author  clasohm 
Mon, 05 Feb 1996 21:27:16 +0100  
changeset 1475  7f5a4cd08209 
parent 1454  d0266c81a85e 
child 1695  0f9b9eda2a2c 
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 * 'b)set => ('b * 'a)set" 
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"^^" :: "[('a * 'b) set, 'a set] => 'b set" (infixl 90) 
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Domain :: "('a * 'b) set => 'a set" 
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Range :: "('a * 'b) set => 'b set" 
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defs 
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id_def "id == {p. ? x. p = (x,x)}" 
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comp_def "r O s == {(x,z). ? y. (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) == {(y,x). (x,y):r}" 
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Domain_def "Domain(r) == {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 