src/HOLCF/Tr1.thy

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+++ b/src/HOLCF/Tr1.thy	Wed Jan 19 17:35:01 1994 +0100
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+(*  Title: 	HOLCF/tr1.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Introduve the domain of truth values tr = {UU,TT,FF}
+
+This type is introduced using a domain isomorphism.
+
+The type axiom 
+
+	arities tr :: pcpo
+
+and the continuity of the Isomorphisms are taken for granted. Since the
+type is not recursive, it could be easily introduced in a purely conservative
+style as it was used for the types sprod, ssum, lift. The definition of the 
+ordering is canonical using abstraction and representation, but this would take
+again a lot of internal constants. It can be easily seen that the axioms below
+are consistent.
+
+Partial Ordering is implicit in isomorphims abs_tr,rep_tr and their continuity
+
+*)
+
+Tr1 = One +
+
+types tr 0
+arities tr :: pcpo
+
+consts
+	abs_tr		:: "one ++ one -> tr"
+	rep_tr		:: "tr -> one ++ one"
+	TT 		:: "tr"
+	FF		:: "tr"
+	tr_when 	:: "'c -> 'c -> tr -> 'c"
+
+rules
+
+  abs_tr_iso	"abs_tr[rep_tr[u]] = u"
+  rep_tr_iso	"rep_tr[abs_tr[x]] = x"
+
+  TT_def	"TT == abs_tr[sinl[one]]"
+  FF_def	"FF == abs_tr[sinr[one]]"
+
+  tr_when_def "tr_when == (LAM e1 e2 t.when[LAM x.e1][LAM y.e2][rep_tr[t]])"
+
+end
+
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