src/HOL/Induct/PropLog.thy

--- /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
+