(* Title: HOL/datatype_codegen.ML
ID: $Id$
Author: Stefan Berghofer & Florian Haftmann, TU Muenchen
Code generator for inductive datatypes.
*)
signature DATATYPE_CODEGEN =
sig
val get_eq: theory -> string -> thm list
val get_eq_datatype: theory -> string -> thm list
val get_cert: theory -> bool * string -> thm list
val get_cert_datatype: theory -> string -> thm list
val dest_case_expr: theory -> term
-> ((string * typ) list * ((term * typ) * (term * term) list)) option
val add_datatype_case_const: string -> theory -> theory
val add_datatype_case_defs: string -> theory -> theory
type hook = (string * (bool * ((string * sort) list * (string * typ list) list))) list
-> theory -> theory
val codetype_hook: hook
val eq_hook: hook
val codetypes_dependency: theory -> (string * bool) list list
val add_codetypes_hook_bootstrap: hook -> theory -> theory
val the_codetypes_mut_specs: theory -> (string * bool) list
-> ((string * sort) list * (string * (bool * (string * typ list) list)) list)
val get_codetypes_arities: theory -> (string * bool) list -> sort
-> (string * (((string * sort list) * sort) * term list)) list option
val prove_codetypes_arities: tactic -> (string * bool) list -> sort
-> (((string * sort list) * sort) list -> (string * term list) list -> theory
-> ((bstring * attribute list) * term) list * theory)
-> (((string * sort list) * sort) list -> (string * term list) list -> theory -> theory)
-> theory -> theory
val setup: theory -> theory
val setup_hooks: theory -> theory
end;
structure DatatypeCodegen : DATATYPE_CODEGEN =
struct
open Codegen;
fun mk_tuple [p] = p
| mk_tuple ps = Pretty.block (Pretty.str "(" ::
List.concat (separate [Pretty.str ",", Pretty.brk 1] (map single ps)) @
[Pretty.str ")"]);
(**** datatype definition ****)
(* find shortest path to constructor with no recursive arguments *)
fun find_nonempty (descr: DatatypeAux.descr) is i =
let
val (_, _, constrs) = valOf (AList.lookup (op =) descr i);
fun arg_nonempty (_, DatatypeAux.DtRec i) = if i mem is then NONE
else Option.map (curry op + 1 o snd) (find_nonempty descr (i::is) i)
| arg_nonempty _ = SOME 0;
fun max xs = Library.foldl
(fn (NONE, _) => NONE
| (SOME i, SOME j) => SOME (Int.max (i, j))
| (_, NONE) => NONE) (SOME 0, xs);
val xs = sort (int_ord o pairself snd)
(List.mapPartial (fn (s, dts) => Option.map (pair s)
(max (map (arg_nonempty o DatatypeAux.strip_dtyp) dts))) constrs)
in case xs of [] => NONE | x :: _ => SOME x end;
fun add_dt_defs thy defs dep module gr (descr: DatatypeAux.descr) =
let
val sg = sign_of thy;
val tab = DatatypePackage.get_datatypes thy;
val descr' = List.filter (can (map DatatypeAux.dest_DtTFree o #2 o snd)) descr;
val rtnames = map (#1 o snd) (List.filter (fn (_, (_, _, cs)) =>
exists (exists DatatypeAux.is_rec_type o snd) cs) descr');
val (_, (tname, _, _)) :: _ = descr';
val node_id = tname ^ " (type)";
val module' = if_library (thyname_of_type tname thy) module;
fun mk_dtdef gr prfx [] = (gr, [])
| mk_dtdef gr prfx ((_, (tname, dts, cs))::xs) =
let
val tvs = map DatatypeAux.dest_DtTFree dts;
val sorts = map (rpair []) tvs;
val cs' = map (apsnd (map (DatatypeAux.typ_of_dtyp descr sorts))) cs;
val (gr', (_, type_id)) = mk_type_id module' tname gr;
val (gr'', ps) =
foldl_map (fn (gr, (cname, cargs)) =>
foldl_map (invoke_tycodegen thy defs node_id module' false)
(gr, cargs) |>>>
mk_const_id module' cname) (gr', cs');
val (gr''', rest) = mk_dtdef gr'' "and " xs
in
(gr''',
Pretty.block (Pretty.str prfx ::
(if null tvs then [] else
[mk_tuple (map Pretty.str tvs), Pretty.str " "]) @
[Pretty.str (type_id ^ " ="), Pretty.brk 1] @
List.concat (separate [Pretty.brk 1, Pretty.str "| "]
(map (fn (ps', (_, cname)) => [Pretty.block
(Pretty.str cname ::
(if null ps' then [] else
List.concat ([Pretty.str " of", Pretty.brk 1] ::
separate [Pretty.str " *", Pretty.brk 1]
(map single ps'))))]) ps))) :: rest)
end;
fun mk_term_of_def gr prfx [] = []
| mk_term_of_def gr prfx ((_, (tname, dts, cs)) :: xs) =
let
val tvs = map DatatypeAux.dest_DtTFree dts;
val sorts = map (rpair []) tvs;
val cs' = map (apsnd (map (DatatypeAux.typ_of_dtyp descr sorts))) cs;
val dts' = map (DatatypeAux.typ_of_dtyp descr sorts) dts;
val T = Type (tname, dts');
val rest = mk_term_of_def gr "and " xs;
val (_, eqs) = foldl_map (fn (prfx, (cname, Ts)) =>
let val args = map (fn i =>
Pretty.str ("x" ^ string_of_int i)) (1 upto length Ts)
in (" | ", Pretty.blk (4,
[Pretty.str prfx, mk_term_of gr module' false T, Pretty.brk 1,
if null Ts then Pretty.str (snd (get_const_id cname gr))
else parens (Pretty.block
[Pretty.str (snd (get_const_id cname gr)),
Pretty.brk 1, mk_tuple args]),
Pretty.str " =", Pretty.brk 1] @
List.concat (separate [Pretty.str " $", Pretty.brk 1]
([Pretty.str ("Const (\"" ^ cname ^ "\","), Pretty.brk 1,
mk_type false (Ts ---> T), Pretty.str ")"] ::
map (fn (x, U) => [Pretty.block [mk_term_of gr module' false U,
Pretty.brk 1, x]]) (args ~~ Ts)))))
end) (prfx, cs')
in eqs @ rest end;
fun mk_gen_of_def gr prfx [] = []
| mk_gen_of_def gr prfx ((i, (tname, dts, cs)) :: xs) =
let
val tvs = map DatatypeAux.dest_DtTFree dts;
val sorts = map (rpair []) tvs;
val (cs1, cs2) =
List.partition (exists DatatypeAux.is_rec_type o snd) cs;
val SOME (cname, _) = find_nonempty descr [i] i;
fun mk_delay p = Pretty.block
[Pretty.str "fn () =>", Pretty.brk 1, p];
fun mk_constr s b (cname, dts) =
let
val gs = map (fn dt => mk_app false (mk_gen gr module' false rtnames s
(DatatypeAux.typ_of_dtyp descr sorts dt))
[Pretty.str (if b andalso DatatypeAux.is_rec_type dt then "0"
else "j")]) dts;
val (_, id) = get_const_id cname gr
in case gs of
_ :: _ :: _ => Pretty.block
[Pretty.str id, Pretty.brk 1, mk_tuple gs]
| _ => mk_app false (Pretty.str id) (map parens gs)
end;
fun mk_choice [c] = mk_constr "(i-1)" false c
| mk_choice cs = Pretty.block [Pretty.str "one_of",
Pretty.brk 1, Pretty.blk (1, Pretty.str "[" ::
List.concat (separate [Pretty.str ",", Pretty.fbrk]
(map (single o mk_delay o mk_constr "(i-1)" false) cs)) @
[Pretty.str "]"]), Pretty.brk 1, Pretty.str "()"];
val gs = map (Pretty.str o suffix "G" o strip_tname) tvs;
val gen_name = "gen_" ^ snd (get_type_id tname gr)
in
Pretty.blk (4, separate (Pretty.brk 1)
(Pretty.str (prfx ^ gen_name ^
(if null cs1 then "" else "'")) :: gs @
(if null cs1 then [] else [Pretty.str "i"]) @
[Pretty.str "j"]) @
[Pretty.str " =", Pretty.brk 1] @
(if not (null cs1) andalso not (null cs2)
then [Pretty.str "frequency", Pretty.brk 1,
Pretty.blk (1, [Pretty.str "[",
mk_tuple [Pretty.str "i", mk_delay (mk_choice cs1)],
Pretty.str ",", Pretty.fbrk,
mk_tuple [Pretty.str "1", mk_delay (mk_choice cs2)],
Pretty.str "]"]), Pretty.brk 1, Pretty.str "()"]
else if null cs2 then
[Pretty.block [Pretty.str "(case", Pretty.brk 1,
Pretty.str "i", Pretty.brk 1, Pretty.str "of",
Pretty.brk 1, Pretty.str "0 =>", Pretty.brk 1,
mk_constr "0" true (cname, valOf (AList.lookup (op =) cs cname)),
Pretty.brk 1, Pretty.str "| _ =>", Pretty.brk 1,
mk_choice cs1, Pretty.str ")"]]
else [mk_choice cs2])) ::
(if null cs1 then []
else [Pretty.blk (4, separate (Pretty.brk 1)
(Pretty.str ("and " ^ gen_name) :: gs @ [Pretty.str "i"]) @
[Pretty.str " =", Pretty.brk 1] @
separate (Pretty.brk 1) (Pretty.str (gen_name ^ "'") :: gs @
[Pretty.str "i", Pretty.str "i"]))]) @
mk_gen_of_def gr "and " xs
end
in
((add_edge_acyclic (node_id, dep) gr
handle Graph.CYCLES _ => gr) handle Graph.UNDEF _ =>
let
val gr1 = add_edge (node_id, dep)
(new_node (node_id, (NONE, "", "")) gr);
val (gr2, dtdef) = mk_dtdef gr1 "datatype " descr';
in
map_node node_id (K (NONE, module',
Pretty.string_of (Pretty.blk (0, separate Pretty.fbrk dtdef @
[Pretty.str ";"])) ^ "\n\n" ^
(if "term_of" mem !mode then
Pretty.string_of (Pretty.blk (0, separate Pretty.fbrk
(mk_term_of_def gr2 "fun " descr') @ [Pretty.str ";"])) ^ "\n\n"
else "") ^
(if "test" mem !mode then
Pretty.string_of (Pretty.blk (0, separate Pretty.fbrk
(mk_gen_of_def gr2 "fun " descr') @ [Pretty.str ";"])) ^ "\n\n"
else ""))) gr2
end,
module')
end;
(**** case expressions ****)
fun pretty_case thy defs gr dep module brack constrs (c as Const (_, T)) ts =
let val i = length constrs
in if length ts <= i then
invoke_codegen thy defs dep module brack (gr, eta_expand c ts (i+1))
else
let
val ts1 = Library.take (i, ts);
val t :: ts2 = Library.drop (i, ts);
val names = foldr add_term_names
(map (fst o fst o dest_Var) (foldr add_term_vars [] ts1)) ts1;
val (Ts, dT) = split_last (Library.take (i+1, fst (strip_type T)));
fun pcase gr [] [] [] = ([], gr)
| pcase gr ((cname, cargs)::cs) (t::ts) (U::Us) =
let
val j = length cargs;
val xs = Name.variant_list names (replicate j "x");
val Us' = Library.take (j, fst (strip_type U));
val frees = map Free (xs ~~ Us');
val (gr0, cp) = invoke_codegen thy defs dep module false
(gr, list_comb (Const (cname, Us' ---> dT), frees));
val t' = Envir.beta_norm (list_comb (t, frees));
val (gr1, p) = invoke_codegen thy defs dep module false (gr0, t');
val (ps, gr2) = pcase gr1 cs ts Us;
in
([Pretty.block [cp, Pretty.str " =>", Pretty.brk 1, p]] :: ps, gr2)
end;
val (ps1, gr1) = pcase gr constrs ts1 Ts;
val ps = List.concat (separate [Pretty.brk 1, Pretty.str "| "] ps1);
val (gr2, p) = invoke_codegen thy defs dep module false (gr1, t);
val (gr3, ps2) = foldl_map (invoke_codegen thy defs dep module true) (gr2, ts2)
in (gr3, (if not (null ts2) andalso brack then parens else I)
(Pretty.block (separate (Pretty.brk 1)
(Pretty.block ([Pretty.str "(case ", p, Pretty.str " of",
Pretty.brk 1] @ ps @ [Pretty.str ")"]) :: ps2))))
end
end;
(**** constructors ****)
fun pretty_constr thy defs gr dep module brack args (c as Const (s, T)) ts =
let val i = length args
in if i > 1 andalso length ts < i then
invoke_codegen thy defs dep module brack (gr, eta_expand c ts i)
else
let
val id = mk_qual_id module (get_const_id s gr);
val (gr', ps) = foldl_map
(invoke_codegen thy defs dep module (i = 1)) (gr, ts);
in (case args of
_ :: _ :: _ => (gr', (if brack then parens else I)
(Pretty.block [Pretty.str id, Pretty.brk 1, mk_tuple ps]))
| _ => (gr', mk_app brack (Pretty.str id) ps))
end
end;
(**** code generators for terms and types ****)
fun datatype_codegen thy defs gr dep module brack t = (case strip_comb t of
(c as Const (s, T), ts) =>
(case Library.find_first (fn (_, {index, descr, case_name, ...}) =>
s = case_name orelse
AList.defined (op =) ((#3 o the o AList.lookup (op =) descr) index) s)
(Symtab.dest (DatatypePackage.get_datatypes thy)) of
NONE => NONE
| SOME (tname, {index, descr, ...}) =>
if is_some (get_assoc_code thy s T) then NONE else
let val SOME (_, _, constrs) = AList.lookup (op =) descr index
in (case (AList.lookup (op =) constrs s, strip_type T) of
(NONE, _) => SOME (pretty_case thy defs gr dep module brack
((#3 o the o AList.lookup (op =) descr) index) c ts)
| (SOME args, (_, Type _)) => SOME (pretty_constr thy defs
(fst (invoke_tycodegen thy defs dep module false
(gr, snd (strip_type T))))
dep module brack args c ts)
| _ => NONE)
end)
| _ => NONE);
fun datatype_tycodegen thy defs gr dep module brack (Type (s, Ts)) =
(case Symtab.lookup (DatatypePackage.get_datatypes thy) s of
NONE => NONE
| SOME {descr, ...} =>
if isSome (get_assoc_type thy s) then NONE else
let
val (gr', ps) = foldl_map
(invoke_tycodegen thy defs dep module false) (gr, Ts);
val (gr'', module') = add_dt_defs thy defs dep module gr' descr;
val (gr''', tyid) = mk_type_id module' s gr''
in SOME (gr''',
Pretty.block ((if null Ts then [] else
[mk_tuple ps, Pretty.str " "]) @
[Pretty.str (mk_qual_id module tyid)]))
end)
| datatype_tycodegen _ _ _ _ _ _ _ = NONE;
(** datatypes for code 2nd generation **)
fun dtyp_of_case_const thy c =
get_first (fn (dtco, { case_name, ... }) => if case_name = c then SOME dtco else NONE)
((Symtab.dest o DatatypePackage.get_datatypes) thy);
fun dest_case_app cs ts tys =
let
val abs = Name.names Name.context "a" (Library.drop (length ts, tys));
val (ts', t) = split_last (ts @ map Free abs);
val (tys', sty) = split_last tys;
fun dest_case ((c, tys_decl), ty) t =
let
val (vs, t') = Term.strip_abs_eta (length tys_decl) t;
val c' = list_comb (Const (c, map snd vs ---> sty), map Free vs);
in (c', t') end;
in (abs, ((t, sty), map2 dest_case (cs ~~ tys') ts')) end;
fun dest_case_expr thy t =
case strip_comb t
of (Const (c, ty), ts) =>
(case dtyp_of_case_const thy c
of SOME dtco =>
let val (vs, cs) = (the o DatatypePackage.get_datatype_spec thy) dtco;
in SOME (dest_case_app cs ts (Library.take (length cs + 1, (fst o strip_type) ty))) end
| _ => NONE)
| _ => NONE;
fun mk_distinct cos =
let
fun sym_product [] = []
| sym_product (x::xs) = map (pair x) xs @ sym_product xs;
fun mk_co_args (co, tys) ctxt =
let
val names = Name.invents ctxt "a" (length tys);
val ctxt' = fold Name.declare names ctxt;
val vs = map2 (curry Free) names tys;
in (vs, ctxt') end;
fun mk_dist ((co1, tys1), (co2, tys2)) =
let
val ((xs1, xs2), _) = Name.context
|> mk_co_args (co1, tys1)
||>> mk_co_args (co2, tys2);
val prem = HOLogic.mk_eq
(list_comb (co1, xs1), list_comb (co2, xs2));
val t = HOLogic.mk_not prem;
in HOLogic.mk_Trueprop t end;
in map mk_dist (sym_product cos) end;
local
val bool_eq_implies = iffD1;
val rew_eq = thm "HOL.atomize_eq" |> Thm.symmetric;
val rew_conj = thm "HOL.atomize_conj" |> Thm.symmetric;
val not_false_true = iffD2 OF [nth (thms "HOL.simp_thms") 7, TrueI];
val not_eq_quodlibet = thm "not_eq_quodlibet";
in
fun get_cert_datatype thy dtco =
let
val SOME (vs, cs) = DatatypePackage.get_datatype_spec thy dtco;
val inject = (#inject o DatatypePackage.the_datatype thy) dtco
|> map (fn thm => bool_eq_implies OF [thm] )
|> map (MetaSimplifier.rewrite_rule [rew_eq, rew_conj]);
val ctxt = ProofContext.init thy;
val simpset = Simplifier.context ctxt
(MetaSimplifier.empty_ss addsimprocs [DatatypePackage.distinct_simproc]);
val cos = map (fn (co, tys) =>
(Const (co, tys ---> Type (dtco, map TFree vs)), tys)) cs;
val tac = ALLGOALS (simp_tac simpset)
THEN ALLGOALS (ProofContext.fact_tac [not_false_true, TrueI]);
val distinct =
mk_distinct cos
|> map (fn t => Goal.prove_global thy [] [] t (K tac))
|> map (fn thm => not_eq_quodlibet OF [thm])
in inject @ distinct end
end;
local
val not_sym = thm "HOL.not_sym";
val not_false_true = iffD2 OF [nth (thms "HOL.simp_thms") 7, TrueI];
val refl = thm "refl";
val eqTrueI = thm "eqTrueI";
in
fun get_eq_datatype thy dtco =
let
val SOME (vs, cs) = DatatypePackage.get_datatype_spec thy dtco;
fun mk_triv_inject co =
let
val ct' = Thm.cterm_of thy
(Const (co, Type (dtco, map (fn (v, sort) => TVar ((v, 0), sort)) vs)))
val cty' = Thm.ctyp_of_term ct';
val SOME (ct, cty) = fold_aterms (fn Var (v, ty) =>
(K o SOME) (Thm.cterm_of thy (Var (v, Thm.typ_of cty')), Thm.ctyp_of thy ty) | _ => I)
(Thm.prop_of refl) NONE;
in eqTrueI OF [Thm.instantiate ([(cty, cty')], [(ct, ct')]) refl] end;
val inject1 = map_filter (fn (co, []) => SOME (mk_triv_inject co) | _ => NONE) cs
val inject2 = (#inject o DatatypePackage.the_datatype thy) dtco;
val ctxt = ProofContext.init thy;
val simpset = Simplifier.context ctxt
(MetaSimplifier.empty_ss addsimprocs [distinct_simproc]);
val cos = map (fn (co, tys) =>
(Const (co, tys ---> Type (dtco, map TFree vs)), tys)) cs;
val tac = ALLGOALS (simp_tac simpset)
THEN ALLGOALS (ProofContext.fact_tac [not_false_true, TrueI]);
val distinct =
mk_distinct cos
|> map (fn t => Goal.prove_global thy [] [] t (K tac))
|> (fn thms => thms @ map (fn thm => not_sym OF [thm]) thms)
in inject1 @ inject2 @ distinct end;
end;
fun add_datatype_case_const dtco thy =
let
val {case_name, index, descr, ...} = DatatypePackage.the_datatype thy dtco;
in
CodegenPackage.add_appconst (case_name, CodegenPackage.appgen_case dest_case_expr) thy
end;
fun add_datatype_case_defs dtco thy =
let
val {case_rewrites, ...} = DatatypePackage.the_datatype thy dtco
in
fold_rev CodegenData.add_func case_rewrites thy
end;
(** codetypes for code 2nd generation **)
(* abstraction over datatypes vs. type copies *)
fun codetypes_dependency thy =
let
val names =
map (rpair true) (Symtab.keys (DatatypePackage.get_datatypes thy))
@ map (rpair false) (TypecopyPackage.get_typecopies thy);
fun add_node (name, is_dt) =
let
fun add_tycos (Type (tyco, tys)) = insert (op =) tyco #> fold add_tycos tys
| add_tycos _ = I;
val tys = if is_dt then
(maps snd o snd o the o DatatypePackage.get_datatype_spec thy) name
else
[(#typ o the o TypecopyPackage.get_typecopy_info thy) name]
val deps = (filter (AList.defined (op =) names) o maps (fn ty =>
add_tycos ty [])) tys;
in
Graph.default_node (name, ())
#> fold (fn name' =>
Graph.default_node (name', ())
#> Graph.add_edge (name', name)
) deps
end
in
Graph.empty
|> fold add_node names
|> Graph.strong_conn
|> map (AList.make (the o AList.lookup (op =) names))
end;
fun get_spec thy (dtco, true) =
(the o DatatypePackage.get_datatype_spec thy) dtco
| get_spec thy (tyco, false) =
TypecopyPackage.get_spec thy tyco;
fun get_cert thy (true, dtco) = get_cert_datatype thy dtco
| get_cert thy (false, dtco) = [TypecopyPackage.get_cert thy dtco];
local
fun get_eq_thms thy tyco = case DatatypePackage.get_datatype thy tyco
of SOME _ => get_eq_datatype thy tyco
| NONE => [TypecopyPackage.get_eq thy tyco];
fun constrain_op_eq_thms thy thms =
let
fun add_eq (Const ("op =", ty)) =
fold (insert (eq_fst (op =)))
(Term.add_tvarsT ty [])
| add_eq _ =
I
val eqs = fold (fold_aterms add_eq o Thm.prop_of) thms [];
val instT = map (fn (v_i, sort) =>
(Thm.ctyp_of thy (TVar (v_i, sort)),
Thm.ctyp_of thy (TVar (v_i, Sorts.inter_sort (Sign.classes_of thy) (sort, [HOLogic.class_eq]))))) eqs;
in
thms
|> map (Thm.instantiate (instT, []))
end;
in
fun get_eq thy tyco =
get_eq_thms thy tyco
|> maps ((#mk o #mk_rews o snd o MetaSimplifier.rep_ss o Simplifier.simpset_of) thy)
|> constrain_op_eq_thms thy
end;
type hook = (string * (bool * ((string * sort) list * (string * typ list) list))) list
-> theory -> theory;
fun add_codetypes_hook_bootstrap hook thy =
let
fun add_spec thy (tyco, is_dt) =
(tyco, (is_dt, get_spec thy (tyco, is_dt)));
fun datatype_hook dtcos thy =
hook (map (add_spec thy) (map (rpair true) dtcos)) thy;
fun typecopy_hook ((tyco, _)) thy =
hook ([(tyco, (false, TypecopyPackage.get_spec thy tyco))]) thy;
in
thy
|> fold hook ((map o map) (add_spec thy) (codetypes_dependency thy))
|> DatatypeHooks.add datatype_hook
|> TypecopyPackage.add_hook typecopy_hook
end;
fun the_codetypes_mut_specs thy ([(tyco, is_dt)]) =
let
val (vs, cs) = get_spec thy (tyco, is_dt)
in (vs, [(tyco, (is_dt, cs))]) end
| the_codetypes_mut_specs thy (tycos' as (tyco, true) :: _) =
let
val tycos = map fst tycos';
val tycos'' = (map (#1 o snd) o #descr o DatatypePackage.the_datatype thy) tyco;
val _ = if gen_subset (op =) (tycos, tycos'') then () else
error ("datatype constructors are not mutually recursive: " ^ (commas o map quote) tycos);
val (vs::_, css) = split_list (map (the o DatatypePackage.get_datatype_spec thy) tycos);
in (vs, map2 (fn (tyco, is_dt) => fn cs => (tyco, (is_dt, cs))) tycos' css) end;
(* registering code types in code generator *)
fun codetype_hook specs =
let
fun add (dtco, (flag, spec)) thy =
let
fun cert thy_ref = (fn () => get_cert (Theory.deref thy_ref) (flag, dtco));
in
CodegenData.add_datatype
(dtco, (spec, CodegenData.lazy (cert (Theory.self_ref thy)))) thy
end;
in fold add specs end;
(* instrumentalizing the sort algebra *)
fun get_codetypes_arities thy tycos sort =
let
val algebra = Sign.classes_of thy;
val (vs_proto, css_proto) = the_codetypes_mut_specs thy tycos;
val vs = map (fn (v, vsort) => (v, Sorts.inter_sort algebra (vsort, sort))) vs_proto;
fun inst_type tyco (c, tys) =
let
val tys' = (map o map_atyps)
(fn TFree (v, _) => TFree (v, the (AList.lookup (op =) vs v))) tys
in (c, tys') end;
val css = map (fn (tyco, (_, cs)) => (tyco, (map (inst_type tyco) cs))) css_proto;
fun mk_arity tyco =
((tyco, map snd vs), sort);
fun typ_of_sort ty =
let
val arities = map (fn (tyco, _) => ((tyco, map snd vs), sort)) css;
in ClassPackage.assume_arities_of_sort thy arities (ty, sort) end;
fun mk_cons tyco (c, tys) =
let
val ts = Name.names Name.context "a" tys;
val ty = tys ---> Type (tyco, map TFree vs);
in list_comb (Const (c, ty), map Free ts) end;
in if forall (fn (_, cs) => forall (fn (_, tys) => forall typ_of_sort tys) cs) css
then SOME (
map (fn (tyco, cs) => (tyco, (mk_arity tyco, map (mk_cons tyco) cs))) css
) else NONE
end;
fun prove_codetypes_arities tac tycos sort f after_qed thy =
case get_codetypes_arities thy tycos sort
of NONE => thy
| SOME insts => let
fun proven ((tyco, asorts), sort) =
Sorts.of_sort (Sign.classes_of thy)
(Type (tyco, map TFree (Name.names Name.context "'a" asorts)), sort);
val (arities, css) = (split_list o map_filter
(fn (tyco, (arity, cs)) => if proven arity
then NONE else SOME (arity, (tyco, cs)))) insts;
in
thy
|> not (null arities) ? (
f arities css
#-> (fn defs =>
ClassPackage.prove_instance_arity tac arities defs
#> after_qed arities css))
end;
(* operational equality *)
fun eq_hook specs =
let
fun add_eq_thms (dtco, (_, (vs, cs))) thy =
let
val thy_ref = Theory.self_ref thy;
val ty = Type (dtco, map TFree vs) |> Logic.varifyT;
val c = CodegenConsts.norm thy ("op =", [ty]);
val get_thms = (fn () => get_eq (Theory.deref thy_ref) dtco |> rev);
in
CodegenData.add_funcl (c, CodegenData.lazy get_thms) thy
end;
in
prove_codetypes_arities (ClassPackage.intro_classes_tac [])
(map (fn (tyco, (is_dt, _)) => (tyco, is_dt)) specs)
[HOLogic.class_eq] ((K o K o pair) []) ((K o K) (fold add_eq_thms specs))
end;
(** theory setup **)
val setup =
add_codegen "datatype" datatype_codegen
#> add_tycodegen "datatype" datatype_tycodegen
#> DatatypeHooks.add (fold add_datatype_case_const)
#> DatatypeHooks.add (fold add_datatype_case_defs)
val setup_hooks =
add_codetypes_hook_bootstrap codetype_hook
#> add_codetypes_hook_bootstrap eq_hook
end;