(*  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 =

       DictConst of string * dict list list

     | DictVar of string list * (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*))

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

   val contains_dictvar: iterm -> bool

   val locally_monomorphic: iterm -> bool

   val add_constnames: 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 * bool)) list)

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

   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 contr_classparam_typs: program -> string -> itype option list

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

   val clean_thms: theory -> thm list -> thm list

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

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

   val cached_program: theory -> naming * program

   val eval_conv: theory

     -> (naming -> program -> ((string * sort) list * typscheme) * iterm -> string list -> cterm -> thm)

     -> cterm -> thm

   val eval: theory -> ((term -> term) -> 'a -> 'a)

     -> (naming -> program -> ((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 =

     DictConst of string * dict list list

   | DictVar of string list * (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*))

 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*)

 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 add_constnames (IConst (c, _)) = insert (op =) c

   | add_constnames (IVar _) = I

   | add_constnames (t1 `$ t2) = add_constnames t1 #> add_constnames t2

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

   | add_constnames (ICase (((t, _), ds), _)) = add_constnames t

       #> fold (fn (pat, body) => add_constnames pat #> add_constnames body) ds;

 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.names ctxt "a" tys);

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

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

   let

     val j = length ts;

     val l = k - j;

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

     val vs_tys = (map o apfst) SOME

       (Name.names ctxt "a" ((curry Library.take l o curry Library.drop j) tys));

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

 fun contains_dictvar t =

   let

     fun cont_dict (DictConst (_, dss)) = (exists o exists) cont_dict dss

       | cont_dict (DictVar _) = 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;

 fun locally_monomorphic (IConst _) = false

   | locally_monomorphic (IVar _) = true

   | locally_monomorphic (t `$ _) = locally_monomorphic t

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

   | locally_monomorphic (ICase ((_, ds), _)) = exists (locally_monomorphic o snd) ds;

 (** namings **)

 (* policies *)

 local

   fun thyname_of thy f x = the (AList.lookup (op =) (f x) Markup.theory_nameN);

   fun thyname_of_class thy =

     thyname_of thy (ProofContext.query_class (ProofContext.init thy));

   fun thyname_of_tyco thy =

     thyname_of thy (Type.the_tags (Sign.tsig_of thy));

   fun thyname_of_instance thy inst = case AxClass.arity_property thy inst Markup.theory_nameN

    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_datatype_of_constr thy c

        of SOME dtco => thyname_of_tyco thy dtco

         | NONE => thyname_of thy (Consts.the_tags (Sign.consts_of thy)) c);

   fun purify_base "op &" = "and"

     | purify_base "op |" = "or"

     | purify_base "op -->" = "implies"

     | purify_base "op :" = "member"

     | purify_base "op =" = "eq"

     | purify_base "*" = "product"

     | purify_base "+" = "sum"

     | 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 (class1, class2) => 

   Long_Name.base_name class2 ^ "_" ^ Long_Name.base_name class1) (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_tyco 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') = yield_singleton Name.variants 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 unfold_fun = unfoldr

   (fn "Pure.fun.tyco" `%% [ty1, ty2] => SOME (ty1, ty2)

     | _ => NONE); (*depends on suffix_tyco and namify_tyco!*)

 end; (* local *)

 (** 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 (head, 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 (curry Int.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 thy 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 thy 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 desymbolize_all_vars thy = desymbolize_tvars thy #> map (desymbolize_vars thy);

 fun clean_thms thy = map (Thm.transfer thy) #> same_arity thy #> desymbolize_all_vars thy;

 (** statements, abstract programs **)

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

 datatype stmt =

     NoStmt

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

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

 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_terms_stmt f NoStmt = NoStmt

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

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

   | 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, (superarities, classparms))) =

       Classinst (arity, (superarities, (map o apfst o apsnd) (fn const =>

         case f (IConst const) of IConst const' => const') classparms));

 fun is_cons program name = case Graph.get_node program name

  of Datatypecons _ => true

   | _ => false;

 fun contr_classparam_typs program name = case Graph.get_node program name

  of Classparam (_, class) => let

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

         val SOME ty = AList.lookup (op =) params name;

         val (tys, res_ty) = unfold_fun ty;

         fun no_tyvar (_ `%% tys) = forall no_tyvar tys

           | no_tyvar (ITyVar _) = false;

       in if no_tyvar res_ty

         then map (fn ty => if no_tyvar ty then NONE else SOME ty) tys

         else []

       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;

 fun not_wellsorted thy thm ty sort e =

   let

     val err_class = Sorts.class_error (Syntax.pp_global thy) e;

     val err_thm = case thm

      of SOME thm => "\n(in code equation " ^ Display.string_of_thm_global thy thm ^ ")" | NONE => "";

     val err_typ = "Type " ^ Syntax.string_of_typ_global thy ty ^ " not of sort "

       ^ Syntax.string_of_sort_global thy sort;

   in error ("Wellsortedness error" ^ err_thm ^ ":\n" ^ err_typ ^ "\n" ^ err_class) end;

 (* translation *)

 fun ensure_tyco thy algbr funcgr tyco =

   let

     val stmt_datatype =

       let

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

       in

         fold_map (translate_tyvar_sort thy algbr funcgr) vs

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

           ensure_const thy algbr funcgr c

           ##>> fold_map (translate_typ thy algbr funcgr) tys) cos

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

       end;

   in ensure_stmt lookup_tyco (declare_tyco thy) stmt_datatype tyco end

 and ensure_const thy algbr funcgr c =

   let

     fun stmt_datatypecons tyco =

       ensure_tyco thy algbr funcgr tyco

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

     fun stmt_classparam class =

       ensure_class thy algbr funcgr class

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

     fun stmt_fun raw_eqns =

       let

         val eqns = burrow_fst (clean_thms thy) raw_eqns;

         val ((vs, ty), _) = Code.typscheme_rhss_eqns thy c (map fst eqns);

       in

         fold_map (translate_tyvar_sort thy algbr funcgr) vs

         ##>> translate_typ thy algbr funcgr ty

         ##>> fold_map (translate_eqn thy algbr funcgr) eqns

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

       end;

     val stmt_const = case Code.get_datatype_of_constr 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.eqns funcgr c))

   in ensure_stmt lookup_const (declare_const thy) stmt_const c end

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

   let

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

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

     val stmt_class =

       fold_map (fn superclass => ensure_class thy algbr funcgr superclass

         ##>> ensure_classrel thy algbr funcgr (class, superclass)) superclasses

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

         ##>> translate_typ thy algbr funcgr 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 funcgr (subclass, superclass) =

   let

     val stmt_classrel =

       ensure_class thy algbr funcgr subclass

       ##>> ensure_class thy algbr funcgr superclass

       #>> Classrel;

   in ensure_stmt lookup_classrel (declare_classrel thy) stmt_classrel (subclass, superclass) end

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

   let

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

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

     val vs = Name.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_superarity superclass =

       ensure_class thy algbr funcgr superclass

       ##>> ensure_classrel thy algbr funcgr (class, superclass)

       ##>> translate_dicts thy algbr funcgr NONE (arity_typ, [superclass])

       #>> (fn ((superclass, classrel), [DictConst (inst, dss)]) =>

             (superclass, (classrel, (inst, dss))));

     fun translate_classparam_inst (c, ty) =

       let

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

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

         val c_ty = (apsnd Logic.unvarifyT o dest_Const o snd

           o Logic.dest_equals o Thm.prop_of) thm;

       in

         ensure_const thy algbr funcgr c

         ##>> translate_const thy algbr funcgr (SOME thm) c_ty

         #>> (fn (c, IConst c_inst) => ((c, c_inst), (thm, true)))

       end;

     val stmt_inst =

       ensure_class thy algbr funcgr class

       ##>> ensure_tyco thy algbr funcgr tyco

       ##>> fold_map (translate_tyvar_sort thy algbr funcgr) vs

       ##>> fold_map translate_superarity superclasses

       ##>> fold_map translate_classparam_inst classparams

       #>> (fn ((((class, tyco), arity), superarities), classparams) =>

              Classinst ((class, (tyco, arity)), (superarities, classparams)));

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

 and translate_typ thy algbr funcgr (TFree (v, _)) =

       pair (ITyVar (unprefix "'" v))

   | translate_typ thy algbr funcgr (Type (tyco, tys)) =

       ensure_tyco thy algbr funcgr tyco

       ##>> fold_map (translate_typ thy algbr funcgr) tys

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

 and translate_term thy algbr funcgr thm (Const (c, ty)) =

       translate_app thy algbr funcgr thm ((c, ty), [])

   | translate_term thy algbr funcgr thm (Free (v, _)) =

       pair (IVar (SOME v))

   | translate_term thy algbr funcgr thm (Abs (v, ty, t)) =

       let

         val (v', t') = Syntax.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 funcgr ty

         ##>> translate_term thy algbr funcgr thm t'

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

       end

   | translate_term thy algbr funcgr thm (t as _ $ _) =

       case strip_comb t

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

             translate_app thy algbr funcgr thm ((c, ty), ts)

         | (t', ts) =>

             translate_term thy algbr funcgr thm t'

             ##>> fold_map (translate_term thy algbr funcgr thm) ts

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

 and translate_eqn thy algbr funcgr (thm, proper) =

   let

     val (args, rhs) = (apfst (snd o strip_comb) o Logic.dest_equals

       o Logic.unvarify o prop_of) thm;

   in

     fold_map (translate_term thy algbr funcgr (SOME thm)) args

     ##>> translate_term thy algbr funcgr (SOME thm) rhs

     #>> rpair (thm, proper)

   end

 and translate_const thy algbr funcgr thm (c, ty) =

   let

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

     val sorts = (map snd o fst o Code_Preproc.typ funcgr) c;

     val tys_args = (fst o Term.strip_type) ty;

   in

     ensure_const thy algbr funcgr c

     ##>> fold_map (translate_typ thy algbr funcgr) tys

     ##>> fold_map (translate_dicts thy algbr funcgr thm) (tys ~~ sorts)

     ##>> fold_map (translate_typ thy algbr funcgr) tys_args

     #>> (fn (((c, tys), iss), tys_args) => IConst (c, ((tys, iss), tys_args)))

   end

 and translate_app_const thy algbr funcgr thm (c_ty, ts) =

   translate_const thy algbr funcgr thm c_ty

   ##>> fold_map (translate_term thy algbr funcgr thm) ts

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

 and translate_case thy algbr funcgr thm (num_args, (t_pos, case_pats)) (c_ty, ts) =

   let

     fun arg_types num_args ty = (fst o chop num_args o fst o strip_type) ty;

     val tys = arg_types num_args (snd c_ty);

     val ty = nth tys t_pos;

     fun mk_constr c t = let val n = Code.args_number thy c

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

     val constrs = if null case_pats then []

       else 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)) (curry Library.take n tys) t)

               (constrs ~~ ts_clause);

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

   in

     translate_const thy algbr funcgr thm c_ty

     ##>> fold_map (fn (constr, n) => translate_const thy algbr funcgr thm constr #>> rpair n) constrs

     ##>> translate_typ thy algbr funcgr ty

     ##>> fold_map (translate_term thy algbr funcgr thm) ts

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

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

   end

 and translate_app_case thy algbr funcgr thm (case_scheme as (num_args, _)) ((c, ty), ts) =

   if length ts < num_args then

     let

       val k = length ts;

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

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

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

     in

       fold_map (translate_typ thy algbr funcgr) tys

       ##>> translate_case thy algbr funcgr 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 funcgr thm case_scheme ((c, ty), Library.take (num_args, ts))

     ##>> fold_map (translate_term thy algbr funcgr thm) (Library.drop (num_args, ts))

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

   else

     translate_case thy algbr funcgr thm case_scheme ((c, ty), ts)

 and translate_app thy algbr funcgr thm (c_ty_ts as ((c, _), _)) =

   case Code.get_case_scheme thy c

    of SOME case_scheme => translate_app_case thy algbr funcgr thm case_scheme c_ty_ts

     | NONE => translate_app_const thy algbr funcgr thm c_ty_ts

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

   fold_map (ensure_class thy algbr funcgr) (proj_sort sort)

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

 and translate_dicts thy (algbr as (proj_sort, algebra)) funcgr thm (ty, sort) =

   let

     datatype typarg =

         Global of (class * string) * typarg list list

       | Local of (class * class) list * (string * (int * sort));

     fun class_relation (Global ((_, tyco), yss), _) class =

           Global ((class, tyco), yss)

       | class_relation (Local (classrels, v), subclass) superclass =

           Local ((subclass, superclass) :: classrels, v);

     fun type_constructor tyco yss class =

       Global ((class, tyco), (map o map) fst yss);

     fun type_variable (TFree (v, sort)) =

       let

         val sort' = proj_sort sort;

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

     val typargs = Sorts.of_sort_derivation algebra

       {class_relation = class_relation, type_constructor = type_constructor,

        type_variable = type_variable} (ty, proj_sort sort)

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

     fun mk_dict (Global (inst, yss)) =

           ensure_inst thy algbr funcgr inst

           ##>> (fold_map o fold_map) mk_dict yss

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

       | mk_dict (Local (classrels, (v, (n, sort)))) =

           fold_map (ensure_classrel thy algbr funcgr) classrels

           #>> (fn classrels => DictVar (classrels, (unprefix "'" v, (n, length sort))))

   in fold_map mk_dict typargs end;

 (* store *)

 structure Program = Code_Data_Fun

 (

   type T = naming * program;

   val empty = (empty_naming, Graph.empty);

   fun purge thy cs (naming, program) =

     let

       val names_delete = cs

         |> map_filter (lookup_const naming)

         |> filter (can (Graph.get_node program))

         |> Graph.all_preds program;

       val program' = Graph.del_nodes names_delete program;

     in (naming, program') end;

 );

 val cached_program = Program.get;

 fun invoke_generation thy (algebra, funcgr) f name =

   Program.change_yield thy (fn naming_program => (NONE, naming_program)

     |> f thy algebra funcgr name

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

 (* program generation *)

 fun consts_program thy cs =

   let

     fun project_consts cs (naming, program) =

       let

         val cs_all = Graph.all_succs program cs;

       in (cs, (naming, Graph.subgraph (member (op =) cs_all) program)) end;

     fun generate_consts thy algebra funcgr =

       fold_map (ensure_const thy algebra funcgr);

   in

     invoke_generation thy (Code_Preproc.obtain thy cs []) generate_consts cs

     |-> project_consts

   end;

 (* value evaluation *)

 fun ensure_value thy algbr funcgr t =

   let

     val ty = fastype_of t;

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

       o dest_TFree))) t [];

     val stmt_value =

       fold_map (translate_tyvar_sort thy algbr funcgr) vs

       ##>> translate_typ thy algbr funcgr ty

       ##>> translate_term thy algbr funcgr NONE t

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

         (Term.dummy_patternN, ((vs, ty), [(([], t), (Drule.dummy_thm, true))])));

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

       let

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

           Graph.get_node program1 Term.dummy_patternN;

         val deps = Graph.imm_succs program1 Term.dummy_patternN;

         val program2 = Graph.del_nodes [Term.dummy_patternN] program1;

         val deps_all = Graph.all_succs program2 deps;

         val program3 = Graph.subgraph (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 base_evaluator thy evaluator algebra funcgr vs t =

   let

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

       invoke_generation thy (algebra, funcgr) ensure_value t;

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

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

 fun eval_conv thy = Code_Preproc.eval_conv thy o base_evaluator thy;

 fun eval thy postproc = Code_Preproc.eval thy postproc o base_evaluator thy;

 (** diagnostic commands **)

 fun read_const_exprs thy =

   let

     fun consts_of some_thyname =

       let

         val thy' = case some_thyname

          of SOME thyname => ThyInfo.the_theory thyname thy

           | NONE => thy;

         val cs = Symtab.fold (fn (c, (_, NONE)) => cons c | _ => I)

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

         fun belongs_here c =

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

       in case some_thyname

        of NONE => cs

         | SOME thyname => filter belongs_here cs

       end;

     fun read_const_expr "*" = ([], consts_of NONE)

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

           then ([], consts_of (SOME (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 thy consts [];

     val select = Graph.all_succs eqngr consts;

   in

     eqngr

     |> not (null consts) ? Graph.subgraph (member (op =) select) 

     |> Graph.map_nodes ((apsnd o map o apfst) (AxClass.overload thy))

   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.imm_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

 structure P = OuterParse

 and K = OuterKeyword

 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 _ =

   OuterSyntax.improper_command "code_thms" "print system of code equations for code" OuterKeyword.diag

     (Scan.repeat P.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 _ =

   OuterSyntax.improper_command "code_deps" "visualize dependencies of code equations for code" OuterKeyword.diag

     (Scan.repeat P.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;