(*  Title:      Pure/Syntax/syn_trans.ML

    Author:     Tobias Nipkow and Markus Wenzel, TU Muenchen

Syntax translation functions.

*)

signature SYN_TRANS0 =

sig

  val eta_contract: bool Unsynchronized.ref

  val atomic_abs_tr': string * typ * term -> term * term

  val preserve_binder_abs_tr': string -> string -> string * (term list -> term)

  val preserve_binder_abs2_tr': string -> string -> string * (term list -> term)

  val mk_binder_tr: string * string -> string * (term list -> term)

  val mk_binder_tr': string * string -> string * (term list -> term)

  val dependent_tr': string * string -> term list -> term

  val antiquote_tr: string -> term -> term

  val quote_tr: string -> term -> term

  val quote_antiquote_tr: string -> string -> string -> string * (term list -> term)

  val antiquote_tr': string -> term -> term

  val quote_tr': string -> term -> term

  val quote_antiquote_tr': string -> string -> string -> string * (term list -> term)

  val mark_bound: string -> term

  val mark_boundT: string * typ -> term

  val bound_vars: (string * typ) list -> term -> term

  val variant_abs: string * typ * term -> string * term

  val variant_abs': string * typ * term -> string * term

end;

signature SYN_TRANS1 =

sig

  include SYN_TRANS0

  val non_typed_tr': (term list -> term) -> bool -> typ -> term list -> term

  val non_typed_tr'': ('a -> term list -> term) -> 'a -> bool -> typ -> term list -> term

  val constrainAbsC: string

  val pure_trfuns:

      (string * (Ast.ast list -> Ast.ast)) list *

      (string * (term list -> term)) list *

      (string * (term list -> term)) list *

      (string * (Ast.ast list -> Ast.ast)) list

  val pure_trfunsT: (string * (bool -> typ -> term list -> term)) list

  val struct_trfuns: string list ->

      (string * (Ast.ast list -> Ast.ast)) list *

      (string * (term list -> term)) list *

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

      (string * (Ast.ast list -> Ast.ast)) list

end;

signature SYN_TRANS =

sig

  include SYN_TRANS1

  val abs_tr': term -> term

  val prop_tr': term -> term

  val appl_ast_tr': Ast.ast * Ast.ast list -> Ast.ast

  val applC_ast_tr': Ast.ast * Ast.ast list -> Ast.ast

  val pts_to_asts: Proof.context ->

    (string -> (Proof.context -> Ast.ast list -> Ast.ast) option) ->

    Parser.parsetree list -> Ast.ast list

  val asts_to_terms: Proof.context ->

    (string -> (Proof.context -> term list -> term) option) -> Ast.ast list -> term list

end;

structure SynTrans: SYN_TRANS =

struct

(** parse (ast) translations **)

(* constify *)

fun constify_ast_tr [Ast.Variable c] = Ast.Constant c

  | constify_ast_tr asts = raise Ast.AST ("constify_ast_tr", asts);

(* application *)

fun appl_ast_tr [f, args] = Ast.Appl (f :: Ast.unfold_ast "_args" args)

  | appl_ast_tr asts = raise Ast.AST ("appl_ast_tr", asts);

fun applC_ast_tr [f, args] = Ast.Appl (f :: Ast.unfold_ast "_cargs" args)

  | applC_ast_tr asts = raise Ast.AST ("applC_ast_tr", asts);

(* abstraction *)

fun idtyp_ast_tr (*"_idtyp"*) [x, ty] = Ast.Appl [Ast.Constant "_constrain", x, ty]

  | idtyp_ast_tr (*"_idtyp"*) asts = raise Ast.AST ("idtyp_ast_tr", asts);

fun idtypdummy_ast_tr (*"_idtypdummy"*) [ty] =

      Ast.Appl [Ast.Constant "_constrain", Ast.Constant "_idtdummy", ty]

  | idtypdummy_ast_tr (*"_idtypdummy"*) asts = raise Ast.AST ("idtyp_ast_tr", asts);

fun lambda_ast_tr (*"_lambda"*) [pats, body] =

      Ast.fold_ast_p "_abs" (Ast.unfold_ast "_pttrns" pats, body)

  | lambda_ast_tr (*"_lambda"*) asts = raise Ast.AST ("lambda_ast_tr", asts);

val constrainAbsC = "_constrainAbs";

fun absfree_proper (x, T, t) =

  if can Name.dest_internal x then error ("Illegal internal variable in abstraction: " ^ quote x)

  else Term.absfree (x, T, t);

fun abs_tr (*"_abs"*) [Free (x, T), t] = absfree_proper (x, T, t)

  | abs_tr (*"_abs"*) [Const ("_idtdummy", T), t] = Term.absdummy (T, t)

  | abs_tr (*"_abs"*) [Const ("_constrain", _) $ Free (x, T) $ tT, t] =

      Lexicon.const constrainAbsC $ absfree_proper (x, T, t) $ tT

  | abs_tr (*"_abs"*) [Const ("_constrain", _) $ Const ("_idtdummy", T) $ tT, t] =

      Lexicon.const constrainAbsC $ Term.absdummy (T, t) $ tT

  | abs_tr (*"_abs"*) ts = raise TERM ("abs_tr", ts);

(* binder *)

fun mk_binder_tr (syn, name) =

  let

    fun tr (Free (x, T), t) = Lexicon.const name $ absfree_proper (x, T, t)

      | tr (Const ("_idtdummy", T), t) = Lexicon.const name $ Term.absdummy (T, t)

      | tr (Const ("_constrain", _) $ Free (x, T) $ tT, t) =

          Lexicon.const name $ (Lexicon.const constrainAbsC $ absfree_proper (x, T, t) $ tT)

      | tr (Const ("_constrain", _) $ Const ("_idtdummy", T) $ tT, t) =

          Lexicon.const name $ (Lexicon.const constrainAbsC $ Term.absdummy (T, t) $ tT)

      | tr (Const ("_idts", _) $ idt $ idts, t) = tr (idt, tr (idts, t))

      | tr (t1, t2) = raise TERM ("binder_tr", [t1, t2]);

    fun binder_tr [idts, body] = tr (idts, body)

      | binder_tr ts = raise TERM ("binder_tr", ts);

  in (syn, binder_tr) end;

(* type propositions *)

fun mk_type ty = Lexicon.const "_constrain" $ Lexicon.const "TYPE" $ (Lexicon.const "itself" $ ty);

fun ofclass_tr (*"_ofclass"*) [ty, cls] = cls $ mk_type ty

  | ofclass_tr (*"_ofclass"*) ts = raise TERM ("ofclass_tr", ts);

fun sort_constraint_tr (*"_sort_constraint"*) [ty] =

      Lexicon.const "Pure.sort_constraint" $ mk_type ty

  | sort_constraint_tr (*"_sort_constraint"*) ts = raise TERM ("sort_constraint_tr", ts);

(* meta propositions *)

fun aprop_tr (*"_aprop"*) [t] = Lexicon.const "_constrain" $ t $ Lexicon.const "prop"

  | aprop_tr (*"_aprop"*) ts = raise TERM ("aprop_tr", ts);

(* meta implication *)

fun bigimpl_ast_tr (*"_bigimpl"*) (asts as [asms, concl]) =

      let val prems =

        (case Ast.unfold_ast_p "_asms" asms of

          (asms', Ast.Appl [Ast.Constant "_asm", asm']) => asms' @ [asm']

        | _ => raise Ast.AST ("bigimpl_ast_tr", asts))

      in Ast.fold_ast_p "==>" (prems, concl) end

  | bigimpl_ast_tr (*"_bigimpl"*) asts = raise Ast.AST ("bigimpl_ast_tr", asts);

(* type/term reflection *)

fun type_tr (*"_TYPE"*) [ty] = mk_type ty

  | type_tr (*"_TYPE"*) ts = raise TERM ("type_tr", ts);

(* dddot *)

fun dddot_tr (*"_DDDOT"*) ts = Term.list_comb (Lexicon.var SynExt.dddot_indexname, ts);

(* quote / antiquote *)

fun antiquote_tr name =

  let

    fun tr i ((t as Const (c, _)) $ u) =

          if c = name then tr i u $ Bound i

          else tr i t $ tr i u

      | tr i (t $ u) = tr i t $ tr i u

      | tr i (Abs (x, T, t)) = Abs (x, T, tr (i + 1) t)

      | tr _ a = a;

  in tr 0 end;

fun quote_tr name t = Abs ("s", dummyT, antiquote_tr name (Term.incr_boundvars 1 t));

fun quote_antiquote_tr quoteN antiquoteN name =

  let

    fun tr [t] = Lexicon.const name $ quote_tr antiquoteN t

      | tr ts = raise TERM ("quote_tr", ts);

  in (quoteN, tr) end;

(* indexed syntax *)

fun struct_ast_tr (*"_struct"*) [Ast.Appl [Ast.Constant "_index", ast]] = ast

  | struct_ast_tr (*"_struct"*) asts = Ast.mk_appl (Ast.Constant "_struct") asts;

fun index_ast_tr ast =

  Ast.mk_appl (Ast.Constant "_index") [Ast.mk_appl (Ast.Constant "_struct") [ast]];

fun indexdefault_ast_tr (*"_indexdefault"*) [] =

      index_ast_tr (Ast.Constant "_indexdefault")

  | indexdefault_ast_tr (*"_indexdefault"*) asts =

      raise Ast.AST ("indexdefault_ast_tr", asts);

fun indexnum_ast_tr (*"_indexnum"*) [ast] =

      index_ast_tr (Ast.mk_appl (Ast.Constant "_indexnum") [ast])

  | indexnum_ast_tr (*"_indexnum"*) asts = raise Ast.AST ("indexnum_ast_tr", asts);

fun indexvar_ast_tr (*"_indexvar"*) [] =

      Ast.mk_appl (Ast.Constant "_index") [Ast.Variable "some_index"]

  | indexvar_ast_tr (*"_indexvar"*) asts = raise Ast.AST ("indexvar_ast_tr", asts);

fun index_tr (*"_index"*) [t] = t

  | index_tr (*"_index"*) ts = raise TERM ("index_tr", ts);

(* implicit structures *)

fun the_struct structs i =

  if 1 <= i andalso i <= length structs then nth structs (i - 1)

  else error ("Illegal reference to implicit structure #" ^ string_of_int i);

fun struct_tr structs (*"_struct"*) [Const ("_indexdefault", _)] =

      Lexicon.free (the_struct structs 1)

  | struct_tr structs (*"_struct"*) [t as (Const ("_indexnum", _) $ Const (s, _))] =

      Lexicon.free (the_struct structs

        (case Lexicon.read_nat s of SOME n => n | NONE => raise TERM ("struct_tr", [t])))

  | struct_tr _ (*"_struct"*) ts = raise TERM ("struct_tr", ts);

(** print (ast) translations **)

(* types *)

fun non_typed_tr' f _ _ ts = f ts;

fun non_typed_tr'' f x _ _ ts = f x ts;

(* application *)

fun appl_ast_tr' (f, []) = raise Ast.AST ("appl_ast_tr'", [f])

  | appl_ast_tr' (f, args) = Ast.Appl [Ast.Constant "_appl", f, Ast.fold_ast "_args" args];

fun applC_ast_tr' (f, []) = raise Ast.AST ("applC_ast_tr'", [f])

  | applC_ast_tr' (f, args) = Ast.Appl [Ast.Constant "_applC", f, Ast.fold_ast "_cargs" args];

(* abstraction *)

fun mark_boundT (x, T) = Const ("_bound", T --> T) $ Free (x, T);

fun mark_bound x = mark_boundT (x, dummyT);

fun bound_vars vars body =

  subst_bounds (map mark_boundT (Term.rename_wrt_term body vars), body);

fun strip_abss vars_of body_of tm =

  let

    val vars = vars_of tm;

    val body = body_of tm;

    val rev_new_vars = Term.rename_wrt_term body vars;

    fun subst (x, T) b =

      if can Name.dest_internal x andalso not (Term.loose_bvar1 (b, 0))

      then (Const ("_idtdummy", T), incr_boundvars ~1 b)

      else (mark_boundT (x, T), Term.subst_bound (mark_bound x, b));

    val (rev_vars', body') = fold_map subst rev_new_vars body;

  in (rev rev_vars', body') end;

(*do (partial) eta-contraction before printing*)

val eta_contract = Unsynchronized.ref true;

fun eta_contr tm =

  let

    fun is_aprop (Const ("_aprop", _)) = true

      | is_aprop _ = false;

    fun eta_abs (Abs (a, T, t)) =

          (case eta_abs t of

            t' as f $ u =>

              (case eta_abs u of

                Bound 0 =>

                  if Term.loose_bvar1 (f, 0) orelse is_aprop f then Abs (a, T, t')

                  else  incr_boundvars ~1 f

              | _ => Abs (a, T, t'))

          | t' => Abs (a, T, t'))

      | eta_abs t = t;

  in

    if ! eta_contract then eta_abs tm else tm

  end;

fun abs_tr' tm =

  uncurry (fold_rev (fn x => fn t => Lexicon.const "_abs" $ x $ t))

    (strip_abss strip_abs_vars strip_abs_body (eta_contr tm));

fun atomic_abs_tr' (x, T, t) =

  let val [xT] = Term.rename_wrt_term t [(x, T)]

  in (mark_boundT xT, subst_bound (mark_bound (fst xT), t)) end;

fun abs_ast_tr' (*"_abs"*) asts =

  (case Ast.unfold_ast_p "_abs" (Ast.Appl (Ast.Constant "_abs" :: asts)) of

    ([], _) => raise Ast.AST ("abs_ast_tr'", asts)

  | (xs, body) => Ast.Appl [Ast.Constant "_lambda", Ast.fold_ast "_pttrns" xs, body]);

fun preserve_binder_abs_tr' name syn = (name, fn (Abs abs :: ts) =>

  let val (x, t) = atomic_abs_tr' abs

  in list_comb (Lexicon.const syn $ x $ t, ts) end);

fun preserve_binder_abs2_tr' name syn = (name, fn (A :: Abs abs :: ts) =>

  let val (x, t) = atomic_abs_tr' abs

  in list_comb (Lexicon.const syn $ x $ A $ t, ts) end);

(* binder *)

fun mk_binder_tr' (name, syn) =

  let

    fun mk_idts [] = raise Match    (*abort translation*)

      | mk_idts [idt] = idt

      | mk_idts (idt :: idts) = Lexicon.const "_idts" $ idt $ mk_idts idts;

    fun tr' t =

      let

        val (xs, bd) = strip_abss (strip_qnt_vars name) (strip_qnt_body name) t;

      in Lexicon.const syn $ mk_idts xs $ bd end;

    fun binder_tr' (t :: ts) = Term.list_comb (tr' (Lexicon.const name $ t), ts)

      | binder_tr' [] = raise Match;

  in (name, binder_tr') end;

(* idtyp constraints *)

fun idtyp_ast_tr' a [Ast.Appl [Ast.Constant c, x, ty], xs] =

      if c = "_constrain" then

        Ast.Appl [Ast.Constant a, Ast.Appl [Ast.Constant "_idtyp", x, ty], xs]

      else raise Match

  | idtyp_ast_tr' _ _ = raise Match;

(* type propositions *)

fun type_prop_tr' _ (*"_type_prop"*) T [Const ("Pure.sort_constraint", _)] =

      Lexicon.const "_sort_constraint" $ TypeExt.term_of_typ true T

  | type_prop_tr' show_sorts (*"_type_prop"*) T [t] =

      Lexicon.const "_ofclass" $ TypeExt.term_of_typ show_sorts T $ t

  | type_prop_tr' _ (*"_type_prop"*) T ts = raise TYPE ("type_prop_tr'", [T], ts);

(* meta propositions *)

fun prop_tr' tm =

  let

    fun aprop t = Lexicon.const "_aprop" $ t;

    fun is_prop Ts t =

      fastype_of1 (Ts, t) = propT handle TERM _ => false;

    fun is_term (Const ("Pure.term", _) $ _) = true

      | is_term _ = false;

    fun tr' _ (t as Const _) = t

      | tr' Ts (t as Const ("_bound", _) $ u) =

          if is_prop Ts u then aprop t else t

      | tr' _ (t as Free (x, T)) =

          if T = propT then aprop (Lexicon.free x) else t

      | tr' _ (t as Var (xi, T)) =

          if T = propT then aprop (Lexicon.var xi) else t

      | tr' Ts (t as Bound _) =

          if is_prop Ts t then aprop t else t

      | tr' Ts (Abs (x, T, t)) = Abs (x, T, tr' (T :: Ts) t)

      | tr' Ts (t as t1 $ (t2 as Const ("TYPE", Type ("itself", [T])))) =

          if is_prop Ts t andalso not (is_term t) then Const ("_type_prop", T) $ tr' Ts t1

          else tr' Ts t1 $ tr' Ts t2

      | tr' Ts (t as t1 $ t2) =

          (if is_Const (Term.head_of t) orelse not (is_prop Ts t)

            then I else aprop) (tr' Ts t1 $ tr' Ts t2);

  in tr' [] tm end;

(* meta implication *)

fun impl_ast_tr' (*"==>"*) asts =

  if TypeExt.no_brackets () then raise Match

  else

    (case Ast.unfold_ast_p "==>" (Ast.Appl (Ast.Constant "==>" :: asts)) of

      (prems as _ :: _ :: _, concl) =>

        let

          val (asms, asm) = split_last prems;

          val asms' = Ast.fold_ast_p "_asms" (asms, Ast.Appl [Ast.Constant "_asm", asm]);

        in Ast.Appl [Ast.Constant "_bigimpl", asms', concl] end

    | _ => raise Match);

(* type reflection *)

fun type_tr' show_sorts (*"TYPE"*) (Type ("itself", [T])) ts =

      Term.list_comb (Lexicon.const "_TYPE" $ TypeExt.term_of_typ show_sorts T, ts)

  | type_tr' _ _ _ = raise Match;

(* type constraints *)

fun type_constraint_tr' show_sorts (*"_type_constraint_"*) (Type ("fun", [T, _])) (t :: ts) =

      Term.list_comb (Lexicon.const SynExt.constrainC $ t $ TypeExt.term_of_typ show_sorts T, ts)

  | type_constraint_tr' _ _ _ = raise Match;

(* dependent / nondependent quantifiers *)

fun var_abs mark (x, T, b) =

  let val ([x'], _) = Name.variants [x] (Term.declare_term_names b Name.context)

  in (x', subst_bound (mark (x', T), b)) end;

val variant_abs = var_abs Free;

val variant_abs' = var_abs mark_boundT;

fun dependent_tr' (q, r) (A :: Abs (x, T, B) :: ts) =

      if Term.loose_bvar1 (B, 0) then

        let val (x', B') = variant_abs' (x, dummyT, B);

        in Term.list_comb (Lexicon.const q $ mark_boundT (x', T) $ A $ B', ts) end

      else Term.list_comb (Lexicon.const r $ A $ B, ts)

  | dependent_tr' _ _ = raise Match;

(* quote / antiquote *)

fun antiquote_tr' name =

  let

    fun tr' i (t $ u) =

      if u aconv Bound i then Lexicon.const name $ tr' i t

      else tr' i t $ tr' i u

      | tr' i (Abs (x, T, t)) = Abs (x, T, tr' (i + 1) t)

      | tr' i a = if a aconv Bound i then raise Match else a;

  in tr' 0 end;

fun quote_tr' name (Abs (_, _, t)) = Term.incr_boundvars ~1 (antiquote_tr' name t)

  | quote_tr' _ _ = raise Match;

fun quote_antiquote_tr' quoteN antiquoteN name =

  let

    fun tr' (t :: ts) = Term.list_comb (Lexicon.const quoteN $ quote_tr' antiquoteN t, ts)

      | tr' _ = raise Match;

  in (name, tr') end;

(* indexed syntax *)

fun index_ast_tr' (*"_index"*) [Ast.Appl [Ast.Constant "_struct", ast]] = ast

  | index_ast_tr' _ = raise Match;

(* implicit structures *)

fun the_struct' structs s =

  [(case Lexicon.read_nat s of

    SOME i => Ast.Variable (the_struct structs i handle ERROR _ => raise Match)

  | NONE => raise Match)] |> Ast.mk_appl (Ast.Constant "_free");

fun struct_ast_tr' structs (*"_struct"*) [Ast.Constant "_indexdefault"] =

      the_struct' structs "1"

  | struct_ast_tr' structs (*"_struct"*) [Ast.Appl [Ast.Constant "_indexnum", Ast.Constant s]] =

      the_struct' structs s

  | struct_ast_tr' _ _ = raise Match;

(** Pure translations **)

val pure_trfuns =

 ([("_constify", constify_ast_tr), ("_appl", appl_ast_tr), ("_applC", applC_ast_tr),

   ("_lambda", lambda_ast_tr), ("_idtyp", idtyp_ast_tr), ("_idtypdummy", idtypdummy_ast_tr),

   ("_bigimpl", bigimpl_ast_tr), ("_indexdefault", indexdefault_ast_tr),

   ("_indexnum", indexnum_ast_tr), ("_indexvar", indexvar_ast_tr), ("_struct", struct_ast_tr)],

  [("_abs", abs_tr), ("_aprop", aprop_tr), ("_ofclass", ofclass_tr),

   ("_sort_constraint", sort_constraint_tr), ("_TYPE", type_tr),

   ("_DDDOT", dddot_tr), ("_index", index_tr)],

  ([]: (string * (term list -> term)) list),

  [("_abs", abs_ast_tr'), ("_idts", idtyp_ast_tr' "_idts"),

   ("_pttrns", idtyp_ast_tr' "_pttrns"), ("==>", impl_ast_tr'),

   ("_index", index_ast_tr')]);

val pure_trfunsT =

  [("_type_prop", type_prop_tr'), ("TYPE", type_tr'), ("_type_constraint_", type_constraint_tr')];

fun struct_trfuns structs =

  ([], [("_struct", struct_tr structs)], [], [("_struct", struct_ast_tr' structs)]);

(** pts_to_asts **)

fun pts_to_asts ctxt trf pts =

  let

    fun trans a args =

      (case trf a of

        NONE => Ast.mk_appl (Ast.Constant a) args

      | SOME f => f ctxt args);

    (*translate pt bottom-up*)

    fun ast_of (Parser.Node (a, pts)) = trans a (map ast_of pts)

      | ast_of (Parser.Tip tok) = Ast.Variable (Lexicon.str_of_token tok);

    val exn_results = map (Exn.capture ast_of) pts;

    val exns = map_filter Exn.get_exn exn_results;

    val results = map_filter Exn.get_result exn_results

  in (case (results, exns) of ([], exn :: _) => reraise exn | _ => results) end;

(** asts_to_terms **)

fun asts_to_terms ctxt trf asts =

  let

    fun trans a args =

      (case trf a of

        NONE => Term.list_comb (Lexicon.const a, args)

      | SOME f => f ctxt args);

    fun term_of (Ast.Constant a) = trans a []

      | term_of (Ast.Variable x) = Lexicon.read_var x

      | term_of (Ast.Appl (Ast.Constant a :: (asts as _ :: _))) =

          trans a (map term_of asts)

      | term_of (Ast.Appl (ast :: (asts as _ :: _))) =

          Term.list_comb (term_of ast, map term_of asts)

      | term_of (ast as Ast.Appl _) = raise Ast.AST ("ast_to_term: malformed ast", [ast]);

    val free_fixed = Term.map_aterms

      (fn t as Const (c, T) =>

          (case try (unprefix Lexicon.fixedN) c of

            NONE => t

          | SOME x => Free (x, T))

        | t => t);

    val exn_results = map (Exn.capture (term_of #> free_fixed)) asts;

    val exns = map_filter Exn.get_exn exn_results;

    val results = map_filter Exn.get_result exn_results

  in (case (results, exns) of ([], exn :: _) => reraise exn | _ => results) end;

end;