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1 (* Title: Relation.thy |
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2 ID: $Id$ |
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3 Author: Riccardo Mattolini, Dip. Sistemi e Informatica |
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4 and Lawrence C Paulson, Cambridge University Computer Laboratory |
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5 Copyright 1994 Universita' di Firenze |
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6 Copyright 1993 University of Cambridge |
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7 |
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8 Functions represented as relations in Higher-Order Set Theory |
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9 *) |
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10 |
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11 Relation = Trancl + |
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12 consts |
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13 converse :: "('a*'a) set => ('a*'a) set" |
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14 "^^" :: "[('a*'a) set,'a set] => 'a set" (infixl 90) |
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15 Domain :: "('a*'a) set => 'a set" |
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16 Range :: "('a*'a) set => 'a set" |
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17 |
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18 defs |
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19 converse_def "converse(r) == {z. (? w:r. ? x y. w=<x,y> & z=<y,x>)}" |
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20 Domain_def "Domain(r) == {z. ! x. (z=x --> (? y. <x,y>:r))}" |
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21 Range_def "Range(r) == Domain(converse(r))" |
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22 Image_def "r ^^ s == {y. y:Range(r) & (? x:s. <x,y>:r)}" |
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23 |
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24 end |
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