--- a/src/HOLCF/stream.thy Sat Apr 05 17:03:38 2003 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,102 +0,0 @@
-(* Title: HOLCF/stream.thy
- ID: $Id$
- Author: Franz Regensburger
- Copyright 1993 Technische Universitaet Muenchen
-
-Theory for streams without defined empty stream
-*)
-
-Stream = Dnat2 +
-
-types stream 1
-
-(* ----------------------------------------------------------------------- *)
-(* arity axiom is validated by semantic reasoning *)
-(* partial ordering is implicit in the isomorphism axioms and their cont. *)
-
-arities stream::(pcpo)pcpo
-
-consts
-
-(* ----------------------------------------------------------------------- *)
-(* essential constants *)
-
-stream_rep :: "('a stream) -> ('a ** ('a stream)u)"
-stream_abs :: "('a ** ('a stream)u) -> ('a stream)"
-
-(* ----------------------------------------------------------------------- *)
-(* abstract constants and auxiliary constants *)
-
-stream_copy :: "('a stream -> 'a stream) ->'a stream -> 'a stream"
-
-scons :: "'a -> 'a stream -> 'a stream"
-stream_when :: "('a -> 'a stream -> 'b) -> 'a stream -> 'b"
-is_scons :: "'a stream -> tr"
-shd :: "'a stream -> 'a"
-stl :: "'a stream -> 'a stream"
-stream_take :: "nat => 'a stream -> 'a stream"
-stream_finite :: "'a stream => bool"
-stream_bisim :: "('a stream => 'a stream => bool) => bool"
-
-rules
-
-(* ----------------------------------------------------------------------- *)
-(* axiomatization of recursive type 'a stream *)
-(* ----------------------------------------------------------------------- *)
-(* ('a stream,stream_abs) is the initial F-algebra where *)
-(* F is the locally continuous functor determined by domain equation *)
-(* X = 'a ** (X)u *)
-(* ----------------------------------------------------------------------- *)
-(* stream_abs is an isomorphism with inverse stream_rep *)
-(* identity is the least endomorphism on 'a stream *)
-
-stream_abs_iso "stream_rep[stream_abs[x]] = x"
-stream_rep_iso "stream_abs[stream_rep[x]] = x"
-stream_copy_def "stream_copy == (LAM f. stream_abs oo \
-\ (ssplit[LAM x y. x ## (lift[up oo f])[y]] oo stream_rep))"
-stream_reach "(fix[stream_copy])[x]=x"
-
-(* ----------------------------------------------------------------------- *)
-(* properties of additional constants *)
-(* ----------------------------------------------------------------------- *)
-(* constructors *)
-
-scons_def "scons == (LAM x l. stream_abs[x##up[l]])"
-
-(* ----------------------------------------------------------------------- *)
-(* discriminator functional *)
-
-stream_when_def
-"stream_when == (LAM f l.ssplit[LAM x l.f[x][lift[ID][l]]][stream_rep[l]])"
-
-(* ----------------------------------------------------------------------- *)
-(* discriminators and selectors *)
-
-is_scons_def "is_scons == stream_when[LAM x l.TT]"
-shd_def "shd == stream_when[LAM x l.x]"
-stl_def "stl == stream_when[LAM x l.l]"
-
-(* ----------------------------------------------------------------------- *)
-(* the taker for streams *)
-
-stream_take_def "stream_take == (%n.iterate(n,stream_copy,UU))"
-
-(* ----------------------------------------------------------------------- *)
-
-stream_finite_def "stream_finite == (%s.? n.stream_take(n)[s]=s)"
-
-(* ----------------------------------------------------------------------- *)
-(* definition of bisimulation is determined by domain equation *)
-(* simplification and rewriting for abstract constants yields def below *)
-
-stream_bisim_def "stream_bisim ==\
-\(%R.!s1 s2.\
-\ R(s1,s2) -->\
-\ ((s1=UU & s2=UU) |\
-\ (? x s11 s21. x~=UU & s1=scons[x][s11] & s2 = scons[x][s21] & R(s11,s21))))"
-
-end
-
-
-
-