INSTALLATION OF INDUCTIVE DEFINITIONS
HOL/ex/MT.thy: now mentions dependence upon Sum.thy
HOL/ex/Acc: new example, borrowed & adapted from ZF
HOL/ex/Simult, ex/Term: updated refs to Sexp intr rules
HOL/Sexp,List,LList,ex/Term: converted as follows
node *set -> item
Sexp -> sexp
LList_corec -> <self>
LList_ -> llist_
LList\> -> llist
List_case -> <self>
List_rec -> <self>
List_ -> list_
List\> -> list
Term_rec -> <self>
Term_ -> term_
Term\> -> term
(* Title: HOL/wf.ML
ID: $Id$
Author: Tobias Nipkow
Copyright 1992 University of Cambridge
Well-founded Recursion
*)
WF = Trancl +
consts
wf :: "('a * 'a)set => bool"
cut :: "['a => 'b, ('a * 'a)set, 'a] => 'a => 'b"
wftrec,wfrec :: "[('a * 'a)set, 'a, ['a,'a=>'b]=>'b] => 'b"
is_recfun :: "[('a * 'a)set, 'a, ['a,'a=>'b]=>'b, 'a=>'b] => bool"
the_recfun :: "[('a * 'a)set, 'a, ['a,'a=>'b]=>'b] => 'a=>'b"
rules
wf_def "wf(r) == (!P. (!x. (!y. <y,x>:r --> P(y)) --> P(x)) --> (!x.P(x)))"
cut_def "cut(f,r,x) == (%y. if(<y,x>:r, f(y), @z.True))"
is_recfun_def "is_recfun(r,a,H,f) == (f = cut(%x.H(x, cut(f,r,x)), r, a))"
the_recfun_def "the_recfun(r,a,H) == (@f.is_recfun(r,a,H,f))"
wftrec_def "wftrec(r,a,H) == H(a, the_recfun(r,a,H))"
(*version not requiring transitivity*)
wfrec_def "wfrec(r,a,H) == wftrec(trancl(r), a, %x f. H(x, cut(f,r,x)))"
end