--- a/ex/PropLog.thy Tue Oct 24 14:59:17 1995 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,45 +0,0 @@
-(* 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 "eval2(false) = (%x.False)"
- eval2_var "eval2(#v) = (%tt.v:tt)"
- eval2_imp "eval2(p->q) = (%tt.eval2(p,tt)-->eval2(q,tt))"
-
-primrec hyps pl
- hyps_false "hyps(false) = (%tt.{})"
- hyps_var "hyps(#v) = (%tt.{if(v:tt, #v, #v->false)})"
- hyps_imp "hyps(p->q) = (%tt.hyps(p,tt) Un hyps(q,tt))"
-
-end