src/FOL/intprover.ML
author haftmann
Mon Jun 05 15:59:41 2017 +0200 (2017-06-05)
changeset 66010 2f7d39285a1a
parent 59529 d881f5288d5a
permissions -rw-r--r--
executable domain membership checks
     1 (*  Title:      FOL/intprover.ML
     2     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     3     Copyright   1992  University of Cambridge
     4 
     5 A naive prover for intuitionistic logic
     6 
     7 BEWARE OF NAME CLASHES WITH CLASSICAL TACTICS -- use IntPr.fast_tac ...
     8 
     9 Completeness (for propositional logic) is proved in
    10 
    11 Roy Dyckhoff.
    12 Contraction-Free Sequent Calculi for Intuitionistic Logic.
    13 J. Symbolic Logic  57(3), 1992, pages 795-807.
    14 
    15 The approach was developed independently by Roy Dyckhoff and L C Paulson.
    16 *)
    17 
    18 signature INT_PROVER =
    19 sig
    20   val best_tac: Proof.context -> int -> tactic
    21   val best_dup_tac: Proof.context -> int -> tactic
    22   val fast_tac: Proof.context -> int -> tactic
    23   val inst_step_tac: Proof.context -> int -> tactic
    24   val safe_step_tac: Proof.context -> int -> tactic
    25   val safe_brls: (bool * thm) list
    26   val safe_tac: Proof.context -> tactic
    27   val step_tac: Proof.context -> int -> tactic
    28   val step_dup_tac: Proof.context -> int -> tactic
    29   val haz_brls: (bool * thm) list
    30   val haz_dup_brls: (bool * thm) list
    31 end;
    32 
    33 
    34 structure IntPr : INT_PROVER   =
    35 struct
    36 
    37 (*Negation is treated as a primitive symbol, with rules notI (introduction),
    38   not_to_imp (converts the assumption ~P to P-->False), and not_impE
    39   (handles double negations).  Could instead rewrite by not_def as the first
    40   step of an intuitionistic proof.
    41 *)
    42 val safe_brls = sort (make_ord lessb)
    43     [ (true, @{thm FalseE}), (false, @{thm TrueI}), (false, @{thm refl}),
    44       (false, @{thm impI}), (false, @{thm notI}), (false, @{thm allI}),
    45       (true, @{thm conjE}), (true, @{thm exE}),
    46       (false, @{thm conjI}), (true, @{thm conj_impE}),
    47       (true, @{thm disj_impE}), (true, @{thm disjE}),
    48       (false, @{thm iffI}), (true, @{thm iffE}), (true, @{thm not_to_imp}) ];
    49 
    50 val haz_brls =
    51     [ (false, @{thm disjI1}), (false, @{thm disjI2}), (false, @{thm exI}),
    52       (true, @{thm allE}), (true, @{thm not_impE}), (true, @{thm imp_impE}), (true, @{thm iff_impE}),
    53       (true, @{thm all_impE}), (true, @{thm ex_impE}), (true, @{thm impE}) ];
    54 
    55 val haz_dup_brls =
    56     [ (false, @{thm disjI1}), (false, @{thm disjI2}), (false, @{thm exI}),
    57       (true, @{thm all_dupE}), (true, @{thm not_impE}), (true, @{thm imp_impE}), (true, @{thm iff_impE}),
    58       (true, @{thm all_impE}), (true, @{thm ex_impE}), (true, @{thm impE}) ];
    59 
    60 (*0 subgoals vs 1 or more: the p in safep is for positive*)
    61 val (safe0_brls, safep_brls) =
    62     List.partition (curry (op =) 0 o subgoals_of_brl) safe_brls;
    63 
    64 (*Attack subgoals using safe inferences -- matching, not resolution*)
    65 fun safe_step_tac ctxt =
    66   FIRST' [
    67     eq_assume_tac,
    68     eq_mp_tac ctxt,
    69     bimatch_tac ctxt safe0_brls,
    70     hyp_subst_tac ctxt,
    71     bimatch_tac ctxt safep_brls];
    72 
    73 (*Repeatedly attack subgoals using safe inferences -- it's deterministic!*)
    74 fun safe_tac ctxt = REPEAT_DETERM_FIRST (safe_step_tac ctxt);
    75 
    76 (*These steps could instantiate variables and are therefore unsafe.*)
    77 fun inst_step_tac ctxt =
    78   assume_tac ctxt APPEND' mp_tac ctxt APPEND'
    79   biresolve_tac ctxt (safe0_brls @ safep_brls);
    80 
    81 (*One safe or unsafe step. *)
    82 fun step_tac ctxt i =
    83   FIRST [safe_tac ctxt, inst_step_tac ctxt i, biresolve_tac ctxt haz_brls i];
    84 
    85 fun step_dup_tac ctxt i =
    86   FIRST [safe_tac ctxt, inst_step_tac ctxt i, biresolve_tac ctxt haz_dup_brls i];
    87 
    88 (*Dumb but fast*)
    89 fun fast_tac ctxt = SELECT_GOAL (DEPTH_SOLVE (step_tac ctxt 1));
    90 
    91 (*Slower but smarter than fast_tac*)
    92 fun best_tac ctxt =
    93   SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, size_of_thm) (step_tac ctxt 1));
    94 
    95 (*Uses all_dupE: allows multiple use of universal assumptions.  VERY slow.*)
    96 fun best_dup_tac ctxt =
    97   SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, size_of_thm) (step_dup_tac ctxt 1));
    98 
    99 
   100 end;
   101