(* Title: Pure/sign.ML
ID: $Id$
Author: Lawrence C Paulson and Markus Wenzel
The abstract type "sg" of signatures.
*)
signature SIGN =
sig
type sg
val rep_sg: sg ->
{tsig: Type.type_sig,
const_tab: typ Symtab.table,
syn: Syntax.syntax,
stamps: string ref list}
val subsig: sg * sg -> bool
val eq_sg: sg * sg -> bool
val same_sg: sg * sg -> bool
val is_draft: sg -> bool
val const_type: sg -> string -> typ option
val classes: sg -> class list
val subsort: sg -> sort * sort -> bool
val nodup_Vars: term -> unit
val norm_sort: sg -> sort -> sort
val nonempty_sort: sg -> sort list -> sort -> bool
val print_sg: sg -> unit
val pretty_sg: sg -> Pretty.T
val pprint_sg: sg -> pprint_args -> unit
val pretty_term: sg -> term -> Pretty.T
val pretty_typ: sg -> typ -> Pretty.T
val pretty_sort: sort -> Pretty.T
val string_of_term: sg -> term -> string
val string_of_typ: sg -> typ -> string
val pprint_term: sg -> term -> pprint_args -> unit
val pprint_typ: sg -> typ -> pprint_args -> unit
val certify_typ: sg -> typ -> typ
val certify_term: sg -> term -> term * typ * int
val read_typ: sg * (indexname -> sort option) -> string -> typ
val infer_types: sg -> (indexname -> typ option) ->
(indexname -> sort option) -> string list -> bool
-> term list * typ -> int * term * (indexname * typ) list
val add_classes: (class * class list) list -> sg -> sg
val add_classrel: (class * class) list -> sg -> sg
val add_defsort: sort -> sg -> sg
val add_types: (string * int * mixfix) list -> sg -> sg
val add_tyabbrs: (string * string list * string * mixfix) list -> sg -> sg
val add_tyabbrs_i: (string * string list * typ * mixfix) list -> sg -> sg
val add_arities: (string * sort list * sort) list -> sg -> sg
val add_consts: (string * string * mixfix) list -> sg -> sg
val add_consts_i: (string * typ * mixfix) list -> sg -> sg
val add_syntax: (string * string * mixfix) list -> sg -> sg
val add_syntax_i: (string * typ * mixfix) list -> sg -> sg
val add_modesyntax: (string * bool) * (string * string * mixfix) list -> sg -> sg
val add_modesyntax_i: (string * bool) * (string * typ * mixfix) list -> sg -> sg
val add_trfuns:
(string * (ast list -> ast)) list *
(string * (term list -> term)) list *
(string * (term list -> term)) list *
(string * (ast list -> ast)) list -> sg -> sg
val add_trfunsT:
(string * (typ -> term list -> term)) list -> sg -> sg
val add_tokentrfuns:
(string * string * (string -> string * int)) list -> sg -> sg
val add_trrules: (string * string) Syntax.trrule list -> sg -> sg
val add_trrules_i: ast Syntax.trrule list -> sg -> sg
val add_name: string -> sg -> sg
val make_draft: sg -> sg
val merge: sg * sg -> sg
val proto_pure: sg
val pure: sg
val cpure: sg
val const_of_class: class -> string
val class_of_const: string -> class
end;
structure Sign : SIGN =
struct
(** datatype sg **)
(*the "ref" in stamps ensures that no two signatures are identical -- it is
impossible to forge a signature*)
datatype sg =
Sg of {
tsig: Type.type_sig, (*order-sorted signature of types*)
const_tab: typ Symtab.table, (*types of constants*)
syn: Syntax.syntax, (*syntax for parsing and printing*)
stamps: string ref list}; (*unique theory indentifier*)
fun rep_sg (Sg args) = args;
val tsig_of = #tsig o rep_sg;
(* inclusion and equality *)
local
(*avoiding polymorphic equality: factor 10 speedup*)
fun mem_stamp (_:string ref, []) = false
| mem_stamp (x, y :: ys) = x = y orelse mem_stamp (x, ys);
fun subset_stamp ([], ys) = true
| subset_stamp (x :: xs, ys) =
mem_stamp (x, ys) andalso subset_stamp (xs, ys);
(*fast partial test*)
fun fast_sub ([]: string ref list, _) = true
| fast_sub (_, []) = false
| fast_sub (x :: xs, y :: ys) =
if x = y then fast_sub (xs, ys)
else fast_sub (x :: xs, ys);
in
fun subsig (Sg {stamps = s1, ...}, Sg {stamps = s2, ...}) =
s1 = s2 orelse subset_stamp (s1, s2);
fun fast_subsig (Sg {stamps = s1, ...}, Sg {stamps = s2, ...}) =
s1 = s2 orelse fast_sub (s1, s2);
fun eq_sg (Sg {stamps = s1, ...}, Sg {stamps = s2, ...}) =
s1 = s2 orelse (subset_stamp (s1, s2) andalso subset_stamp (s2, s1));
end;
(*test if same theory names are contained in signatures' stamps,
i.e. if signatures belong to same theory but not necessarily to the
same version of it*)
fun same_sg (Sg {stamps = s1, ...}, Sg {stamps = s2, ...}) =
eq_set_string (pairself (map (op !)) (s1, s2));
(*test for drafts*)
fun is_draft (Sg {stamps = ref "#" :: _, ...}) = true
| is_draft _ = false;
(* consts *)
fun const_type (Sg {const_tab, ...}) c = Symtab.lookup (const_tab, c);
(* classes and sorts *)
val classes = #classes o Type.rep_tsig o tsig_of;
val subsort = Type.subsort o tsig_of;
val norm_sort = Type.norm_sort o tsig_of;
val nonempty_sort = Type.nonempty_sort o tsig_of;
(* FIXME move to Sorts? *)
fun pretty_sort [c] = Pretty.str c
| pretty_sort cs = Pretty.str_list "{" "}" cs;
(** print signature **)
fun stamp_names stamps = rev (map ! stamps);
fun print_sg sg =
let
fun prt_typ syn ty = Pretty.quote (Syntax.pretty_typ syn ty);
fun pretty_classrel (cl, cls) = Pretty.block
(Pretty.str (cl ^ " <") :: Pretty.brk 1 ::
Pretty.commas (map Pretty.str cls));
fun pretty_default cls = Pretty.block
[Pretty.str "default:", Pretty.brk 1, pretty_sort cls];
fun pretty_ty (ty, n) = Pretty.str (ty ^ " " ^ string_of_int n);
fun pretty_abbr syn (ty, (vs, rhs)) = Pretty.block
[prt_typ syn (Type (ty, map (fn v => TVar ((v, 0), [])) vs)),
Pretty.str " =", Pretty.brk 1, prt_typ syn rhs];
fun pretty_arity ty (cl, []) = Pretty.block
[Pretty.str (ty ^ " ::"), Pretty.brk 1, Pretty.str cl]
| pretty_arity ty (cl, srts) = Pretty.block
[Pretty.str (ty ^ " ::"), Pretty.brk 1,
Pretty.list "(" ")" (map pretty_sort srts),
Pretty.brk 1, Pretty.str cl];
fun pretty_arities (ty, ars) = map (pretty_arity ty) ars;
fun pretty_const syn (c, ty) = Pretty.block
[Pretty.str (quote c ^ " ::"), Pretty.brk 1, prt_typ syn ty];
val Sg {tsig, const_tab, syn, stamps} = sg;
val {classes, classrel, default, tycons, abbrs, arities} =
Type.rep_tsig tsig;
in
Pretty.writeln (Pretty.strs ("stamps:" :: stamp_names stamps));
Pretty.writeln (Pretty.strs ("classes:" :: classes));
Pretty.writeln (Pretty.big_list "classrel:" (map pretty_classrel classrel));
Pretty.writeln (pretty_default default);
Pretty.writeln (Pretty.big_list "types:" (map pretty_ty tycons));
Pretty.writeln (Pretty.big_list "abbrs:" (map (pretty_abbr syn) abbrs));
Pretty.writeln (Pretty.big_list "arities:"
(List.concat (map pretty_arities arities)));
Pretty.writeln (Pretty.big_list "consts:"
(map (pretty_const syn) (Symtab.dest const_tab)))
end;
fun pretty_sg (Sg {stamps, ...}) =
Pretty.str_list "{" "}" (stamp_names stamps);
val pprint_sg = Pretty.pprint o pretty_sg;
(** pretty printing of terms and types **)
fun pretty_term (Sg {syn, stamps, ...}) =
let val curried = "CPure" mem_string (map ! stamps);
in Syntax.pretty_term curried syn end;
fun pretty_typ (Sg {syn, ...}) = Syntax.pretty_typ syn;
fun string_of_term (Sg {syn, stamps, ...}) =
let val curried = "CPure" mem_string (map ! stamps);
in Syntax.string_of_term curried syn end;
fun string_of_typ (Sg {syn, ...}) = Syntax.string_of_typ syn;
fun pprint_term sg = Pretty.pprint o Pretty.quote o (pretty_term sg);
fun pprint_typ sg = Pretty.pprint o Pretty.quote o (pretty_typ sg);
(** read types **) (*exception ERROR*)
fun err_in_type s =
error ("The error(s) above occurred in type " ^ quote s);
fun read_raw_typ syn tsig sort_of str =
Syntax.read_typ syn (Type.eq_sort tsig) (Type.get_sort tsig sort_of) str
handle ERROR => err_in_type str;
(*read and certify typ wrt a signature*)
fun read_typ (Sg {tsig, syn, ...}, sort_of) str =
Type.cert_typ tsig (read_raw_typ syn tsig sort_of str)
handle TYPE (msg, _, _) => (writeln msg; err_in_type str);
(** certify types and terms **) (*exception TYPE*)
fun certify_typ (Sg {tsig, ...}) ty = Type.cert_typ tsig ty;
(*check for duplicate TVars with distinct sorts*)
fun nodup_TVars (tvars, T) =
(case T of
Type (_, Ts) => nodup_TVars_list (tvars, Ts)
| TFree _ => tvars
| TVar (v as (a, S)) =>
(case assoc_string_int (tvars, a) of
Some S' =>
if S = S' then tvars
else raise_type ("Type variable " ^ Syntax.string_of_vname a ^
" has two distinct sorts") [TVar (a, S'), T] []
| None => v :: tvars))
(*equivalent to foldl nodup_TVars_list, but 3X faster under Poly/ML*)
and nodup_TVars_list (tvars, []) = tvars
| nodup_TVars_list (tvars, T :: Ts) =
nodup_TVars_list (nodup_TVars (tvars, T), Ts);
(*check for duplicate Vars with distinct types*)
fun nodup_Vars tm =
let
fun nodups vars tvars tm =
(case tm of
Const (c, T) => (vars, nodup_TVars (tvars, T))
| Free (a, T) => (vars, nodup_TVars (tvars, T))
| Var (v as (ixn, T)) =>
(case assoc_string_int (vars, ixn) of
Some T' =>
if T = T' then (vars, nodup_TVars (tvars, T))
else raise_type ("Variable " ^ Syntax.string_of_vname ixn ^
" has two distinct types") [T', T] []
| None => (v :: vars, tvars))
| Bound _ => (vars, tvars)
| Abs(_, T, t) => nodups vars (nodup_TVars (tvars, T)) t
| s $ t =>
let val (vars',tvars') = nodups vars tvars s in
nodups vars' tvars' t
end);
in nodups [] [] tm; () end;
fun mapfilt_atoms f (Abs (_, _, t)) = mapfilt_atoms f t
| mapfilt_atoms f (t $ u) = mapfilt_atoms f t @ mapfilt_atoms f u
| mapfilt_atoms f a = (case f a of Some y => [y] | None => []);
fun certify_term (sg as Sg {tsig, ...}) tm =
let
fun valid_const a T =
(case const_type sg a of
Some U => Type.typ_instance (tsig, T, U)
| _ => false);
fun atom_err (Const (a, T)) =
if valid_const a T then None
else Some ("Illegal type for constant " ^ quote a ^ " :: " ^
quote (string_of_typ sg T))
| atom_err (Var ((x, i), _)) =
if i < 0 then Some ("Negative index for Var " ^ quote x) else None
| atom_err _ = None;
val norm_tm =
(case it_term_types (Type.typ_errors tsig) (tm, []) of
[] => map_term_types (Type.norm_typ tsig) tm
| errs => raise_type (cat_lines errs) [] [tm]);
val _ = nodup_Vars norm_tm;
in
(case mapfilt_atoms atom_err norm_tm of
[] => (norm_tm, type_of norm_tm, maxidx_of_term norm_tm)
| errs => raise_type (cat_lines errs) [] [norm_tm])
end;
(** infer_types **) (*exception ERROR*)
(*
ts: list of alternative parses (hopefully only one is type-correct)
T: expected type
def_type: partial map from indexnames to types (constrains Frees, Vars)
def_sort: partial map from indexnames to sorts (constrains TFrees, TVars)
used: list of already used type variables
freeze: if true then generated parameters are turned into TFrees, else TVars
*)
fun infer_types sg def_type def_sort used freeze (ts, T) =
let
val Sg {tsig, ...} = sg;
val prt = setmp Syntax.show_brackets true (pretty_term sg);
val prT = pretty_typ sg;
val infer = Type.infer_types prt prT tsig (const_type sg)
def_type def_sort used freeze;
val T' = certify_typ sg T handle TYPE (msg, _, _) => error msg;
fun warn () =
if length ts > 1 andalso length ts <= ! Syntax.ambiguity_level
then (*no warning shown yet*)
warning "Currently parsed input \
\produces more than one parse tree.\n\
\For more information lower Syntax.ambiguity_level."
else ();
datatype result =
One of int * term * (indexname * typ) list |
Errs of string list |
Ambigs of term list;
fun process_term (res, (t, i)) =
let val ([u], tye) = infer [T'] [t] in
(case res of
One (_, t0, _) => Ambigs ([u, t0])
| Errs _ => One (i, u, tye)
| Ambigs us => Ambigs (u :: us))
end handle TYPE (msg, _, _) =>
(case res of
Errs errs => Errs (msg :: errs)
| _ => res);
in
(case foldl process_term (Errs [], ts ~~ (0 upto (length ts - 1))) of
One res =>
(if length ts > ! Syntax.ambiguity_level then
writeln "Fortunately, only one parse tree is type correct.\n\
\It helps (speed!) if you disambiguate your grammar or your input."
else (); res)
| Errs errs => (warn (); error (cat_lines errs))
| Ambigs us =>
(warn (); error ("Error: More than one term is type correct:\n" ^
(cat_lines (map (Pretty.string_of o prt) us)))))
end;
(** extend signature **) (*exception ERROR*)
(** signature extension functions **) (*exception ERROR*)
fun decls_of name_of mfixs =
map (fn (x, y, mx) => (name_of x mx, y)) mfixs;
(* add default sort *)
fun ext_defsort (syn, tsig, ctab) defsort =
(syn, Type.ext_tsig_defsort tsig defsort, ctab);
(* add type constructors *)
fun ext_types (syn, tsig, ctab) types =
(Syntax.extend_type_gram syn types,
Type.ext_tsig_types tsig (decls_of Syntax.type_name types),
ctab);
(* add type abbreviations *)
fun read_abbr syn tsig (t, vs, rhs_src) =
(t, vs, read_raw_typ syn tsig (K None) rhs_src)
handle ERROR => error ("in type abbreviation " ^ t);
fun ext_abbrs rd_abbr (syn, tsig, ctab) abbrs =
let
fun mfix_of (t, vs, _, mx) = (t, length vs, mx);
val syn1 = Syntax.extend_type_gram syn (map mfix_of abbrs);
fun decl_of (t, vs, rhs, mx) =
rd_abbr syn1 tsig (Syntax.type_name t mx, vs, rhs);
in
(syn1, Type.ext_tsig_abbrs tsig (map decl_of abbrs), ctab)
end;
fun ext_tyabbrs_i arg = ext_abbrs (K (K I)) arg;
fun ext_tyabbrs arg = ext_abbrs read_abbr arg;
(* add type arities *)
fun ext_arities (syn, tsig, ctab) arities =
let
val tsig1 = Type.ext_tsig_arities tsig arities;
val log_types = Type.logical_types tsig1;
in
(Syntax.extend_log_types syn log_types, tsig1, ctab)
end;
(* add term constants and syntax *)
fun err_in_const c =
error ("in declaration of constant " ^ quote c);
fun err_dup_consts cs =
error ("Duplicate declaration of constant(s) " ^ commas_quote cs);
fun read_const syn tsig (c, ty_src, mx) =
(c, read_raw_typ syn tsig (K None) ty_src, mx)
handle ERROR => err_in_const (Syntax.const_name c mx);
fun ext_cnsts rd_const syn_only prmode (syn, tsig, ctab) raw_consts =
let
fun prep_const (c, ty, mx) =
(c, compress_type (Type.varifyT (Type.cert_typ tsig (Type.no_tvars ty))), mx)
handle TYPE (msg, _, _)
=> (writeln msg; err_in_const (Syntax.const_name c mx));
val consts = map (prep_const o rd_const syn tsig) raw_consts;
val decls =
if syn_only then []
else filter_out (equal "" o fst) (decls_of Syntax.const_name consts);
in
(Syntax.extend_const_gram syn prmode consts, tsig,
Symtab.extend_new (ctab, decls)
handle Symtab.DUPS cs => err_dup_consts cs)
end;
val ext_consts_i = ext_cnsts (K (K I)) false ("", true);
val ext_consts = ext_cnsts read_const false ("", true);
val ext_syntax_i = ext_cnsts (K (K I)) true ("", true);
val ext_syntax = ext_cnsts read_const true ("", true);
fun ext_modesyntax_i sg (prmode, consts) = ext_cnsts (K (K I)) true prmode sg consts;
fun ext_modesyntax sg (prmode, consts) = ext_cnsts read_const true prmode sg consts;
(* add type classes *)
fun const_of_class c = c ^ "_class";
fun class_of_const c_class =
let
val c = implode (take (size c_class - 6, explode c_class));
in
if const_of_class c = c_class then c
else raise_term ("class_of_const: bad name " ^ quote c_class) []
end;
fun ext_classes (syn, tsig, ctab) classes =
let
val names = map fst classes;
val consts =
map (fn c => (const_of_class c, a_itselfT --> propT, NoSyn)) names;
in
ext_consts_i
(Syntax.extend_consts syn names, Type.ext_tsig_classes tsig classes, ctab)
consts
end;
(* add to classrel *)
fun ext_classrel (syn, tsig, ctab) pairs =
(syn, Type.ext_tsig_classrel tsig pairs, ctab);
(* add to syntax *)
fun ext_syn extfun (syn, tsig, ctab) args =
(extfun syn args, tsig, ctab);
(* build signature *)
fun ext_stamps stamps name =
let
val stmps = (case stamps of ref "#" :: ss => ss | ss => ss);
in
if exists (equal name o !) stmps then
error ("Theory already contains a " ^ quote name ^ " component")
else ref name :: stmps
end;
fun make_sign (syn, tsig, ctab) stamps name =
Sg {tsig = tsig, const_tab = ctab, syn = syn,
stamps = ext_stamps stamps name};
fun extend_sign extfun name decls (Sg {tsig, const_tab, syn, stamps}) =
make_sign (extfun (syn, tsig, const_tab) decls) stamps name;
(* the external interfaces *)
val add_classes = extend_sign ext_classes "#";
val add_classrel = extend_sign ext_classrel "#";
val add_defsort = extend_sign ext_defsort "#";
val add_types = extend_sign ext_types "#";
val add_tyabbrs = extend_sign ext_tyabbrs "#";
val add_tyabbrs_i = extend_sign ext_tyabbrs_i "#";
val add_arities = extend_sign ext_arities "#";
val add_consts = extend_sign ext_consts "#";
val add_consts_i = extend_sign ext_consts_i "#";
val add_syntax = extend_sign ext_syntax "#";
val add_syntax_i = extend_sign ext_syntax_i "#";
val add_modesyntax = extend_sign ext_modesyntax "#";
val add_modesyntax_i = extend_sign ext_modesyntax_i "#";
val add_trfuns = extend_sign (ext_syn Syntax.extend_trfuns) "#";
val add_trfunsT = extend_sign (ext_syn Syntax.extend_trfunsT) "#";
val add_tokentrfuns = extend_sign (ext_syn Syntax.extend_tokentrfuns) "#";
val add_trrules = extend_sign (ext_syn Syntax.extend_trrules) "#";
val add_trrules_i = extend_sign (ext_syn Syntax.extend_trrules_i) "#";
fun add_name name sg = extend_sign K name () sg;
val make_draft = add_name "#";
(** merge signatures **) (*exception TERM*) (*exception ERROR (* FIXME *)*)
fun merge (sg1, sg2) =
if fast_subsig (sg2, sg1) then sg1
else if fast_subsig (sg1, sg2) then sg2
else if subsig (sg2, sg1) then sg1
else if subsig (sg1, sg2) then sg2
else if is_draft sg1 orelse is_draft sg2 then
raise_term "Illegal merge of draft signatures" []
else
(*neither is union already; must form union*)
let
val Sg {tsig = tsig1, const_tab = const_tab1, syn = syn1,
stamps = stamps1} = sg1;
val Sg {tsig = tsig2, const_tab = const_tab2, syn = syn2,
stamps = stamps2} = sg2;
val stamps = merge_rev_lists stamps1 stamps2;
val _ =
(case duplicates (stamp_names stamps) of
[] => ()
| dups => raise_term ("Attempt to merge different versions of theories "
^ commas_quote dups) []);
val tsig = Type.merge_tsigs (tsig1, tsig2);
val const_tab = Symtab.merge (op =) (const_tab1, const_tab2)
handle Symtab.DUPS cs =>
raise_term ("Incompatible types for constant(s) " ^ commas_quote cs) [];
val syn = Syntax.merge_syntaxes syn1 syn2;
in
Sg {tsig = tsig, const_tab = const_tab, syn = syn, stamps = stamps}
end;
(** the Pure signature **)
val proto_pure =
make_sign (Syntax.pure_syn, Type.tsig0, Symtab.null) [] "#"
|> add_types
(("fun", 2, NoSyn) ::
("prop", 0, NoSyn) ::
("itself", 1, NoSyn) ::
Syntax.pure_types)
|> add_classes [(logicC, [])]
|> add_defsort logicS
|> add_arities
[("fun", [logicS, logicS], logicS),
("prop", [], logicS),
("itself", [logicS], logicS)]
|> add_syntax Syntax.pure_syntax
|> add_modesyntax (("symbols", true), Syntax.pure_sym_syntax)
|> add_trfuns Syntax.pure_trfuns
|> add_trfunsT Syntax.pure_trfunsT
|> add_consts
[("==", "['a::{}, 'a] => prop", InfixrName ("==", 2)),
("=?=", "['a::{}, 'a] => prop", InfixrName ("=?=", 2)),
("==>", "[prop, prop] => prop", Mixfix ("(_/ ==> _)", [2, 1], 1)),
("all", "('a => prop) => prop", Binder ("!!", 0, 0)),
("TYPE", "'a itself", NoSyn)]
|> add_syntax
[("==>", "[prop, prop] => prop", Delimfix "op ==>")]
|> add_name "ProtoPure";
val pure = proto_pure
|> add_syntax Syntax.pure_appl_syntax
|> add_name "Pure";
val cpure = proto_pure
|> add_syntax Syntax.pure_applC_syntax
|> add_name "CPure";
end;