src/FOL/intprover.ML
author oheimb
Thu May 15 15:51:09 1997 +0200 (1997-05-15 ago)
changeset 3206 a3de7f32728c
parent 2601 b301958c465d
child 4440 9ed4098074bc
permissions -rw-r--r--
renamed addss to addSss, unsafe_addss to addss, extended auto_tac
     1 (*  Title:      FOL/int-prover
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1992  University of Cambridge
     5 
     6 A naive prover for intuitionistic logic
     7 
     8 BEWARE OF NAME CLASHES WITH CLASSICAL TACTICS -- use IntPr.fast_tac ...
     9 
    10 Completeness (for propositional logic) is proved in 
    11 
    12 Roy Dyckhoff.
    13 Contraction-Free Sequent Calculi for Intuitionistic Logic.
    14 J. Symbolic Logic  57(3), 1992, pages 795-807.
    15 
    16 The approach was developed independently by Roy Dyckhoff and L C Paulson.
    17 *)
    18 
    19 signature INT_PROVER = 
    20   sig
    21   val best_tac: int -> tactic
    22   val fast_tac: int -> tactic
    23   val inst_step_tac: int -> tactic
    24   val safe_step_tac: int -> tactic
    25   val safe_brls: (bool * thm) list
    26   val safe_tac: tactic
    27   val step_tac: int -> tactic
    28   val haz_brls: (bool * thm) list
    29   end;
    30 
    31 
    32 structure IntPr : INT_PROVER   = 
    33 struct
    34 
    35 (*Negation is treated as a primitive symbol, with rules notI (introduction),
    36   not_to_imp (converts the assumption ~P to P-->False), and not_impE
    37   (handles double negations).  Could instead rewrite by not_def as the first
    38   step of an intuitionistic proof.
    39 *)
    40 val safe_brls = sort lessb 
    41     [ (true,FalseE), (false,TrueI), (false,refl),
    42       (false,impI), (false,notI), (false,allI),
    43       (true,conjE), (true,exE),
    44       (false,conjI), (true,conj_impE),
    45       (true,disj_impE), (true,disjE), 
    46       (false,iffI), (true,iffE), (true,not_to_imp) ];
    47 
    48 val haz_brls =
    49     [ (false,disjI1), (false,disjI2), (false,exI), 
    50       (true,allE), (true,not_impE), (true,imp_impE), (true,iff_impE),
    51       (true,all_impE), (true,ex_impE), (true,impE) ];
    52 
    53 (*0 subgoals vs 1 or more: the p in safep is for positive*)
    54 val (safe0_brls, safep_brls) =
    55     partition (apl(0,op=) o subgoals_of_brl) safe_brls;
    56 
    57 (*Attack subgoals using safe inferences -- matching, not resolution*)
    58 val safe_step_tac = FIRST' [eq_assume_tac,
    59                             eq_mp_tac,
    60                             bimatch_tac safe0_brls,
    61                             hyp_subst_tac,
    62                             bimatch_tac safep_brls] ;
    63 
    64 (*Repeatedly attack subgoals using safe inferences -- it's deterministic!*)
    65 val safe_tac = REPEAT_DETERM_FIRST safe_step_tac;
    66 
    67 (*These steps could instantiate variables and are therefore unsafe.*)
    68 val inst_step_tac =
    69   assume_tac APPEND' mp_tac APPEND' 
    70   biresolve_tac (safe0_brls @ safep_brls);
    71 
    72 (*One safe or unsafe step. *)
    73 fun step_tac i = FIRST [safe_tac, inst_step_tac i, biresolve_tac haz_brls i];
    74 
    75 (*Dumb but fast*)
    76 val fast_tac = SELECT_GOAL (DEPTH_SOLVE (step_tac 1));
    77 
    78 (*Slower but smarter than fast_tac*)
    79 val best_tac = 
    80   SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, size_of_thm) (step_tac 1));
    81 
    82 end;
    83