(* Title: HOL/Transitive_Closure.thy
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1992 University of Cambridge
Relfexive and Transitive closure of a relation
rtrancl is reflexive/transitive closure;
trancl is transitive closure
reflcl is reflexive closure
These postfix operators have MAXIMUM PRIORITY, forcing their operands
to be atomic.
*)
Transitive_Closure = Lfp + Relation +
constdefs
rtrancl :: "('a * 'a) set => ('a * 'a) set" ("(_^*)" [1000] 999)
"r^* == lfp (%s. Id Un (r O s))"
trancl :: "('a * 'a) set => ('a * 'a) set" ("(_^+)" [1000] 999)
"r^+ == r O rtrancl r"
syntax
"_reflcl" :: "('a * 'a) set => ('a * 'a) set" ("(_^=)" [1000] 999)
translations
"r^=" == "r Un Id"
syntax (xsymbols)
rtrancl :: "('a * 'a) set => ('a * 'a) set" ("(_\\<^sup>*)" [1000] 999)
trancl :: "('a * 'a) set => ('a * 'a) set" ("(_\\<^sup>+)" [1000] 999)
"_reflcl" :: "('a * 'a) set => ('a * 'a) set" ("(_\\<^sup>=)" [1000] 999)
end