src/HOL/Transitive_Closure.thy
author wenzelm
Wed Oct 25 18:32:02 2000 +0200 (2000-10-25)
changeset 10331 7411e4659d4a
parent 10213 01c2744a3786
child 10565 7f7c1c3511e2
permissions -rw-r--r--
more "xsymbols" syntax;
nipkow@10213
     1
(*  Title:      HOL/Transitive_Closure.thy
nipkow@10213
     2
    ID:         $Id$
nipkow@10213
     3
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
nipkow@10213
     4
    Copyright   1992  University of Cambridge
nipkow@10213
     5
nipkow@10213
     6
Relfexive and Transitive closure of a relation
nipkow@10213
     7
nipkow@10213
     8
rtrancl is reflexive/transitive closure;
nipkow@10213
     9
trancl  is transitive closure
nipkow@10213
    10
reflcl  is reflexive closure
nipkow@10213
    11
wenzelm@10331
    12
These postfix operators have MAXIMUM PRIORITY, forcing their operands
wenzelm@10331
    13
to be atomic.
nipkow@10213
    14
*)
nipkow@10213
    15
nipkow@10213
    16
Transitive_Closure = Lfp + Relation + 
nipkow@10213
    17
nipkow@10213
    18
constdefs
wenzelm@10331
    19
  rtrancl :: "('a * 'a) set => ('a * 'a) set"    ("(_^*)" [1000] 999)
wenzelm@10331
    20
  "r^* == lfp (%s. Id Un (r O s))"
nipkow@10213
    21
wenzelm@10331
    22
  trancl :: "('a * 'a) set => ('a * 'a) set"    ("(_^+)" [1000] 999)
wenzelm@10331
    23
  "r^+ ==  r O rtrancl r"
nipkow@10213
    24
nipkow@10213
    25
syntax
wenzelm@10331
    26
  "_reflcl" :: "('a * 'a) set => ('a * 'a) set"    ("(_^=)" [1000] 999)
nipkow@10213
    27
translations
nipkow@10213
    28
  "r^=" == "r Un Id"
nipkow@10213
    29
wenzelm@10331
    30
syntax (xsymbols)
wenzelm@10331
    31
  rtrancl :: "('a * 'a) set => ('a * 'a) set"    ("(_\\<^sup>*)" [1000] 999)
wenzelm@10331
    32
  trancl :: "('a * 'a) set => ('a * 'a) set"    ("(_\\<^sup>+)" [1000] 999)
wenzelm@10331
    33
  "_reflcl" :: "('a * 'a) set => ('a * 'a) set"    ("(_\\<^sup>=)" [1000] 999)
wenzelm@10331
    34
nipkow@10213
    35
end