src/FOLP/intprover.ML
author wenzelm
Mon Nov 10 21:49:48 2014 +0100 (2014-11-10)
changeset 58963 26bf09b95dda
parent 52457 c3b4b74a54fd
child 59498 50b60f501b05
permissions -rw-r--r--
proper context for assume_tac (atac remains as fall-back without context);
     1 (*  Title:      FOLP/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 (in press)
    14 *)
    15 
    16 signature INT_PROVER = 
    17   sig
    18   val best_tac: Proof.context -> int -> tactic
    19   val fast_tac: Proof.context -> int -> tactic
    20   val inst_step_tac: Proof.context -> int -> tactic
    21   val safe_step_tac: Proof.context -> int -> tactic
    22   val safe_brls: (bool * thm) list
    23   val safe_tac: Proof.context -> tactic
    24   val step_tac: Proof.context -> int -> tactic
    25   val haz_brls: (bool * thm) list
    26   end;
    27 
    28 
    29 structure IntPr : INT_PROVER   = 
    30 struct
    31 
    32 (*Negation is treated as a primitive symbol, with rules notI (introduction),
    33   not_to_imp (converts the assumption ~P to P-->False), and not_impE
    34   (handles double negations).  Could instead rewrite by not_def as the first
    35   step of an intuitionistic proof.
    36 *)
    37 val safe_brls = sort (make_ord lessb)
    38     [ (true, @{thm FalseE}), (false, @{thm TrueI}), (false, @{thm refl}),
    39       (false, @{thm impI}), (false, @{thm notI}), (false, @{thm allI}),
    40       (true, @{thm conjE}), (true, @{thm exE}),
    41       (false, @{thm conjI}), (true, @{thm conj_impE}),
    42       (true, @{thm disj_impE}), (true, @{thm disjE}), 
    43       (false, @{thm iffI}), (true, @{thm iffE}), (true, @{thm not_to_imp}) ];
    44 
    45 val haz_brls =
    46     [ (false, @{thm disjI1}), (false, @{thm disjI2}), (false, @{thm exI}), 
    47       (true, @{thm allE}), (true, @{thm not_impE}), (true, @{thm imp_impE}), (true, @{thm iff_impE}),
    48       (true, @{thm all_impE}), (true, @{thm ex_impE}), (true, @{thm impE}) ];
    49 
    50 (*0 subgoals vs 1 or more: the p in safep is for positive*)
    51 val (safe0_brls, safep_brls) =
    52     List.partition (curry (op =) 0 o subgoals_of_brl) safe_brls;
    53 
    54 (*Attack subgoals using safe inferences*)
    55 fun safe_step_tac ctxt = FIRST' [uniq_assume_tac ctxt,
    56                             int_uniq_mp_tac ctxt,
    57                             biresolve_tac safe0_brls,
    58                             hyp_subst_tac,
    59                             biresolve_tac safep_brls] ;
    60 
    61 (*Repeatedly attack subgoals using safe inferences*)
    62 fun safe_tac ctxt = DETERM (REPEAT_FIRST (safe_step_tac ctxt));
    63 
    64 (*These steps could instantiate variables and are therefore unsafe.*)
    65 fun inst_step_tac ctxt = assume_tac ctxt APPEND' mp_tac ctxt;
    66 
    67 (*One safe or unsafe step. *)
    68 fun step_tac ctxt i = FIRST [safe_tac ctxt, inst_step_tac ctxt i, biresolve_tac haz_brls i];
    69 
    70 (*Dumb but fast*)
    71 fun fast_tac ctxt = SELECT_GOAL (DEPTH_SOLVE (step_tac ctxt 1));
    72 
    73 (*Slower but smarter than fast_tac*)
    74 fun best_tac ctxt =
    75   SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, size_of_thm) (step_tac ctxt 1));
    76 
    77 end;