(*  Title:      Tools/Code/code_thingol.ML

    Author:     Florian Haftmann, TU Muenchen

Intermediate language ("Thin-gol") representing executable code.

Representation and translation.

*)

infix 8 `%%;

infix 4 `$;

infix 4 `$$;

infixr 3 `|=>;

infixr 3 `|==>;

signature BASIC_CODE_THINGOL =

sig

  type vname = string;

  datatype dict =

      Dict of string list * plain_dict

  and plain_dict = 

      Dict_Const of string * dict list list

    | Dict_Var of vname * (int * int)

  datatype itype =

      `%% of string * itype list

    | ITyVar of vname;

  type const = string * (((itype list * dict list list) * (itype list * itype)) * bool)

    (* (f [T1..Tn] {dicts} (_::S1) .. (_::Sm)) :: S =^= (f, ((([T1..Tn], dicts), ([S1..Sm], S)), ambiguous)) *)

  datatype iterm =

      IConst of const

    | IVar of vname option

    | `$ of iterm * iterm

    | `|=> of (vname option * itype) * iterm

    | ICase of ((iterm * itype) * (iterm * iterm) list) * iterm;

        (*((term, type), [(selector pattern, body term )]), primitive term)*)

  val `$$ : iterm * iterm list -> iterm;

  val `|==> : (vname option * itype) list * iterm -> iterm;

  type typscheme = (vname * sort) list * itype;

end;

signature CODE_THINGOL =

sig

  include BASIC_CODE_THINGOL

  val fun_tyco: string

  val unfoldl: ('a -> ('a * 'b) option) -> 'a -> 'a * 'b list

  val unfoldr: ('a -> ('b * 'a) option) -> 'a -> 'b list * 'a

  val unfold_fun: itype -> itype list * itype

  val unfold_fun_n: int -> itype -> itype list * itype

  val unfold_app: iterm -> iterm * iterm list

  val unfold_abs: iterm -> (vname option * itype) list * iterm

  val split_let: iterm -> (((iterm * itype) * iterm) * iterm) option

  val unfold_let: iterm -> ((iterm * itype) * iterm) list * iterm

  val split_pat_abs: iterm -> ((iterm * itype) * iterm) option

  val unfold_pat_abs: iterm -> (iterm * itype) list * iterm

  val unfold_const_app: iterm -> (const * iterm list) option

  val is_IVar: iterm -> bool

  val is_IAbs: iterm -> bool

  val eta_expand: int -> const * iterm list -> iterm

  val contains_dict_var: iterm -> bool

  val add_constnames: iterm -> string list -> string list

  val add_tyconames: iterm -> string list -> string list

  val fold_varnames: (string -> 'a -> 'a) -> iterm -> 'a -> 'a

  type naming

  val empty_naming: naming

  val lookup_class: naming -> class -> string option

  val lookup_classrel: naming -> class * class -> string option

  val lookup_tyco: naming -> string -> string option

  val lookup_instance: naming -> class * string -> string option

  val lookup_const: naming -> string -> string option

  val ensure_declared_const: theory -> string -> naming -> string * naming

  datatype stmt =

      NoStmt

    | Fun of string * ((typscheme * ((iterm list * iterm) * (thm option * bool)) list) * thm option)

    | Datatype of string * ((vname * sort) list *

        ((string * vname list (*type argument wrt. canonical order*)) * itype list) list)

    | Datatypecons of string * string

    | Class of class * (vname * ((class * string) list * (string * itype) list))

    | Classrel of class * class

    | Classparam of string * class

    | Classinst of (class * (string * (vname * sort) list) (*class and arity*))

          * ((class * (string * (string * dict list list))) list (*super instances*)

        * (((string * const) * (thm * bool)) list (*class parameter instances*)

          * ((string * const) * (thm * bool)) list (*super class parameter instances*)))

  type program = stmt Graph.T

  val empty_funs: program -> string list

  val map_terms_bottom_up: (iterm -> iterm) -> iterm -> iterm

  val map_terms_stmt: (iterm -> iterm) -> stmt -> stmt

  val is_cons: program -> string -> bool

  val is_case: stmt -> bool

  val labelled_name: theory -> program -> string -> string

  val group_stmts: theory -> program

    -> ((string * stmt) list * (string * stmt) list

      * ((string * stmt) list * (string * stmt) list)) list

  val read_const_exprs: theory -> string list -> string list * string list

  val consts_program: theory -> bool -> string list -> string list * (naming * program)

  val dynamic_conv: theory -> (naming -> program

    -> ((string * sort) list * typscheme) * iterm -> string list -> conv)

    -> conv

  val dynamic_value: theory -> ((term -> term) -> 'a -> 'a) -> (naming -> program

    -> ((string * sort) list * typscheme) * iterm -> string list -> 'a)

    -> term -> 'a

  val static_conv: theory -> string list -> (naming -> program -> string list

    -> ((string * sort) list * typscheme) * iterm -> string list -> conv)

    -> conv

  val static_conv_simple: theory -> string list

    -> (program -> (string * sort) list -> term -> conv) -> conv

  val static_value: theory -> ((term -> term) -> 'a -> 'a) -> string list ->

    (naming -> program -> string list

      -> ((string * sort) list * typscheme) * iterm -> string list -> 'a)

    -> term -> 'a

end;

structure Code_Thingol: CODE_THINGOL =

struct

(** auxiliary **)

fun unfoldl dest x =

  case dest x

   of NONE => (x, [])

    | SOME (x1, x2) =>

        let val (x', xs') = unfoldl dest x1 in (x', xs' @ [x2]) end;

fun unfoldr dest x =

  case dest x

   of NONE => ([], x)

    | SOME (x1, x2) =>

        let val (xs', x') = unfoldr dest x2 in (x1::xs', x') end;

(** language core - types, terms **)

type vname = string;

datatype dict =

    Dict of string list * plain_dict

and plain_dict = 

    Dict_Const of string * dict list list

  | Dict_Var of vname * (int * int)

datatype itype =

    `%% of string * itype list

  | ITyVar of vname;

type const = string * (((itype list * dict list list) *

  (itype list (*types of arguments*) * itype (*result type*))) * bool (*requires type annotation*))

datatype iterm =

    IConst of const

  | IVar of vname option

  | `$ of iterm * iterm

  | `|=> of (vname option * itype) * iterm

  | ICase of ((iterm * itype) * (iterm * iterm) list) * iterm;

    (*see also signature*)

fun is_IVar (IVar _) = true

  | is_IVar _ = false;

fun is_IAbs (_ `|=> _) = true

  | is_IAbs _ = false;

val op `$$ = Library.foldl (op `$);

val op `|==> = Library.foldr (op `|=>);

val unfold_app = unfoldl

  (fn op `$ t => SOME t

    | _ => NONE);

val unfold_abs = unfoldr

  (fn op `|=> t => SOME t

    | _ => NONE);

val split_let = 

  (fn ICase (((td, ty), [(p, t)]), _) => SOME (((p, ty), td), t)

    | _ => NONE);

val unfold_let = unfoldr split_let;

fun unfold_const_app t =

 case unfold_app t

  of (IConst c, ts) => SOME (c, ts)

   | _ => NONE;

fun fold_constexprs f =

  let

    fun fold' (IConst c) = f c

      | fold' (IVar _) = I

      | fold' (t1 `$ t2) = fold' t1 #> fold' t2

      | fold' (_ `|=> t) = fold' t

      | fold' (ICase (((t, _), ds), _)) = fold' t

          #> fold (fn (pat, body) => fold' pat #> fold' body) ds

  in fold' end;

val add_constnames = fold_constexprs (fn (c, _) => insert (op =) c);

fun add_tycos (tyco `%% tys) = insert (op =) tyco #> fold add_tycos tys

  | add_tycos (ITyVar _) = I;

val add_tyconames = fold_constexprs (fn (_, (((tys, _), _), _)) => fold add_tycos tys);

fun fold_varnames f =

  let

    fun fold_aux add f =

      let

        fun fold_term _ (IConst _) = I

          | fold_term vs (IVar (SOME v)) = if member (op =) vs v then I else f v

          | fold_term _ (IVar NONE) = I

          | fold_term vs (t1 `$ t2) = fold_term vs t1 #> fold_term vs t2

          | fold_term vs ((SOME v, _) `|=> t) = fold_term (insert (op =) v vs) t

          | fold_term vs ((NONE, _) `|=> t) = fold_term vs t

          | fold_term vs (ICase (((t, _), ds), _)) = fold_term vs t #> fold (fold_case vs) ds

        and fold_case vs (p, t) = fold_term (add p vs) t;

      in fold_term [] end;

    fun add t = fold_aux add (insert (op =)) t;

  in fold_aux add f end;

fun exists_var t v = fold_varnames (fn w => fn b => v = w orelse b) t false;

fun split_pat_abs ((NONE, ty) `|=> t) = SOME ((IVar NONE, ty), t)

  | split_pat_abs ((SOME v, ty) `|=> t) = SOME (case t

     of ICase (((IVar (SOME w), _), [(p, t')]), _) =>

          if v = w andalso (exists_var p v orelse not (exists_var t' v))

          then ((p, ty), t')

          else ((IVar (SOME v), ty), t)

      | _ => ((IVar (SOME v), ty), t))

  | split_pat_abs _ = NONE;

val unfold_pat_abs = unfoldr split_pat_abs;

fun unfold_abs_eta [] t = ([], t)

  | unfold_abs_eta (_ :: tys) (v_ty `|=> t) =

      let

        val (vs_tys, t') = unfold_abs_eta tys t;

      in (v_ty :: vs_tys, t') end

  | unfold_abs_eta tys t =

      let

        val ctxt = fold_varnames Name.declare t Name.context;

        val vs_tys = (map o apfst) SOME (Name.invent_names ctxt "a" tys);

      in (vs_tys, t `$$ map (IVar o fst) vs_tys) end;

fun eta_expand k (c as (name, ((_, (tys, _)), _)), ts) =

  let

    val j = length ts;

    val l = k - j;

    val _ = if l > length tys

      then error ("Impossible eta-expansion for constant " ^ quote name) else ();

    val ctxt = (fold o fold_varnames) Name.declare ts Name.context;

    val vs_tys = (map o apfst) SOME

      (Name.invent_names ctxt "a" ((take l o drop j) tys));

  in vs_tys `|==> IConst c `$$ ts @ map (IVar o fst) vs_tys end;

fun contains_dict_var t =

  let

    fun cont_dict (Dict (_, d)) = cont_plain_dict d

    and cont_plain_dict (Dict_Const (_, dss)) = (exists o exists) cont_dict dss

      | cont_plain_dict (Dict_Var _) = true;

    fun cont_term (IConst (_, (((_, dss), _), _))) = (exists o exists) cont_dict dss

      | cont_term (IVar _) = false

      | cont_term (t1 `$ t2) = cont_term t1 orelse cont_term t2

      | cont_term (_ `|=> t) = cont_term t

      | cont_term (ICase (_, t)) = cont_term t;

  in cont_term t end;

(** namings **)

(* policies *)

local

  fun thyname_of_type thy = #theory_name o Name_Space.the_entry (Sign.type_space thy);

  fun thyname_of_class thy = #theory_name o Name_Space.the_entry (Sign.class_space thy);

  fun thyname_of_instance thy inst = case AxClass.thynames_of_arity thy inst

   of [] => error ("No such instance: " ^ quote (snd inst ^ " :: " ^ fst inst))

    | thyname :: _ => thyname;

  fun thyname_of_const thy c = case AxClass.class_of_param thy c

   of SOME class => thyname_of_class thy class

    | NONE => (case Code.get_type_of_constr_or_abstr thy c

       of SOME (tyco, _) => thyname_of_type thy tyco

        | NONE => #theory_name (Name_Space.the_entry (Sign.const_space thy) c));

  fun purify_base "==>" = "follows"

    | purify_base "==" = "meta_eq"

    | purify_base s = Name.desymbolize false s;

  fun namify thy get_basename get_thyname name =

    let

      val prefix = get_thyname thy name;

      val base = (purify_base o get_basename) name;

    in Long_Name.append prefix base end;

in

fun namify_class thy = namify thy Long_Name.base_name thyname_of_class;

fun namify_classrel thy = namify thy (fn (sub_class, super_class) => 

    Long_Name.base_name super_class ^ "_" ^ Long_Name.base_name sub_class)

  (fn thy => thyname_of_class thy o fst);

  (*order fits nicely with composed projections*)

fun namify_tyco thy "fun" = "Pure.fun"

  | namify_tyco thy tyco = namify thy Long_Name.base_name thyname_of_type tyco;

fun namify_instance thy = namify thy (fn (class, tyco) => 

  Long_Name.base_name class ^ "_" ^ Long_Name.base_name tyco) thyname_of_instance;

fun namify_const thy = namify thy Long_Name.base_name thyname_of_const;

end; (* local *)

(* data *)

datatype naming = Naming of {

  class: class Symtab.table * Name.context,

  classrel: string Symreltab.table * Name.context,

  tyco: string Symtab.table * Name.context,

  instance: string Symreltab.table * Name.context,

  const: string Symtab.table * Name.context

}

fun dest_Naming (Naming naming) = naming;

val empty_naming = Naming {

  class = (Symtab.empty, Name.context),

  classrel = (Symreltab.empty, Name.context),

  tyco = (Symtab.empty, Name.context),

  instance = (Symreltab.empty, Name.context),

  const = (Symtab.empty, Name.context)

};

local

  fun mk_naming (class, classrel, tyco, instance, const) =

    Naming { class = class, classrel = classrel,

      tyco = tyco, instance = instance, const = const };

  fun map_naming f (Naming { class, classrel, tyco, instance, const }) =

    mk_naming (f (class, classrel, tyco, instance, const));

in

  fun map_class f = map_naming

    (fn (class, classrel, tyco, inst, const) =>

      (f class, classrel, tyco, inst, const));

  fun map_classrel f = map_naming

    (fn (class, classrel, tyco, inst, const) =>

      (class, f classrel, tyco, inst, const));

  fun map_tyco f = map_naming

    (fn (class, classrel, tyco, inst, const) =>

      (class, classrel, f tyco, inst, const));

  fun map_instance f = map_naming

    (fn (class, classrel, tyco, inst, const) =>

      (class, classrel, tyco, f inst, const));

  fun map_const f = map_naming

    (fn (class, classrel, tyco, inst, const) =>

      (class, classrel, tyco, inst, f const));

end; (*local*)

fun add_variant update (thing, name) (tab, used) =

  let

    val (name', used') = Name.variant name used;

    val tab' = update (thing, name') tab;

  in (tab', used') end;

fun declare thy mapp lookup update namify thing =

  mapp (add_variant update (thing, namify thy thing))

  #> `(fn naming => the (lookup naming thing));

(* lookup and declare *)

local

val suffix_class = "class";

val suffix_classrel = "classrel"

val suffix_tyco = "tyco";

val suffix_instance = "inst";

val suffix_const = "const";

fun add_suffix nsp NONE = NONE

  | add_suffix nsp (SOME name) = SOME (Long_Name.append name nsp);

in

val lookup_class = add_suffix suffix_class

  oo Symtab.lookup o fst o #class o dest_Naming;

val lookup_classrel = add_suffix suffix_classrel

  oo Symreltab.lookup o fst o #classrel o dest_Naming;

val lookup_tyco = add_suffix suffix_tyco

  oo Symtab.lookup o fst o #tyco o dest_Naming;

val lookup_instance = add_suffix suffix_instance

  oo Symreltab.lookup o fst o #instance o dest_Naming;

val lookup_const = add_suffix suffix_const

  oo Symtab.lookup o fst o #const o dest_Naming;

fun declare_class thy = declare thy map_class

  lookup_class Symtab.update_new namify_class;

fun declare_classrel thy = declare thy map_classrel

  lookup_classrel Symreltab.update_new namify_classrel;

fun declare_tyco thy = declare thy map_tyco

  lookup_tyco Symtab.update_new namify_tyco;

fun declare_instance thy = declare thy map_instance

  lookup_instance Symreltab.update_new namify_instance;

fun declare_const thy = declare thy map_const

  lookup_const Symtab.update_new namify_const;

fun ensure_declared_const thy const naming =

  case lookup_const naming const

   of SOME const' => (const', naming)

    | NONE => declare_const thy const naming;

val fun_tyco = Long_Name.append (namify_tyco Pure.thy "fun") suffix_tyco

  (*depends on add_suffix*);

val unfold_fun = unfoldr

  (fn tyco `%% [ty1, ty2] => if tyco = fun_tyco then SOME (ty1, ty2) else NONE

    | _ => NONE);

fun unfold_fun_n n ty =

  let

    val (tys1, ty1) = unfold_fun ty;

    val (tys3, tys2) = chop n tys1;

    val ty3 = Library.foldr (fn (ty1, ty2) => fun_tyco `%% [ty1, ty2]) (tys2, ty1);

  in (tys3, ty3) end;

end; (* local *)

(** statements, abstract programs **)

type typscheme = (vname * sort) list * itype;

datatype stmt =

    NoStmt

  | Fun of string * ((typscheme * ((iterm list * iterm) * (thm option * bool)) list) * thm option)

  | Datatype of string * ((vname * sort) list * ((string * vname list) * itype list) list)

  | Datatypecons of string * string

  | Class of class * (vname * ((class * string) list * (string * itype) list))

  | Classrel of class * class

  | Classparam of string * class

  | Classinst of (class * (string * (vname * sort) list))

        * ((class * (string * (string * dict list list))) list

      * (((string * const) * (thm * bool)) list

        * ((string * const) * (thm * bool)) list))

      (*see also signature*);

type program = stmt Graph.T;

fun empty_funs program =

  Graph.fold (fn (name, (Fun (c, ((_, []), _)), _)) => cons c

               | _ => I) program [];

fun map_terms_bottom_up f (t as IConst _) = f t

  | map_terms_bottom_up f (t as IVar _) = f t

  | map_terms_bottom_up f (t1 `$ t2) = f

      (map_terms_bottom_up f t1 `$ map_terms_bottom_up f t2)

  | map_terms_bottom_up f ((v, ty) `|=> t) = f

      ((v, ty) `|=> map_terms_bottom_up f t)

  | map_terms_bottom_up f (ICase (((t, ty), ps), t0)) = f

      (ICase (((map_terms_bottom_up f t, ty), (map o pairself)

        (map_terms_bottom_up f) ps), map_terms_bottom_up f t0));

fun map_classparam_instances_as_term f =

  (map o apfst o apsnd) (fn const => case f (IConst const) of IConst const' => const')

fun map_terms_stmt f NoStmt = NoStmt

  | map_terms_stmt f (Fun (c, ((tysm, eqs), case_cong))) = Fun (c, ((tysm, (map o apfst)

      (fn (ts, t) => (map f ts, f t)) eqs), case_cong))

  | map_terms_stmt f (stmt as Datatype _) = stmt

  | map_terms_stmt f (stmt as Datatypecons _) = stmt

  | map_terms_stmt f (stmt as Class _) = stmt

  | map_terms_stmt f (stmt as Classrel _) = stmt

  | map_terms_stmt f (stmt as Classparam _) = stmt

  | map_terms_stmt f (Classinst (arity, (super_instances, classparam_instances))) =

      Classinst (arity, (super_instances, (pairself o map_classparam_instances_as_term) f classparam_instances));

fun is_cons program name = case Graph.get_node program name

 of Datatypecons _ => true

  | _ => false;

fun is_case (Fun (_, (_, SOME _))) = true

  | is_case _ = false;

fun labelled_name thy program name =

  let val ctxt = Proof_Context.init_global thy in

    case Graph.get_node program name of

      Fun (c, _) => quote (Code.string_of_const thy c)

    | Datatype (tyco, _) => "type " ^ quote (Proof_Context.extern_type ctxt tyco)

    | Datatypecons (c, _) => quote (Code.string_of_const thy c)

    | Class (class, _) => "class " ^ quote (Proof_Context.extern_class ctxt class)

    | Classrel (sub, super) =>

        let

          val Class (sub, _) = Graph.get_node program sub;

          val Class (super, _) = Graph.get_node program super;

        in

          quote (Proof_Context.extern_class ctxt sub ^ " < " ^ Proof_Context.extern_class ctxt super)

        end

    | Classparam (c, _) => quote (Code.string_of_const thy c)

    | Classinst ((class, (tyco, _)), _) =>

        let

          val Class (class, _) = Graph.get_node program class;

          val Datatype (tyco, _) = Graph.get_node program tyco;

        in

          quote (Proof_Context.extern_type ctxt tyco ^ " :: " ^ Proof_Context.extern_class ctxt class)

        end

  end;

fun linear_stmts program =

  rev (Graph.strong_conn program)

  |> map (AList.make (Graph.get_node program));

fun group_stmts thy program =

  let

    fun is_fun (_, Fun _) = true | is_fun _ = false;

    fun is_datatypecons (_, Datatypecons _) = true | is_datatypecons _ = false;

    fun is_datatype (_, Datatype _) = true | is_datatype _ = false;

    fun is_class (_, Class _) = true | is_class _ = false;

    fun is_classrel (_, Classrel _) = true | is_classrel _ = false;

    fun is_classparam (_, Classparam _) = true | is_classparam _ = false;

    fun is_classinst (_, Classinst _) = true | is_classinst _ = false;

    fun group stmts =

      if forall (is_datatypecons orf is_datatype) stmts

      then (filter is_datatype stmts, [], ([], []))

      else if forall (is_class orf is_classrel orf is_classparam) stmts

      then ([], filter is_class stmts, ([], []))

      else if forall (is_fun orf is_classinst) stmts

      then ([], [], List.partition is_fun stmts)

      else error ("Illegal mutual dependencies: " ^

        (commas o map (labelled_name thy program o fst)) stmts)

  in

    linear_stmts program

    |> map group

  end;

(** translation kernel **)

(* generic mechanisms *)

fun ensure_stmt lookup declare generate thing (dep, (naming, program)) =

  let

    fun add_dep name = case dep of NONE => I

      | SOME dep => Graph.add_edge (dep, name);

    val (name, naming') = case lookup naming thing

     of SOME name => (name, naming)

      | NONE => declare thing naming;

  in case try (Graph.get_node program) name

   of SOME stmt => program

        |> add_dep name

        |> pair naming'

        |> pair dep

        |> pair name

    | NONE => program

        |> Graph.default_node (name, NoStmt)

        |> add_dep name

        |> pair naming'

        |> curry generate (SOME name)

        ||> snd

        |-> (fn stmt => (apsnd o Graph.map_node name) (K stmt))

        |> pair dep

        |> pair name

  end;

exception PERMISSIVE of unit;

fun translation_error thy permissive some_thm msg sub_msg =

  if permissive

  then raise PERMISSIVE ()

  else

    let

      val err_thm =

        (case some_thm of

          SOME thm => "\n(in code equation " ^ Display.string_of_thm_global thy thm ^ ")"

        | NONE => "");

    in error (msg ^ err_thm ^ ":\n" ^ sub_msg) end;

fun not_wellsorted thy permissive some_thm ty sort e =

  let

    val err_class = Sorts.class_error (Context.pretty_global thy) e;

    val err_typ =

      "Type " ^ Syntax.string_of_typ_global thy ty ^ " not of sort " ^

        Syntax.string_of_sort_global thy sort;

  in

    translation_error thy permissive some_thm "Wellsortedness error"

      (err_typ ^ "\n" ^ err_class)

  end;

(* inference of type annotations for disambiguation with type classes *)

fun mk_tagged_type (true, T) = Type ("", [T])

  | mk_tagged_type (false, T) = T;

fun dest_tagged_type (Type ("", [T])) = (true, T)

  | dest_tagged_type T = (false, T);

val untag_term = map_types (snd o dest_tagged_type);

fun tag_term (proj_sort, _) eqngr =

  let

    val has_sort_constraints = exists (not o null) o map proj_sort o Code_Preproc.sortargs eqngr;

    fun tag (Const (c', T')) (Const (c, T)) =

        Const (c,

          mk_tagged_type (not (null (Term.add_tvarsT T' [])) andalso has_sort_constraints c, T))

      | tag (t1 $ u1) (t $ u) = tag t1 t $ tag u1 u

      | tag (Abs (_, _, t1)) (Abs (x, T, t)) = Abs (x, T, tag t1 t)

      | tag (Free _) (t as Free _) = t

      | tag (Var _) (t as Var _) = t

      | tag (Bound _) (t as Bound _) = t;

  in

    tag

  end

fun annotate thy algbr eqngr (c, ty) args rhs =

  let

    val ctxt = Proof_Context.init_global thy |> Config.put Type_Infer_Context.const_sorts false

    val erase = map_types (fn _ => Type_Infer.anyT [])

    val reinfer = singleton (Type_Infer_Context.infer_types ctxt)

    val lhs = list_comb (Const (c, ty), map (map_types Type.strip_sorts o fst) args)

    val reinferred_rhs = snd (Logic.dest_equals (reinfer (Logic.mk_equals (lhs, erase rhs))))

  in

    tag_term algbr eqngr reinferred_rhs rhs

  end

fun annotate_eqns thy algbr eqngr (c, ty) eqns = 

  map (apfst (fn (args, (rhs, some_abs)) => (args,

    (annotate thy algbr eqngr (c, ty) args rhs, some_abs)))) eqns

(* translation *)

fun ensure_tyco thy algbr eqngr permissive tyco =

  let

    val ((vs, cos), _) = Code.get_type thy tyco;

    val stmt_datatype =

      fold_map (translate_tyvar_sort thy algbr eqngr permissive) vs

      ##>> fold_map (fn (c, (vs, tys)) =>

        ensure_const thy algbr eqngr permissive c

        ##>> pair (map (unprefix "'" o fst) vs)

        ##>> fold_map (translate_typ thy algbr eqngr permissive) tys) cos

      #>> (fn info => Datatype (tyco, info));

  in ensure_stmt lookup_tyco (declare_tyco thy) stmt_datatype tyco end

and ensure_const thy algbr eqngr permissive c =

  let

    fun stmt_datatypecons tyco =

      ensure_tyco thy algbr eqngr permissive tyco

      #>> (fn tyco => Datatypecons (c, tyco));

    fun stmt_classparam class =

      ensure_class thy algbr eqngr permissive class

      #>> (fn class => Classparam (c, class));

    fun stmt_fun cert =

      let

        val ((vs, ty), eqns) = Code.equations_of_cert thy cert;

        val eqns' = annotate_eqns thy algbr eqngr (c, ty) eqns

        val some_case_cong = Code.get_case_cong thy c;

      in

        fold_map (translate_tyvar_sort thy algbr eqngr permissive) vs

        ##>> translate_typ thy algbr eqngr permissive ty

        ##>> translate_eqns thy algbr eqngr permissive eqns'

        #>> (fn info => Fun (c, (info, some_case_cong)))

      end;

    val stmt_const = case Code.get_type_of_constr_or_abstr thy c

     of SOME (tyco, _) => stmt_datatypecons tyco

      | NONE => (case AxClass.class_of_param thy c

         of SOME class => stmt_classparam class

          | NONE => stmt_fun (Code_Preproc.cert eqngr c))

  in ensure_stmt lookup_const (declare_const thy) stmt_const c end

and ensure_class thy (algbr as (_, algebra)) eqngr permissive class =

  let

    val super_classes = (Sorts.minimize_sort algebra o Sorts.super_classes algebra) class;

    val cs = #params (AxClass.get_info thy class);

    val stmt_class =

      fold_map (fn super_class => ensure_class thy algbr eqngr permissive super_class

        ##>> ensure_classrel thy algbr eqngr permissive (class, super_class)) super_classes

      ##>> fold_map (fn (c, ty) => ensure_const thy algbr eqngr permissive c

        ##>> translate_typ thy algbr eqngr permissive ty) cs

      #>> (fn info => Class (class, (unprefix "'" Name.aT, info)))

  in ensure_stmt lookup_class (declare_class thy) stmt_class class end

and ensure_classrel thy algbr eqngr permissive (sub_class, super_class) =

  let

    val stmt_classrel =

      ensure_class thy algbr eqngr permissive sub_class

      ##>> ensure_class thy algbr eqngr permissive super_class

      #>> Classrel;

  in ensure_stmt lookup_classrel (declare_classrel thy) stmt_classrel (sub_class, super_class) end

and ensure_inst thy (algbr as (_, algebra)) eqngr permissive (class, tyco) =

  let

    val super_classes = (Sorts.minimize_sort algebra o Sorts.super_classes algebra) class;

    val these_classparams = these o try (#params o AxClass.get_info thy);

    val classparams = these_classparams class;

    val further_classparams = maps these_classparams

      ((Sorts.complete_sort algebra o Sorts.super_classes algebra) class);

    val vs = Name.invent_names Name.context "'a" (Sorts.mg_domain algebra tyco [class]);

    val sorts' = Sorts.mg_domain (Sign.classes_of thy) tyco [class];

    val vs' = map2 (fn (v, sort1) => fn sort2 => (v,

      Sorts.inter_sort (Sign.classes_of thy) (sort1, sort2))) vs sorts';

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

    val arity_typ' = Type (tyco, map (fn (v, sort) => TVar ((v, 0), sort)) vs');

    fun translate_super_instance super_class =

      ensure_class thy algbr eqngr permissive super_class

      ##>> ensure_classrel thy algbr eqngr permissive (class, super_class)

      ##>> translate_dicts thy algbr eqngr permissive NONE (arity_typ, [super_class])

      #>> (fn ((super_class, classrel), [Dict ([], Dict_Const (inst, dss))]) =>

            (super_class, (classrel, (inst, dss))));

    fun translate_classparam_instance (c, ty) =

      let

        val raw_const = Const (c, map_type_tfree (K arity_typ') ty);

        val thm = AxClass.unoverload_conv thy (Thm.cterm_of thy raw_const);

        val const = (apsnd Logic.unvarifyT_global o dest_Const o snd

          o Logic.dest_equals o Thm.prop_of) thm;

      in

        ensure_const thy algbr eqngr permissive c

        ##>> translate_const thy algbr eqngr permissive (SOME thm) (const, NONE)

        #>> (fn (c, IConst const') => ((c, const'), (thm, true)))

      end;

    val stmt_inst =

      ensure_class thy algbr eqngr permissive class

      ##>> ensure_tyco thy algbr eqngr permissive tyco

      ##>> fold_map (translate_tyvar_sort thy algbr eqngr permissive) vs

      ##>> fold_map translate_super_instance super_classes

      ##>> fold_map translate_classparam_instance classparams

      ##>> fold_map translate_classparam_instance further_classparams

      #>> (fn (((((class, tyco), arity_args), super_instances),

        classparam_instances), further_classparam_instances) =>

          Classinst ((class, (tyco, arity_args)), (super_instances,

            (classparam_instances, further_classparam_instances))));

  in ensure_stmt lookup_instance (declare_instance thy) stmt_inst (class, tyco) end

and translate_typ thy algbr eqngr permissive (TFree (v, _)) =

      pair (ITyVar (unprefix "'" v))

  | translate_typ thy algbr eqngr permissive (Type (tyco, tys)) =

      ensure_tyco thy algbr eqngr permissive tyco

      ##>> fold_map (translate_typ thy algbr eqngr permissive) tys

      #>> (fn (tyco, tys) => tyco `%% tys)

and translate_term thy algbr eqngr permissive some_thm (Const (c, ty), some_abs) =

      translate_app thy algbr eqngr permissive some_thm (((c, ty), []), some_abs)

  | translate_term thy algbr eqngr permissive some_thm (Free (v, _), some_abs) =

      pair (IVar (SOME v))

  | translate_term thy algbr eqngr permissive some_thm (Abs (v, ty, t), some_abs) =

      let

        val (v', t') = Syntax_Trans.variant_abs (Name.desymbolize false v, ty, t);

        val v'' = if member (op =) (Term.add_free_names t' []) v'

          then SOME v' else NONE

      in

        translate_typ thy algbr eqngr permissive ty

        ##>> translate_term thy algbr eqngr permissive some_thm (t', some_abs)

        #>> (fn (ty, t) => (v'', ty) `|=> t)

      end

  | translate_term thy algbr eqngr permissive some_thm (t as _ $ _, some_abs) =

      case strip_comb t

       of (Const (c, ty), ts) =>

            translate_app thy algbr eqngr permissive some_thm (((c, ty), ts), some_abs)

        | (t', ts) =>

            translate_term thy algbr eqngr permissive some_thm (t', some_abs)

            ##>> fold_map (translate_term thy algbr eqngr permissive some_thm o rpair NONE) ts

            #>> (fn (t, ts) => t `$$ ts)

and translate_eqn thy algbr eqngr permissive ((args, (rhs, some_abs)), (some_thm, proper)) =

  fold_map (translate_term thy algbr eqngr permissive some_thm) args

  ##>> translate_term thy algbr eqngr permissive some_thm (rhs, some_abs)

  #>> rpair (some_thm, proper)

and translate_eqns thy algbr eqngr permissive eqns prgrm =

  prgrm |> fold_map (translate_eqn thy algbr eqngr permissive) eqns

    handle PERMISSIVE () => ([], prgrm)

and translate_const thy algbr eqngr permissive some_thm ((c, ty), some_abs) =

  let

    val _ = if (case some_abs of NONE => true | SOME abs => not (c = abs))

        andalso Code.is_abstr thy c

        then translation_error thy permissive some_thm

          "Abstraction violation" ("constant " ^ Code.string_of_const thy c)

      else ()

    val (annotate, ty') = dest_tagged_type ty

    val arg_typs = Sign.const_typargs thy (c, ty');

    val sorts = Code_Preproc.sortargs eqngr c;

    val (function_typs, body_typ) = Term.strip_type ty';

  in

    ensure_const thy algbr eqngr permissive c

    ##>> fold_map (translate_typ thy algbr eqngr permissive) arg_typs

    ##>> fold_map (translate_dicts thy algbr eqngr permissive some_thm) (arg_typs ~~ sorts)

    ##>> fold_map (translate_typ thy algbr eqngr permissive) (body_typ :: function_typs)

    #>> (fn (((c, arg_typs), dss), body_typ :: function_typs) =>

      IConst (c, (((arg_typs, dss), (function_typs, body_typ)), annotate)))

  end

and translate_app_const thy algbr eqngr permissive some_thm ((c_ty, ts), some_abs) =

  translate_const thy algbr eqngr permissive some_thm (c_ty, some_abs)

  ##>> fold_map (translate_term thy algbr eqngr permissive some_thm o rpair NONE) ts

  #>> (fn (t, ts) => t `$$ ts)

and translate_case thy algbr eqngr permissive some_thm (num_args, (t_pos, case_pats)) (c_ty, ts) =

  let

    fun arg_types num_args ty = fst (chop num_args (binder_types ty));

    val tys = arg_types num_args (snd c_ty);

    val ty = nth tys t_pos;

    fun mk_constr NONE t = NONE

      | mk_constr (SOME c) t =

          let

            val n = Code.args_number thy c;

          in SOME ((c, arg_types n (fastype_of (untag_term t)) ---> ty), n) end;

    val constrs =

      if null case_pats then []

      else map_filter I (map2 mk_constr case_pats (nth_drop t_pos ts));

    fun casify naming constrs ty ts =

      let

        val undefineds = map_filter (lookup_const naming) (Code.undefineds thy);

        fun collapse_clause vs_map ts body =

          let

          in case body

           of IConst (c, _) => if member (op =) undefineds c

                then []

                else [(ts, body)]

            | ICase (((IVar (SOME v), _), subclauses), _) =>

                if forall (fn (pat', body') => exists_var pat' v

                  orelse not (exists_var body' v)) subclauses

                then case AList.lookup (op =) vs_map v

                 of SOME i => maps (fn (pat', body') =>

                      collapse_clause (AList.delete (op =) v vs_map)

                        (nth_map i (K pat') ts) body') subclauses

                  | NONE => [(ts, body)]

                else [(ts, body)]

            | _ => [(ts, body)]

          end;

        fun mk_clause mk tys t =

          let

            val (vs, body) = unfold_abs_eta tys t;

            val vs_map = fold_index (fn (i, (SOME v, _)) => cons (v, i) | _ => I) vs [];

            val ts = map (IVar o fst) vs;

          in map mk (collapse_clause vs_map ts body) end;

        val t = nth ts t_pos;

        val ts_clause = nth_drop t_pos ts;

        val clauses = if null case_pats

          then mk_clause (fn ([t], body) => (t, body)) [ty] (the_single ts_clause)

          else maps (fn ((constr as IConst (_, ((_, (tys, _)), _)), n), t) =>

            mk_clause (fn (ts, body) => (constr `$$ ts, body)) (take n tys) t)

              (constrs ~~ (map_filter (fn (NONE, _) => NONE | (SOME _, t) => SOME t)

                (case_pats ~~ ts_clause)));

      in ((t, ty), clauses) end;

  in

    translate_const thy algbr eqngr permissive some_thm (c_ty, NONE)

    ##>> fold_map (fn (constr, n) => translate_const thy algbr eqngr permissive some_thm (constr, NONE)

      #>> rpair n) constrs

    ##>> translate_typ thy algbr eqngr permissive ty

    ##>> fold_map (translate_term thy algbr eqngr permissive some_thm o rpair NONE) ts

    #-> (fn (((t, constrs), ty), ts) =>

      `(fn (_, (naming, _)) => ICase (casify naming constrs ty ts, t `$$ ts)))

  end

and translate_app_case thy algbr eqngr permissive some_thm (case_scheme as (num_args, _)) ((c, ty), ts) =

  if length ts < num_args then

    let

      val k = length ts;

      val tys = (take (num_args - k) o drop k o fst o strip_type) ty;

      val ctxt = (fold o fold_aterms) Term.declare_term_frees ts Name.context;

      val vs = Name.invent_names ctxt "a" tys;

    in

      fold_map (translate_typ thy algbr eqngr permissive) tys

      ##>> translate_case thy algbr eqngr permissive some_thm case_scheme ((c, ty), ts @ map Free vs)

      #>> (fn (tys, t) => map2 (fn (v, _) => pair (SOME v)) vs tys `|==> t)

    end

  else if length ts > num_args then

    translate_case thy algbr eqngr permissive some_thm case_scheme ((c, ty), take num_args ts)

    ##>> fold_map (translate_term thy algbr eqngr permissive some_thm o rpair NONE) (drop num_args ts)

    #>> (fn (t, ts) => t `$$ ts)

  else

    translate_case thy algbr eqngr permissive some_thm case_scheme ((c, ty), ts)

and translate_app thy algbr eqngr permissive some_thm (c_ty_ts as ((c, _), _), some_abs) =

  case Code.get_case_scheme thy c

   of SOME case_scheme => translate_app_case thy algbr eqngr permissive some_thm case_scheme c_ty_ts

    | NONE => translate_app_const thy algbr eqngr permissive some_thm (c_ty_ts, some_abs)

and translate_tyvar_sort thy (algbr as (proj_sort, _)) eqngr permissive (v, sort) =

  fold_map (ensure_class thy algbr eqngr permissive) (proj_sort sort)

  #>> (fn sort => (unprefix "'" v, sort))

and translate_dicts thy (algbr as (proj_sort, algebra)) eqngr permissive some_thm (ty, sort) =

  let

    datatype typarg_witness =

        Weakening of (class * class) list * plain_typarg_witness

    and plain_typarg_witness =

        Global of (class * string) * typarg_witness list list

      | Local of string * (int * sort);

    fun class_relation ((Weakening (classrels, x)), sub_class) super_class =

      Weakening ((sub_class, super_class) :: classrels, x);

    fun type_constructor (tyco, _) dss class =

      Weakening ([], Global ((class, tyco), (map o map) fst dss));

    fun type_variable (TFree (v, sort)) =

      let

        val sort' = proj_sort sort;

      in map_index (fn (n, class) => (Weakening ([], Local (v, (n, sort'))), class)) sort' end;

    val typarg_witnesses = Sorts.of_sort_derivation algebra

      {class_relation = K (Sorts.classrel_derivation algebra class_relation),

       type_constructor = type_constructor,

       type_variable = type_variable} (ty, proj_sort sort)

      handle Sorts.CLASS_ERROR e => not_wellsorted thy permissive some_thm ty sort e;

    fun mk_dict (Weakening (classrels, x)) =

          fold_map (ensure_classrel thy algbr eqngr permissive) classrels

          ##>> mk_plain_dict x

          #>> Dict 

    and mk_plain_dict (Global (inst, dss)) =

          ensure_inst thy algbr eqngr permissive inst

          ##>> (fold_map o fold_map) mk_dict dss

          #>> (fn (inst, dss) => Dict_Const (inst, dss))

      | mk_plain_dict (Local (v, (n, sort))) =

          pair (Dict_Var (unprefix "'" v, (n, length sort)))

  in fold_map mk_dict typarg_witnesses end;

(* store *)

structure Program = Code_Data

(

  type T = naming * program;

  val empty = (empty_naming, Graph.empty);

);

fun invoke_generation ignore_cache thy (algebra, eqngr) generate thing =

  Program.change_yield (if ignore_cache then NONE else SOME thy)

    (fn naming_program => (NONE, naming_program)

      |> generate thy algebra eqngr thing

      |-> (fn thing => fn (_, naming_program) => (thing, naming_program)));

(* program generation *)

fun consts_program thy permissive consts =

  let

    fun project_consts consts (naming, program) =

      if permissive then (consts, (naming, program))

      else (consts, (naming, Graph.restrict

        (member (op =) (Graph.all_succs program consts)) program));

    fun generate_consts thy algebra eqngr =

      fold_map (ensure_const thy algebra eqngr permissive);

  in

    invoke_generation permissive thy (Code_Preproc.obtain false thy consts [])

      generate_consts consts

    |-> project_consts

  end;

(* value evaluation *)

fun ensure_value thy algbr eqngr t =

  let

    val ty = fastype_of t;

    val vs = fold_term_types (K (fold_atyps (insert (eq_fst op =)

      o dest_TFree))) t [];

    val t' = annotate thy algbr eqngr (Term.dummy_patternN, ty) [] t;

    val stmt_value =

      fold_map (translate_tyvar_sort thy algbr eqngr false) vs

      ##>> translate_typ thy algbr eqngr false ty

      ##>> translate_term thy algbr eqngr false NONE (t', NONE)

      #>> (fn ((vs, ty), t) => Fun

        (Term.dummy_patternN, (((vs, ty), [(([], t), (NONE, true))]), NONE)));

    fun term_value (dep, (naming, program1)) =

      let

        val Fun (_, ((vs_ty, [(([], t), _)]), _)) =

          Graph.get_node program1 Term.dummy_patternN;

        val deps = Graph.immediate_succs program1 Term.dummy_patternN;

        val program2 = Graph.del_node Term.dummy_patternN program1;

        val deps_all = Graph.all_succs program2 deps;

        val program3 = Graph.restrict (member (op =) deps_all) program2;

      in (((naming, program3), ((vs_ty, t), deps)), (dep, (naming, program2))) end;

  in

    ensure_stmt ((K o K) NONE) pair stmt_value Term.dummy_patternN

    #> snd

    #> term_value

  end;

fun original_sorts vs =

  map (fn (v, _) => (v, (the o AList.lookup (op =) vs o prefix "'") v));

fun dynamic_evaluator thy evaluator algebra eqngr vs t =

  let

    val (((naming, program), (((vs', ty'), t'), deps)), _) =

      invoke_generation false thy (algebra, eqngr) ensure_value t;

  in evaluator naming program ((original_sorts vs vs', (vs', ty')), t') deps end;

fun dynamic_conv thy evaluator =

  Code_Preproc.dynamic_conv thy (dynamic_evaluator thy evaluator);

fun dynamic_value thy postproc evaluator =

  Code_Preproc.dynamic_value thy postproc (dynamic_evaluator thy evaluator);

fun lift_evaluation thy evaluation' algebra eqngr naming program vs t =

  let

    val (((_, program'), (((vs', ty'), t'), deps)), _) =

      ensure_value thy algebra eqngr t (NONE, (naming, program));

  in evaluation' ((original_sorts vs vs', (vs', ty')), t') deps end;

fun lift_evaluator thy evaluator' consts algebra eqngr =

  let

    fun generate_consts thy algebra eqngr =

      fold_map (ensure_const thy algebra eqngr false);

    val (consts', (naming, program)) =

      invoke_generation true thy (algebra, eqngr) generate_consts consts;

    val evaluation' = evaluator' naming program consts';

  in lift_evaluation thy evaluation' algebra eqngr naming program end;

fun lift_evaluator_simple thy evaluator' consts algebra eqngr =

  let

    fun generate_consts thy algebra eqngr =

      fold_map (ensure_const thy algebra eqngr false);

    val (consts', (naming, program)) =

      invoke_generation true thy (algebra, eqngr) generate_consts consts;

  in evaluator' program end;

fun static_conv thy consts conv =

  Code_Preproc.static_conv thy consts (lift_evaluator thy conv consts);

fun static_conv_simple thy consts conv =

  Code_Preproc.static_conv thy consts (lift_evaluator_simple thy conv consts);