author  wenzelm 
Wed, 22 Apr 2020 19:22:43 +0200  
changeset 71787  acfe72ff00c2 
parent 59529  d881f5288d5a 
permissions  rwrr 
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(* Title: FOL/intprover.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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A naive prover for intuitionistic logic 

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Renamed structure Int (intuitionistic prover) to IntPr to prevent clash
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BEWARE OF NAME CLASHES WITH CLASSICAL TACTICS  use IntPr.fast_tac ... 
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Completeness (for propositional logic) is proved in 
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Roy Dyckhoff. 

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ContractionFree Sequent Calculi for Intuitionistic Logic. 

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J. Symbolic Logic 57(3), 1992, pages 795807. 
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The approach was developed independently by Roy Dyckhoff and L C Paulson. 

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*) 
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signature INT_PROVER = 
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sig 
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val best_tac: Proof.context > int > tactic 

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val best_dup_tac: Proof.context > int > tactic 

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val fast_tac: Proof.context > int > tactic 

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val inst_step_tac: Proof.context > int > tactic 
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val safe_step_tac: Proof.context > int > tactic 
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val safe_brls: (bool * thm) list 
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val safe_tac: Proof.context > tactic 
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val step_tac: Proof.context > int > tactic 

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val step_dup_tac: Proof.context > int > tactic 

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val haz_brls: (bool * thm) list 
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val haz_dup_brls: (bool * thm) list 
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end; 
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structure IntPr : INT_PROVER = 
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struct 
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(*Negation is treated as a primitive symbol, with rules notI (introduction), 

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not_to_imp (converts the assumption ~P to P>False), and not_impE 

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(handles double negations). Could instead rewrite by not_def as the first 

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step of an intuitionistic proof. 

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*) 

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val safe_brls = sort (make_ord lessb) 
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[ (true, @{thm FalseE}), (false, @{thm TrueI}), (false, @{thm refl}), 
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(false, @{thm impI}), (false, @{thm notI}), (false, @{thm allI}), 

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(true, @{thm conjE}), (true, @{thm exE}), 

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(false, @{thm conjI}), (true, @{thm conj_impE}), 

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(true, @{thm disj_impE}), (true, @{thm disjE}), 
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(false, @{thm iffI}), (true, @{thm iffE}), (true, @{thm not_to_imp}) ]; 
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val haz_brls = 

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[ (false, @{thm disjI1}), (false, @{thm disjI2}), (false, @{thm exI}), 
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(true, @{thm allE}), (true, @{thm not_impE}), (true, @{thm imp_impE}), (true, @{thm iff_impE}), 
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(true, @{thm all_impE}), (true, @{thm ex_impE}), (true, @{thm impE}) ]; 

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val haz_dup_brls = 
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[ (false, @{thm disjI1}), (false, @{thm disjI2}), (false, @{thm exI}), 
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(true, @{thm all_dupE}), (true, @{thm not_impE}), (true, @{thm imp_impE}), (true, @{thm iff_impE}), 

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(true, @{thm all_impE}), (true, @{thm ex_impE}), (true, @{thm impE}) ]; 

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(*0 subgoals vs 1 or more: the p in safep is for positive*) 
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val (safe0_brls, safep_brls) = 

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List.partition (curry (op =) 0 o subgoals_of_brl) safe_brls; 
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(*Attack subgoals using safe inferences  matching, not resolution*) 

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fun safe_step_tac ctxt = 
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FIRST' [ 

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eq_assume_tac, 

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eq_mp_tac ctxt, 
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bimatch_tac ctxt safe0_brls, 
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hyp_subst_tac ctxt, 
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bimatch_tac ctxt safep_brls]; 
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(*Repeatedly attack subgoals using safe inferences  it's deterministic!*) 

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fun safe_tac ctxt = REPEAT_DETERM_FIRST (safe_step_tac ctxt); 
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(*These steps could instantiate variables and are therefore unsafe.*) 

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fun inst_step_tac ctxt = 
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assume_tac ctxt APPEND' mp_tac ctxt APPEND' 
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biresolve_tac ctxt (safe0_brls @ safep_brls); 
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(*One safe or unsafe step. *) 

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fun step_tac ctxt i = 
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FIRST [safe_tac ctxt, inst_step_tac ctxt i, biresolve_tac ctxt haz_brls i]; 
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fun step_dup_tac ctxt i = 
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FIRST [safe_tac ctxt, inst_step_tac ctxt i, biresolve_tac ctxt haz_dup_brls i]; 
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(*Dumb but fast*) 
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fun fast_tac ctxt = SELECT_GOAL (DEPTH_SOLVE (step_tac ctxt 1)); 
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(*Slower but smarter than fast_tac*) 

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fun best_tac ctxt = 
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SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, size_of_thm) (step_tac ctxt 1)); 

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(*Uses all_dupE: allows multiple use of universal assumptions. VERY slow.*) 
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fun best_dup_tac ctxt = 
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SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, size_of_thm) (step_dup_tac ctxt 1)); 

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end; 
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