src/HOL/Lex/RegExp2NA.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Lex/RegExp2NA.thy	Mon Aug 17 11:00:57 1998 +0200
@@ -0,0 +1,60 @@
+(*  Title:      HOL/Lex/RegExp2NA.thy
+    ID:         $Id$
+    Author:     Tobias Nipkow
+    Copyright   1998 TUM
+
+Conversion of regular expressions *directly*
+into nondeterministic automata *without* epsilon transitions
+*)
+
+RegExp2NA = NA + RegExp +
+
+types 'a bitsNA = ('a,bool list)na
+
+syntax "##" :: 'a => 'a list set => 'a list set (infixr 65)
+translations "x ## S" == "op # x `` S"
+
+constdefs
+ atom  :: 'a => 'a bitsNA
+"atom a == ([True],
+            %b s. if s=[True] & b=a then {[False]} else {},
+            %s. s=[False])"
+
+ union :: 'a bitsNA => 'a bitsNA => 'a bitsNA
+"union == %(ql,dl,fl)(qr,dr,fr).
+   ([],
+    %a s. case s of
+            [] => (True ## dl a ql) Un (False ## dr a qr)
+          | left#s => if left then True ## dl a s
+                              else False ## dr a s,
+    %s. case s of [] => (fl ql | fr qr)
+                | left#s => if left then fl s else fr s)"
+
+ conc :: 'a bitsNA => 'a bitsNA => 'a bitsNA
+"conc == %(ql,dl,fl)(qr,dr,fr).
+   (True#ql,
+    %a s. case s of
+            [] => {}
+          | left#s => if left then (True ## dl a s) Un
+                                   (if fl s then False ## dr a qr else {})
+                              else False ## dr a s,
+    %s. case s of [] => False | left#s => left & fl s & fr qr | ~left & fr s)"
+
+ epsilon :: 'a bitsNA
+"epsilon == ([],%a s. {}, %s. s=[])"
+
+ plus :: 'a bitsNA => 'a bitsNA
+"plus == %(q,d,f). (q, %a s. d a s Un (if f s then d a q else {}), f)"
+
+ star :: 'a bitsNA => 'a bitsNA
+"star A == union epsilon (plus A)"
+
+consts rexp2na :: 'a rexp => 'a bitsNA
+primrec
+"rexp2na Empty      = ([], %a s. {}, %s. False)"
+"rexp2na(Atom a)    = atom a"
+"rexp2na(Union r s) = union (rexp2na r) (rexp2na s)"
+"rexp2na(Conc r s)  = conc  (rexp2na r) (rexp2na s)"
+"rexp2na(Star r)    = star  (rexp2na r)"
+
+end