author  nipkow 
Fri, 26 May 1995 18:11:47 +0200  
changeset 1128  64b30e3cc6d4 
child 1454  d0266c81a85e 
permissions  rwrr 
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(* Title: Relation.thy 
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ID: $Id$ 
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Author: Riccardo Mattolini, Dip. Sistemi e Informatica 
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and Lawrence C Paulson, Cambridge University Computer Laboratory 
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Copyright 1994 Universita' di Firenze 
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Copyright 1993 University of Cambridge 
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*) 
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Relation = Prod + 
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consts 
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id :: "('a * 'a)set" (*the identity relation*) 
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O :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60) 
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trans :: "('a * 'a)set => bool" (*transitivity predicate*) 
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converse :: "('a*'a) set => ('a*'a) set" 
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"^^" :: "[('a*'a) set,'a set] => 'a set" (infixl 90) 
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Domain :: "('a*'a) set => 'a set" 
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Range :: "('a*'a) set => 'a set" 
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defs 
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id_def "id == {p. ? x. p = (x,x)}" 
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comp_def (*composition of relations*) 
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"r O s == {xz. ? x y z. xz = (x,z) & (x,y):s & (y,z):r}" 
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trans_def "trans(r) == (!x y z. (x,y):r > (y,z):r > (x,z):r)" 
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converse_def "converse(r) == {z. (? w:r. ? x y. w=(x,y) & z=(y,x))}" 
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Domain_def "Domain(r) == {z. ! x. (z=x > (? y. (x,y):r))}" 
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Range_def "Range(r) == Domain(converse(r))" 
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Image_def "r ^^ s == {y. y:Range(r) & (? x:s. (x,y):r)}" 
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end 