
diff -r b38cfbabfda4 -r 6f463d16cbd0 src/ZF/Induct/PropLog.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/ZF/Induct/PropLog.thy	Wed Nov 07 12:29:07 2001 +0100
@@ -0,0 +1,68 @@
+(*  Title:      ZF/ex/PropLog.thy
+    ID:         $Id$
+    Author:     Tobias Nipkow & Lawrence C Paulson
+    Copyright   1993  University of Cambridge
+
+Datatype definition of propositional logic formulae and inductive definition
+of the propositional tautologies.
+*)
+
+PropLog = Main +
+
+(** The datatype of propositions; note mixfix syntax **)
+consts
+  prop     :: i
+
+datatype
+  "prop" = Fls
+         | Var ("n \\<in> nat")                       ("#_" [100] 100)
+         | "=>" ("p \\<in> prop", "q \\<in> prop")          (infixr 90)
+
+(** The proof system **)
+consts
+  thms     :: i => i
+
+syntax
+  "|-"     :: [i,i] => o                        (infixl 50)
+
+translations
+  "H |- p" == "p \\<in> thms(H)"
+
+inductive
+  domains "thms(H)" <= "prop"
+  intrs
+    H  "[| p \\<in> H;  p \\<in> prop |] ==> H |- p"
+    K  "[| p \\<in> prop;  q \\<in> prop |] ==> H |- p=>q=>p"
+    S  "[| p \\<in> prop;  q \\<in> prop;  r \\<in> prop |] ==> H |- (p=>q=>r) => (p=>q) => p=>r"
+    DN "p \\<in> prop ==> H |- ((p=>Fls) => Fls) => p"
+    MP "[| H |- p=>q;  H |- p;  p \\<in> prop;  q \\<in> prop |] ==> H |- q"
+  type_intrs "prop.intrs"
+
+
+(** The semantics **)
+consts
+  "|="        :: [i,i] => o                        (infixl 50)
+  hyps        :: [i,i] => i
+  is_true_fun :: [i,i] => i
+
+constdefs (*this definitionis necessary since predicates can't be recursive*)
+  is_true     :: [i,i] => o
+    "is_true(p,t) == is_true_fun(p,t)=1"
+
+defs
+  (*Logical consequence: for every valuation, if all elements of H are true
+     then so is p*)
+  logcon_def  "H |= p == \\<forall>t. (\\<forall>q \\<in> H. is_true(q,t)) --> is_true(p,t)"
+
+primrec (** A finite set of hypotheses from t and the Vars in p **)
+  "hyps(Fls, t)    = 0"
+  "hyps(Var(v), t) = (if v \\<in> t then {#v} else {#v=>Fls})"
+  "hyps(p=>q, t)   = hyps(p,t) Un hyps(q,t)"
+ 
+primrec (** Semantics of propositional logic **)
+  "is_true_fun(Fls, t)    = 0"
+  "is_true_fun(Var(v), t) = (if v \\<in> t then 1 else 0)"
+  "is_true_fun(p=>q, t)   = (if is_true_fun(p,t)=1 then is_true_fun(q,t)
+			     else 1)"
+
+end




