?*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1115 
val tac' = tac(updated, dup, true) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1116 
(*if recur then perhaps shouldn't call rotate_tac: new 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1117 
formulae should be last, but that's WRONG if the new 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1118 
formulae are Goals, since they remain in the first 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1119 
position*) 
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1120 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1121 
in 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1122 
if lim'<0 andalso not (null prems) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1123 
then (*it's faster to kill ALL the alternatives*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1124 
(traceMsg"Excessive branching: KILLED"; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1125 
clearTo ntrl; raise NEWBRANCHES) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1126 
else 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1127 
traceNew prems; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1128 
if !trace andalso dup then immediate_output" (duplicating)" 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1129 
else (); 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1130 
if !trace andalso recur then immediate_output" (recursive)" 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1131 
else (); 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1132 
traceVars sign ntrl; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1133 
if null prems then nclosed := !nclosed + 1 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1134 
else ntried := !ntried + length prems  1; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1135 
prv(tac' :: tacs, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1136 
brs0::trs, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1137 
(ntrl, length brs0, PRV) :: choices, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1138 
newBr (vars', P, dup, lim') prems) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1139 
handle PRV => 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1140 
if mayUndo 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1141 
then (*reset Vars and try another rule*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1142 
(clearTo ntrl; deeper grls) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1143 
else (*backtrack to previous level*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1144 
backtrack choices 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1145 
end 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1146 
else deeper grls 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1147 
in tracing sign brs0; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1148 
if lim<1 then (traceMsg "Limit reached. "; backtrack choices) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1149 
else deeper rules 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1150 
handle NEWBRANCHES => 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1151 
(*cannot close branch: move H to literals*) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1152 
prv (tacs, brs0::trs, choices, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1153 
{pairs = [([], Hs)], 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1154 
lits = H::lits, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1155 
vars = vars, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1156 
lim = lim} :: brs) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1157 
end 
2854  1158 
 prv (tacs, trs, choices, _ :: brs) = backtrack choices 
12346  1159 
in prv ([], [], [(!ntrail, length brs, PROVE)], brs) end; 
2854  1160 

1161 

2883  1162 
(*Construct an initial branch.*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1163 
fun initBranch (ts,lim) = 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1164 
{pairs = [(map (fn t => (t,true)) ts, [])], 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1165 
lits = [], 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1166 
vars = add_terms_vars (ts,[]), 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1167 
lim = lim}; 
2854  1168 

1169 

1170 
(*** Conversion & Skolemization of the Isabelle proof state ***) 

1171 

1172 
(*Make a list of all the parameters in a subgoal, even if nested*) 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1173 
local open Term 
2854  1174 
in 
1175 
fun discard_foralls (Const("all",_)$Abs(a,T,t)) = discard_foralls t 

1176 
 discard_foralls t = t; 

1177 
end; 

1178 

1179 
(*List of variables not appearing as arguments to the given parameter*) 

1180 
fun getVars [] i = [] 

20664  1181 
 getVars ((_,(v,is))::alist) (i: int) = 
1182 
if member (op =) is i then getVars alist i 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1183 
else v :: getVars alist i; 
2854  1184 

4233
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

1185 
exception TRANS of string; 
2854  1186 

4233
85d004a96b98
Rationalized error handling: if lowlevel tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset

1187 
(*Translation of a subgoal: Skolemize all parameters*) 
4065  1188 
fun fromSubgoal t = 
1189 
let val alistVar = ref [] 

1190 
and alistTVar = ref [] 

2854  1191 
fun hdvar ((ix,(v,is))::_) = v 
1192 
fun from lev t = 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1193 
let val (ht,ts) = Term.strip_comb t 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1194 
fun apply u = list_comb (u, map (from lev) ts) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1195 
fun bounds [] = [] 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1196 
 bounds (Term.Bound i::ts) = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1197 
if i<lev then raise TRANS 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1198 
"Function unknown's argument not a parameter" 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1199 
else ilev :: bounds ts 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1200 
 bounds ts = raise TRANS 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1201 
"Function unknown's argument not a bound variable" 
2854  1202 
in 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1203 
case ht of 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1204 
Term.Const aT => apply (fromConst alistTVar aT) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1205 
 Term.Free (a,_) => apply (Free a) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1206 
 Term.Bound i => apply (Bound i) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1207 
 Term.Var (ix,_) => 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1208 
(case (AList.lookup (op =) (!alistVar) ix) of 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1209 
NONE => (alistVar := (ix, (ref NONE, bounds ts)) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1210 
:: !alistVar; 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1211 
Var (hdvar(!alistVar))) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1212 
 SOME(v,is) => if is=bounds ts then Var v 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1213 
else raise TRANS 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1214 
("Discrepancy among occurrences of " 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1215 
^ Syntax.string_of_vname ix)) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1216 
 Term.Abs (a,_,body) => 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1217 
if null ts then Abs(a, from (lev+1) body) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1218 
else raise TRANS "argument not in normal form" 
2854  1219 
end 
1220 

1221 
val npars = length (Logic.strip_params t) 

1222 

1223 
(*Skolemize a subgoal from a proof state*) 

1224 
fun skoSubgoal i t = 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1225 
if i<npars then 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1226 
skoSubgoal (i+1) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1227 
(subst_bound (Skolem (gensym "T_", getVars (!alistVar) i), 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1228 
t)) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1229 
else t 
2854  1230 

1231 
in skoSubgoal 0 (from 0 (discard_foralls t)) end; 

1232 

1233 

18533  1234 
fun reject_const thy c = 
1235 
if is_some (Sign.const_type thy c) then 

1236 
error ("Blast: theory contains illegal constant " ^ quote c) 

1237 
else (); 

1238 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1239 
fun initialize thy = 
18533  1240 
(fullTrace:=[]; trail := []; ntrail := 0; 
1241 
nclosed := 0; ntried := 1; typargs := Sign.const_typargs thy; 

1242 
reject_const thy "*Goal*"; reject_const thy "*False*"); 

4300  1243 

1244 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1245 
(*Tactic using tableau engine and proof reconstruction. 
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1246 
"start" is CPU time at start, for printing SEARCH time 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1247 
(also prints reconstruction time) 
2854  1248 
"lim" is depth limit.*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1249 
fun timing_depth_tac start cs lim i st0 = 
16774
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset

1250 
let val st = (initialize (theory_of_thm st0); ObjectLogic.atomize_goal i st0); 
9486
2df511ebb956
handle actual objectlogic rules by atomizing the goal;
wenzelm
parents:
9170
diff
changeset

1251 
val {sign,...} = rep_thm st 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1252 
val skoprem = fromSubgoal (List.nth(prems_of st, i1)) 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1253 
val hyps = strip_imp_prems skoprem 
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1254 
and concl = strip_imp_concl skoprem 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1255 
fun cont (tacs,_,choices) = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1256 
let val start = startTiming() 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1257 
in 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1258 
case Seq.pull(EVERY' (rev tacs) i st) of 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1259 
NONE => (writeln ("PROOF FAILED for depth " ^ 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1260 
Int.toString lim); 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1261 
if !trace then error "************************\n" 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1262 
else (); 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1263 
backtrack choices) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1264 
 cell => (if (!trace orelse !stats) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1265 
then writeln (endTiming start ^ " for reconstruction") 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1266 
else (); 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1267 
Seq.make(fn()=> cell)) 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1268 
end 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1269 
in prove (sign, start, cs, [initBranch (mkGoal concl :: hyps, lim)], cont) 
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset

1270 
end 
16774
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset

1271 
handle PROVE => Seq.empty; 
2854  1272 

4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1273 
(*Public version with fixed depth*) 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1274 
fun depth_tac cs lim i st = timing_depth_tac (startTiming()) cs lim i st; 
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset

1275 

15162
670ab8497818
depth limit (previously hardcoded with a value of 20) made a reference
webertj
parents:
14984
diff
changeset

1276 
val depth_limit = ref 20; 
670ab8497818
depth limit (previously hardcoded with a value of 20) made a reference
webertj
parents:
14984
diff
changeset

1277 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1278 
fun blast_tac cs i st = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1279 
((DEEPEN (1, !depth_limit) (timing_depth_tac (startTiming()) cs) 0) i 
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset

1280 
THEN flexflex_tac) st 
14466  1281 
handle TRANS s => 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1282 
((if !trace then warning ("blast: " ^ s) else ()); 
14466  1283 
Seq.empty); 
2854  1284 

4078  1285 
fun Blast_tac i = blast_tac (Data.claset()) i; 
2854  1286 

2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1287 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1288 
(*** For debugging: these apply the prover to a subgoal and return 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1289 
the resulting tactics, trace, etc. ***) 
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1290 

af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1291 
(*Translate subgoal i from a proof state*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1292 
fun trygl cs lim i = 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1293 
let val st = topthm() 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1294 
val {sign,...} = rep_thm st 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1295 
val skoprem = (initialize (theory_of_thm st); 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1296 
fromSubgoal (List.nth(prems_of st, i1))) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1297 
val hyps = strip_imp_prems skoprem 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1298 
and concl = strip_imp_concl skoprem 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1299 
in timeap prove (sign, startTiming(), cs, 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1300 
[initBranch (mkGoal concl :: hyps, lim)], I) 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1301 
end 
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1302 
handle Subscript => error("There is no subgoal " ^ Int.toString i); 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1303 

4078  1304 
fun Trygl lim i = trygl (Data.claset()) lim i; 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1305 

af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1306 
(*Read a string to make an initial, singleton branch*) 
18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1307 
fun readGoal thy s = Sign.read_prop thy s > fromTerm > rand > mkGoal; 
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset

1308 

18525
ce1ae48c320f
avoid implicit assumptions about consts Not, op =, *Goal*, *False*;
wenzelm
parents:
18177
diff
changeset

1309 
fun tryInThy thy lim s = 
16774
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset

1310< 