src/HOLCF/dlist.thy
changeset 13897 f62f9a75f685
parent 13896 717bd79b976f
child 13898 9410d2eb9563
--- a/src/HOLCF/dlist.thy	Sat Apr 05 17:03:38 2003 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,111 +0,0 @@
-(*  Title: 	HOLCF/dlist.thy
-
-    Author: 	Franz Regensburger
-    ID:         $ $
-    Copyright   1994 Technische Universitaet Muenchen
-
-Theory for lists
-*)
-
-Dlist = Stream2 +
-
-types dlist 1
-
-(* ----------------------------------------------------------------------- *)
-(* arity axiom is validated by semantic reasoning                          *)
-(* partial ordering is implicit in the isomorphism axioms and their cont.  *)
-
-arities dlist::(pcpo)pcpo
-
-consts
-
-(* ----------------------------------------------------------------------- *)
-(* essential constants                                                     *)
-
-dlist_rep	:: "('a dlist) -> (one ++ 'a ** 'a dlist)"
-dlist_abs	:: "(one ++ 'a ** 'a dlist) -> ('a dlist)"
-
-(* ----------------------------------------------------------------------- *)
-(* abstract constants and auxiliary constants                              *)
-
-dlist_copy	:: "('a dlist -> 'a dlist) ->'a dlist -> 'a dlist"
-
-dnil            :: "'a dlist"
-dcons		:: "'a -> 'a dlist -> 'a dlist"
-dlist_when	:: " 'b -> ('a -> 'a dlist -> 'b) -> 'a dlist -> 'b"
-is_dnil    	:: "'a dlist -> tr"
-is_dcons	:: "'a dlist -> tr"
-dhd		:: "'a dlist -> 'a"
-dtl		:: "'a dlist -> 'a dlist"
-dlist_take	:: "nat => 'a dlist -> 'a dlist"
-dlist_finite	:: "'a dlist => bool"
-dlist_bisim	:: "('a dlist => 'a dlist => bool) => bool"
-
-rules
-
-(* ----------------------------------------------------------------------- *)
-(* axiomatization of recursive type 'a dlist                               *)
-(* ----------------------------------------------------------------------- *)
-(* ('a dlist,dlist_abs) is the initial F-algebra where                     *)
-(* F is the locally continuous functor determined by domain equation       *)
-(* X = one ++ 'a ** X                                                      *)
-(* ----------------------------------------------------------------------- *)
-(* dlist_abs is an isomorphism with inverse dlist_rep                      *)
-(* identity is the least endomorphism on 'a dlist                          *)
-
-dlist_abs_iso	"dlist_rep[dlist_abs[x]] = x"
-dlist_rep_iso	"dlist_abs[dlist_rep[x]] = x"
-dlist_copy_def	"dlist_copy == (LAM f. dlist_abs oo \
-\ 		(when[sinl][sinr oo (ssplit[LAM x y. x ## f[y]])])\
-\                                oo dlist_rep)"
-dlist_reach	"(fix[dlist_copy])[x]=x"
-
-(* ----------------------------------------------------------------------- *)
-(* properties of additional constants                                      *)
-(* ----------------------------------------------------------------------- *)
-(* constructors                                                            *)
-
-dnil_def	"dnil  == dlist_abs[sinl[one]]"
-dcons_def	"dcons == (LAM x l. dlist_abs[sinr[x##l]])"
-
-(* ----------------------------------------------------------------------- *)
-(* discriminator functional                                                *)
-
-dlist_when_def 
-"dlist_when == (LAM f1 f2 l.\
-\   when[LAM x.f1][ssplit[LAM x l.f2[x][l]]][dlist_rep[l]])"
-
-(* ----------------------------------------------------------------------- *)
-(* discriminators and selectors                                            *)
-
-is_dnil_def	"is_dnil  == dlist_when[TT][LAM x l.FF]"
-is_dcons_def	"is_dcons == dlist_when[FF][LAM x l.TT]"
-dhd_def		"dhd == dlist_when[UU][LAM x l.x]"
-dtl_def		"dtl == dlist_when[UU][LAM x l.l]"
-
-(* ----------------------------------------------------------------------- *)
-(* the taker for dlists                                                   *)
-
-dlist_take_def "dlist_take == (%n.iterate(n,dlist_copy,UU))"
-
-(* ----------------------------------------------------------------------- *)
-
-dlist_finite_def	"dlist_finite == (%s.? n.dlist_take(n)[s]=s)"
-
-(* ----------------------------------------------------------------------- *)
-(* definition of bisimulation is determined by domain equation             *)
-(* simplification and rewriting for abstract constants yields def below    *)
-
-dlist_bisim_def "dlist_bisim ==\
-\ ( %R.!l1 l2.\
-\ 	R(l1,l2) -->\
-\  ((l1=UU & l2=UU) |\
-\   (l1=dnil & l2=dnil) |\
-\   (? x l11 l21. x~=UU & l11~=UU & l21~=UU & \
-\               l1=dcons[x][l11] & l2 = dcons[x][l21] & R(l11,l21))))"
-
-end
-
-
-
-