src/FOL/intprover.ML

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−(*  Title:      FOL/int-prover
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−    ID:         $Id$
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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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−
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−A naive prover for intuitionistic logic
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−
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−BEWARE OF NAME CLASHES WITH CLASSICAL TACTICS -- use IntPr.fast_tac ...
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−
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−Completeness (for propositional logic) is proved in 
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−
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−Roy Dyckhoff.
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−Contraction-Free Sequent Calculi for Intuitionistic Logic.
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−J. Symbolic Logic  57(3), 1992, pages 795-807.
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−
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−The approach was developed independently by Roy Dyckhoff and L C Paulson.
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−*)
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−
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−signature INT_PROVER = 
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−  sig
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−  val best_tac: int -> tactic
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−  val fast_tac: int -> tactic
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−  val inst_step_tac: int -> tactic
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−  val safe_step_tac: int -> tactic
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−  val safe_brls: (bool * thm) list
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−  val safe_tac: tactic
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−  val step_tac: int -> tactic
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−  val haz_brls: (bool * thm) list
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−  end;
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−
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−
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−structure IntPr : INT_PROVER   = 
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−struct
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−
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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 lessb 
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−    [ (true,FalseE), (false,TrueI), (false,refl),
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−      (false,impI), (false,notI), (false,allI),
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−      (true,conjE), (true,exE),
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−      (false,conjI), (true,conj_impE),
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−      (true,disj_impE), (true,disjE), 
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−      (false,iffI), (true,iffE), (true,not_to_imp) ];
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−
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−val haz_brls =
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−    [ (false,disjI1), (false,disjI2), (false,exI), 
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−      (true,allE), (true,not_impE), (true,imp_impE), (true,iff_impE),
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−      (true,all_impE), (true,ex_impE), (true,impE) ];
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−
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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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−    partition (apl(0,op=) o subgoals_of_brl) safe_brls;
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−
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−(*Attack subgoals using safe inferences -- matching, not resolution*)
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−val safe_step_tac = FIRST' [eq_assume_tac,
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−                            eq_mp_tac,
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−                            bimatch_tac safe0_brls,
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−                            hyp_subst_tac,
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−                            bimatch_tac safep_brls] ;
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−
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−(*Repeatedly attack subgoals using safe inferences -- it's deterministic!*)
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−val safe_tac = REPEAT_DETERM_FIRST safe_step_tac;
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−
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−(*These steps could instantiate variables and are therefore unsafe.*)
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−val inst_step_tac =
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−  assume_tac APPEND' mp_tac APPEND' 
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−  biresolve_tac (safe0_brls @ safep_brls);
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−
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−(*One safe or unsafe step. *)
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−fun step_tac i = FIRST [safe_tac, inst_step_tac i, biresolve_tac haz_brls i];
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−
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−(*Dumb but fast*)
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−val fast_tac = SELECT_GOAL (DEPTH_SOLVE (step_tac 1));
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−
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−(*Slower but smarter than fast_tac*)
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−val best_tac = 
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−  SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, size_of_thm) (step_tac 1));
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−
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−end;
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−