src/HOL/Lambda/Commutation.thy
 changeset 1278 7e6189fc833c child 1302 ddfdcc9ce667
```     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/src/HOL/Lambda/Commutation.thy	Wed Oct 11 10:09:56 1995 +0100
1.3 @@ -0,0 +1,31 @@
1.4 +(*  Title: 	HOL/Lambda/Commutation.thy
1.5 +    ID:         \$Id\$
1.6 +    Author: 	Tobias Nipkow
1.7 +    Copyright   1995  TU Muenchen
1.8 +
1.9 +Abstract commutation and confluence notions.
1.10 +*)
1.11 +
1.12 +Commutation = Trancl +
1.13 +
1.14 +consts
1.15 +  reflcl  :: "('a*'a)set => ('a*'a)set"               ("(_^=)" [100] 100)
1.16 +  square  :: "[('a*'a)set,('a*'a)set,('a*'a)set,('a*'a)set] => bool"
1.17 +  commute :: "[('a*'a)set,('a*'a)set] => bool"
1.18 +  confluent, diamond, Church_Rosser :: "('a*'a)set => bool"
1.19 +
1.20 +defs
1.21 +  square_def
1.22 + "square R S T U == !x y.(x,y):R --> (!z.(x,z):S --> (? u. (y,u):T & (z,u):U))"
1.23 +
1.24 +  commute_def "commute R S == square R S S R"
1.25 +  diamond_def "diamond R   == commute R R"
1.26 +
1.27 +  Church_Rosser_def "Church_Rosser(R) ==
1.28 +  !x y. (x,y) : (R Un converse(R))^* --> (? z. (x,z) : R^* & (y,z) : R^*)"
1.29 +
1.30 +translations
1.31 +  "r^="   == "r Un id"
1.32 +  "confluent R" == "diamond(R^*)"
1.33 +
1.34 +end
```