--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Induct/PropLog.thy Wed May 07 12:50:26 1997 +0200
@@ -0,0 +1,46 @@
+(* Title: HOL/ex/PropLog.thy
+ ID: $Id$
+ Author: Tobias Nipkow
+ Copyright 1994 TU Muenchen
+
+Inductive definition of propositional logic.
+*)
+
+PropLog = Finite +
+datatype
+ 'a pl = false | var 'a ("#_" [1000]) | "->" ('a pl) ('a pl) (infixr 90)
+consts
+ thms :: 'a pl set => 'a pl set
+ "|-" :: ['a pl set, 'a pl] => bool (infixl 50)
+ "|=" :: ['a pl set, 'a pl] => bool (infixl 50)
+ eval2 :: ['a pl, 'a set] => bool
+ eval :: ['a set, 'a pl] => bool ("_[_]" [100,0] 100)
+ hyps :: ['a pl, 'a set] => 'a pl set
+
+translations
+ "H |- p" == "p : thms(H)"
+
+inductive "thms(H)"
+ intrs
+ H "p:H ==> H |- p"
+ K "H |- p->q->p"
+ S "H |- (p->q->r) -> (p->q) -> p->r"
+ DN "H |- ((p->false) -> false) -> p"
+ MP "[| H |- p->q; H |- p |] ==> H |- q"
+
+defs
+ sat_def "H |= p == (!tt. (!q:H. tt[q]) --> tt[p])"
+ eval_def "tt[p] == eval2 p tt"
+
+primrec eval2 pl
+ "eval2(false) = (%x.False)"
+ "eval2(#v) = (%tt.v:tt)"
+ "eval2(p->q) = (%tt.eval2 p tt-->eval2 q tt)"
+
+primrec hyps pl
+ "hyps(false) = (%tt.{})"
+ "hyps(#v) = (%tt.{if v:tt then #v else #v->false})"
+ "hyps(p->q) = (%tt.hyps p tt Un hyps q tt)"
+
+end
+