author  hoelzl 
Mon, 08 Aug 2016 14:13:14 +0200  
changeset 63627  6ddb43c6b711 
parent 59582  0fbed69ff081 
child 69593  3dda49e08b9d 
permissions  rwrr 
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(* Title: Sequents/modal.ML 
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory 
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Copyright 1992 University of Cambridge 

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Simple modal reasoner. 
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*) 
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signature MODAL_PROVER_RULE = 

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sig 

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val rewrite_rls : thm list 
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val safe_rls : thm list 

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val unsafe_rls : thm list 

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val bound_rls : thm list 

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val aside_rls : thm list 

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end; 
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signature MODAL_PROVER = 
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sig 
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val rule_tac : Proof.context > thm list > int >tactic 
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val step_tac : Proof.context > int > tactic 

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val solven_tac : Proof.context > int > int > tactic 

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val solve_tac : Proof.context > int > tactic 

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end; 
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functor Modal_ProverFun (Modal_Rule: MODAL_PROVER_RULE) : MODAL_PROVER = 
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struct 
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(*Returns the list of all formulas in the sequent*) 

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fun forms_of_seq (Const(@{const_name SeqO'},_) $ P $ u) = P :: forms_of_seq u 
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 forms_of_seq (H $ u) = forms_of_seq u 
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 forms_of_seq _ = []; 

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(*Tests whether two sequences (left or right sides) could be resolved. 

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seqp is a premise (subgoal), seqc is a conclusion of an objectrule. 

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Assumes each formula in seqc is surrounded by sequence variables 

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 checks that each concl formula looks like some subgoal formula.*) 

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fun could_res (seqp,seqc) = 

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forall (fn Qc => exists (fn Qp => Term.could_unify (Qp,Qc)) 
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(forms_of_seq seqp)) 
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(forms_of_seq seqc); 

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(*Tests whether two sequents GH could be resolved, comparing each side.*) 

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fun could_resolve_seq (prem,conc) = 

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case (prem,conc) of 

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(_ $ Abs(_,_,leftp) $ Abs(_,_,rightp), 

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_ $ Abs(_,_,leftc) $ Abs(_,_,rightc)) => 

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could_res (leftp,leftc) andalso could_res (rightp,rightc) 

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 _ => false; 

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(*Like filt_resolve_tac, using could_resolve_seq 

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Much faster than resolve_tac when there are many rules. 

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Resolve subgoal i using the rules, unless more than maxr are compatible. *) 

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fun filseq_resolve_tac ctxt rules maxr = SUBGOAL(fn (prem,i) => 
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let val rls = filter_thms could_resolve_seq (maxr+1, prem, rules) 
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in if length rls > maxr then no_tac else resolve_tac ctxt rls i 
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end); 
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fun fresolve_tac ctxt rls n = filseq_resolve_tac ctxt rls 999 n; 
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(* NB No back tracking possible with aside rules *) 

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val aside_net = Tactic.build_net Modal_Rule.aside_rls; 
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fun aside_tac ctxt n = DETERM (REPEAT (filt_resolve_from_net_tac ctxt 999 aside_net n)); 

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fun rule_tac ctxt rls n = fresolve_tac ctxt rls n THEN aside_tac ctxt n; 
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fun fres_safe_tac ctxt = fresolve_tac ctxt Modal_Rule.safe_rls; 
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fun fres_unsafe_tac ctxt = fresolve_tac ctxt Modal_Rule.unsafe_rls THEN' aside_tac ctxt; 
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fun fres_bound_tac ctxt = fresolve_tac ctxt Modal_Rule.bound_rls; 
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fun UPTOGOAL n tf = let fun tac i = if i<n then all_tac 

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else tf(i) THEN tac(i1) 

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in fn st => tac (Thm.nprems_of st) st end; 
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(* Depth first search bounded by d *) 

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fun solven_tac ctxt d n st = st > 
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(if d < 0 then no_tac 

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else if Thm.nprems_of st = 0 then all_tac 
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else (DETERM(fres_safe_tac ctxt n) THEN UPTOGOAL n (solven_tac ctxt d)) ORELSE 
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((fres_unsafe_tac ctxt n THEN UPTOGOAL n (solven_tac ctxt d)) APPEND 
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(fres_bound_tac ctxt n THEN UPTOGOAL n (solven_tac ctxt (d  1))))); 
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fun solve_tac ctxt d = 
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rewrite_goals_tac ctxt Modal_Rule.rewrite_rls THEN solven_tac ctxt d 1; 

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fun step_tac ctxt n = 
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COND (has_fewer_prems 1) all_tac 

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(DETERM(fres_safe_tac ctxt n) ORELSE 
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(fres_unsafe_tac ctxt n APPEND fres_bound_tac ctxt n)); 
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end; 