4 Copyright 1996 University of Cambridge |
4 Copyright 1996 University of Cambridge |
5 *) |
5 *) |
6 |
6 |
7 Relation = Prod + |
7 Relation = Prod + |
8 |
8 |
9 consts |
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10 O :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60) |
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11 converse :: "('a*'b) set => ('b*'a) set" ("(_^-1)" [1000] 999) |
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12 "^^" :: "[('a*'b) set,'a set] => 'b set" (infixl 90) |
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13 |
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14 defs |
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15 comp_def "r O s == {(x,z). ? y. (x,y):s & (y,z):r}" |
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16 converse_def "r^-1 == {(y,x). (x,y):r}" |
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17 Image_def "r ^^ s == {y. ? x:s. (x,y):r}" |
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18 |
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19 constdefs |
9 constdefs |
20 Id :: "('a * 'a)set" (*the identity relation*) |
10 converse :: "('a*'b) set => ('b*'a) set" ("(_^-1)" [1000] 999) |
21 "Id == {p. ? x. p = (x,x)}" |
11 "r^-1 == {(y,x). (x,y):r}" |
22 |
12 |
23 diag :: "'a set => ('a * 'a)set" |
13 comp :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr "O" 60) |
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14 "r O s == {(x,z). ? y. (x,y):s & (y,z):r}" |
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15 |
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16 Image :: "[('a*'b) set,'a set] => 'b set" (infixl "^^" 90) |
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17 "r ^^ s == {y. ? x:s. (x,y):r}" |
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18 |
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19 Id :: "('a * 'a)set" (*the identity relation*) |
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20 "Id == {p. ? x. p = (x,x)}" |
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21 |
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22 diag :: "'a set => ('a * 'a)set" (*diagonal: identity over a set*) |
24 "diag(A) == UN x:A. {(x,x)}" |
23 "diag(A) == UN x:A. {(x,x)}" |
25 |
24 |
26 Domain :: "('a*'b) set => 'a set" |
25 Domain :: "('a*'b) set => 'a set" |
27 "Domain(r) == {x. ? y. (x,y):r}" |
26 "Domain(r) == {x. ? y. (x,y):r}" |
28 |
27 |