(* Title: Pure/Syntax/syn_trans.ML
ID: $Id$
Author: Tobias Nipkow and Markus Wenzel, TU Muenchen
Syntax translation functions.
*)
signature SYN_TRANS0 =
sig
val eta_contract: bool ref
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
end;
signature SYN_TRANS1 =
sig
include SYN_TRANS0
structure Parser: PARSER
local open Parser.SynExt.Ast in
val constrainAbsC: string
val pure_trfuns:
(string * (ast list -> ast)) list *
(string * (term list -> term)) list *
(string * (term list -> term)) list *
(string * (ast list -> ast)) list
end
end;
signature SYN_TRANS =
sig
include SYN_TRANS1
local open Parser Parser.SynExt Parser.SynExt.Ast in
val abs_tr': term -> term
val prop_tr': bool -> term -> term
val appl_ast_tr': ast * ast list -> ast
val applC_ast_tr': ast * ast list -> ast
val pt_to_ast: (string -> (ast list -> ast) option) -> parsetree -> ast
val ast_to_term: (string -> (term list -> term) option) -> ast -> term
end
end;
functor SynTransFun(structure TypeExt: TYPE_EXT and Parser: PARSER
sharing TypeExt.SynExt = Parser.SynExt): SYN_TRANS =
struct
structure Parser = Parser;
open TypeExt Parser.Lexicon Parser.SynExt.Ast Parser.SynExt Parser;
(** parse (ast) translations **)
(* application *)
fun appl_ast_tr [f, args] = Appl (f :: unfold_ast "_args" args)
| appl_ast_tr asts = raise_ast "appl_ast_tr" asts;
fun applC_ast_tr [f, arg] =
let fun unfold_ast_c (y as Appl (Constant _ :: _)) = [y]
| unfold_ast_c (Appl xs) = xs
| unfold_ast_c y = [y];
in Appl ((unfold_ast_c f) @ [arg]) end
| applC_ast_tr asts = raise_ast "applC_ast_tr" asts;
(* abstraction *)
fun idtyp_ast_tr (*"_idtyp"*) [x, ty] = Appl [Constant constrainC, x, ty]
| idtyp_ast_tr (*"_idtyp"*) asts = raise_ast "idtyp_ast_tr" asts;
fun lambda_ast_tr (*"_lambda"*) [idts, body] =
fold_ast_p "_abs" (unfold_ast "_idts" idts, body)
| lambda_ast_tr (*"_lambda"*) asts = raise_ast "lambda_ast_tr" asts;
val constrainAbsC = "_constrainAbs";
fun abs_tr (*"_abs"*) [Free (x, T), body] = absfree (x, T, body)
| abs_tr (*"_abs"*) (ts as [Const (c, _) $ Free (x, T) $ tT, body]) =
if c = constrainC
then const constrainAbsC $ absfree (x, T, body) $ tT
else raise_term "abs_tr" ts
| abs_tr (*"_abs"*) ts = raise_term "abs_tr" ts;
(* nondependent abstraction *)
fun k_tr (*"_K"*) [t] = Abs ("uu", dummyT, incr_boundvars 1 t)
| k_tr (*"_K"*) ts = raise_term "k_tr" ts;
(* binder *)
fun mk_binder_tr (sy, name) =
let
fun tr (Free (x, T), t) = const name $ absfree (x, T, t)
| tr (Const ("_idts", _) $ idt $ idts, t) = tr (idt, tr (idts, t))
| tr (t1 as Const (c, _) $ Free (x, T) $ tT, t) =
if c = constrainC then
const name $ (const constrainAbsC $ absfree (x, T, t) $ tT)
else raise_term "binder_tr" [t1, t]
| tr (t1, t2) = raise_term "binder_tr" [t1, t2];
fun binder_tr (*sy*) [idts, body] = tr (idts, body)
| binder_tr (*sy*) ts = raise_term "binder_tr" ts;
in
(sy, binder_tr)
end;
(* meta propositions *)
fun aprop_tr (*"_aprop"*) [t] = const constrainC $ t $ const "prop"
| aprop_tr (*"_aprop"*) ts = raise_term "aprop_tr" ts;
fun ofclass_tr (*"_ofclass"*) [ty, cls] =
cls $ (const constrainC $ const "TYPE" $ (const "itself" $ ty))
| ofclass_tr (*"_ofclass"*) ts = raise_term "ofclass_tr" ts;
(* meta implication *)
fun bigimpl_ast_tr (*"_bigimpl"*) [asms, concl] =
fold_ast_p "==>" (unfold_ast "_asms" asms, concl)
| bigimpl_ast_tr (*"_bigimpl"*) asts = raise_ast "bigimpl_ast_tr" asts;
(** print (ast) translations **)
(* application *)
fun appl_ast_tr' (f, []) = raise_ast "appl_ast_tr'" [f]
| appl_ast_tr' (f, args) = Appl [Constant "_appl", f, fold_ast "_args" args];
fun applC_ast_tr' (f, []) = raise_ast "applC_ast_tr'" [f]
| applC_ast_tr' (f, arg::args) =
let (* fold curried function application *)
fun fold [] result = result
| fold (x :: xs) result =
fold xs (Appl [Constant "_applC", result, x]);
in fold args (Appl [Constant "_applC", f, arg]) end;
(*
f a b c ()
("_applC" f a)
b c ("_applC" f a)
("_applC" ("_applC" f a) b)
c ("_applC" ("_applC" f a) b)
("_applC" ("_applC" ("_applC" f a) b) c)
*)
(* abstraction *)
fun strip_abss vars_of body_of tm =
let
val vars = vars_of tm;
val body = body_of tm;
val rev_new_vars = rename_wrt_term body vars;
in
(map Free (rev rev_new_vars),
subst_bounds (map (free o #1) rev_new_vars, body))
end;
(*do (partial) eta-contraction before printing*)
val eta_contract = ref false;
fun eta_contr tm =
let
fun eta_abs (Abs (a, T, t)) =
(case eta_abs t of
t' as f $ u =>
(case eta_abs u of
Bound 0 =>
if not (0 mem loose_bnos f) then incr_boundvars ~1 f
else Abs (a, T, t')
| _ => 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 =
foldr (fn (x, t) => const "_abs" $ x $ t)
(strip_abss strip_abs_vars strip_abs_body (eta_contr tm));
fun abs_ast_tr' (*"_abs"*) asts =
(case unfold_ast_p "_abs" (Appl (Constant "_abs" :: asts)) of
([], _) => raise_ast "abs_ast_tr'" asts
| (xs, body) => Appl [Constant "_lambda", fold_ast "_idts" xs, body]);
(* binder *)
fun mk_binder_tr' (name, sy) =
let
fun mk_idts [] = raise Match (*abort translation*)
| mk_idts [idt] = idt
| mk_idts (idt :: idts) = 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
const sy $ mk_idts xs $ bd
end;
fun binder_tr' (*name*) (t :: ts) =
list_comb (tr' (const name $ t), ts)
| binder_tr' (*name*) [] = raise Match;
in
(name, binder_tr')
end;
(* idts *)
fun idts_ast_tr' (*"_idts"*) [Appl [Constant c, x, ty], xs] =
if c = constrainC then
Appl [Constant "_idts", Appl [Constant "_idtyp", x, ty], xs]
else raise Match
| idts_ast_tr' (*"_idts"*) _ = raise Match;
(* meta propositions *)
fun prop_tr' show_sorts tm =
let
fun aprop t = const "_aprop" $ t;
fun is_prop tys t =
fastype_of1 (tys, t) = propT handle TERM _ => false;
fun tr' _ (t as Const _) = t
| tr' _ (t as Free (x, ty)) =
if ty = propT then aprop (free x) else t
| tr' _ (t as Var (xi, ty)) =
if ty = propT then aprop (var xi) else t
| tr' tys (t as Bound _) =
if is_prop tys t then aprop t else t
| tr' tys (Abs (x, ty, t)) = Abs (x, ty, tr' (ty :: tys) t)
| tr' tys (t as t1 $ (t2 as Const ("TYPE", Type ("itself", [ty])))) =
if is_prop tys t then
const "_ofclass" $ term_of_typ show_sorts ty $ tr' tys t1
else tr' tys t1 $ tr' tys t2
| tr' tys (t as t1 $ t2) =
(if is_Const (head_of t) orelse not (is_prop tys t)
then I else aprop) (tr' tys t1 $ tr' tys t2);
in
tr' [] tm
end;
(* meta implication *)
fun impl_ast_tr' (*"==>"*) asts =
(case unfold_ast_p "==>" (Appl (Constant "==>" :: asts)) of
(asms as _ :: _ :: _, concl)
=> Appl [Constant "_bigimpl", fold_ast "_asms" asms, concl]
| _ => raise Match);
(* dependent / nondependent quantifiers *)
fun dependent_tr' (q, r) (A :: Abs (x, T, B) :: ts) =
if 0 mem (loose_bnos B) then
let val (x', B') = variant_abs (x, dummyT, B);
in list_comb (const q $ Free (x', T) $ A $ B', ts) end
else list_comb (const r $ A $ B, ts)
| dependent_tr' _ _ = raise Match;
(** pure_trfuns **)
val pure_trfuns =
([("_appl", appl_ast_tr), ("_applC", applC_ast_tr),
("_lambda", lambda_ast_tr), ("_idtyp", idtyp_ast_tr),
("_bigimpl", bigimpl_ast_tr)],
[("_abs", abs_tr), ("_aprop", aprop_tr), ("_ofclass", ofclass_tr),
("_K", k_tr)],
[],
[("_abs", abs_ast_tr'), ("_idts", idts_ast_tr'), ("==>", impl_ast_tr')]);
(** pt_to_ast **)
fun pt_to_ast trf pt =
let
fun trans a args =
(case trf a of
None => mk_appl (Constant a) args
| Some f => f args handle exn
=> (writeln ("Error in parse ast translation for " ^ quote a); raise exn));
fun ast_of (Node (a, pts)) = trans a (map ast_of pts)
| ast_of (Tip tok) = Variable (str_of_token tok);
in
ast_of pt
end;
(** ast_to_term **)
fun ast_to_term trf ast =
let
fun trans a args =
(case trf a of
None => list_comb (const a, args)
| Some f => f args handle exn
=> (writeln ("Error in parse translation for " ^ quote a); raise exn));
fun term_of (Constant a) = trans a []
| term_of (Variable x) = scan_var x
| term_of (Appl (Constant a :: (asts as _ :: _))) =
trans a (map term_of asts)
| term_of (Appl (ast :: (asts as _ :: _))) =
list_comb (term_of ast, map term_of asts)
| term_of (ast as Appl _) = raise_ast "ast_to_term: malformed ast" [ast];
in
term_of ast
end;
end;