src/FOL/int-prover.ML
 author clasohm Fri, 13 Oct 1995 11:48:40 +0100 changeset 1280 909079af97b7 parent 0 a5a9c433f639 permissions -rw-r--r--
corrected spelling of title
```
(*  Title: 	FOL/int-prover
ID:         \$Id\$
Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory

A naive prover for intuitionistic logic

BEWARE OF NAME CLASHES WITH CLASSICAL TACTICS -- use Int.fast_tac ...

Completeness (for propositional logic) is proved in

Roy Dyckhoff.
Contraction-Free Sequent Calculi for Intuitionistic Logic.
J. Symbolic Logic (in press)
*)

signature INT_PROVER =
sig
val best_tac: int -> tactic
val fast_tac: int -> tactic
val inst_step_tac: int -> tactic
val safe_step_tac: int -> tactic
val safe_brls: (bool * thm) list
val safe_tac: tactic
val step_tac: int -> tactic
val haz_brls: (bool * thm) list
end;

structure Int : INT_PROVER   =
struct

(*Negation is treated as a primitive symbol, with rules notI (introduction),
not_to_imp (converts the assumption ~P to P-->False), and not_impE
(handles double negations).  Could instead rewrite by not_def as the first
step of an intuitionistic proof.
*)
val safe_brls = sort lessb
[ (true,FalseE), (false,TrueI), (false,refl),
(false,impI), (false,notI), (false,allI),
(true,conjE), (true,exE),
(false,conjI), (true,conj_impE),
(true,disj_impE), (true,ex_impE),
(true,disjE), (false,iffI), (true,iffE), (true,not_to_imp) ];

val haz_brls =
[ (false,disjI1), (false,disjI2), (false,exI),
(true,allE), (true,not_impE), (true,imp_impE), (true,iff_impE),
(true,all_impE), (true,impE) ];

(*0 subgoals vs 1 or more: the p in safep is for positive*)
val (safe0_brls, safep_brls) =
partition (apl(0,op=) o subgoals_of_brl) safe_brls;

(*Attack subgoals using safe inferences -- matching, not resolution*)
val safe_step_tac = FIRST' [eq_assume_tac,
eq_mp_tac,
bimatch_tac safe0_brls,
hyp_subst_tac,
bimatch_tac safep_brls] ;

(*Repeatedly attack subgoals using safe inferences -- it's deterministic!*)
val safe_tac = DETERM (REPEAT_FIRST safe_step_tac);

(*These steps could instantiate variables and are therefore unsafe.*)
val inst_step_tac =
assume_tac APPEND' mp_tac APPEND'
biresolve_tac (safe0_brls @ safep_brls);

(*One safe or unsafe step. *)
fun step_tac i = FIRST [safe_tac, inst_step_tac i, biresolve_tac haz_brls i];

(*Dumb but fast*)
val fast_tac = SELECT_GOAL (DEPTH_SOLVE (step_tac 1));

(*Slower but smarter than fast_tac*)
val best_tac =
SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, size_of_thm) (step_tac 1));

end;

```