src/CCL/Wfd.thy
author wenzelm
Fri, 10 Oct 1997 17:10:12 +0200
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(*  Title:      CCL/wfd.thy
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    ID:         $Id$
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    Author:     Martin Coen, Cambridge University Computer Laboratory
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    Copyright   1993  University of Cambridge
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Well-founded relations in CCL.
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*)
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Wfd = Trancl + Type +
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consts
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      (*** Predicates ***)
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  Wfd        ::       "[i set] => o"
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      (*** Relations ***)
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  wf         ::       "[i set] => i set"
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  wmap       ::       "[i=>i,i set] => i set"
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  "**"       ::       "[i set,i set] => i set"      (infixl 70)
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  NatPR      ::       "i set"
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  ListPR     ::       "i set => i set"
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rules
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  Wfd_def
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  "Wfd(R) == ALL P.(ALL x.(ALL y.<y,x> : R --> y:P) --> x:P) --> (ALL a. a:P)"
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  wf_def         "wf(R) == {x. x:R & Wfd(R)}"
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  wmap_def       "wmap(f,R) == {p. EX x y. p=<x,y>  &  <f(x),f(y)> : R}"
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  lex_def
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  "ra**rb == {p. EX a a' b b'. p = <<a,b>,<a',b'>> & (<a,a'> : ra | (a=a' & <b,b'> : rb))}"
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  NatPR_def      "NatPR == {p. EX x:Nat. p=<x,succ(x)>}"
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  ListPR_def     "ListPR(A) == {p. EX h:A. EX t:List(A). p=<t,h$t>}"
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end