# Theory Compat

theory Compat
imports Main
```(*  Title:      HOL/Datatype_Examples/Compat.thy
Author:     Jasmin Blanchette, TU Muenchen

Tests for compatibility with the old datatype package.
*)

section ‹Tests for Compatibility with the Old Datatype Package›

theory Compat
imports Main
begin

subsection ‹Viewing and Registering New-Style Datatypes as Old-Style Ones›

ML ‹
fun check_len n xs label =
length xs = n orelse error ("Expected length " ^ string_of_int (length xs) ^ " for " ^ label);

fun check_lens (n1, n2, n3) (xs1, xs2, xs3) =
check_len n1 xs1 "old" andalso check_len n2 xs2 "unfold" andalso check_len n3 xs3 "keep";

fun get_descrs thy lens T_name =
(these (Option.map #descr (Old_Datatype_Data.get_info thy T_name)),
these (Option.map #descr (BNF_LFP_Compat.get_info thy [] T_name)),
these (Option.map #descr (BNF_LFP_Compat.get_info thy [BNF_LFP_Compat.Keep_Nesting] T_name)))
|> tap (check_lens lens);
›

datatype 'b w = W | W' "'b w × 'b list"

ML ‹get_descrs @{theory} (0, 1, 1) @{type_name w}›

datatype_compat w

ML ‹get_descrs @{theory} (2, 2, 1) @{type_name w}›

datatype ('c, 'b) s = L 'c | R 'b

ML ‹get_descrs @{theory} (0, 1, 1) @{type_name s}›

datatype 'd x = X | X' "('d x list, 'd list) s"

ML ‹get_descrs @{theory} (0, 1, 1) @{type_name x}›

datatype_compat s

ML ‹get_descrs @{theory} (1, 1, 1) @{type_name s}›
ML ‹get_descrs @{theory} (0, 1, 1) @{type_name x}›

datatype_compat x

ML ‹get_descrs @{theory} (3, 3, 1) @{type_name x}›

thm x.induct x.rec
thm compat_x.induct compat_x.rec

datatype 'a tttre = TTTre 'a "'a tttre list list list"

ML ‹get_descrs @{theory} (0, 1, 1) @{type_name tttre}›

datatype_compat tttre

ML ‹get_descrs @{theory} (4, 4, 1) @{type_name tttre}›

thm tttre.induct tttre.rec
thm compat_tttre.induct compat_tttre.rec

datatype 'a ftre = FEmp | FTre "'a ⇒ 'a ftre list"

ML ‹get_descrs @{theory} (0, 1, 1) @{type_name ftre}›

datatype_compat ftre

ML ‹get_descrs @{theory} (2, 2, 1) @{type_name ftre}›

thm ftre.induct ftre.rec
thm compat_ftre.induct compat_ftre.rec

datatype 'a btre = BTre 'a "'a btre list" "'a btre list"

ML ‹get_descrs @{theory} (0, 1, 1) @{type_name btre}›

datatype_compat btre

ML ‹get_descrs @{theory} (3, 3, 1) @{type_name btre}›

thm btre.induct btre.rec
thm compat_btre.induct compat_btre.rec

datatype 'a foo = Foo | Foo' 'a "'a bar" and 'a bar = Bar | Bar' 'a "'a foo"

ML ‹get_descrs @{theory} (0, 2, 2) @{type_name foo}›
ML ‹get_descrs @{theory} (0, 2, 2) @{type_name bar}›

datatype_compat foo bar

ML ‹get_descrs @{theory} (2, 2, 2) @{type_name foo}›
ML ‹get_descrs @{theory} (2, 2, 2) @{type_name bar}›

datatype 'a tre = Tre 'a "'a tre list"

ML ‹get_descrs @{theory} (0, 1, 1) @{type_name tre}›

datatype_compat tre

ML ‹get_descrs @{theory} (2, 2, 1) @{type_name tre}›

thm tre.induct tre.rec
thm compat_tre.induct compat_tre.rec

datatype 'a f = F 'a and 'a g = G 'a

ML ‹get_descrs @{theory} (0, 2, 2) @{type_name f}›
ML ‹get_descrs @{theory} (0, 2, 2) @{type_name g}›

datatype h = H "h f" | H'

ML ‹get_descrs @{theory} (0, 1, 1) @{type_name h}›

datatype_compat f g

ML ‹get_descrs @{theory} (2, 2, 2) @{type_name f}›
ML ‹get_descrs @{theory} (2, 2, 2) @{type_name g}›
ML ‹get_descrs @{theory} (0, 1, 1) @{type_name h}›

datatype_compat h

ML ‹get_descrs @{theory} (3, 3, 1) @{type_name h}›

thm h.induct h.rec
thm compat_h.induct compat_h.rec

datatype myunit = MyUnity

ML ‹get_descrs @{theory} (0, 1, 1) @{type_name myunit}›

datatype_compat myunit

ML ‹get_descrs @{theory} (1, 1, 1) @{type_name myunit}›

datatype mylist = MyNil | MyCons nat mylist

ML ‹get_descrs @{theory} (0, 1, 1) @{type_name mylist}›

datatype_compat mylist

ML ‹get_descrs @{theory} (1, 1, 1) @{type_name mylist}›

datatype foo' = FooNil | FooCons bar' foo' and bar' = Bar

ML ‹get_descrs @{theory} (0, 2, 2) @{type_name foo'}›
ML ‹get_descrs @{theory} (0, 2, 2) @{type_name bar'}›

datatype_compat bar' foo'

ML ‹get_descrs @{theory} (2, 2, 2) @{type_name foo'}›
ML ‹get_descrs @{theory} (2, 2, 2) @{type_name bar'}›

datatype tree = Tree "tree foo"

ML ‹get_descrs @{theory} (0, 1, 1) @{type_name tree}›

datatype_compat tree

ML ‹get_descrs @{theory} (3, 3, 1) @{type_name tree}›

thm tree.induct tree.rec
thm compat_tree.induct compat_tree.rec

subsection ‹Creating New-Style Datatypes Using Old-Style Interfaces›

ML ‹
val l_specs =
[((@{binding l}, [("'a", @{sort type})], NoSyn),
[(@{binding N}, [], NoSyn),
(@{binding C}, [@{typ 'a}, Type (Sign.full_name @{theory} @{binding l}, [@{typ 'a}])],
NoSyn)])];
›

setup ‹snd o BNF_LFP_Compat.add_datatype [] l_specs›

ML ‹get_descrs @{theory} (1, 1, 1) @{type_name l}›

thm l.exhaust l.map l.induct l.rec l.size

ML ‹
val t_specs =
[((@{binding t}, [("'b", @{sort type})], NoSyn),
[(@{binding T}, [@{typ 'b},
Type (@{type_name l}, [Type (Sign.full_name @{theory} @{binding t}, [@{typ 'b}])])],
NoSyn)])];
›

setup ‹snd o BNF_LFP_Compat.add_datatype [] t_specs›

ML ‹get_descrs @{theory} (2, 2, 1) @{type_name t}›

thm t.exhaust t.map t.induct t.rec t.size
thm compat_t.induct compat_t.rec

ML ‹
val ft_specs =
[((@{binding ft}, [("'a", @{sort type})], NoSyn),
[(@{binding FT0}, [], NoSyn),
(@{binding FT}, [@{typ 'a} --> Type (Sign.full_name @{theory} @{binding ft}, [@{typ 'a}])],
NoSyn)])];
›

setup ‹snd o BNF_LFP_Compat.add_datatype [] ft_specs›

ML ‹get_descrs @{theory} (1, 1, 1) @{type_name ft}›

thm ft.exhaust ft.induct ft.rec ft.size
thm compat_ft.induct compat_ft.rec

end
```