header {* Small examples for evaluation mechanisms *}
theory Eval_Examples
imports Complex_Main
begin
text {* evaluation oracle *}
lemma "True ∨ False" by eval
lemma "Suc 0 ≠ Suc 1" by eval
lemma "[] = ([] :: int list)" by eval
lemma "[()] = [()]" by eval
lemma "fst ([] :: nat list, Suc 0) = []" by eval
text {* normalization *}
lemma "True ∨ False" by normalization
lemma "Suc 0 ≠ Suc 1" by normalization
lemma "[] = ([] :: int list)" by normalization
lemma "[()] = [()]" by normalization
lemma "fst ([] :: nat list, Suc 0) = []" by normalization
text {* term evaluation *}
value "(Suc 2 + 1) * 4"
value "(Suc 2 + Suc 0) * Suc 3"
value "nat 100"
value "(10::int) ≤ 12"
value "max (2::int) 4"
value "of_int 2 / of_int 4 * (1::rat)"
value "[] :: nat list"
value "[(nat 100, ())]"
text {* a fancy datatype *}
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