(* Author: Florian Haftmann, TU Muenchen *)
section \<open>Small examples for evaluation mechanisms\<close>
theory Eval_Examples
imports Complex_Main
begin
text \<open>evaluation oracle\<close>
lemma "True \<or> False" by eval
lemma "Suc 0 \<noteq> Suc 1" by eval
lemma "[] = ([] :: int list)" by eval
lemma "[()] = [()]" by eval
lemma "fst ([] :: nat list, Suc 0) = []" by eval
text \<open>normalization\<close>
lemma "True \<or> False" by normalization
lemma "Suc 0 \<noteq> Suc 1" by normalization
lemma "[] = ([] :: int list)" by normalization
lemma "[()] = [()]" by normalization
lemma "fst ([] :: nat list, Suc 0) = []" by normalization
text \<open>term evaluation\<close>
value "(Suc 2 + 1) * 4"
value "(Suc 2 + Suc 0) * Suc 3"
value "nat 100"
value "(10::int) \<le> 12"
value "max (2::int) 4"
value "of_int 2 / of_int 4 * (1::rat)"
value "[] :: nat list"
value "[(nat 100, ())]"
text \<open>a fancy datatype\<close>
datatype ('a, 'b) foo =
Foo "'a::order" 'b
| Bla "('a, 'b) bar"
| Dummy nat
and ('a, 'b) bar =
Bar 'a 'b
| Blubb "('a, 'b) foo"
value "Bla (Bar (4::nat) [Suc 0])"
end