Theory Ex2

section Example 3.8

theory Ex2
imports "../LCF"
begin

axiomatization
  P     :: "'a  tr" and
  F     :: "'b  'b" and
  G     :: "'a  'a" and
  H     :: "'a  'b  'b" and
  K     :: "('a  'b  'b)  ('a  'b  'b)"
where
  F_strict:     "F(UU) = UU" and
  K:            "K = (λh x y. P(x)  y | F(h(G(x),y)))" and
  H:            "H = FIX(K)"

declare F_strict [simp] K [simp]

lemma example: "x. F(H(x::'a,y::'b)) = H(x,F(y))"
  apply (simplesubst H)
  apply (induct "K:: ('a'b'b)  ('a'b'b)")
  apply simp
  apply (simp split: COND_cases_iff)
  done

end