(*  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 is_IVar: iterm -> bool

  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 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 * 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 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 expand_eta: theory -> int -> thm -> thm

  val canonize_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*)

fun is_IVar (IVar _) = true

  | is_IVar _ = 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.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 canonize_thms thy = map (Thm.transfer thy)

  #> Code.same_typscheme thy #> desymbolize_tvars thy

  #> same_arity thy #> map (desymbolize_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

  | _ => [];

fun labelled_name thy program name = case Graph.get_node program name

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

  | Datatype (tyco, _) => "type " ^ quote (Sign.extern_type thy tyco)

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

  | Class (class, _) => "class " ^ quote (Sign.extern_class thy class)

  | Classrel (sub, super) => let

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

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

      in quote (Sign.extern_class thy sub ^ " < " ^ Sign.extern_class thy 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 (Sign.extern_type thy tyco ^ " :: " ^ Sign.extern_class thy class) end

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

    rev (Graph.strong_conn program)

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

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 eqngr tyco =

  let

    val stmt_datatype =

      let

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

      in

        fold_map (translate_tyvar_sort thy algbr eqngr) vs

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

          ensure_const thy algbr eqngr c

          ##>> fold_map (translate_typ thy algbr eqngr) 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 eqngr c =

  let

    fun stmt_datatypecons tyco =

      ensure_tyco thy algbr eqngr tyco

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

    fun stmt_classparam class =

      ensure_class thy algbr eqngr class

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

    fun stmt_fun raw_eqns =

      let

        val eqns = burrow_fst (canonize_thms thy) raw_eqns;

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

      in

        fold_map (translate_tyvar_sort thy algbr eqngr) vs

        ##>> translate_typ thy algbr eqngr ty

        ##>> fold_map (translate_eqn thy algbr eqngr) 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 eqngr c))

  in ensure_stmt lookup_const (declare_const thy) stmt_const c end

and ensure_class thy (algbr as (_, algebra)) eqngr 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 eqngr superclass

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

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

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

  let

    val stmt_classrel =

      ensure_class thy algbr eqngr subclass

      ##>> ensure_class thy algbr eqngr superclass

      #>> Classrel;

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

and ensure_inst thy (algbr as (_, algebra)) eqngr (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 eqngr superclass

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

      ##>> translate_dicts thy algbr eqngr 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 eqngr c

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

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

      end;

    val stmt_inst =

      ensure_class thy algbr eqngr class

      ##>> ensure_tyco thy algbr eqngr tyco

      ##>> fold_map (translate_tyvar_sort thy algbr eqngr) 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 eqngr (TFree (v, _)) =

      pair (ITyVar (unprefix "'" v))

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

      ensure_tyco thy algbr eqngr tyco

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

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

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

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

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

      pair (IVar (SOME v))

  | translate_term thy algbr eqngr 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 eqngr ty

        ##>> translate_term thy algbr eqngr thm t'

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

      end

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

      case strip_comb t

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

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

        | (t', ts) =>

            translate_term thy algbr eqngr thm t'

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

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

and translate_eqn thy algbr eqngr (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 eqngr (SOME thm)) args

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

    #>> rpair (thm, proper)

  end

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

  let

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

    val sorts = Code_Preproc.sortargs eqngr c;

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

  in

    ensure_const thy algbr eqngr c

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

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

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

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

  end

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

  translate_const thy algbr eqngr thm c_ty

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

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

and translate_case thy algbr eqngr 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 eqngr thm c_ty

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

    ##>> translate_typ thy algbr eqngr ty

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

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

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

  end

and translate_app_case thy algbr eqngr 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 eqngr) tys

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

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

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

  else

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

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

  case Code.get_case_scheme thy c

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

    | NONE => translate_app_const thy algbr eqngr thm c_ty_ts

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

  fold_map (ensure_class thy algbr eqngr) (proj_sort sort)

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

and translate_dicts thy (algbr as (proj_sort, algebra)) eqngr 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 eqngr 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 eqngr) 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, eqngr) f name =

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

    |> f thy algebra eqngr 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 eqngr =

      fold_map (ensure_const thy algebra eqngr);

  in

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

    |-> 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 stmt_value =

      fold_map (translate_tyvar_sort thy algbr eqngr) vs

      ##>> translate_typ thy algbr eqngr ty

      ##>> translate_term thy algbr eqngr 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 eqngr vs t =

  let

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

      invoke_generation thy (algebra, eqngr) 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