(* Title: Pure/Syntax/syntax_trans.ML
Author: Tobias Nipkow and Markus Wenzel, TU Muenchen
Syntax translation functions.
*)
signature BASIC_SYNTAX_TRANS =
sig
val eta_contract: bool Config.T
end
signature SYNTAX_TRANS =
sig
include BASIC_SYNTAX_TRANS
val bracketsN: string
val no_bracketsN: string
val no_brackets: unit -> bool
val type_bracketsN: string
val no_type_bracketsN: string
val no_type_brackets: unit -> bool
val abs_tr: term list -> term
val mk_binder_tr: string * string -> string * (Proof.context -> term list -> term)
val antiquote_tr: string -> term -> term
val quote_tr: string -> term -> term
val quote_antiquote_tr: string -> string -> string ->
string * (Proof.context -> term list -> term)
val non_typed_tr': (Proof.context -> term list -> term) ->
Proof.context -> typ -> term list -> term
val tappl_ast_tr': Ast.ast * Ast.ast list -> Ast.ast
val appl_ast_tr': Ast.ast * Ast.ast list -> Ast.ast
val applC_ast_tr': Ast.ast * Ast.ast list -> Ast.ast
val declare_term_names: Proof.context -> term -> Name.context -> Name.context
val variant_bounds: Proof.context -> term -> (string * 'a) list -> (string * 'a) list
val mark_bound_abs: string * typ -> term
val mark_bound_body: string * typ -> term
val bound_vars: Proof.context -> (string * typ) list -> term -> term
val abs_tr': Proof.context -> term -> term
val atomic_abs_tr': Proof.context -> string * typ * term -> term * term
val const_abs_tr': term -> term
val mk_binder_tr': string * string -> string * (Proof.context -> term list -> term)
val preserve_binder_abs_tr': string -> Proof.context -> typ -> term list -> term
val preserve_binder_abs2_tr': string -> Proof.context -> typ -> term list -> term
val print_abs: string * typ * term -> string * 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 * (Proof.context -> term list -> term)
val update_name_tr': term -> term
val get_idents: Proof.context -> {structs: string list, fixes: string list}
val put_idents: {structs: string list, fixes: string list} -> Proof.context -> Proof.context
val default_struct: Proof.context -> string option
val pure_parse_ast_translation: (string * (Proof.context -> Ast.ast list -> Ast.ast)) list
val pure_parse_translation: (string * (Proof.context -> term list -> term)) list
val pure_print_ast_translation: (string * (Proof.context -> Ast.ast list -> Ast.ast)) list
end;
structure Syntax_Trans: SYNTAX_TRANS =
struct
structure Syntax = Lexicon.Syntax;
(* print mode *)
val bracketsN = "brackets";
val no_bracketsN = "no_brackets";
fun no_brackets () =
find_first (fn mode => mode = bracketsN orelse mode = no_bracketsN)
(print_mode_value ()) = SOME no_bracketsN;
val type_bracketsN = "type_brackets";
val no_type_bracketsN = "no_type_brackets";
fun no_type_brackets () =
find_first (fn mode => mode = type_bracketsN orelse mode = no_type_bracketsN)
(print_mode_value ()) <> SOME type_bracketsN;
(** parse (ast) translations **)
(* strip_positions *)
fun strip_positions_ast_tr [ast] = Ast.strip_positions ast
| strip_positions_ast_tr asts = raise Ast.AST ("strip_positions_ast_tr", asts);
(* constify *)
fun constify_ast_tr [Ast.Appl [c as Ast.Constant "_constrain", ast1, ast2]] =
Ast.Appl [c, constify_ast_tr [ast1], ast2]
| constify_ast_tr [Ast.Variable c] = Ast.Constant c
| constify_ast_tr asts = raise Ast.AST ("constify_ast_tr", asts);
(* type syntax *)
fun tapp_ast_tr [ty, c] = Ast.Appl [c, ty]
| tapp_ast_tr asts = raise Ast.AST ("tapp_ast_tr", asts);
fun tappl_ast_tr [ty, tys, c] = Ast.mk_appl c (ty :: Ast.unfold_ast "_types" tys)
| tappl_ast_tr asts = raise Ast.AST ("tappl_ast_tr", asts);
fun bracket_ast_tr [dom, cod] = Ast.fold_ast_p "\<^type>fun" (Ast.unfold_ast "_types" dom, cod)
| bracket_ast_tr asts = raise Ast.AST ("bracket_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 [x, ty] = Ast.Appl [Ast.Constant "_constrain", x, ty]
| idtyp_ast_tr asts = raise Ast.AST ("idtyp_ast_tr", asts);
fun lambda_ast_tr [pats, body] = Ast.fold_ast_p "_abs" (Ast.unfold_ast "_pttrns" pats, body)
| lambda_ast_tr asts = raise Ast.AST ("lambda_ast_tr", asts);
fun absfree_proper (x, T) t =
if Name.is_internal x
then error ("Illegal internal variable in abstraction: " ^ quote x)
else absfree (x, T) t;
fun abs_tr [Free x, t] = absfree_proper x t
| abs_tr [Const ("_idtdummy", T), t] = absdummy T t
| abs_tr [Const ("_constrain", _) $ x $ tT, t] = Syntax.const "_constrainAbs" $ abs_tr [x, t] $ tT
| abs_tr ts = raise TERM ("abs_tr", ts);
(* binder *)
fun mk_binder_tr (syn, name) =
let
fun err ts = raise TERM ("binder_tr: " ^ syn, ts)
fun binder_tr [Const ("_idts", _) $ idt $ idts, t] = binder_tr [idt, binder_tr [idts, t]]
| binder_tr [x, t] = Syntax.const name $ (abs_tr [x, t] handle TERM _ => err [x, t])
| binder_tr ts = err ts;
in (syn, fn _ => binder_tr) end;
(* type propositions *)
fun mk_type ty =
Syntax.const "_constrain" $
Syntax.const "\<^const>Pure.type" $ (Syntax.const "\<^type>itself" $ ty);
fun ofclass_tr [ty, cls] = cls $ mk_type ty
| ofclass_tr ts = raise TERM ("ofclass_tr", ts);
fun sort_constraint_tr [ty] = Syntax.const "\<^const>Pure.sort_constraint" $ mk_type ty
| sort_constraint_tr ts = raise TERM ("sort_constraint_tr", ts);
(* meta propositions *)
fun aprop_tr [t] = Syntax.const "_constrain" $ t $ Syntax.const "\<^type>prop"
| aprop_tr ts = raise TERM ("aprop_tr", ts);
(* meta implication *)
fun bigimpl_ast_tr (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 "\<^const>Pure.imp" (prems, concl) end
| bigimpl_ast_tr asts = raise Ast.AST ("bigimpl_ast_tr", asts);
(* type/term reflection *)
fun type_tr [ty] = mk_type ty
| type_tr ts = raise TERM ("type_tr", 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] = Syntax.const name $ quote_tr antiquoteN t
| tr ts = raise TERM ("quote_tr", ts);
in (quoteN, fn _ => tr) end;
(* corresponding updates *)
fun update_name_tr (Free (x, T) :: ts) = list_comb (Free (suffix "_update" x, T), ts)
| update_name_tr (Const (x, T) :: ts) = list_comb (Const (suffix "_update" x, T), ts)
| update_name_tr (((c as Const ("_constrain", _)) $ t $ ty) :: ts) =
if Term_Position.detect_position ty then list_comb (c $ update_name_tr [t] $ ty, ts)
else
list_comb (c $ update_name_tr [t] $
(Lexicon.fun_type $
(Lexicon.fun_type $ Lexicon.dummy_type $ ty) $ Lexicon.dummy_type), ts)
| update_name_tr ts = raise TERM ("update_name_tr", ts);
(* indexed syntax *)
structure Idents = Proof_Data
(
type T = {structs: string list, fixes: string list};
fun init _ : T = {structs = [], fixes = []};
);
val get_idents = Idents.get;
val put_idents = Idents.put;
val default_struct = try hd o #structs o get_idents;
fun indexdefault_ast_tr [] =
Ast.Appl [Ast.Constant "_index",
Ast.Appl [Ast.Constant "_struct", Ast.Constant "_indexdefault"]]
| indexdefault_ast_tr asts = raise Ast.AST ("indexdefault_ast_tr", asts);
fun indexvar_ast_tr [] = Ast.Appl [Ast.Constant "_index", Ast.Variable "some_index"]
| indexvar_ast_tr asts = raise Ast.AST ("indexvar_ast_tr", asts);
fun struct_ast_tr [Ast.Appl [Ast.Constant "_index", ast]] = ast
| struct_ast_tr asts = Ast.mk_appl (Ast.Constant "_struct") asts;
fun index_tr [t] = t
| index_tr ts = raise TERM ("index_tr", ts);
fun struct_tr ctxt [Const ("_indexdefault", _)] =
(case default_struct ctxt of
SOME x => Syntax.const (Lexicon.mark_fixed x)
| NONE => error "Illegal reference to implicit structure")
| struct_tr _ ts = raise TERM ("struct_tr", ts);
(** print (ast) translations **)
(* types *)
fun non_typed_tr' f ctxt _ ts = f ctxt ts;
(* type syntax *)
fun tappl_ast_tr' (f, []) = raise Ast.AST ("tappl_ast_tr'", [f])
| tappl_ast_tr' (f, [ty]) = Ast.Appl [Ast.Constant "_tapp", ty, f]
| tappl_ast_tr' (f, ty :: tys) =
Ast.Appl [Ast.Constant "_tappl", ty, Ast.fold_ast "_types" tys, f];
fun fun_ast_tr' asts =
if no_brackets () orelse no_type_brackets () then raise Match
else
(case Ast.unfold_ast_p "\<^type>fun" (Ast.Appl (Ast.Constant "\<^type>fun" :: asts)) of
(dom as _ :: _ :: _, cod)
=> Ast.Appl [Ast.Constant "_bracket", Ast.fold_ast "_types" dom, cod]
| _ => raise Match);
(* 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];
(* partial eta-contraction before printing *)
fun eta_abs (Abs (a, T, t)) =
(case eta_abs t of
t' as Const ("_aprop", _) $ _ => Abs (a, T, t')
| t' as f $ u =>
(case eta_abs u of
Bound 0 =>
if Term.is_dependent f then Abs (a, T, t')
else incr_boundvars ~1 f
| _ => Abs (a, T, t'))
| t' => Abs (a, T, t'))
| eta_abs t = t;
val eta_contract = Config.declare_option_bool ("eta_contract", \<^here>);
fun eta_contr ctxt = Config.get ctxt eta_contract ? eta_abs;
(* renaming variables *)
fun declare_term_names ctxt =
let
val s = the_default "" (default_struct ctxt);
fun declare (Const ("_struct", _) $ Const ("_indexdefault", _)) = Name.declare s
| declare (Const (c, _)) =
if Lexicon.is_fixed c then Name.declare (Lexicon.unmark_fixed c) else I
| declare (Free (x, _)) = Name.declare x
| declare (t $ u) = declare t #> declare u
| declare (Abs (_, _, t)) = declare t
| declare _ = I;
in declare end;
fun variant_bounds ctxt =
Name.variant_names_build o declare_term_names ctxt;
(* abstraction *)
fun mark_bound_abs (x, T) = Const ("_bound", T --> T) $ Free (x, T);
fun mark_bound_body (x, T) = Const ("_bound", dummyT) $ Free (x, T);
fun bound_vars ctxt vars body =
subst_bounds (map mark_bound_abs (rev (variant_bounds ctxt body vars)), body);
fun strip_abss ctxt vars_of body_of tm =
let
val vars = vars_of tm;
val body = body_of tm;
val new_vars = variant_bounds ctxt body vars;
fun subst (x, T) b =
if Name.is_internal x andalso not (Term.is_dependent b)
then (Const ("_idtdummy", T), incr_boundvars ~1 b)
else (mark_bound_abs (x, T), Term.subst_bound (mark_bound_body (x, T), b));
val (rev_vars', body') = fold_map subst (rev new_vars) body;
in (rev rev_vars', body') end;
fun abs_tr' ctxt tm =
uncurry (fold_rev (fn x => fn t => Syntax.const "_abs" $ x $ t))
(strip_abss ctxt strip_abs_vars strip_abs_body (eta_contr ctxt tm));
fun atomic_abs_tr' ctxt (x, T, t) =
let val xT = singleton (variant_bounds ctxt t) (x, T)
in (mark_bound_abs xT, subst_bound (mark_bound_body xT, t)) end;
fun abs_ast_tr' 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 const_abs_tr' t =
(case eta_abs t of
Abs (_, _, t') =>
if Term.is_dependent t' then raise Match
else incr_boundvars ~1 t'
| _ => raise Match);
(* binders *)
fun mk_binder_tr' (name, syn) =
let
fun mk_idts [] = raise Match (*abort translation*)
| mk_idts [idt] = idt
| mk_idts (idt :: idts) = Syntax.const "_idts" $ idt $ mk_idts idts;
fun tr' ctxt t =
let
val (xs, bd) = strip_abss ctxt (strip_qnt_vars name) (strip_qnt_body name) t;
in Syntax.const syn $ mk_idts xs $ bd end;
fun binder_tr' ctxt (t :: ts) = Term.list_comb (tr' ctxt (Syntax.const name $ t), ts)
| binder_tr' _ [] = raise Match;
in (name, binder_tr') end;
fun preserve_binder_abs_tr' syn ctxt ty (Abs abs :: ts) =
let val (x, t) = atomic_abs_tr' ctxt abs
in list_comb (Const (syn, ty) $ x $ t, ts) end;
fun preserve_binder_abs2_tr' syn ctxt ty (A :: Abs abs :: ts) =
let val (x, t) = atomic_abs_tr' ctxt abs
in list_comb (Const (syn, ty) $ x $ A $ t, ts) end;
(* idtyp constraints *)
fun idtyp_ast_tr' a [Ast.Appl [Ast.Constant "_constrain", x, ty], xs] =
Ast.Appl [Ast.Constant a, Ast.Appl [Ast.Constant "_idtyp", x, ty], xs]
| idtyp_ast_tr' _ _ = raise Match;
(* meta implication *)
fun impl_ast_tr' asts =
if no_brackets () then raise Match
else
(case Ast.unfold_ast_p "\<^const>Pure.imp"
(Ast.Appl (Ast.Constant "\<^const>Pure.imp" :: 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);
(* dependent / nondependent quantifiers *)
fun print_abs (x, T, b) =
let val x' = #1 (Name.variant x (Name.build_context (Term.declare_free_names b)))
in (x', subst_bound (mark_bound_abs (x', T), b)) end;
fun dependent_tr' (q, r) (A :: Abs (x, T, B) :: ts) =
if Term.is_dependent B then
let val (x', B') = print_abs (x, dummyT, B);
in Term.list_comb (Syntax.const q $ mark_bound_abs (x', T) $ A $ B', ts) end
else Term.list_comb (Syntax.const r $ A $ incr_boundvars ~1 B, ts)
| dependent_tr' _ _ = raise Match;
(* quote / antiquote *)
fun antiquote_tr' name =
let
fun tr' i (t $ u) =
if u aconv Bound i then Syntax.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 (Syntax.const quoteN $ quote_tr' antiquoteN t, ts)
| tr' _ = raise Match;
in (name, fn _ => tr') end;
(* corresponding updates *)
local
fun upd_type (Type ("fun", [Type ("fun", [_, T]), _])) = T
| upd_type _ = dummyT;
fun upd_tr' (x_upd, T) =
(case try (unsuffix "_update") x_upd of
SOME x => (x, upd_type T)
| NONE => raise Match);
in
fun update_name_tr' (Free x) = Free (upd_tr' x)
| update_name_tr' ((c as Const ("_free", _)) $ Free x) = c $ Free (upd_tr' x)
| update_name_tr' (Const x) = Const (upd_tr' x)
| update_name_tr' _ = raise Match;
end;
(* indexed syntax *)
fun index_ast_tr' [Ast.Appl [Ast.Constant "_struct", ast]] = ast
| index_ast_tr' _ = raise Match;
fun struct_ast_tr' ctxt [Ast.Constant "_indexdefault"] =
(case default_struct ctxt of
SOME x => Ast.Appl [Ast.Constant "_free", Ast.Variable x]
| NONE => raise Match)
| struct_ast_tr' _ _ = raise Match;
(** Pure translations **)
val pure_parse_ast_translation =
[("_strip_positions", fn _ => strip_positions_ast_tr),
("_constify", fn _ => constify_ast_tr),
("_tapp", fn _ => tapp_ast_tr),
("_tappl", fn _ => tappl_ast_tr),
("_bracket", fn _ => bracket_ast_tr),
("_appl", fn _ => appl_ast_tr),
("_applC", fn _ => applC_ast_tr),
("_lambda", fn _ => lambda_ast_tr),
("_idtyp", fn _ => idtyp_ast_tr),
("_bigimpl", fn _ => bigimpl_ast_tr),
("_indexdefault", fn _ => indexdefault_ast_tr),
("_indexvar", fn _ => indexvar_ast_tr),
("_struct", fn _ => struct_ast_tr)];
val pure_parse_translation =
[("_abs", fn _ => abs_tr),
("_aprop", fn _ => aprop_tr),
("_ofclass", fn _ => ofclass_tr),
("_sort_constraint", fn _ => sort_constraint_tr),
("_TYPE", fn _ => type_tr),
("_update_name", fn _ => update_name_tr),
("_index", fn _ => index_tr),
("_struct", struct_tr)];
val pure_print_ast_translation =
[("\<^type>fun", fn _ => fun_ast_tr'),
("_abs", fn _ => abs_ast_tr'),
("_idts", fn _ => idtyp_ast_tr' "_idts"),
("_pttrns", fn _ => idtyp_ast_tr' "_pttrns"),
("\<^const>Pure.imp", fn _ => impl_ast_tr'),
("_index", fn _ => index_ast_tr'),
("_struct", struct_ast_tr')];
end;
structure Basic_Syntax_Trans: BASIC_SYNTAX_TRANS = Syntax_Trans;
open Basic_Syntax_Trans;