src/FOLP/intprover.ML
author wenzelm
Tue Mar 18 22:19:18 2008 +0100 (2008-03-18)
changeset 26322 eaf634e975fa
parent 24584 01e83ffa6c54
child 35762 af3ff2ba4c54
permissions -rw-r--r--
converted legacy ML scripts;
     1 (*  Title:      FOLP/intprover.ML
     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 IntPruitionistic Logic.
    14 J. Symbolic Logic (in press)
    15 *)
    16 
    17 signature INT_PROVER = 
    18   sig
    19   val best_tac: int -> tactic
    20   val fast_tac: int -> tactic
    21   val inst_step_tac: int -> tactic
    22   val safe_step_tac: int -> tactic
    23   val safe_brls: (bool * thm) list
    24   val safe_tac: tactic
    25   val step_tac: int -> tactic
    26   val haz_brls: (bool * thm) list
    27   end;
    28 
    29 
    30 structure IntPr : INT_PROVER   = 
    31 struct
    32 
    33 (*Negation is treated as a primitive symbol, with rules notI (introduction),
    34   not_to_imp (converts the assumption ~P to P-->False), and not_impE
    35   (handles double negations).  Could instead rewrite by not_def as the first
    36   step of an intuitionistic proof.
    37 *)
    38 val safe_brls = sort (make_ord lessb)
    39     [ (true, @{thm FalseE}), (false, @{thm TrueI}), (false, @{thm refl}),
    40       (false, @{thm impI}), (false, @{thm notI}), (false, @{thm allI}),
    41       (true, @{thm conjE}), (true, @{thm exE}),
    42       (false, @{thm conjI}), (true, @{thm conj_impE}),
    43       (true, @{thm disj_impE}), (true, @{thm disjE}), 
    44       (false, @{thm iffI}), (true, @{thm iffE}), (true, @{thm not_to_imp}) ];
    45 
    46 val haz_brls =
    47     [ (false, @{thm disjI1}), (false, @{thm disjI2}), (false, @{thm exI}), 
    48       (true, @{thm allE}), (true, @{thm not_impE}), (true, @{thm imp_impE}), (true, @{thm iff_impE}),
    49       (true, @{thm all_impE}), (true, @{thm ex_impE}), (true, @{thm impE}) ];
    50 
    51 (*0 subgoals vs 1 or more: the p in safep is for positive*)
    52 val (safe0_brls, safep_brls) =
    53     List.partition (curry (op =) 0 o subgoals_of_brl) safe_brls;
    54 
    55 (*Attack subgoals using safe inferences*)
    56 val safe_step_tac = FIRST' [uniq_assume_tac,
    57                             int_uniq_mp_tac,
    58                             biresolve_tac safe0_brls,
    59                             hyp_subst_tac,
    60                             biresolve_tac safep_brls] ;
    61 
    62 (*Repeatedly attack subgoals using safe inferences*)
    63 val safe_tac = DETERM (REPEAT_FIRST safe_step_tac);
    64 
    65 (*These steps could instantiate variables and are therefore unsafe.*)
    66 val inst_step_tac = assume_tac APPEND' mp_tac;
    67 
    68 (*One safe or unsafe step. *)
    69 fun step_tac i = FIRST [safe_tac, inst_step_tac i, biresolve_tac haz_brls i];
    70 
    71 (*Dumb but fast*)
    72 val fast_tac = SELECT_GOAL (DEPTH_SOLVE (step_tac 1));
    73 
    74 (*Slower but smarter than fast_tac*)
    75 val best_tac = 
    76   SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, size_of_thm) (step_tac 1));
    77 
    78 end;