(* Title: HOL/UNITY/Extend.thy
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1998 University of Cambridge
Extending of state sets
function f (forget) maps the extended state to the original state
function g (forgotten) maps the extended state to the "extending part"
*)
Extend = Guar +
constdefs
extend_set :: "['a*'b => 'c, 'a set] => 'c set"
"extend_set h A == h `` (A Times UNIV)"
project_set :: "['a*'b => 'c, 'c set] => 'a set"
"project_set h C == {x. EX y. h(x,y) : C}"
extend_act :: "['a*'b => 'c, ('a*'a) set] => ('c*'c) set"
"extend_act h act == UN (s,s'): act. UN y. {(h(s,y), h(s',y))}"
project_act :: "['a*'b => 'c, ('c*'c) set] => ('a*'a) set"
"project_act h act == {(x,x'). EX y y'. (h(x,y), h(x',y')) : act}"
extend :: "['a*'b => 'c, 'a program] => 'c program"
"extend h F == mk_program (extend_set h (Init F),
extend_act h `` Acts F)"
project :: "['a*'b => 'c, 'c program] => 'a program"
"project h F == mk_program (project_set h (Init F),
project_act h `` Acts F)"
locale Extend =
fixes
f :: 'c => 'a
g :: 'c => 'b
h :: "'a*'b => 'c" (*isomorphism between 'a * 'b and 'c *)
slice :: ['c set, 'b] => 'a set
f_act :: "('c * 'c) set => ('a*'a) set"
assumes
bij_h "bij h"
defines
f_def "f z == fst (inv h z)"
g_def "g z == snd (inv h z)"
slice_def "slice Z y == {x. h(x,y) : Z}"
f_act_def "f_act act == (%(z,z'). (f z, f z')) `` act"
end