src/HOL/Transitive_Closure.thy
changeset 10213 01c2744a3786
child 10331 7411e4659d4a
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/HOL/Transitive_Closure.thy	Thu Oct 12 18:44:35 2000 +0200
     1.3 @@ -0,0 +1,31 @@
     1.4 +(*  Title:      HOL/Transitive_Closure.thy
     1.5 +    ID:         $Id$
     1.6 +    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     1.7 +    Copyright   1992  University of Cambridge
     1.8 +
     1.9 +Relfexive and Transitive closure of a relation
    1.10 +
    1.11 +rtrancl is reflexive/transitive closure;
    1.12 +trancl  is transitive closure
    1.13 +reflcl  is reflexive closure
    1.14 +
    1.15 +These postfix operators have MAXIMUM PRIORITY, forcing their operands to be
    1.16 +      atomic.
    1.17 +*)
    1.18 +
    1.19 +Transitive_Closure = Lfp + Relation + 
    1.20 +
    1.21 +constdefs
    1.22 +  rtrancl :: "('a * 'a)set => ('a * 'a)set"   ("(_^*)" [1000] 999)
    1.23 +  "r^*  ==  lfp(%s. Id Un (r O s))"
    1.24 +
    1.25 +  trancl  :: "('a * 'a)set => ('a * 'a)set"   ("(_^+)" [1000] 999)
    1.26 +  "r^+  ==  r O rtrancl(r)"
    1.27 +
    1.28 +syntax
    1.29 +  "_reflcl"  :: "('a*'a)set => ('a*'a)set"       ("(_^=)" [1000] 999)
    1.30 +
    1.31 +translations
    1.32 +  "r^=" == "r Un Id"
    1.33 +
    1.34 +end