author  paulson 
Thu, 12 Sep 1996 10:36:06 +0200  
changeset 1983  f3f7bf0079fa 
parent 1695  0f9b9eda2a2c 
child 3439  54785105178c 
permissions  rwrr 
1475  1 
(* Title: Relation.thy 
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset

2 
ID: $Id$ 
1983  3 
Author: Lawrence C Paulson, Cambridge University Computer Laboratory 
4 
Copyright 1996 University of Cambridge 

1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset

5 
*) 
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset

6 

64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset

7 
Relation = Prod + 
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset

8 
consts 
1475  9 
id :: "('a * 'a)set" (*the identity relation*) 
10 
O :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60) 

11 
trans :: "('a * 'a)set => bool" (*transitivity predicate*) 

1695
0f9b9eda2a2c
Generalized types of some of the operators (thanks to Norbert Voelker)
nipkow
parents:
1475
diff
changeset

12 
converse :: "('a*'b) set => ('b*'a) set" 
0f9b9eda2a2c
Generalized types of some of the operators (thanks to Norbert Voelker)
nipkow
parents:
1475
diff
changeset

13 
"^^" :: "[('a*'b) set,'a set] => 'b set" (infixl 90) 
0f9b9eda2a2c
Generalized types of some of the operators (thanks to Norbert Voelker)
nipkow
parents:
1475
diff
changeset

14 
Domain :: "('a*'b) set => 'a set" 
0f9b9eda2a2c
Generalized types of some of the operators (thanks to Norbert Voelker)
nipkow
parents:
1475
diff
changeset

15 
Range :: "('a*'b) set => 'b set" 
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset

16 
defs 
1983  17 
id_def "id == {p. ? x. p = (x,x)}" 
18 
comp_def "r O s == {(x,z). ? y. (x,y):s & (y,z):r}" 

1475  19 
trans_def "trans(r) == (!x y z. (x,y):r > (y,z):r > (x,z):r)" 
1454
d0266c81a85e
Streamlined defs in Relation and added new intro/elim rules to do with
nipkow
parents:
1128
diff
changeset

20 
converse_def "converse(r) == {(y,x). (x,y):r}" 
d0266c81a85e
Streamlined defs in Relation and added new intro/elim rules to do with
nipkow
parents:
1128
diff
changeset

21 
Domain_def "Domain(r) == {x. ? y. (x,y):r}" 
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset

22 
Range_def "Range(r) == Domain(converse(r))" 
1983  23 
Image_def "r ^^ s == {y. ? x:s. (x,y):r}" 
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset

24 
end 