src/CCL/fix.thy

Installation of new simplfier. Previously appeared to set up the old
simplifier to rewrite with the partial ordering [=, something not possible
with the new simplifier. But such rewriting appears not to have actually
been used, and there were few complications. In terms.ML setloop was used
to avoid infinite rewriting with the letrec rule. Congruence rules were
deleted, and an occasional SIMP_TAC had to become asm_simp_tac.

(*  Title: 	CCL/Lazy/fix.thy
    ID:         $Id$
    Author: 	Martin Coen
    Copyright   1993  University of Cambridge

Tentative attempt at including fixed point induction.
Justified by Smith.
*)

Fix = Type + 

consts

  idgen      ::	      "[i]=>i"
  INCL      :: "[i=>o]=>o"

rules

  idgen_def
  "idgen(f) == lam t.case(t,true,false,%x y.<f`x, f`y>,%u.lam x.f ` u(x))"

  INCL_def   "INCL(%x.P(x)) == (ALL f.(ALL n:Nat.P(f^n`bot)) --> P(fix(f)))"
  po_INCL    "INCL(%x.a(x) [= b(x))"
  INCL_subst "INCL(P) ==> INCL(%x.P((g::i=>i)(x)))"

end