src/FOL/int-prover.ML
 author clasohm Thu Sep 16 12:20:38 1993 +0200 (1993-09-16) changeset 0 a5a9c433f639 permissions -rw-r--r--
Initial revision
```     1 (*  Title: 	FOL/int-prover
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```     2     ID:         \$Id\$
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```     3     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
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```     4     Copyright   1992  University of Cambridge
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```     5
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```     6 A naive prover for intuitionistic logic
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```     7
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```     8 BEWARE OF NAME CLASHES WITH CLASSICAL TACTICS -- use Int.fast_tac ...
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```     9
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```    10 Completeness (for propositional logic) is proved in
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```    11
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```    12 Roy Dyckhoff.
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```    13 Contraction-Free Sequent Calculi for Intuitionistic Logic.
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```    14 J. Symbolic Logic (in press)
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```    15 *)
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```    16
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```    17 signature INT_PROVER =
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```    18   sig
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```    19   val best_tac: int -> tactic
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```    20   val fast_tac: int -> tactic
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```    21   val inst_step_tac: int -> tactic
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```    22   val safe_step_tac: int -> tactic
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```    23   val safe_brls: (bool * thm) list
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```    24   val safe_tac: tactic
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```    25   val step_tac: int -> tactic
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```    26   val haz_brls: (bool * thm) list
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```    27   end;
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```    28
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```    29
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```    30 structure Int : INT_PROVER   =
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```    31 struct
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```    32
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```    33 (*Negation is treated as a primitive symbol, with rules notI (introduction),
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```    34   not_to_imp (converts the assumption ~P to P-->False), and not_impE
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```    35   (handles double negations).  Could instead rewrite by not_def as the first
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```    36   step of an intuitionistic proof.
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```    37 *)
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```    38 val safe_brls = sort lessb
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```    39     [ (true,FalseE), (false,TrueI), (false,refl),
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```    40       (false,impI), (false,notI), (false,allI),
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```    41       (true,conjE), (true,exE),
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```    42       (false,conjI), (true,conj_impE),
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```    43       (true,disj_impE), (true,ex_impE),
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```    44       (true,disjE), (false,iffI), (true,iffE), (true,not_to_imp) ];
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```    45
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```    46 val haz_brls =
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```    47     [ (false,disjI1), (false,disjI2), (false,exI),
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```    48       (true,allE), (true,not_impE), (true,imp_impE), (true,iff_impE),
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```    49       (true,all_impE), (true,impE) ];
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```    50
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```    51 (*0 subgoals vs 1 or more: the p in safep is for positive*)
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```    52 val (safe0_brls, safep_brls) =
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```    53     partition (apl(0,op=) o subgoals_of_brl) safe_brls;
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```    54
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```    55 (*Attack subgoals using safe inferences -- matching, not resolution*)
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```    56 val safe_step_tac = FIRST' [eq_assume_tac,
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```    57 			    eq_mp_tac,
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```    58 			    bimatch_tac safe0_brls,
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```    59 			    hyp_subst_tac,
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```    60 			    bimatch_tac safep_brls] ;
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```    61
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```    62 (*Repeatedly attack subgoals using safe inferences -- it's deterministic!*)
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```    63 val safe_tac = DETERM (REPEAT_FIRST safe_step_tac);
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```    64
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```    65 (*These steps could instantiate variables and are therefore unsafe.*)
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```    66 val inst_step_tac =
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```    67   assume_tac APPEND' mp_tac APPEND'
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```    68   biresolve_tac (safe0_brls @ safep_brls);
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```    69
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```    70 (*One safe or unsafe step. *)
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```    71 fun step_tac i = FIRST [safe_tac, inst_step_tac i, biresolve_tac haz_brls i];
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```    72
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```    73 (*Dumb but fast*)
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```    74 val fast_tac = SELECT_GOAL (DEPTH_SOLVE (step_tac 1));
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```    75
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```    76 (*Slower but smarter than fast_tac*)
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```    77 val best_tac =
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```    78   SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, size_of_thm) (step_tac 1));
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```    79
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```    80 end;
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```    81
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