author  blanchet 
Mon, 20 Dec 2010 14:17:49 +0100  
changeset 41317  fc48faccd77b 
parent 38500  d5477ee35820 
child 41449  7339f0e7c513 
permissions  rwrr 
24584  1 
(* 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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29269
5c25a2012975
moved term order operations to structure TermOrd (cf. Pure/term_ord.ML);
wenzelm
parents:
24584
diff
changeset

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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 : thm list > int >tactic 

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val step_tac : int > tactic 

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val solven_tac : int > int > tactic 

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val solve_tac : 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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local open Modal_Rule 

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in 

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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) = 

29269
5c25a2012975
moved term order operations to structure TermOrd (cf. Pure/term_ord.ML);
wenzelm
parents:
24584
diff
changeset

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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 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 rls i 

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end); 

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fun fresolve_tac rls n = filseq_resolve_tac rls 999 n; 

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(* NB No back tracking possible with aside rules *) 

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fun aside_tac n = DETERM(REPEAT (filt_resolve_tac aside_rls 999 n)); 

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fun rule_tac rls n = fresolve_tac rls n THEN aside_tac n; 

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val fres_safe_tac = fresolve_tac safe_rls; 

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val fres_unsafe_tac = fresolve_tac unsafe_rls THEN' aside_tac; 

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val fres_bound_tac = fresolve_tac 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 (nprems_of st) st end; 

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(* Depth first search bounded by d *) 

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fun solven_tac d n state = state > 

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(if d<0 then no_tac 

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else if (nprems_of state = 0) then all_tac 

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else (DETERM(fres_safe_tac n) THEN UPTOGOAL n (solven_tac d)) ORELSE 

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((fres_unsafe_tac n THEN UPTOGOAL n (solven_tac d)) APPEND 

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(fres_bound_tac n THEN UPTOGOAL n (solven_tac (d1))))); 

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fun solve_tac d = rewrite_goals_tac rewrite_rls THEN solven_tac d 1; 

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fun step_tac n = 

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COND (has_fewer_prems 1) all_tac 

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(DETERM(fres_safe_tac n) ORELSE 

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(fres_unsafe_tac n APPEND fres_bound_tac n)); 
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end; 

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end; 