src/FOLP/int-prover.ML
 changeset 0 a5a9c433f639
```--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOLP/int-prover.ML	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,79 @@
+(*  Title: 	FOL/int-prover
+    ID:         \$Id\$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1992  University of Cambridge
+
+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*)
+val safe_step_tac = FIRST' [uniq_assume_tac,
+			    IFOLP_Lemmas.uniq_mp_tac,
+			    biresolve_tac safe0_brls,
+			    hyp_subst_tac,
+			    biresolve_tac safep_brls] ;
+
+(*Repeatedly attack subgoals using safe inferences*)
+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;
+
+(*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;
+```