theory Datatype_Record_Examples
imports "HOL-Library.Datatype_Records"
begin
text \<open>Standard usage\<close>
datatype_record ('a, 'b) foo =
field_1 :: 'a
field_2 :: 'b
lemma "\<lparr> field_1 = 3, field_2 = () \<rparr> = (make_foo 3 () :: (nat, unit) foo)" ..
lemma "(make_foo a b) \<lparr> field_1 := y \<rparr> = make_foo y b"
by (simp add: datatype_record_update)
lemma "(make_foo a b) \<lparr> foo.field_1 := y \<rparr> = make_foo y b"
by (simp add: datatype_record_update)
text \<open>Existing datatypes\<close>
datatype x = X (a: int) (b: int)
lemma "\<lparr> a = 1, b = 2 \<rparr> = X 1 2" ..
local_setup \<open>Datatype_Records.mk_update_defs \<^type_name>\<open>x\<close>\<close>
lemma "(X 1 2) \<lparr> b := 3 \<rparr> = X 1 3"
by (simp add: datatype_record_update)
text \<open>Nested recursion\<close>
datatype_record 'a container =
content :: "'a option"
datatype 'a contrived = Contrived "'a contrived container"
term "Contrived \<lparr> content = None \<rparr>"
text \<open>Supports features of @{command datatype}\<close>
datatype_record (plugins del: code) (dead 'a :: finite, b_set: 'b) rec =
field_1 :: 'a
field_2 :: 'b
lemma "b_set \<lparr> field_1 = True, field_2 = False \<rparr> = {False}"
by simp
text \<open>More tests\<close>
datatype_record ('a, 'b) test1 =
field_t11 :: 'a
field_t12 :: 'b
field_t13 :: nat
field_t14 :: int
thm test1.record_simps
definition ID where "ID x = x"
lemma ID_cong[cong]: "ID x = ID x" by (rule refl)
lemma "update_field_t11 f (update_field_t12 g (update_field_t11 h x)) = ID (update_field_t12 g (update_field_t11 (\<lambda>x. f (h x)) x))"
apply (simp only: test1.record_simps)
apply (subst ID_def)
apply (rule refl)
done
end