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