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