src/FOLP/intprover.ML
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`     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*)`
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`    56 val safe_step_tac = FIRST' [uniq_assume_tac,`
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`    57 			    IFOLP_Lemmas.uniq_mp_tac,`
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`    58 			    biresolve_tac safe0_brls,`
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`    59 			    hyp_subst_tac,`
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`    60 			    biresolve_tac safep_brls] ;`
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`    61 `
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`    62 (*Repeatedly attack subgoals using safe inferences*)`
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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 = assume_tac APPEND' mp_tac;`
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`    67 `
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`    68 (*One safe or unsafe step. *)`
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`    69 fun step_tac i = FIRST [safe_tac, inst_step_tac i, biresolve_tac haz_brls i];`
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`    70 `
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`    71 (*Dumb but fast*)`
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`    72 val fast_tac = SELECT_GOAL (DEPTH_SOLVE (step_tac 1));`
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`    73 `
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`    74 (*Slower but smarter than fast_tac*)`
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`    75 val best_tac = `
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`    76   SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, size_of_thm) (step_tac 1));`
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`    77 `
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`    78 end;`
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`    79 `