(*  Title:      Pure/Isar/code.ML

     Author:     Florian Haftmann, TU Muenchen

 Abstract executable ingredients of theory.  Management of data

 dependent on executable ingredients as synchronized cache; purged

 on any change of underlying executable ingredients.

 *)

 signature CODE =

 sig

   (*constants*)

   val check_const: theory -> term -> string

   val read_bare_const: theory -> string -> string * typ

   val read_const: theory -> string -> string

   val string_of_const: theory -> string -> string

   val cert_signature: theory -> typ -> typ

   val read_signature: theory -> string -> typ

   val const_typ: theory -> string -> typ

   val subst_signatures: theory -> term -> term

   val args_number: theory -> string -> int

   (*constructor sets*)

   val constrset_of_consts: theory -> (string * typ) list

     -> string * ((string * sort) list * (string * ((string * sort) list * typ list)) list)

   (*code equations and certificates*)

   val mk_eqn: theory -> thm * bool -> thm * bool

   val mk_eqn_warning: theory -> thm -> (thm * bool) option

   val mk_eqn_liberal: theory -> thm -> (thm * bool) option

   val assert_eqn: theory -> thm * bool -> thm * bool

   val const_typ_eqn: theory -> thm -> string * typ

   val expand_eta: theory -> int -> thm -> thm

   type cert

   val empty_cert: theory -> string -> cert

   val cert_of_eqns: theory -> string -> (thm * bool) list -> cert

   val constrain_cert: theory -> sort list -> cert -> cert

   val typargs_deps_of_cert: theory -> cert -> (string * sort) list * (string * typ list) list

   val equations_of_cert: theory -> cert -> ((string * sort) list * typ)

     * (((term * string option) list * (term * string option)) * (thm option * bool)) list

   val bare_thms_of_cert: theory -> cert -> thm list

   val pretty_cert: theory -> cert -> Pretty.T list

   (*executable code*)

   val add_type: string -> theory -> theory

   val add_type_cmd: string -> theory -> theory

   val add_signature: string * typ -> theory -> theory

   val add_signature_cmd: string * string -> theory -> theory

   val add_datatype: (string * typ) list -> theory -> theory

   val add_datatype_cmd: string list -> theory -> theory

   val datatype_interpretation:

     (string * ((string * sort) list * (string * ((string * sort) list * typ list)) list)

       -> theory -> theory) -> theory -> theory

   val add_abstype: thm -> theory -> theory

   val abstype_interpretation:

     (string * ((string * sort) list * ((string * ((string * sort) list * typ)) * (string * thm)))

       -> theory -> theory) -> theory -> theory

   val add_eqn: thm -> theory -> theory

   val add_nbe_eqn: thm -> theory -> theory

   val add_default_eqn: thm -> theory -> theory

   val add_default_eqn_attribute: attribute

   val add_default_eqn_attrib: Attrib.src

   val add_nbe_default_eqn: thm -> theory -> theory

   val add_nbe_default_eqn_attribute: attribute

   val add_nbe_default_eqn_attrib: Attrib.src

   val del_eqn: thm -> theory -> theory

   val del_eqns: string -> theory -> theory

   val add_case: thm -> theory -> theory

   val add_undefined: string -> theory -> theory

   val get_type: theory -> string

     -> ((string * sort) list * (string * ((string * sort) list * typ list)) list) * bool

   val get_type_of_constr_or_abstr: theory -> string -> (string * bool) option

   val is_constr: theory -> string -> bool

   val is_abstr: theory -> string -> bool

   val get_cert: theory -> ((thm * bool) list -> (thm * bool) list) -> string -> cert

   val get_case_scheme: theory -> string -> (int * (int * string list)) option

   val get_case_cong: theory -> string -> thm option

   val undefineds: theory -> string list

   val print_codesetup: theory -> unit

   (*infrastructure*)

   val set_code_target_attr: (string -> thm -> theory -> theory) -> theory -> theory

 end;

 signature CODE_DATA_ARGS =

 sig

   type T

   val empty: T

 end;

 signature CODE_DATA =

 sig

   type T

   val change: theory option -> (T -> T) -> T

   val change_yield: theory option -> (T -> 'a * T) -> 'a * T

 end;

 signature PRIVATE_CODE =

 sig

   include CODE

   val declare_data: Object.T -> serial

   val change_yield_data: serial * ('a -> Object.T) * (Object.T -> 'a)

     -> theory -> ('a -> 'b * 'a) -> 'b * 'a

 end;

 structure Code : PRIVATE_CODE =

 struct

 (** auxiliary **)

 (* printing *)

 fun string_of_typ thy =

   Syntax.string_of_typ (Config.put show_sorts true (Syntax.init_pretty_global thy));

 fun string_of_const thy c =

   let val ctxt = Proof_Context.init_global thy in

     case AxClass.inst_of_param thy c of

       SOME (c, tyco) =>

         Proof_Context.extern_const ctxt c ^ " " ^ enclose "[" "]"

           (Proof_Context.extern_type ctxt tyco)

     | NONE => Proof_Context.extern_const ctxt c

   end;

 (* constants *)

 fun typ_equiv tys = Type.raw_instance tys andalso Type.raw_instance (swap tys);

 fun check_bare_const thy t = case try dest_Const t

  of SOME c_ty => c_ty

   | NONE => error ("Not a constant: " ^ Syntax.string_of_term_global thy t);

 fun check_unoverload thy (c, ty) =

   let

     val c' = AxClass.unoverload_const thy (c, ty);

     val ty_decl = Sign.the_const_type thy c';

   in if Sign.typ_equiv thy

       (Type.strip_sorts ty_decl, Type.strip_sorts (Logic.varifyT_global ty)) then c'

     else error ("Type\n" ^ string_of_typ thy ty

       ^ "\nof constant " ^ quote c

       ^ "\nis too specific compared to declared type\n"

       ^ string_of_typ thy ty_decl)

   end; 

 fun check_const thy = check_unoverload thy o check_bare_const thy;

 fun read_bare_const thy = check_bare_const thy o Syntax.read_term_global thy;

 fun read_const thy = check_unoverload thy o read_bare_const thy;

 (** data store **)

 (* datatypes *)

 datatype typ_spec = Constructors of (string * ((string * sort) list * typ list)) list

   | Abstractor of (string * ((string * sort) list * typ)) * (string * thm);

 fun constructors_of (Constructors cos) = (cos, false)

   | constructors_of (Abstractor ((co, (vs, ty)), _)) = ([(co, (vs, [ty]))], true);

 (* functions *)

 datatype fun_spec = Default of (thm * bool) list * (thm * bool) list lazy

   | Eqns of (thm * bool) list

   | Proj of term * string

   | Abstr of thm * string;

 val empty_fun_spec = Default ([], Lazy.value []);

 fun is_default (Default _) = true

   | is_default _ = false;

 fun associated_abstype (Abstr (_, tyco)) = SOME tyco

   | associated_abstype _ = NONE;

 (* executable code data *)

 datatype spec = Spec of {

   history_concluded: bool,

   signatures: int Symtab.table * typ Symtab.table,

   functions: ((bool * fun_spec) * (serial * fun_spec) list) Symtab.table

     (*with explicit history*),

   types: ((serial * ((string * sort) list * typ_spec)) list) Symtab.table

     (*with explicit history*),

   cases: ((int * (int * string list)) * thm) Symtab.table * unit Symtab.table

 };

 fun make_spec (history_concluded, ((signatures, functions), (types, cases))) =

   Spec { history_concluded = history_concluded,

     signatures = signatures, functions = functions, types = types, cases = cases };

 fun map_spec f (Spec { history_concluded = history_concluded, signatures = signatures,

   functions = functions, types = types, cases = cases }) =

   make_spec (f (history_concluded, ((signatures, functions), (types, cases))));

 fun merge_spec (Spec { history_concluded = _, signatures = (tycos1, sigs1), functions = functions1,

     types = types1, cases = (cases1, undefs1) },

   Spec { history_concluded = _, signatures = (tycos2, sigs2), functions = functions2,

     types = types2, cases = (cases2, undefs2) }) =

   let

     val signatures = (Symtab.merge (op =) (tycos1, tycos2),

       Symtab.merge typ_equiv (sigs1, sigs2));

     val types = Symtab.join (K (AList.merge (op =) (K true))) (types1, types2);

     fun merge_functions ((_, history1), (_, history2)) =

       let

         val raw_history = AList.merge (op = : serial * serial -> bool)

           (K true) (history1, history2);

         val filtered_history = filter_out (is_default o snd) raw_history;

         val history = if null filtered_history

           then raw_history else filtered_history;

       in ((false, (snd o hd) history), history) end;

     val all_constructors =

       maps (map fst o fst o constructors_of o snd o snd o hd o snd) (Symtab.dest types);

     val functions = Symtab.join (K merge_functions) (functions1, functions2)

       |> fold (fn c => Symtab.map_entry c (apfst (K (true, empty_fun_spec)))) all_constructors;

     val cases = (Symtab.merge (K true) (cases1, cases2),

       Symtab.merge (K true) (undefs1, undefs2));

   in make_spec (false, ((signatures, functions), (types, cases))) end;

 fun history_concluded (Spec { history_concluded, ... }) = history_concluded;

 fun the_signatures (Spec { signatures, ... }) = signatures;

 fun the_functions (Spec { functions, ... }) = functions;

 fun the_types (Spec { types, ... }) = types;

 fun the_cases (Spec { cases, ... }) = cases;

 val map_history_concluded = map_spec o apfst;

 val map_signatures = map_spec o apsnd o apfst o apfst;

 val map_functions = map_spec o apsnd o apfst o apsnd;

 val map_typs = map_spec o apsnd o apsnd o apfst;

 val map_cases = map_spec o apsnd o apsnd o apsnd;

 (* data slots dependent on executable code *)

 (*private copy avoids potential conflict of table exceptions*)

 structure Datatab = Table(type key = int val ord = int_ord);

 local

 type kind = { empty: Object.T };

 val kinds = Unsynchronized.ref (Datatab.empty: kind Datatab.table);

 fun invoke f k = case Datatab.lookup (! kinds) k

  of SOME kind => f kind

   | NONE => raise Fail "Invalid code data identifier";

 in

 fun declare_data empty =

   let

     val k = serial ();

     val kind = { empty = empty };

     val _ = CRITICAL (fn () => Unsynchronized.change kinds (Datatab.update (k, kind)));

   in k end;

 fun invoke_init k = invoke (fn kind => #empty kind) k;

 end; (*local*)

 (* theory store *)

 local

 type data = Object.T Datatab.table;

 fun empty_dataref () = Synchronized.var "code data" (NONE : (data * theory_ref) option);

 structure Code_Data = Theory_Data

 (

   type T = spec * (data * theory_ref) option Synchronized.var;

   val empty = (make_spec (false, (((Symtab.empty, Symtab.empty), Symtab.empty),

     (Symtab.empty, (Symtab.empty, Symtab.empty)))), empty_dataref ());

   val extend = I  (* FIXME empty_dataref!?! *)

   fun merge ((spec1, _), (spec2, _)) =

     (merge_spec (spec1, spec2), empty_dataref ());

 );

 in

 (* access to executable code *)

 val the_exec = fst o Code_Data.get;

 fun map_exec_purge f = Code_Data.map (fn (exec, _) => (f exec, empty_dataref ()));

 fun change_fun_spec delete c f = (map_exec_purge o map_functions

   o (if delete then Symtab.map_entry c else Symtab.map_default (c, ((false, empty_fun_spec), [])))

     o apfst) (fn (_, spec) => (true, f spec));

 (* tackling equation history *)

 fun continue_history thy = if (history_concluded o the_exec) thy

   then thy

     |> (Code_Data.map o apfst o map_history_concluded) (K false)

     |> SOME

   else NONE;

 fun conclude_history thy = if (history_concluded o the_exec) thy

   then NONE

   else thy

     |> (Code_Data.map o apfst)

         ((map_functions o Symtab.map) (fn _ => fn ((changed, current), history) =>

           ((false, current),

             if changed then (serial (), current) :: history else history))

         #> map_history_concluded (K true))

     |> SOME;

 val _ = Context.>> (Context.map_theory (Theory.at_begin continue_history #> Theory.at_end conclude_history));

 (* access to data dependent on abstract executable code *)

 fun change_yield_data (kind, mk, dest) theory f =

   let

     val dataref = (snd o Code_Data.get) theory;

     val (datatab, thy_ref) = case Synchronized.value dataref

      of SOME (datatab, thy_ref) => if Theory.eq_thy (theory, Theory.deref thy_ref)

           then (datatab, thy_ref)

           else (Datatab.empty, Theory.check_thy theory)

       | NONE => (Datatab.empty, Theory.check_thy theory)

     val data = case Datatab.lookup datatab kind

      of SOME data => data

       | NONE => invoke_init kind;

     val result as (_, data') = f (dest data);

     val _ = Synchronized.change dataref

       ((K o SOME) (Datatab.update (kind, mk data') datatab, thy_ref));

   in result end;

 end; (*local*)

 (** foundation **)

 (* constants *)

 fun arity_number thy tyco = case Symtab.lookup ((fst o the_signatures o the_exec) thy) tyco

  of SOME n => n

   | NONE => Sign.arity_number thy tyco;

 fun build_tsig thy =

   let

     val ctxt = Syntax.init_pretty_global thy;

     val (tycos, _) = the_signatures (the_exec thy);

     val decls = #types (Type.rep_tsig (Sign.tsig_of thy))

       |> snd 

       |> Symtab.fold (fn (tyco, n) =>

           Symtab.update (tyco, Type.LogicalType n)) tycos;

   in

     Type.empty_tsig

     |> Symtab.fold (fn (tyco, Type.LogicalType n) => Type.add_type ctxt Name_Space.default_naming

         (Binding.qualified_name tyco, n) | _ => I) decls

   end;

 fun cert_signature thy =

   Logic.varifyT_global o Type.cert_typ (build_tsig thy) o Type.no_tvars;

 fun read_signature thy =

   cert_signature thy o Type.strip_sorts o Syntax.parse_typ (Proof_Context.init_global thy);

 fun expand_signature thy = Type.cert_typ_mode Type.mode_syntax (Sign.tsig_of thy);

 fun lookup_typ thy = Symtab.lookup ((snd o the_signatures o the_exec) thy);

 fun const_typ thy c = case lookup_typ thy c

  of SOME ty => ty

   | NONE => (Type.strip_sorts o Sign.the_const_type thy) c;

 fun args_number thy = length o binder_types o const_typ thy;

 fun subst_signature thy c ty =

   let

     fun mk_subst (Type (_, tys1)) (Type (_, tys2)) =

           fold2 mk_subst tys1 tys2

       | mk_subst ty (TVar (v, _)) = Vartab.update (v, ([], ty))

   in case lookup_typ thy c

    of SOME ty' => Envir.subst_type (mk_subst ty (expand_signature thy ty') Vartab.empty) ty'

     | NONE => ty

   end;

 fun subst_signatures thy = map_aterms (fn Const (c, ty) => Const (c, subst_signature thy c ty) | t => t);

 fun logical_typscheme thy (c, ty) =

   (map dest_TFree (Sign.const_typargs thy (c, ty)), Type.strip_sorts ty);

 fun typscheme thy (c, ty) = logical_typscheme thy (c, subst_signature thy c ty);

 (* datatypes *)

 fun no_constr thy s (c, ty) = error ("Not a datatype constructor:\n" ^ string_of_const thy c

   ^ " :: " ^ string_of_typ thy ty ^ "\n" ^ enclose "(" ")" s);

 fun analyze_constructor thy (c, raw_ty) =

   let

     val _ = Thm.cterm_of thy (Const (c, raw_ty));

     val ty = subst_signature thy c raw_ty;

     val ty_decl = (Logic.unvarifyT_global o const_typ thy) c;

     fun last_typ c_ty ty =

       let

         val tfrees = Term.add_tfreesT ty [];

         val (tyco, vs) = (apsnd o map) dest_TFree (dest_Type (body_type ty))

           handle TYPE _ => no_constr thy "bad type" c_ty

         val _ = if tyco = "fun" then no_constr thy "bad type" c_ty else ();

         val _ = if has_duplicates (eq_fst (op =)) vs

           then no_constr thy "duplicate type variables in datatype" c_ty else ();

         val _ = if length tfrees <> length vs

           then no_constr thy "type variables missing in datatype" c_ty else ();

       in (tyco, vs) end;

     val (tyco, _) = last_typ (c, ty) ty_decl;

     val (_, vs) = last_typ (c, ty) ty;

   in ((tyco, map snd vs), (c, (map fst vs, ty))) end;

 fun constrset_of_consts thy cs =

   let

     val _ = map (fn (c, _) => if (is_some o AxClass.class_of_param thy) c

       then error ("Is a class parameter: " ^ string_of_const thy c) else ()) cs;

     fun add ((tyco', sorts'), c) ((tyco, sorts), cs) =

       let

         val _ = if (tyco' : string) <> tyco

           then error "Different type constructors in constructor set"

           else ();

         val sorts'' =

           map2 (curry (Sorts.inter_sort (Sign.classes_of thy))) sorts' sorts

       in ((tyco, sorts''), c :: cs) end;

     fun inst vs' (c, (vs, ty)) =

       let

         val the_v = the o AList.lookup (op =) (vs ~~ vs');

         val ty' = map_type_tfree (fn (v, _) => TFree (the_v v)) ty;

         val (vs'', _) = logical_typscheme thy (c, ty');

       in (c, (vs'', binder_types ty')) end;

     val c' :: cs' = map (analyze_constructor thy) cs;

     val ((tyco, sorts), cs'') = fold add cs' (apsnd single c');

     val vs = Name.names Name.context Name.aT sorts;

     val cs''' = map (inst vs) cs'';

   in (tyco, (vs, rev cs''')) end;

 fun get_type_entry thy tyco = case these (Symtab.lookup ((the_types o the_exec) thy) tyco)

  of (_, entry) :: _ => SOME entry

   | _ => NONE;

 fun get_type thy tyco = case get_type_entry thy tyco

  of SOME (vs, spec) => apfst (pair vs) (constructors_of spec)

   | NONE => arity_number thy tyco

       |> Name.invents Name.context Name.aT

       |> map (rpair [])

       |> rpair []

       |> rpair false;

 fun get_abstype_spec thy tyco = case get_type_entry thy tyco

  of SOME (vs, Abstractor spec) => (vs, spec)

   | _ => error ("Not an abstract type: " ^ tyco);

 fun get_type_of_constr_or_abstr thy c =

   case (body_type o const_typ thy) c

    of Type (tyco, _) => let val ((_, cos), abstract) = get_type thy tyco

         in if member (op =) (map fst cos) c then SOME (tyco, abstract) else NONE end

     | _ => NONE;

 fun is_constr thy c = case get_type_of_constr_or_abstr thy c

  of SOME (_, false) => true

    | _ => false;

 fun is_abstr thy c = case get_type_of_constr_or_abstr thy c

  of SOME (_, true) => true

    | _ => false;

 (* bare code equations *)

 (* convention for variables:

     ?x ?'a   for free-floating theorems (e.g. in the data store)

     ?x  'a   for certificates

      x  'a   for final representation of equations

 *)

 exception BAD_THM of string;

 fun bad_thm msg = raise BAD_THM msg;

 fun error_thm f thm = f thm handle BAD_THM msg => error msg;

 fun warning_thm f thm = SOME (f thm) handle BAD_THM msg => (warning msg; NONE)

 fun try_thm f thm = SOME (f thm) handle BAD_THM _ => NONE;

 fun is_linear thm =

   let val (_, args) = (strip_comb o fst o Logic.dest_equals o Thm.plain_prop_of) thm

   in not (has_duplicates (op =) ((fold o fold_aterms)

     (fn Var (v, _) => cons v | _ => I) args [])) end;

 fun check_decl_ty thy (c, ty) =

   let

     val ty_decl = Sign.the_const_type thy c;

   in if Sign.typ_equiv thy (Type.strip_sorts ty_decl, Type.strip_sorts ty) then ()

     else bad_thm ("Type\n" ^ string_of_typ thy ty

       ^ "\nof constant " ^ quote c

       ^ "\nis too specific compared to declared type\n"

       ^ string_of_typ thy ty_decl)

   end; 

 fun check_eqn thy { allow_nonlinear, allow_consts, allow_pats } thm (lhs, rhs) =

   let

     fun bad s = bad_thm (s ^ ":\n" ^ Display.string_of_thm_global thy thm);

     fun vars_of t = fold_aterms (fn Var (v, _) => insert (op =) v

       | Free _ => bad "Illegal free variable in equation"

       | _ => I) t [];

     fun tvars_of t = fold_term_types (fn _ =>

       fold_atyps (fn TVar (v, _) => insert (op =) v

         | TFree _ => bad "Illegal free type variable in equation")) t [];

     val lhs_vs = vars_of lhs;

     val rhs_vs = vars_of rhs;

     val lhs_tvs = tvars_of lhs;

     val rhs_tvs = tvars_of rhs;

     val _ = if null (subtract (op =) lhs_vs rhs_vs)

       then ()

       else bad "Free variables on right hand side of equation";

     val _ = if null (subtract (op =) lhs_tvs rhs_tvs)

       then ()

       else bad "Free type variables on right hand side of equation";

     val (head, args) = strip_comb lhs;

     val (c, ty) = case head

      of Const (c_ty as (_, ty)) => (AxClass.unoverload_const thy c_ty, ty)

       | _ => bad "Equation not headed by constant";

     fun check _ (Abs _) = bad "Abstraction on left hand side of equation"

       | check 0 (Var _) = ()

       | check _ (Var _) = bad "Variable with application on left hand side of equation"

       | check n (t1 $ t2) = (check (n+1) t1; check 0 t2)

       | check n (Const (c_ty as (c, ty))) =

           if allow_pats then let

             val c' = AxClass.unoverload_const thy c_ty

           in if n = (length o binder_types o subst_signature thy c') ty

             then if allow_consts orelse is_constr thy c'

               then ()

               else bad (quote c ^ " is not a constructor, on left hand side of equation")

             else bad ("Partially applied constant " ^ quote c ^ " on left hand side of equation")

           end else bad ("Pattern not allowed here, but constant " ^ quote c ^ " encountered on left hand side")

     val _ = map (check 0) args;

     val _ = if allow_nonlinear orelse is_linear thm then ()

       else bad "Duplicate variables on left hand side of equation";

     val _ = if (is_none o AxClass.class_of_param thy) c then ()

       else bad "Overloaded constant as head in equation";

     val _ = if not (is_constr thy c) then ()

       else bad "Constructor as head in equation";

     val _ = if not (is_abstr thy c) then ()

       else bad "Abstractor as head in equation";

     val _ = check_decl_ty thy (c, ty);

   in () end;

 fun gen_assert_eqn thy check_patterns (thm, proper) =

   let

     fun bad s = bad_thm (s ^ ":\n" ^ Display.string_of_thm_global thy thm);

     val (lhs, rhs) = (Logic.dest_equals o Thm.plain_prop_of) thm

       handle TERM _ => bad "Not an equation"

            | THM _ => bad "Not a proper equation";

     val _ = check_eqn thy { allow_nonlinear = not proper,

       allow_consts = not (proper andalso check_patterns), allow_pats = true } thm (lhs, rhs);

   in (thm, proper) end;

 fun assert_abs_eqn thy some_tyco thm =

   let

     fun bad s = bad_thm (s ^ ":\n" ^ Display.string_of_thm_global thy thm);

     val (full_lhs, rhs) = (Logic.dest_equals o Thm.plain_prop_of) thm

       handle TERM _ => bad "Not an equation"

            | THM _ => bad "Not a proper equation";

     val (rep, lhs) = dest_comb full_lhs

       handle TERM _ => bad "Not an abstract equation";

     val (rep_const, ty) = dest_Const rep;

     val (tyco, Ts) = (dest_Type o domain_type) ty

       handle TERM _ => bad "Not an abstract equation"

            | TYPE _ => bad "Not an abstract equation";

     val _ = case some_tyco of SOME tyco' => if tyco = tyco' then ()

           else bad ("Abstract type mismatch:" ^ quote tyco ^ " vs. " ^ quote tyco')

       | NONE => ();

     val (vs', (_, (rep', _))) = get_abstype_spec thy tyco;

     val _ = if rep_const = rep' then ()

       else bad ("Projection mismatch: " ^ quote rep_const ^ " vs. " ^ quote rep');

     val _ = check_eqn thy { allow_nonlinear = false,

       allow_consts = false, allow_pats = false } thm (lhs, rhs);

     val _ = if forall2 (fn T => fn (_, sort) => Sign.of_sort thy (T, sort)) Ts vs' then ()

       else error ("Type arguments do not satisfy sort constraints of abstype certificate.");

   in (thm, tyco) end;

 fun assert_eqn thy = error_thm (gen_assert_eqn thy true);

 fun meta_rewrite thy = Local_Defs.meta_rewrite_rule (Proof_Context.init_global thy);

 fun mk_eqn thy = error_thm (gen_assert_eqn thy false) o

   apfst (meta_rewrite thy);

 fun mk_eqn_warning thy = Option.map (fn (thm, _) => (thm, is_linear thm))

   o warning_thm (gen_assert_eqn thy false) o rpair false o meta_rewrite thy;

 fun mk_eqn_liberal thy = Option.map (fn (thm, _) => (thm, is_linear thm))

   o try_thm (gen_assert_eqn thy false) o rpair false o meta_rewrite thy;

 fun mk_abs_eqn thy = error_thm (assert_abs_eqn thy NONE) o meta_rewrite thy;

 val head_eqn = dest_Const o fst o strip_comb o fst o Logic.dest_equals o Thm.plain_prop_of;

 fun const_typ_eqn thy thm =

   let

     val (c, ty) = head_eqn thm;

     val c' = AxClass.unoverload_const thy (c, ty);

       (*permissive wrt. to overloaded constants!*)

   in (c', ty) end;

 fun const_eqn thy = fst o const_typ_eqn thy;

 fun const_abs_eqn thy = AxClass.unoverload_const thy o dest_Const o fst o strip_comb o snd

   o dest_comb o fst o Logic.dest_equals o Thm.plain_prop_of;

 fun mk_proj tyco vs ty abs rep =

   let

     val ty_abs = Type (tyco, map TFree vs);

     val xarg = Var (("x", 0), ty);

   in Logic.mk_equals (Const (rep, ty_abs --> ty) $ (Const (abs, ty --> ty_abs) $ xarg), xarg) end;

 (* technical transformations of code equations *)

 fun expand_eta thy k thm =

   let

     val (lhs, rhs) = (Logic.dest_equals o Thm.plain_prop_of) thm;

     val (_, args) = strip_comb lhs;

     val l = if k = ~1

       then (length o fst o strip_abs) rhs

       else Int.max (0, k - length args);

     val (raw_vars, _) = Term.strip_abs_eta l rhs;

     val vars = burrow_fst (Name.variant_list (map (fst o fst) (Term.add_vars lhs [])))

       raw_vars;

     fun expand (v, ty) thm = Drule.fun_cong_rule thm

       (Thm.cterm_of thy (Var ((v, 0), ty)));

   in

     thm

     |> fold expand vars

     |> Conv.fconv_rule Drule.beta_eta_conversion

   end;

 fun same_arity thy thms =

   let

     val num_args_of = length o snd o strip_comb o fst o Logic.dest_equals;

     val k = fold (Integer.max o num_args_of o Thm.prop_of) thms 0;

   in map (expand_eta thy k) thms end;

 fun mk_desymbolization pre post mk vs =

   let

     val names = map (pre o fst o fst) vs

       |> map (Name.desymbolize false)

       |> Name.variant_list []

       |> map post;

   in map_filter (fn (((v, i), x), v') =>

     if v = v' andalso i = 0 then NONE

     else SOME (((v, i), x), mk ((v', 0), x))) (vs ~~ names)

   end;

 fun desymbolize_tvars thms =

   let

     val tvs = fold (Term.add_tvars o Thm.prop_of) thms [];

     val tvar_subst = mk_desymbolization (unprefix "'") (prefix "'") TVar tvs;

   in map (Thm.certify_instantiate (tvar_subst, [])) thms end;

 fun desymbolize_vars thm =

   let

     val vs = Term.add_vars (Thm.prop_of thm) [];

     val var_subst = mk_desymbolization I I Var vs;

   in Thm.certify_instantiate ([], var_subst) thm end;

 fun canonize_thms thy = desymbolize_tvars #> same_arity thy #> map desymbolize_vars;

 (* abstype certificates *)

 fun check_abstype_cert thy proto_thm =

   let

     val thm = (AxClass.unoverload thy o meta_rewrite thy) proto_thm;

     fun bad s = bad_thm (s ^ ":\n" ^ Display.string_of_thm_global thy thm);

     val (lhs, rhs) = Logic.dest_equals (Thm.plain_prop_of thm)

       handle TERM _ => bad "Not an equation"

            | THM _ => bad "Not a proper equation";

     val ((abs, raw_ty), ((rep, rep_ty), param)) = (apsnd (apfst dest_Const o dest_comb)

         o apfst dest_Const o dest_comb) lhs

       handle TERM _ => bad "Not an abstype certificate";

     val _ = pairself (fn c => if (is_some o AxClass.class_of_param thy) c

       then error ("Is a class parameter: " ^ string_of_const thy c) else ()) (abs, rep);

     val _ = check_decl_ty thy (abs, raw_ty);

     val _ = check_decl_ty thy (rep, rep_ty);

     val _ = (fst o dest_Var) param

       handle TERM _ => bad "Not an abstype certificate";

     val _ = if param = rhs then () else bad "Not an abstype certificate";

     val ((tyco, sorts), (abs, (vs, ty'))) = analyze_constructor thy (abs, Logic.unvarifyT_global raw_ty);

     val ty = domain_type ty';

     val (vs', _) = logical_typscheme thy (abs, ty');

   in (tyco, (vs ~~ sorts, ((abs, (vs', ty)), (rep, thm)))) end;

 (* code equation certificates *)

 fun build_head thy (c, ty) =

   Thm.cterm_of thy (Logic.mk_equals (Free ("HEAD", ty), Const (c, ty)));

 fun get_head thy cert_thm =

   let

     val [head] = (#hyps o Thm.crep_thm) cert_thm;

     val (_, Const (c, ty)) = (Logic.dest_equals o Thm.term_of) head;

   in (typscheme thy (c, ty), head) end;

 fun typscheme_projection thy =

   typscheme thy o dest_Const o fst o dest_comb o fst o Logic.dest_equals;

 fun typscheme_abs thy =

   typscheme thy o dest_Const o fst o strip_comb o snd o dest_comb o fst o Logic.dest_equals o Thm.prop_of;

 fun constrain_thm thy vs sorts thm =

   let

     val mapping = map2 (fn (v, sort) => fn sort' =>

       (v, Sorts.inter_sort (Sign.classes_of thy) (sort, sort'))) vs sorts;

     val inst = map2 (fn (v, sort) => fn (_, sort') =>

       (((v, 0), sort), TFree (v, sort'))) vs mapping;

     val subst = (map_types o map_type_tfree)

       (fn (v, _) => TFree (v, the (AList.lookup (op =) mapping v)));

   in

     thm

     |> Thm.varifyT_global

     |> Thm.certify_instantiate (inst, [])

     |> pair subst

   end;

 fun concretify_abs thy tyco abs_thm =

   let

     val (_, ((c, _), (_, cert))) = get_abstype_spec thy tyco;

     val lhs = (fst o Logic.dest_equals o Thm.prop_of) abs_thm

     val ty = fastype_of lhs;

     val ty_abs = (fastype_of o snd o dest_comb) lhs;

     val abs = Thm.cterm_of thy (Const (c, ty --> ty_abs));

     val raw_concrete_thm = Drule.transitive_thm OF [Thm.symmetric cert, Thm.combination (Thm.reflexive abs) abs_thm];

   in (c, (Thm.varifyT_global o zero_var_indexes) raw_concrete_thm) end;

 fun add_rhss_of_eqn thy t =

   let

     val (args, rhs) = (apfst (snd o strip_comb) o Logic.dest_equals o subst_signatures thy) t;

     fun add_const (Const (c, ty)) = insert (op =) (c, Sign.const_typargs thy (c, ty))

       | add_const _ = I

     val add_consts = fold_aterms add_const

   in add_consts rhs o fold add_consts args end;

 fun dest_eqn thy =

   apfst (snd o strip_comb) o Logic.dest_equals o subst_signatures thy o Logic.unvarify_global;

 abstype cert = Equations of thm * bool list

   | Projection of term * string

   | Abstract of thm * string

 with

 fun empty_cert thy c = 

   let

     val raw_ty = Logic.unvarifyT_global (const_typ thy c);

     val (vs, _) = logical_typscheme thy (c, raw_ty);

     val sortargs = case AxClass.class_of_param thy c

      of SOME class => [[class]]

       | NONE => (case get_type_of_constr_or_abstr thy c

          of SOME (tyco, _) => (map snd o fst o the)

               (AList.lookup (op =) ((snd o fst o get_type thy) tyco) c)

           | NONE => replicate (length vs) []);

     val the_sort = the o AList.lookup (op =) (map fst vs ~~ sortargs);

     val ty = map_type_tfree (fn (v, _) => TFree (v, the_sort v)) raw_ty

     val chead = build_head thy (c, ty);

   in Equations (Thm.weaken chead Drule.dummy_thm, []) end;

 fun cert_of_eqns thy c [] = empty_cert thy c

   | cert_of_eqns thy c raw_eqns = 

       let

         val eqns = burrow_fst (canonize_thms thy) raw_eqns;

         val _ = map (assert_eqn thy) eqns;

         val (thms, propers) = split_list eqns;

         val _ = map (fn thm => if c = const_eqn thy thm then ()

           else error ("Wrong head of code equation,\nexpected constant "

             ^ string_of_const thy c ^ "\n" ^ Display.string_of_thm_global thy thm)) thms;

         fun tvars_of T = rev (Term.add_tvarsT T []);

         val vss = map (tvars_of o snd o head_eqn) thms;

         fun inter_sorts vs =

           fold (curry (Sorts.inter_sort (Sign.classes_of thy)) o snd) vs [];

         val sorts = map_transpose inter_sorts vss;

         val vts = Name.names Name.context Name.aT sorts;

         val thms' =

           map2 (fn vs => Thm.certify_instantiate (vs ~~ map TFree vts, [])) vss thms;

         val head_thm = Thm.symmetric (Thm.assume (build_head thy (head_eqn (hd thms'))));

         fun head_conv ct = if can Thm.dest_comb ct

           then Conv.fun_conv head_conv ct

           else Conv.rewr_conv head_thm ct;

         val rewrite_head = Conv.fconv_rule (Conv.arg1_conv head_conv);

         val cert_thm = Conjunction.intr_balanced (map rewrite_head thms');

       in Equations (cert_thm, propers) end;

 fun cert_of_proj thy c tyco =

   let

     val (vs, ((abs, (_, ty)), (rep, _))) = get_abstype_spec thy tyco;

     val _ = if c = rep then () else

       error ("Wrong head of projection,\nexpected constant " ^ string_of_const thy rep);

   in Projection (mk_proj tyco vs ty abs rep, tyco) end;

 fun cert_of_abs thy tyco c raw_abs_thm =

   let

     val abs_thm = singleton (canonize_thms thy) raw_abs_thm;

     val _ = assert_abs_eqn thy (SOME tyco) abs_thm;

     val _ = if c = const_abs_eqn thy abs_thm then ()

       else error ("Wrong head of abstract code equation,\nexpected constant "

         ^ string_of_const thy c ^ "\n" ^ Display.string_of_thm_global thy abs_thm);

   in Abstract (Thm.legacy_freezeT abs_thm, tyco) end;

 fun constrain_cert thy sorts (Equations (cert_thm, propers)) =

       let

         val ((vs, _), head) = get_head thy cert_thm;

         val (subst, cert_thm') = cert_thm

           |> Thm.implies_intr head

           |> constrain_thm thy vs sorts;

         val head' = Thm.term_of head

           |> subst

           |> Thm.cterm_of thy;

         val cert_thm'' = cert_thm'

           |> Thm.elim_implies (Thm.assume head');

       in Equations (cert_thm'', propers) end

   | constrain_cert thy _ (cert as Projection _) =

       cert

   | constrain_cert thy sorts (Abstract (abs_thm, tyco)) =

       Abstract (snd (constrain_thm thy (fst (typscheme_abs thy abs_thm)) sorts abs_thm), tyco);

 fun typscheme_of_cert thy (Equations (cert_thm, _)) =

       fst (get_head thy cert_thm)

   | typscheme_of_cert thy (Projection (proj, _)) =

       typscheme_projection thy proj

   | typscheme_of_cert thy (Abstract (abs_thm, _)) =

       typscheme_abs thy abs_thm;

 fun typargs_deps_of_cert thy (Equations (cert_thm, propers)) =

       let

         val vs = (fst o fst) (get_head thy cert_thm);

         val equations = if null propers then [] else

           Thm.prop_of cert_thm

           |> Logic.dest_conjunction_balanced (length propers);

       in (vs, fold (add_rhss_of_eqn thy) equations []) end

   | typargs_deps_of_cert thy (Projection (t, _)) =

       (fst (typscheme_projection thy t), add_rhss_of_eqn thy t [])

   | typargs_deps_of_cert thy (Abstract (abs_thm, tyco)) =

       let

         val vs = fst (typscheme_abs thy abs_thm);

         val (_, concrete_thm) = concretify_abs thy tyco abs_thm;

       in (vs, add_rhss_of_eqn thy (map_types Logic.unvarifyT_global (Thm.prop_of concrete_thm)) []) end;

 fun equations_of_cert thy (cert as Equations (cert_thm, propers)) =

       let

         val tyscm = typscheme_of_cert thy cert;

         val thms = if null propers then [] else

           cert_thm

           |> Local_Defs.expand [snd (get_head thy cert_thm)]

           |> Thm.varifyT_global

           |> Conjunction.elim_balanced (length propers);

         fun abstractions (args, rhs) = (map (rpair NONE) args, (rhs, NONE));

       in (tyscm, map (abstractions o dest_eqn thy o Thm.prop_of) thms ~~ (map SOME thms ~~ propers)) end

   | equations_of_cert thy (Projection (t, tyco)) =

       let

         val (_, ((abs, _), _)) = get_abstype_spec thy tyco;

         val tyscm = typscheme_projection thy t;

         val t' = map_types Logic.varifyT_global t;

         fun abstractions (args, rhs) = (map (rpair (SOME abs)) args, (rhs, NONE));

       in (tyscm, [((abstractions o dest_eqn thy) t', (NONE, true))]) end

   | equations_of_cert thy (Abstract (abs_thm, tyco)) =

       let

         val tyscm = typscheme_abs thy abs_thm;

         val (abs, concrete_thm) = concretify_abs thy tyco abs_thm;

         fun abstractions (args, rhs) = (map (rpair NONE) args, (rhs, (SOME abs)));

       in

         (tyscm, [((abstractions o dest_eqn thy o Thm.prop_of) concrete_thm,

           (SOME (Thm.varifyT_global abs_thm), true))])

       end;

 fun pretty_cert thy (cert as Equations _) =

       (map_filter (Option.map (Display.pretty_thm_global thy o AxClass.overload thy) o fst o snd)

          o snd o equations_of_cert thy) cert

   | pretty_cert thy (Projection (t, _)) =

       [Syntax.pretty_term_global thy (map_types Logic.varifyT_global t)]

   | pretty_cert thy (Abstract (abs_thm, _)) =

       [(Display.pretty_thm_global thy o AxClass.overload thy o Thm.varifyT_global) abs_thm];

 fun bare_thms_of_cert thy (cert as Equations _) =

       (map_filter (fn (_, (some_thm, proper)) => if proper then some_thm else NONE)

         o snd o equations_of_cert thy) cert

   | bare_thms_of_cert thy (Projection _) = []

   | bare_thms_of_cert thy (Abstract (abs_thm, tyco)) =

       [Thm.varifyT_global (snd (concretify_abs thy tyco abs_thm))];

 end;

 (* code certificate access *)

 fun retrieve_raw thy c =

   Symtab.lookup ((the_functions o the_exec) thy) c

   |> Option.map (snd o fst)

   |> the_default empty_fun_spec

 fun get_cert thy f c = case retrieve_raw thy c

  of Default (_, eqns_lazy) => Lazy.force eqns_lazy

       |> (map o apfst) (Thm.transfer thy)

       |> f

       |> (map o apfst) (AxClass.unoverload thy)

       |> cert_of_eqns thy c

   | Eqns eqns => eqns

       |> (map o apfst) (Thm.transfer thy)

       |> f

       |> (map o apfst) (AxClass.unoverload thy)

       |> cert_of_eqns thy c

   | Proj (_, tyco) =>

       cert_of_proj thy c tyco

   | Abstr (abs_thm, tyco) => abs_thm

       |> Thm.transfer thy

       |> AxClass.unoverload thy

       |> cert_of_abs thy tyco c;

 (* cases *)

 fun case_certificate thm =

   let

     val ((head, raw_case_expr), cases) = (apfst Logic.dest_equals

       o apsnd Logic.dest_conjunctions o Logic.dest_implies o Thm.plain_prop_of) thm;

     val _ = case head of Free _ => true

       | Var _ => true

       | _ => raise TERM ("case_cert", []);

     val ([(case_var, _)], case_expr) = Term.strip_abs_eta 1 raw_case_expr;

     val (Const (case_const, _), raw_params) = strip_comb case_expr;

     val n = find_index (fn Free (v, _) => v = case_var | _ => false) raw_params;

     val _ = if n = ~1 then raise TERM ("case_cert", []) else ();

     val params = map (fst o dest_Var) (nth_drop n raw_params);

     fun dest_case t =

       let

         val (head' $ t_co, rhs) = Logic.dest_equals t;

         val _ = if head' = head then () else raise TERM ("case_cert", []);

         val (Const (co, _), args) = strip_comb t_co;

         val (Var (param, _), args') = strip_comb rhs;

         val _ = if args' = args then () else raise TERM ("case_cert", []);

       in (param, co) end;

     fun analyze_cases cases =

       let

         val co_list = fold (AList.update (op =) o dest_case) cases [];

       in map (the o AList.lookup (op =) co_list) params end;

     fun analyze_let t =

       let

         val (head' $ arg, Var (param', _) $ arg') = Logic.dest_equals t;

         val _ = if head' = head then () else raise TERM ("case_cert", []);

         val _ = if arg' = arg then () else raise TERM ("case_cert", []);

         val _ = if [param'] = params then () else raise TERM ("case_cert", []);

       in [] end;

     fun analyze (cases as [let_case]) =

           (analyze_cases cases handle Bind => analyze_let let_case)

       | analyze cases = analyze_cases cases;

   in (case_const, (n, analyze cases)) end;

 fun case_cert thm = case_certificate thm

   handle Bind => error "bad case certificate"

        | TERM _ => error "bad case certificate";

 fun get_case_scheme thy = Option.map fst o Symtab.lookup ((fst o the_cases o the_exec) thy);

 fun get_case_cong thy = Option.map snd o Symtab.lookup ((fst o the_cases o the_exec) thy);

 val undefineds = Symtab.keys o snd o the_cases o the_exec;

 (* diagnostic *)

 fun print_codesetup thy =

   let

     val ctxt = Proof_Context.init_global thy;

     val exec = the_exec thy;

     fun pretty_equations const thms =

       (Pretty.block o Pretty.fbreaks) (

         Pretty.str (string_of_const thy const) :: map (Display.pretty_thm ctxt) thms

       );

     fun pretty_function (const, Default (_, eqns_lazy)) = pretty_equations const (map fst (Lazy.force eqns_lazy))

       | pretty_function (const, Eqns eqns) = pretty_equations const (map fst eqns)

       | pretty_function (const, Proj (proj, _)) = Pretty.block

           [Pretty.str (string_of_const thy const), Pretty.fbrk, Syntax.pretty_term ctxt proj]

       | pretty_function (const, Abstr (thm, _)) = pretty_equations const [thm];

     fun pretty_typ (tyco, vs) = Pretty.str

       (string_of_typ thy (Type (tyco, map TFree vs)));

     fun pretty_typspec (typ, (cos, abstract)) = if null cos

       then pretty_typ typ

       else (Pretty.block o Pretty.breaks) (

         pretty_typ typ

         :: Pretty.str "="

         :: (if abstract then [Pretty.str "(abstract)"] else [])

         @ separate (Pretty.str "|") (map (fn (c, (_, [])) => Pretty.str (string_of_const thy c)

              | (c, (_, tys)) =>

                  (Pretty.block o Pretty.breaks)

                     (Pretty.str (string_of_const thy c)

                       :: Pretty.str "of"

                       :: map (Pretty.quote o Syntax.pretty_typ_global thy) tys)) cos)

       );

     fun pretty_case (const, ((_, (_, [])), _)) = Pretty.str (string_of_const thy const)

       | pretty_case (const, ((_, (_, cos)), _)) = (Pretty.block o Pretty.breaks) [

           Pretty.str (string_of_const thy const), Pretty.str "with",

           (Pretty.block o Pretty.commas o map (Pretty.str o string_of_const thy)) cos];

     val functions = the_functions exec

       |> Symtab.dest

       |> (map o apsnd) (snd o fst)

       |> sort (string_ord o pairself fst);

     val datatypes = the_types exec

       |> Symtab.dest

       |> map (fn (tyco, (_, (vs, spec)) :: _) =>

           ((tyco, vs), constructors_of spec))

       |> sort (string_ord o pairself (fst o fst));

     val cases = Symtab.dest ((fst o the_cases o the_exec) thy);

     val undefineds = Symtab.keys ((snd o the_cases o the_exec) thy);

   in

     (Pretty.writeln o Pretty.chunks) [

       Pretty.block (

         Pretty.str "code equations:" :: Pretty.fbrk

         :: (Pretty.fbreaks o map pretty_function) functions

       ),

       Pretty.block (

         Pretty.str "datatypes:" :: Pretty.fbrk

         :: (Pretty.fbreaks o map pretty_typspec) datatypes

       ),

       Pretty.block (

         Pretty.str "cases:" :: Pretty.fbrk

         :: (Pretty.fbreaks o map pretty_case) cases

       ),

       Pretty.block (

         Pretty.str "undefined:" :: Pretty.fbrk

         :: (Pretty.commas o map (Pretty.str o string_of_const thy)) undefineds

       )

     ]

   end;

 (** declaring executable ingredients **)

 (* constant signatures *)

 fun add_type tyco thy =

   case Symtab.lookup ((snd o #types o Type.rep_tsig o Sign.tsig_of) thy) tyco

    of SOME (Type.Abbreviation (vs, _, _)) =>

           (map_exec_purge o map_signatures o apfst)

             (Symtab.update (tyco, length vs)) thy

     | _ => error ("No such type abbreviation: " ^ quote tyco);

 fun add_type_cmd s thy = add_type (Sign.intern_type thy s) thy;

 fun gen_add_signature prep_const prep_signature (raw_c, raw_ty) thy =

   let

     val c = prep_const thy raw_c;

     val ty = prep_signature thy raw_ty;

     val ty' = expand_signature thy ty;

     val ty'' = Sign.the_const_type thy c;

     val _ = if typ_equiv (ty', ty'') then () else

       error ("Illegal constant signature: " ^ Syntax.string_of_typ_global thy ty);

   in

     thy

     |> (map_exec_purge o map_signatures o apsnd) (Symtab.update (c, ty))

   end;

 val add_signature = gen_add_signature (K I) cert_signature;

 val add_signature_cmd = gen_add_signature read_const read_signature;

 (* code equations *)

 fun gen_add_eqn default (raw_thm, proper) thy =

   let

     val thm = Thm.close_derivation raw_thm;

     val c = const_eqn thy thm;

     fun update_subsume thy (thm, proper) eqns = 

       let

         val args_of = snd o chop_while is_Var o rev o snd o strip_comb

           o map_types Type.strip_sorts o fst o Logic.dest_equals o Thm.plain_prop_of;

         val args = args_of thm;

         val incr_idx = Logic.incr_indexes ([], Thm.maxidx_of thm + 1);

         fun matches_args args' =

           let

             val k = length args' - length args

           in if k >= 0

             then Pattern.matchess thy (args, (map incr_idx o drop k) args')

             else false

           end;

         fun drop (thm', proper') = if (proper orelse not proper')

           andalso matches_args (args_of thm') then 

             (warning ("Code generator: dropping subsumed code equation\n" ^

                 Display.string_of_thm_global thy thm'); true)

           else false;

       in (thm, proper) :: filter_out drop eqns end;

     fun natural_order thy_ref eqns =

       (eqns, Lazy.lazy (fn () => fold (update_subsume (Theory.deref thy_ref)) eqns []))

     fun add_eqn' true (Default (eqns, _)) =

           Default (natural_order (Theory.check_thy thy) ((thm, proper) :: eqns))

           (*this restores the natural order and drops syntactic redundancies*)

       | add_eqn' true fun_spec = fun_spec

       | add_eqn' false (Eqns eqns) = Eqns (update_subsume thy (thm, proper) eqns)

       | add_eqn' false _ = Eqns [(thm, proper)];

   in change_fun_spec false c (add_eqn' default) thy end;

 fun add_eqn thm thy =

   gen_add_eqn false (mk_eqn thy (thm, true)) thy;

 fun add_warning_eqn thm thy =

   case mk_eqn_warning thy thm

    of SOME eqn => gen_add_eqn false eqn thy

     | NONE => thy;

 fun add_nbe_eqn thm thy =

   gen_add_eqn false (mk_eqn thy (thm, false)) thy;

 fun add_default_eqn thm thy =

   case mk_eqn_liberal thy thm

    of SOME eqn => gen_add_eqn true eqn thy

     | NONE => thy;

 val add_default_eqn_attribute = Thm.declaration_attribute

   (fn thm => Context.mapping (add_default_eqn thm) I);

 val add_default_eqn_attrib = Attrib.internal (K add_default_eqn_attribute);

 fun add_nbe_default_eqn thm thy =

   gen_add_eqn true (mk_eqn thy (thm, false)) thy;

 val add_nbe_default_eqn_attribute = Thm.declaration_attribute

   (fn thm => Context.mapping (add_nbe_default_eqn thm) I);

 val add_nbe_default_eqn_attrib = Attrib.internal (K add_nbe_default_eqn_attribute);

 fun add_abs_eqn raw_thm thy =

   let

     val (abs_thm, tyco) = (apfst Thm.close_derivation o mk_abs_eqn thy) raw_thm;

     val c = const_abs_eqn thy abs_thm;

   in change_fun_spec false c (K (Abstr (abs_thm, tyco))) thy end;

 fun del_eqn thm thy = case mk_eqn_liberal thy thm

  of SOME (thm, _) => let

         fun del_eqn' (Default _) = empty_fun_spec

           | del_eqn' (Eqns eqns) =

               Eqns (filter_out (fn (thm', _) => Thm.eq_thm_prop (thm, thm')) eqns)

           | del_eqn' spec = spec

       in change_fun_spec true (const_eqn thy thm) del_eqn' thy end

   | NONE => thy;

 fun del_eqns c = change_fun_spec true c (K empty_fun_spec);

 (* cases *)

 fun case_cong thy case_const (num_args, (pos, _)) =

   let

     val ([x, y], ctxt) = fold_map Name.variant ["A", "A'"] Name.context;

     val (zs, _) = fold_map Name.variant (replicate (num_args - 1) "") ctxt;

     val (ws, vs) = chop pos zs;

     val T = Logic.unvarifyT_global (Sign.the_const_type thy case_const);

     val Ts = binder_types T;

     val T_cong = nth Ts pos;

     fun mk_prem z = Free (z, T_cong);

     fun mk_concl z = list_comb (Const (case_const, T), map2 (curry Free) (ws @ z :: vs) Ts);

     val (prem, concl) = pairself Logic.mk_equals (pairself mk_prem (x, y), pairself mk_concl (x, y));

     fun tac { context, prems } = Simplifier.rewrite_goals_tac prems

       THEN ALLGOALS (Proof_Context.fact_tac [Drule.reflexive_thm]);

   in Skip_Proof.prove_global thy (x :: y :: zs) [prem] concl tac end;

 fun add_case thm thy =

   let

     val (case_const, (k, case_pats)) = case_cert thm;

     val _ = case filter_out (is_constr thy) case_pats

      of [] => ()

       | cs => error ("Non-constructor(s) in case certificate: " ^ commas (map quote cs));

     val entry = (1 + Int.max (1, length case_pats), (k, case_pats));

   in

     thy

     |> Theory.checkpoint

     |> `(fn thy => case_cong thy case_const entry)

     |-> (fn cong => (map_exec_purge o map_cases o apfst) (Symtab.update (case_const, (entry, cong))))

   end;

 fun add_undefined c thy =

   (map_exec_purge o map_cases o apsnd) (Symtab.update (c, ())) thy;

 (* types *)

 fun register_type (tyco, vs_spec) thy =

   let

     val (old_constrs, some_old_proj) =

       case these (Symtab.lookup ((the_types o the_exec) thy) tyco)

        of (_, (_, Constructors cos)) :: _ => (map fst cos, NONE)

         | (_, (_, Abstractor ((co, _), (proj, _)))) :: _ => ([co], SOME proj)

         | [] => ([], NONE)

     val outdated_funs = case some_old_proj

      of NONE => old_constrs

       | SOME old_proj => Symtab.fold

           (fn (c, ((_, spec), _)) =>

             if member (op =) (the_list (associated_abstype spec)) tyco

             then insert (op =) c else I)

             ((the_functions o the_exec) thy) (old_proj :: old_constrs);

     fun drop_outdated_cases cases = fold Symtab.delete_safe

       (Symtab.fold (fn (c, ((_, (_, cos)), _)) =>

         if exists (member (op =) old_constrs) cos

           then insert (op =) c else I) cases []) cases;

   in

     thy

     |> fold del_eqns outdated_funs

     |> map_exec_purge

         ((map_typs o Symtab.map_default (tyco, [])) (cons (serial (), vs_spec))

         #> (map_cases o apfst) drop_outdated_cases)

   end;

 fun unoverload_const_typ thy (c, ty) = (AxClass.unoverload_const thy (c, ty), ty);

 structure Datatype_Interpretation =

   Interpretation(type T = string * serial val eq = eq_snd (op =) : T * T -> bool);

 fun datatype_interpretation f = Datatype_Interpretation.interpretation

   (fn (tyco, _) => fn thy => f (tyco, fst (get_type thy tyco)) thy);

 fun add_datatype proto_constrs thy =

   let

     val constrs = map (unoverload_const_typ thy) proto_constrs;

     val (tyco, (vs, cos)) = constrset_of_consts thy constrs;

   in

     thy

     |> fold (del_eqns o fst) constrs

     |> register_type (tyco, (vs, Constructors cos))

     |> Datatype_Interpretation.data (tyco, serial ())

   end;

 fun add_datatype_cmd raw_constrs thy =

   add_datatype (map (read_bare_const thy) raw_constrs) thy;

 structure Abstype_Interpretation =

   Interpretation(type T = string * serial val eq = eq_snd (op =) : T * T -> bool);

 fun abstype_interpretation f = Abstype_Interpretation.interpretation

   (fn (tyco, _) => fn thy => f (tyco, get_abstype_spec thy tyco) thy);

 fun add_abstype proto_thm thy =

   let

     val (tyco, (vs, (abs_ty as (abs, (_, ty)), (rep, cert)))) =

       error_thm (check_abstype_cert thy) proto_thm;

   in

     thy

     |> del_eqns abs

     |> register_type (tyco, (vs, Abstractor (abs_ty, (rep, cert))))

     |> change_fun_spec false rep ((K o Proj)

         (map_types Logic.varifyT_global (mk_proj tyco vs ty abs rep), tyco))

     |> Abstype_Interpretation.data (tyco, serial ())

   end;

 (** infrastructure **)

 (* cf. src/HOL/Tools/recfun_codegen.ML *)

 structure Code_Target_Attr = Theory_Data

 (

   type T = (string -> thm -> theory -> theory) option;

   val empty = NONE;

   val extend = I;

   val merge = merge_options;

 );

 fun set_code_target_attr f = Code_Target_Attr.map (K (SOME f));

 fun code_target_attr prefix thm thy =

   let

     val attr = the_default ((K o K) I) (Code_Target_Attr.get thy);

   in thy |> add_warning_eqn thm |> attr prefix thm end;

 (* setup *)

 val _ = Context.>> (Context.map_theory

   (let

     fun mk_attribute f = Thm.declaration_attribute (fn thm => Context.mapping (f thm) I);

     val code_attribute_parser =

       Args.del |-- Scan.succeed (mk_attribute del_eqn)

       || Args.$$$ "nbe" |-- Scan.succeed (mk_attribute add_nbe_eqn)

       || Args.$$$ "abstype" |-- Scan.succeed (mk_attribute add_abstype)

       || Args.$$$ "abstract" |-- Scan.succeed (mk_attribute add_abs_eqn)

       || (Args.$$$ "target" |-- Args.colon |-- Args.name >>

            (mk_attribute o code_target_attr))

       || Scan.succeed (mk_attribute add_warning_eqn);

   in

     Datatype_Interpretation.init

     #> Attrib.setup (Binding.name "code") (Scan.lift code_attribute_parser)

         "declare theorems for code generation"

   end));

 end; (*struct*)

 (* type-safe interfaces for data dependent on executable code *)

 functor Code_Data(Data: CODE_DATA_ARGS): CODE_DATA =

 struct

 type T = Data.T;

 exception Data of T;

 fun dest (Data x) = x

 val kind = Code.declare_data (Data Data.empty);

 val data_op = (kind, Data, dest);

 fun change_yield (SOME thy) f = Code.change_yield_data data_op thy f

   | change_yield NONE f = f Data.empty

 fun change some_thy f = snd (change_yield some_thy (pair () o f));

 end;

 structure Code : CODE = struct open Code; end;