(*  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);

 fun static_value thy postproc consts evaluator =

   Code_Preproc.static_value thy postproc consts (lift_evaluator thy evaluator consts);

 (** diagnostic commands **)

 fun read_const_exprs thy =

   let

     fun consts_of thy' = Symtab.fold (fn (c, (_, NONE)) => cons c | _ => I)

       ((snd o #constants o Consts.dest o Sign.consts_of) thy') [];

     fun belongs_here thy' c = forall

       (fn thy'' => not (Sign.declared_const thy'' c)) (Theory.parents_of thy');

     fun consts_of_select thy' = filter (belongs_here thy') (consts_of thy');

     fun read_const_expr "_" = ([], consts_of thy)

       | read_const_expr s = if String.isSuffix "._" s

           then ([], consts_of_select (Context.this_theory thy (unsuffix "._" s)))

           else ([Code.read_const thy s], []);

   in pairself flat o split_list o map read_const_expr end;

 fun code_depgr thy consts =

   let

     val (_, eqngr) = Code_Preproc.obtain true thy consts [];

     val all_consts = Graph.all_succs eqngr consts;

   in Graph.restrict (member (op =) all_consts) eqngr end;

 fun code_thms thy = Pretty.writeln o Code_Preproc.pretty thy o code_depgr thy;

 fun code_deps thy consts =

   let

     val eqngr = code_depgr thy consts;

     val constss = Graph.strong_conn eqngr;

     val mapping = Symtab.empty |> fold (fn consts => fold (fn const =>

       Symtab.update (const, consts)) consts) constss;

     fun succs consts = consts

       |> maps (Graph.immediate_succs eqngr)

       |> subtract (op =) consts

       |> map (the o Symtab.lookup mapping)

       |> distinct (op =);

     val conn = [] |> fold (fn consts => cons (consts, succs consts)) constss;

     fun namify consts = map (Code.string_of_const thy) consts

       |> commas;

     val prgr = map (fn (consts, constss) =>

       { name = namify consts, ID = namify consts, dir = "", unfold = true,

         path = "", parents = map namify constss }) conn;

   in Present.display_graph prgr end;

 local

 fun code_thms_cmd thy = code_thms thy o op @ o read_const_exprs thy;

 fun code_deps_cmd thy = code_deps thy o op @ o read_const_exprs thy;

 in

 val _ =

   Outer_Syntax.improper_command @{command_spec "code_thms"}

     "print system of code equations for code"

     (Scan.repeat1 Parse.term_group

       >> (fn cs => Toplevel.no_timing o Toplevel.unknown_theory

         o Toplevel.keep ((fn thy => code_thms_cmd thy cs) o Toplevel.theory_of)));

 val _ =

   Outer_Syntax.improper_command @{command_spec "code_deps"}

     "visualize dependencies of code equations for code"

     (Scan.repeat1 Parse.term_group

       >> (fn cs => Toplevel.no_timing o Toplevel.unknown_theory

         o Toplevel.keep ((fn thy => code_deps_cmd thy cs) o Toplevel.theory_of)));

 end;

 end; (*struct*)

 structure Basic_Code_Thingol: BASIC_CODE_THINGOL = Code_Thingol;