floor and ceiling definitions are not code equations -- this enables trivial evaluation of floor and ceiling
header {* Example 3.8 *}
theory Ex2
imports LCF
begin
consts
P :: "'a => tr"
F :: "'a => 'a"
G :: "'a => 'a"
H :: "'a => 'b => 'b"
K :: "('a => 'b => 'b) => ('a => 'b => 'b)"
axioms
F_strict: "F(UU) = UU"
K: "K = (%h x y. P(x) => y | F(h(G(x),y)))"
H: "H = FIX(K)"
declare F_strict [simp] K [simp]
lemma example: "ALL x. F(H(x::'a,y::'b)) = H(x,F(y))"
apply (simplesubst H)
apply (tactic {* induct_tac @{context} "K:: ('a=>'b=>'b) => ('a=>'b=>'b)" 1 *})
apply (simp (no_asm))
apply (simp (no_asm_simp) split: COND_cases_iff)
done
end