src/Pure/type.ML
author wenzelm
Thu Jun 16 12:04:33 1994 +0200 (1994-06-16 ago)
changeset 422 8f194014a9c8
parent 416 12f9f36e4484
child 450 382b5368ec21
permissions -rw-r--r--
added ext_tsig_subclass, ext_tsig_defsort;
minor internal rearrangements;
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(*  Title:      Pure/type.ML
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    ID:         $Id$
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    Author:     Tobias Nipkow & Lawrence C Paulson
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Type classes and sorts. Type signatures. Type unification and inference.
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TODO:
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  move type unification and inference to type_unify.ML (TypeUnify) (?)
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  rename args -> tycons, coreg -> arities (?)
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  clean err msgs
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*)
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signature TYPE =
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sig
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  structure Symtab: SYMTAB
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  val str_of_sort: sort -> string
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  val str_of_arity: string * sort list * sort -> string
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  type type_sig
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  val rep_tsig: type_sig ->
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    {classes: class list,
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     subclass: (class * class list) list,
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     default: sort,
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     args: (string * int) list,
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     abbrs: (string * (indexname list * typ)) list,
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     coreg: (string * (class * sort list) list) list}
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  val defaultS: type_sig -> sort
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  val tsig0: type_sig
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  val logical_types: type_sig -> string list
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  val extend_tsig: type_sig ->
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    (class * class list) list * sort * (string list * int) list *
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    (string list * (sort list * class)) list -> type_sig
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  val ext_tsig_subclass: type_sig -> (class * class) list -> type_sig
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  val ext_tsig_defsort: type_sig -> sort -> type_sig
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  val ext_tsig_abbrs: type_sig -> (string * (indexname list * typ)) list
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    -> type_sig
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  val merge_tsigs: type_sig * type_sig -> type_sig
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  val subsort: type_sig -> sort * sort -> bool
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  val norm_sort: type_sig -> sort -> sort
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  val rem_sorts: typ -> typ
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  val cert_typ: type_sig -> typ -> typ
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  val norm_typ: type_sig -> typ -> typ
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  val freeze: (indexname -> bool) -> term -> term
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  val freeze_vars: typ -> typ
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  val infer_types: type_sig * typ Symtab.table * (indexname -> typ option) *
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    (indexname -> sort option) * typ * term -> term * (indexname * typ) list
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  val inst_term_tvars: type_sig * (indexname * typ) list -> term -> term
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  val thaw_vars: typ -> typ
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  val typ_errors: type_sig -> typ * string list -> string list
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  val typ_instance: type_sig * typ * typ -> bool
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  val typ_match: type_sig -> (indexname * typ) list * (typ * typ)
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    -> (indexname * typ) list
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  val unify: type_sig -> (typ * typ) * (indexname * typ) list
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    -> (indexname * typ) list
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  val varifyT: typ -> typ
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  val varify: term * string list -> term
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  exception TUNIFY
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  exception TYPE_MATCH
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end;
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functor TypeFun(structure Symtab: SYMTAB and Syntax: SYNTAX): TYPE =
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struct
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structure Symtab = Symtab;
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(*** type classes and sorts ***)
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(*
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  Classes denote (possibly empty) collections of types (e.g. sets of types)
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  and are partially ordered by 'inclusion'. They are represented by strings.
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  Sorts are intersections of finitely many classes. They are represented by
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  lists of classes.
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*)
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type domain = sort list;
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(* print sorts and arities *)
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fun str_of_sort [c] = c
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  | str_of_sort cs = parents "{" "}" (commas cs);
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fun str_of_dom dom = parents "(" ")" (commas (map str_of_sort dom));
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fun str_of_arity (t, [], S) = t ^ " :: " ^ str_of_sort S
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  | str_of_arity (t, SS, S) =
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      t ^ " :: " ^ str_of_dom SS ^ " " ^ str_of_sort S;
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(*** type signatures ***)
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(*
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  classes:
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    a list of all declared classes;
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  subclass:
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    an association list representing the subclass relation; (c, cs) is
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    interpreted as "c is a proper subclass of all elemenst of cs"; note that
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    c itself is not a memeber of cs;
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  default:
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    the default sort attached to all unconstrained type vars;
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  args:
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    an association list of all declared types with the number of their
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    arguments;
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  abbrs:
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    an association list of type abbreviations;
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  coreg:
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    a two-fold association list of all type arities; (t, al) means that type
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    constructor t has the arities in al; an element (c, ss) of al represents
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    the arity (ss)c;
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*)
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datatype type_sig =
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  TySg of {
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    classes: class list,
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    subclass: (class * class list) list,
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    default: sort,
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    args: (string * int) list,
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    abbrs: (string * (indexname list * typ)) list,
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    coreg: (string * (class * domain) list) list};
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fun rep_tsig (TySg comps) = comps;
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fun defaultS (TySg {default, ...}) = default;
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(* error messages *)    (* FIXME move? *)
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fun undcl_class c = "Undeclared class " ^ quote c;
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val err_undcl_class = error o undcl_class;
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fun err_dup_classes cs =
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  error ("Duplicate declaration of class(es) " ^ commas_quote cs);
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fun undcl_type c = "Undeclared type constructor " ^ quote c;
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val err_undcl_type = error o undcl_type;
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fun err_dup_tycon c =
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  error ("Duplicate declaration of type constructor " ^ quote c);
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fun err_neg_args c =
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  error ("Negative number of arguments of type constructor " ^ quote c);
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fun err_dup_tyabbr c =
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  error ("Duplicate declaration of type abbreviation " ^ quote c);
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fun ty_confl c = "Conflicting type constructor and abbreviation " ^ quote c;
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val err_ty_confl = error o ty_confl;
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(* 'leq' checks the partial order on classes according to the
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   statements in the association list 'a' (i.e.'subclass')
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*)
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fun less a (C, D) = case assoc (a, C) of
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     Some(ss) => D mem ss
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   | None => err_undcl_class (C) ;
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fun leq a (C, D)  =  C = D orelse less a (C, D);
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(* logical_types *)
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(*return all logical types of tsig, i.e. all types t with some arity t::(ss)c
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  and c <= logic*)
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fun logical_types tsig =
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  let
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    val TySg {subclass, coreg, args, ...} = tsig;
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    fun log_class c = leq subclass (c, logicC);
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    fun log_type t = exists (log_class o #1) (assocs coreg t);
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  in
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    filter log_type (map #1 args)
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  end;
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(* 'sortorder' checks the ordering on sets of classes, i.e. on sorts:
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   S1 <= S2 , iff for every class C2 in S2 there exists a class C1 in S1
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   with C1 <= C2 (according to an association list 'a')
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*)
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fun sortorder a (S1, S2) =
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  forall  (fn C2 => exists  (fn C1 => leq a (C1, C2))  S1)  S2;
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(* 'inj' inserts a new class C into a given class set S (i.e.sort) only if
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  there exists no class in S which is <= C;
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  the resulting set is minimal if S was minimal
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*)
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fun inj a (C, S) =
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  let fun inj1 [] = [C]
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        | inj1 (D::T) = if leq a (D, C) then D::T
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                        else if leq a (C, D) then inj1 T
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                             else D::(inj1 T)
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  in inj1 S end;
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(* 'union_sort' forms the minimal union set of two sorts S1 and S2
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   under the assumption that S2 is minimal *)
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(* FIXME rename to inter_sort (?) *)
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fun union_sort a = foldr (inj a);
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(* 'elementwise_union' forms elementwise the minimal union set of two
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   sort lists under the assumption that the two lists have the same length
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*)
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fun elementwise_union a (Ss1, Ss2) = map (union_sort a) (Ss1~~Ss2);
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(* 'lew' checks for two sort lists the ordering for all corresponding list
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   elements (i.e. sorts) *)
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fun lew a (w1, w2) = forall (sortorder a)  (w1~~w2);
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(* 'is_min' checks if a class C is minimal in a given sort S under the
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   assumption that S contains C *)
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fun is_min a S C = not (exists (fn (D) => less a (D, C)) S);
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(* 'min_sort' reduces a sort to its minimal classes *)
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fun min_sort a S = distinct(filter (is_min a S) S);
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(* 'min_domain' minimizes the domain sorts of type declarationsl;
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   the function will be applied on the type declarations in extensions *)
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fun min_domain subclass =
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  let fun one_min (f, (doms, ran)) = (f, (map (min_sort subclass) doms, ran))
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  in map one_min end;
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(* 'min_filter' filters a list 'ars' consisting of arities (domain * class)
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   and gives back a list of those range classes whose domains meet the
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   predicate 'pred' *)
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fun min_filter a pred ars =
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  let fun filt ([], l) = l
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        | filt ((c, x)::xs, l) = if pred(x) then filt (xs, inj a (c, l))
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                               else filt (xs, l)
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  in filt (ars, []) end;
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(* 'cod_above' filters all arities whose domains are elementwise >= than
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   a given domain 'w' and gives back a list of the corresponding range
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   classes *)
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fun cod_above (a, w, ars) = min_filter a (fn w' => lew a (w, w')) ars;
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(*Instantiation of type variables in types*)
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(*Pre: instantiations obey restrictions! *)
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fun inst_typ tye =
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  let fun inst(Type(a, Ts)) = Type(a, map inst Ts)
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        | inst(T as TFree _) = T
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        | inst(T as TVar(v, _)) =
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            (case assoc(tye, v) of Some U => inst U | None => T)
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  in inst end;
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(* 'least_sort' returns for a given type its maximum sort:
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   - type variables, free types: the sort brought with
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   - type constructors: recursive determination of the maximum sort of the
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                    arguments if the type is declared in 'coreg' of the
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                    given type signature  *)
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fun least_sort (tsig as TySg{subclass, coreg, ...}) =
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  let fun ls(T as Type(a, Ts)) =
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                 (case assoc (coreg, a) of
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                          Some(ars) => cod_above(subclass, map ls Ts, ars)
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                        | None => raise TYPE(undcl_type a, [T], []))
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        | ls(TFree(a, S)) = S
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        | ls(TVar(a, S)) = S
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  in ls end;
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fun check_has_sort(tsig as TySg{subclass, coreg, ...}, T, S) =
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  if sortorder subclass ((least_sort tsig T), S) then ()
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  else raise TYPE("Type not of sort " ^ (str_of_sort S), [T], [])
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(*Instantiation of type variables in types *)
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fun inst_typ_tvars(tsig, tye) =
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  let fun inst(Type(a, Ts)) = Type(a, map inst Ts)
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        | inst(T as TFree _) = T
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        | inst(T as TVar(v, S)) = (case assoc(tye, v) of
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                None => T | Some(U) => (check_has_sort(tsig, U, S); U))
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  in inst end;
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(*Instantiation of type variables in terms *)
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fun inst_term_tvars(tsig, tye) = map_term_types (inst_typ_tvars(tsig, tye));
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(* expand_typ *)
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fun expand_typ (TySg {abbrs, ...}) ty =
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  let
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    fun exptyp (Type (a, Ts)) =
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          (case assoc (abbrs, a) of
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            Some (vs, U) => exptyp (inst_typ (vs ~~ Ts) U)
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          | None => Type (a, map exptyp Ts))
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      | exptyp T = T
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  in
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    exptyp ty
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  end;
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(* norm_typ *)      (* FIXME norm sorts *)
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val norm_typ = expand_typ;
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(** type matching **)
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exception TYPE_MATCH;
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(*typ_match (s, (U, T)) = s' <==> s'(U) = T and s' is an extension of s*)
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fun typ_match tsig =
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  let
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    fun match (subs, (TVar (v, S), T)) =
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          (case assoc (subs, v) of
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            None => ((v, (check_has_sort (tsig, T, S); T)) :: subs
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              handle TYPE _ => raise TYPE_MATCH)
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          | Some U => if U = T then subs else raise TYPE_MATCH)
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      | match (subs, (Type (a, Ts), Type (b, Us))) =
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          if a <> b then raise TYPE_MATCH
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          else foldl match (subs, Ts ~~ Us)
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      | match (subs, (TFree x, TFree y)) =
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          if x = y then subs else raise TYPE_MATCH
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      | match _ = raise TYPE_MATCH;
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  in match end;
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fun typ_instance (tsig, T, U) =
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  (typ_match tsig ([], (U, T)); true) handle TYPE_MATCH => false;
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(** build type signatures **)
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fun make_tsig (classes, subclass, default, args, abbrs, coreg) =
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  TySg {classes = classes, subclass = subclass, default = default,
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    args = args, abbrs = abbrs, coreg = coreg};
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val tsig0 = make_tsig ([], [], [], [], [], []);
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(* sorts *)
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fun subsort (TySg {subclass, ...}) (S1, S2) =
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  sortorder subclass (S1, S2);
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fun norm_sort (TySg {subclass, ...}) S =
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  sort_strings (min_sort subclass S);
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fun rem_sorts (Type (a, tys)) = Type (a, map rem_sorts tys)
wenzelm@416
   370
  | rem_sorts (TFree (x, _)) = TFree (x, [])
wenzelm@416
   371
  | rem_sorts (TVar (xi, _)) = TVar (xi, []);
wenzelm@401
   372
wenzelm@401
   373
clasohm@0
   374
clasohm@0
   375
fun twice(a) = error("Type constructor " ^a^ " has already been declared.");
clasohm@0
   376
wenzelm@256
   377
fun tyab_conflict(a) = error("Can't declare type "^(quote a)^"!\nAn abbreviation with this name exists already.");
clasohm@0
   378
clasohm@0
   379
wenzelm@416
   380
(* typ_errors *)
wenzelm@256
   381
wenzelm@416
   382
(*check validity of (not necessarily normal) type; accumulate error messages*)
wenzelm@256
   383
wenzelm@416
   384
fun typ_errors tsig (typ, errors) =
wenzelm@256
   385
  let
wenzelm@416
   386
    val TySg {classes, args, abbrs, ...} = tsig;
wenzelm@416
   387
wenzelm@416
   388
    fun class_err (errs, c) =
wenzelm@416
   389
      if c mem classes then errs
wenzelm@416
   390
      else undcl_class c ins errs;
wenzelm@256
   391
wenzelm@256
   392
    val sort_err = foldl class_err;
clasohm@0
   393
wenzelm@256
   394
    fun typ_errs (Type (c, Us), errs) =
wenzelm@256
   395
          let
wenzelm@256
   396
            val errs' = foldr typ_errs (Us, errs);
wenzelm@256
   397
            fun nargs n =
wenzelm@256
   398
              if n = length Us then errs'
wenzelm@416
   399
              else ("Wrong number of arguments: " ^ quote c) ins errs';
wenzelm@256
   400
          in
wenzelm@256
   401
            (case assoc (args, c) of
wenzelm@256
   402
              Some n => nargs n
wenzelm@256
   403
            | None =>
wenzelm@256
   404
                (case assoc (abbrs, c) of
wenzelm@256
   405
                  Some (vs, _) => nargs (length vs)
wenzelm@416
   406
                | None => undcl_type c ins errs))
wenzelm@256
   407
          end
wenzelm@256
   408
    | typ_errs (TFree (_, S), errs) = sort_err (errs, S)
wenzelm@416
   409
    | typ_errs (TVar ((x, i), S), errs) =
wenzelm@416
   410
        if i < 0 then
wenzelm@416
   411
          ("Negative index for TVar " ^ quote x) ins sort_err (errs, S)
wenzelm@416
   412
        else sort_err (errs, S);
wenzelm@256
   413
  in
wenzelm@416
   414
    typ_errs (typ, errors)
wenzelm@256
   415
  end;
wenzelm@256
   416
wenzelm@256
   417
wenzelm@256
   418
(* cert_typ *)
wenzelm@256
   419
wenzelm@256
   420
(*check and normalize typ wrt. tsig; errors are indicated by exception TYPE*)
wenzelm@256
   421
wenzelm@256
   422
fun cert_typ tsig ty =
wenzelm@256
   423
  (case typ_errors tsig (ty, []) of
wenzelm@256
   424
    [] => norm_typ tsig ty
wenzelm@256
   425
  | errs => raise_type (cat_lines errs) [ty] []);
wenzelm@256
   426
wenzelm@256
   427
wenzelm@256
   428
wenzelm@422
   429
(** merge type signatures **)
wenzelm@256
   430
wenzelm@422
   431
(*'assoc_union' merges two association lists if the contents associated
wenzelm@422
   432
  the keys are lists*)
clasohm@0
   433
wenzelm@422
   434
fun assoc_union (as1, []) = as1
wenzelm@422
   435
  | assoc_union (as1, (key, l2) :: as2) =
wenzelm@422
   436
      (case assoc (as1, key) of
wenzelm@422
   437
        Some l1 => assoc_union (overwrite (as1, (key, l1 union l2)), as2)
wenzelm@422
   438
      | None => assoc_union ((key, l2) :: as1, as2));
clasohm@0
   439
clasohm@0
   440
wenzelm@422
   441
(* merge subclass *)
clasohm@0
   442
wenzelm@422
   443
fun merge_subclass (subclass1, subclass2) =
wenzelm@422
   444
  let val subclass = transitive_closure (assoc_union (subclass1, subclass2)) in
wenzelm@422
   445
    if exists (op mem) subclass then
wenzelm@422
   446
      error ("Cyclic class structure!")   (* FIXME improve msg, raise TERM *)
wenzelm@422
   447
    else subclass
wenzelm@416
   448
  end;
wenzelm@416
   449
wenzelm@416
   450
wenzelm@422
   451
(* coregularity *)
clasohm@0
   452
clasohm@0
   453
(* 'is_unique_decl' checks if there exists just one declaration t:(Ss)C *)
clasohm@0
   454
wenzelm@256
   455
fun is_unique_decl coreg (t, (s, w)) = case assoc2 (coreg, (t, s)) of
clasohm@0
   456
      Some(w1) => if w = w1 then () else
wenzelm@256
   457
        error("There are two declarations\n" ^
wenzelm@416
   458
              str_of_arity(t, w, [s]) ^ " and\n" ^
wenzelm@416
   459
              str_of_arity(t, w1, [s]) ^ "\n" ^
clasohm@0
   460
              "with the same result class.")
clasohm@0
   461
    | None => ();
clasohm@0
   462
clasohm@0
   463
(* 'restr2' checks if there are two declarations t:(Ss1)C1 and t:(Ss2)C2
clasohm@0
   464
   such that C1 >= C2 then Ss1 >= Ss2 (elementwise) *)
clasohm@0
   465
wenzelm@256
   466
fun subs (classes, subclass) C =
wenzelm@256
   467
  let fun sub (rl, l) = if leq subclass (l, C) then l::rl else rl
wenzelm@256
   468
  in foldl sub ([], classes) end;
clasohm@0
   469
wenzelm@256
   470
fun coreg_err(t, (w1, C), (w2, D)) =
wenzelm@416
   471
    error("Declarations " ^ str_of_arity(t, w1, [C]) ^ " and "
wenzelm@416
   472
                          ^ str_of_arity(t, w2, [D]) ^ " are in conflict");
clasohm@0
   473
wenzelm@256
   474
fun restr2 classes (subclass, coreg) (t, (s, w)) =
wenzelm@256
   475
  let fun restr ([], test) = ()
wenzelm@416
   476
        | restr (s1::Ss, test) =
wenzelm@416
   477
            (case assoc2 (coreg, (t, s1)) of
wenzelm@416
   478
              Some dom =>
wenzelm@416
   479
                if lew subclass (test (w, dom))
wenzelm@416
   480
                then restr (Ss, test)
wenzelm@416
   481
                else coreg_err (t, (w, s), (dom, s1))
wenzelm@256
   482
            | None => restr (Ss, test))
wenzelm@256
   483
      fun forward (t, (s, w)) =
wenzelm@256
   484
        let val s_sups = case assoc (subclass, s) of
wenzelm@256
   485
                   Some(s_sups) => s_sups | None => err_undcl_class(s);
wenzelm@256
   486
        in restr (s_sups, I) end
wenzelm@256
   487
      fun backward (t, (s, w)) =
wenzelm@256
   488
        let val s_subs = subs (classes, subclass) s
wenzelm@256
   489
        in restr (s_subs, fn (x, y) => (y, x)) end
wenzelm@256
   490
  in (backward (t, (s, w)); forward (t, (s, w))) end;
clasohm@0
   491
clasohm@0
   492
wenzelm@256
   493
fun varying_decls t =
wenzelm@256
   494
  error ("Type constructor " ^ quote t ^ " has varying number of arguments");
clasohm@0
   495
clasohm@0
   496
wenzelm@422
   497
(* 'merge_coreg' builds the union of two 'coreg' lists;
wenzelm@422
   498
   it only checks the two restriction conditions and inserts afterwards
wenzelm@422
   499
   all elements of the second list into the first one *)
wenzelm@422
   500
wenzelm@422
   501
fun merge_coreg classes subclass1 =
wenzelm@422
   502
  let fun test_ar classes (t, ars1) (coreg1, (s, w)) =
wenzelm@422
   503
        (is_unique_decl coreg1 (t, (s, w));
wenzelm@422
   504
         restr2 classes (subclass1, coreg1) (t, (s, w));
wenzelm@422
   505
         overwrite (coreg1, (t, (s, w) ins ars1)));
wenzelm@422
   506
wenzelm@422
   507
      fun merge_c (coreg1, (c as (t, ars2))) = case assoc (coreg1, t) of
wenzelm@422
   508
          Some(ars1) => foldl (test_ar classes (t, ars1)) (coreg1, ars2)
wenzelm@422
   509
        | None => c::coreg1
wenzelm@422
   510
  in foldl merge_c end;
wenzelm@422
   511
wenzelm@422
   512
fun merge_args (args, (t, n)) =
wenzelm@422
   513
  (case assoc (args, t) of
wenzelm@422
   514
    Some m => if m = n then args else varying_decls t
wenzelm@422
   515
  | None => (t, n) :: args);
wenzelm@422
   516
wenzelm@422
   517
(* FIXME raise TERM *)
wenzelm@422
   518
fun merge_abbrs (abbrs1, abbrs2) =
wenzelm@422
   519
  let
wenzelm@422
   520
    val abbrs = abbrs1 union abbrs2;
wenzelm@422
   521
    val names = map fst abbrs;
wenzelm@422
   522
  in
wenzelm@422
   523
    (case duplicates names of
wenzelm@422
   524
      [] => abbrs
wenzelm@422
   525
    | dups => error ("Duplicate declaration of type abbreviations: " ^
wenzelm@422
   526
        commas_quote dups))
wenzelm@422
   527
  end;
wenzelm@422
   528
wenzelm@422
   529
wenzelm@422
   530
(* 'merge_tsigs' takes the above declared functions to merge two type
wenzelm@422
   531
  signatures *)
wenzelm@422
   532
wenzelm@422
   533
fun merge_tsigs(TySg{classes=classes1, default=default1, subclass=subclass1, args=args1,
wenzelm@422
   534
           coreg=coreg1, abbrs=abbrs1},
wenzelm@422
   535
          TySg{classes=classes2, default=default2, subclass=subclass2, args=args2,
wenzelm@422
   536
           coreg=coreg2, abbrs=abbrs2}) =
wenzelm@422
   537
  let val classes' = classes1 union classes2;
wenzelm@422
   538
      val subclass' = merge_subclass (subclass1, subclass2);
wenzelm@422
   539
      val args' = foldl merge_args (args1, args2)
wenzelm@422
   540
      val coreg' = merge_coreg classes' subclass' (coreg1, coreg2);
wenzelm@422
   541
      val default' = min_sort subclass' (default1 @ default2);
wenzelm@422
   542
      val abbrs' = merge_abbrs(abbrs1, abbrs2);
wenzelm@422
   543
  in TySg{classes=classes' , default=default', subclass=subclass', args=args',
wenzelm@422
   544
          coreg=coreg' , abbrs = abbrs' }
wenzelm@422
   545
  end;
wenzelm@422
   546
wenzelm@422
   547
wenzelm@422
   548
wenzelm@422
   549
(*** extend type signatures ***)
wenzelm@422
   550
wenzelm@422
   551
(** add classes **)
wenzelm@422
   552
wenzelm@422
   553
(* FIXME use? *)
wenzelm@422
   554
fun add_classes classes cs =
wenzelm@422
   555
  (case cs inter classes of
wenzelm@422
   556
    [] => cs @ classes
wenzelm@422
   557
  | dups => err_dup_classes cs);
wenzelm@422
   558
wenzelm@422
   559
wenzelm@422
   560
(* 'add_class' adds a new class to the list of all existing classes *)
wenzelm@422
   561
wenzelm@422
   562
fun add_class (classes, (s, _)) =
wenzelm@422
   563
  if s mem classes then error("Class " ^ s ^ " declared twice.")
wenzelm@422
   564
  else s :: classes;
wenzelm@422
   565
wenzelm@422
   566
wenzelm@422
   567
(*'add_subclass' adds a tuple consisting of a new class (the new class has
wenzelm@422
   568
  already been inserted into the 'classes' list) and its superclasses (they
wenzelm@422
   569
  must be declared in 'classes' too) to the 'subclass' list of the given type
wenzelm@422
   570
  signature; furthermore all inherited superclasses according to the
wenzelm@422
   571
  superclasses brought with are inserted and there is a check that there are
wenzelm@422
   572
  no cycles (i.e. C <= D <= C, with C <> D);*)
wenzelm@422
   573
wenzelm@422
   574
fun add_subclass classes (subclass, (s, ges)) =
wenzelm@422
   575
let fun upd (subclass, s') = if s' mem classes then
wenzelm@422
   576
        let val ges' = the (assoc (subclass, s))
wenzelm@422
   577
        in case assoc (subclass, s') of
wenzelm@422
   578
             Some sups => if s mem sups
wenzelm@422
   579
                           then error(" Cycle :" ^ s^" <= "^ s'^" <= "^ s )
wenzelm@422
   580
                           else overwrite (subclass, (s, sups union ges'))
wenzelm@422
   581
           | None => subclass
wenzelm@422
   582
         end
wenzelm@422
   583
         else err_undcl_class(s')
wenzelm@422
   584
in foldl upd (subclass@[(s, ges)], ges) end;
wenzelm@422
   585
wenzelm@422
   586
wenzelm@422
   587
(* 'extend_classes' inserts all new classes into the corresponding
wenzelm@422
   588
   lists ('classes', 'subclass') if possible *)
wenzelm@422
   589
wenzelm@422
   590
fun extend_classes (classes, subclass, newclasses) =
wenzelm@422
   591
  if newclasses = [] then (classes, subclass) else
wenzelm@422
   592
  let val classes' = foldl add_class (classes, newclasses);
wenzelm@422
   593
      val subclass' = foldl (add_subclass classes') (subclass, newclasses);
wenzelm@422
   594
  in (classes', subclass') end;
wenzelm@422
   595
wenzelm@422
   596
wenzelm@422
   597
(* ext_tsig_subclass *)
wenzelm@422
   598
wenzelm@422
   599
fun ext_tsig_subclass tsig pairs =
wenzelm@422
   600
  let
wenzelm@422
   601
    val TySg {classes, subclass, default, args, abbrs, coreg} = tsig;
wenzelm@422
   602
wenzelm@422
   603
    (* FIXME clean! *)
wenzelm@422
   604
    val subclass' =
wenzelm@422
   605
      merge_subclass (subclass, map (fn (c1, c2) => (c1, [c2])) pairs);
wenzelm@422
   606
  in
wenzelm@422
   607
    make_tsig (classes, subclass', default, args, abbrs, coreg)
wenzelm@422
   608
  end;
wenzelm@422
   609
wenzelm@422
   610
wenzelm@422
   611
(* ext_tsig_defsort *)
wenzelm@422
   612
wenzelm@422
   613
fun ext_tsig_defsort (TySg {classes, subclass, args, abbrs, coreg, ...}) default =
wenzelm@422
   614
  make_tsig (classes, subclass, default, args, abbrs, coreg);
wenzelm@422
   615
wenzelm@422
   616
wenzelm@422
   617
wenzelm@422
   618
(** add arities **)
wenzelm@422
   619
clasohm@0
   620
(* 'coregular' checks
clasohm@0
   621
   - the two restriction conditions 'is_unique_decl' and 'restr2'
wenzelm@256
   622
   - if the classes in the new type declarations are known in the
clasohm@0
   623
     given type signature
clasohm@0
   624
   - if one type constructor has always the same number of arguments;
wenzelm@256
   625
   if one type declaration has passed all checks it is inserted into
clasohm@0
   626
   the 'coreg' association list of the given type signatrure  *)
clasohm@0
   627
wenzelm@256
   628
fun coregular (classes, subclass, args) =
wenzelm@256
   629
  let fun ex C = if C mem classes then () else err_undcl_class(C);
clasohm@0
   630
wenzelm@256
   631
      fun addar(w, C) (coreg, t) = case assoc(args, t) of
clasohm@0
   632
            Some(n) => if n <> length w then varying_decls(t) else
wenzelm@256
   633
                     (is_unique_decl coreg (t, (C, w));
wenzelm@256
   634
                      (seq o seq) ex w;
wenzelm@256
   635
                      restr2 classes (subclass, coreg) (t, (C, w));
wenzelm@416
   636
                      let val ars = the (assoc(coreg, t))
wenzelm@256
   637
                      in overwrite(coreg, (t, (C, w) ins ars)) end)
wenzelm@256
   638
          | None => err_undcl_type(t);
clasohm@0
   639
wenzelm@256
   640
      fun addts(coreg, (ts, ar)) = foldl (addar ar) (coreg, ts)
clasohm@0
   641
clasohm@0
   642
  in addts end;
clasohm@0
   643
clasohm@0
   644
clasohm@0
   645
(* 'close' extends the 'coreg' association list after all new type
clasohm@0
   646
   declarations have been inserted successfully:
clasohm@0
   647
   for every declaration t:(Ss)C , for all classses D with C <= D:
clasohm@0
   648
      if there is no declaration t:(Ss')C' with C < C' and C' <= D
clasohm@0
   649
      then insert the declaration t:(Ss)D into 'coreg'
clasohm@0
   650
   this means, if there exists a declaration t:(Ss)C and there is
clasohm@0
   651
   no declaration t:(Ss')D with C <=D then the declaration holds
wenzelm@256
   652
   for all range classes more general than C *)
wenzelm@256
   653
wenzelm@256
   654
fun close (coreg, subclass) =
wenzelm@256
   655
  let fun check sl (l, (s, dom)) = case assoc (subclass, s) of
clasohm@0
   656
          Some(sups) =>
wenzelm@256
   657
            let fun close_sup (l, sup) =
wenzelm@256
   658
                  if exists (fn s'' => less subclass (s, s'') andalso
wenzelm@256
   659
                                       leq subclass (s'', sup)) sl
clasohm@0
   660
                  then l
wenzelm@256
   661
                  else (sup, dom)::l
wenzelm@256
   662
            in foldl close_sup (l, sups) end
clasohm@0
   663
        | None => l;
wenzelm@256
   664
      fun ext (s, l) = (s, foldl (check (map #1 l)) (l, l));
clasohm@0
   665
  in map ext coreg end;
clasohm@0
   666
wenzelm@422
   667
wenzelm@422
   668
(** add types **)
wenzelm@422
   669
wenzelm@416
   670
fun add_types (aca, (ts, n)) =
wenzelm@416
   671
  let
wenzelm@416
   672
    fun add_type ((args, coreg, abbrs), t) =
wenzelm@416
   673
      case assoc(args, t) of              (* FIXME from new *)
wenzelm@416
   674
        Some _ => twice(t)
wenzelm@416
   675
      | None =>
wenzelm@416
   676
          (case assoc(abbrs, t) of
wenzelm@416
   677
            Some _ => tyab_conflict(t)
wenzelm@416
   678
          | None => ((t, n)::args, (t, [])::coreg, abbrs))
wenzelm@416
   679
  in
wenzelm@416
   680
    if n < 0 then     (* FIXME err_neg_args *)
wenzelm@416
   681
      error ("Type constructor cannot have negative number of arguments")
wenzelm@416
   682
    else foldl add_type (aca, ts)
clasohm@0
   683
  end;
clasohm@0
   684
wenzelm@256
   685
wenzelm@422
   686
wenzelm@422
   687
(** add type abbreviations **)
wenzelm@256
   688
wenzelm@416
   689
fun abbr_errors tsig (a, (lhs_vs, rhs)) =
wenzelm@416
   690
  let
wenzelm@416
   691
    val TySg {args, abbrs, ...} = tsig;
wenzelm@416
   692
    val rhs_vs = map #1 (typ_tvars rhs);
wenzelm@416
   693
    val show_idxs = commas_quote o map fst;
wenzelm@416
   694
wenzelm@416
   695
    val dup_lhs_vars =
wenzelm@416
   696
      (case duplicates lhs_vs of
wenzelm@416
   697
        [] => []
wenzelm@416
   698
      | vs => ["Duplicate variables on lhs: " ^ show_idxs vs]);
wenzelm@416
   699
wenzelm@416
   700
    val extra_rhs_vars =
wenzelm@416
   701
      (case gen_rems (op =) (rhs_vs, lhs_vs) of
wenzelm@416
   702
        [] => []
wenzelm@416
   703
      | vs => ["Extra variables on rhs: " ^ show_idxs vs]);
wenzelm@416
   704
wenzelm@416
   705
    val tycon_confl =
wenzelm@416
   706
      if is_none (assoc (args, a)) then []
wenzelm@416
   707
      else [ty_confl a];
wenzelm@416
   708
wenzelm@416
   709
    val dup_abbr =
wenzelm@416
   710
      if is_none (assoc (abbrs, a)) then []
wenzelm@416
   711
      else ["Duplicate declaration of abbreviation"];
wenzelm@416
   712
  in
wenzelm@416
   713
    dup_lhs_vars @ extra_rhs_vars @ tycon_confl @ dup_abbr @
wenzelm@416
   714
      typ_errors tsig (rhs, [])
wenzelm@416
   715
  end;
wenzelm@416
   716
wenzelm@416
   717
fun add_abbr (tsig, abbr as (a, _)) =
wenzelm@422
   718
  let val TySg {classes, subclass, default, args, coreg, abbrs} = tsig in
wenzelm@416
   719
    (case abbr_errors tsig abbr of
wenzelm@416
   720
      [] => make_tsig (classes, subclass, default, args, abbr :: abbrs, coreg)
wenzelm@416
   721
    | errs => (seq writeln errs;
wenzelm@416
   722
        error ("The error(s) above occurred in type abbreviation " ^ quote a)))
wenzelm@416
   723
  end;
wenzelm@416
   724
wenzelm@416
   725
fun ext_tsig_abbrs tsig abbrs = foldl add_abbr (tsig, abbrs);
wenzelm@416
   726
wenzelm@416
   727
nipkow@200
   728
wenzelm@256
   729
(* 'extend_tsig' takes the above described check- and extend-functions to
clasohm@0
   730
   extend a given type signature with new classes and new type declarations *)
clasohm@0
   731
wenzelm@256
   732
fun extend_tsig (TySg{classes, default, subclass, args, coreg, abbrs})
wenzelm@256
   733
            (newclasses, newdefault, types, arities) =
wenzelm@416
   734
  let
wenzelm@416
   735
    val (classes', subclass') = extend_classes(classes, subclass, newclasses);
wenzelm@256
   736
    val (args', coreg', _) = foldl add_types ((args, coreg, abbrs), types);
wenzelm@422
   737
clasohm@0
   738
    val old_coreg = map #1 coreg;
wenzelm@416
   739
    val coreg'' =
wenzelm@416
   740
      foldl (coregular (classes', subclass', args'))
wenzelm@416
   741
        (coreg', min_domain subclass' arities);
wenzelm@256
   742
    val coreg''' = close (coreg'', subclass');
wenzelm@422
   743
clasohm@0
   744
    val default' = if null newdefault then default else newdefault;
wenzelm@416
   745
  in
wenzelm@416
   746
    TySg {classes = classes', subclass = subclass', default = default',
wenzelm@416
   747
      args = args', coreg = coreg''', abbrs = abbrs}
wenzelm@416
   748
  end;
clasohm@0
   749
clasohm@0
   750
wenzelm@416
   751
wenzelm@416
   752
wenzelm@416
   753
(*** type unification and inference ***)
clasohm@0
   754
clasohm@0
   755
(*
clasohm@0
   756
clasohm@0
   757
Input:
clasohm@0
   758
- a 'raw' term which contains only dummy types and some explicit type
clasohm@0
   759
  constraints encoded as terms.
clasohm@0
   760
- the expected type of the term.
clasohm@0
   761
clasohm@0
   762
Output:
clasohm@0
   763
- the correctly typed term
clasohm@0
   764
- the substitution needed to unify the actual type of the term with its
clasohm@0
   765
  expected type; only the TVars in the expected type are included.
clasohm@0
   766
clasohm@0
   767
During type inference all TVars in the term have negative index. This keeps
clasohm@0
   768
them apart from normal TVars, which is essential, because at the end the type
clasohm@0
   769
of the term is unified with the expected type, which contains normal TVars.
clasohm@0
   770
clasohm@0
   771
1. Add initial type information to the term (add_types).
clasohm@0
   772
   This freezes (freeze_vars) TVars in explicitly provided types (eg
clasohm@0
   773
   constraints or defaults) by turning them into TFrees.
clasohm@0
   774
2. Carry out type inference, possibly introducing new negative TVars.
clasohm@0
   775
3. Unify actual and expected type.
clasohm@0
   776
4. Turn all (negative) TVars into unique new TFrees (freeze).
clasohm@0
   777
5. Thaw all TVars frozen in step 1 (thaw_vars).
clasohm@0
   778
clasohm@0
   779
*)
clasohm@0
   780
clasohm@0
   781
(*Raised if types are not unifiable*)
clasohm@0
   782
exception TUNIFY;
clasohm@0
   783
clasohm@0
   784
val tyvar_count = ref(~1);
clasohm@0
   785
clasohm@0
   786
fun tyinit() = (tyvar_count := ~1);
clasohm@0
   787
clasohm@0
   788
fun new_tvar_inx() = (tyvar_count := !tyvar_count-1; !tyvar_count)
clasohm@0
   789
clasohm@0
   790
(*
clasohm@0
   791
Generate new TVar.  Index is < ~1 to distinguish it from TVars generated from
clasohm@0
   792
variable names (see id_type).  Name is arbitrary because index is new.
clasohm@0
   793
*)
clasohm@0
   794
wenzelm@256
   795
fun gen_tyvar(S) = TVar(("'a", new_tvar_inx()), S);
clasohm@0
   796
clasohm@0
   797
(*Occurs check: type variable occurs in type?*)
clasohm@0
   798
fun occ v tye =
wenzelm@256
   799
  let fun occ(Type(_, Ts)) = exists occ Ts
clasohm@0
   800
        | occ(TFree _) = false
wenzelm@256
   801
        | occ(TVar(w, _)) = v=w orelse
wenzelm@256
   802
                           (case assoc(tye, w) of
clasohm@0
   803
                              None   => false
clasohm@0
   804
                            | Some U => occ U);
clasohm@0
   805
  in occ end;
clasohm@0
   806
wenzelm@256
   807
(*Chase variable assignments in tye.
wenzelm@256
   808
  If devar (T, tye) returns a type var then it must be unassigned.*)
wenzelm@256
   809
fun devar (T as TVar(v, _), tye) = (case  assoc(tye, v)  of
wenzelm@256
   810
          Some U =>  devar (U, tye)
clasohm@0
   811
        | None   =>  T)
wenzelm@256
   812
  | devar (T, tye) = T;
clasohm@0
   813
clasohm@0
   814
clasohm@0
   815
(* 'dom' returns for a type constructor t the list of those domains
clasohm@0
   816
   which deliver a given range class C *)
clasohm@0
   817
wenzelm@256
   818
fun dom coreg t C = case assoc2 (coreg, (t, C)) of
clasohm@0
   819
    Some(Ss) => Ss
clasohm@0
   820
  | None => raise TUNIFY;
clasohm@0
   821
clasohm@0
   822
clasohm@0
   823
(* 'Dom' returns the union of all domain lists of 'dom' for a given sort S
clasohm@0
   824
   (i.e. a set of range classes ); the union is carried out elementwise
clasohm@0
   825
   for the seperate sorts in the domains *)
clasohm@0
   826
wenzelm@256
   827
fun Dom (subclass, coreg) (t, S) =
clasohm@0
   828
  let val domlist = map (dom coreg t) S;
clasohm@0
   829
  in if null domlist then []
wenzelm@256
   830
     else foldl (elementwise_union subclass) (hd domlist, tl domlist)
clasohm@0
   831
  end;
clasohm@0
   832
clasohm@0
   833
wenzelm@256
   834
fun W ((T, S), tsig as TySg{subclass, coreg, ...}, tye) =
wenzelm@256
   835
  let fun Wd ((T, S), tye) = W ((devar (T, tye), S), tsig, tye)
wenzelm@256
   836
      fun Wk(T as TVar(v, S')) =
wenzelm@256
   837
              if sortorder subclass (S', S) then tye
wenzelm@256
   838
              else (v, gen_tyvar(union_sort subclass (S', S)))::tye
wenzelm@256
   839
        | Wk(T as TFree(v, S')) = if sortorder subclass (S', S) then tye
wenzelm@256
   840
                                 else raise TUNIFY
wenzelm@256
   841
        | Wk(T as Type(f, Ts)) =
wenzelm@256
   842
           if null S then tye
wenzelm@256
   843
           else foldr Wd (Ts~~(Dom (subclass, coreg) (f, S)) , tye)
clasohm@0
   844
  in Wk(T) end;
clasohm@0
   845
clasohm@0
   846
clasohm@0
   847
(* Order-sorted Unification of Types (U)  *)
clasohm@0
   848
clasohm@0
   849
(* Precondition: both types are well-formed w.r.t. type constructor arities *)
wenzelm@256
   850
fun unify (tsig as TySg{subclass, coreg, ...}) =
wenzelm@256
   851
  let fun unif ((T, U), tye) =
wenzelm@256
   852
        case (devar(T, tye), devar(U, tye)) of
wenzelm@256
   853
          (T as TVar(v, S1), U as TVar(w, S2)) =>
clasohm@0
   854
             if v=w then tye else
wenzelm@256
   855
             if sortorder subclass (S1, S2) then (w, T)::tye else
wenzelm@256
   856
             if sortorder subclass (S2, S1) then (v, U)::tye
wenzelm@256
   857
             else let val nu = gen_tyvar (union_sort subclass (S1, S2))
wenzelm@256
   858
                  in (v, nu)::(w, nu)::tye end
wenzelm@256
   859
        | (T as TVar(v, S), U) =>
wenzelm@256
   860
             if occ v tye U then raise TUNIFY else W ((U, S), tsig, (v, U)::tye)
wenzelm@256
   861
        | (U, T as TVar (v, S)) =>
wenzelm@256
   862
             if occ v tye U then raise TUNIFY else W ((U, S), tsig, (v, U)::tye)
wenzelm@256
   863
        | (Type(a, Ts), Type(b, Us)) =>
wenzelm@256
   864
             if a<>b then raise TUNIFY else foldr unif (Ts~~Us, tye)
wenzelm@256
   865
        | (T, U) => if T=U then tye else raise TUNIFY
clasohm@0
   866
  in unif end;
clasohm@0
   867
clasohm@0
   868
clasohm@0
   869
(*Type inference for polymorphic term*)
clasohm@0
   870
fun infer tsig =
wenzelm@256
   871
  let fun inf(Ts, Const (_, T), tye) = (T, tye)
wenzelm@256
   872
        | inf(Ts, Free  (_, T), tye) = (T, tye)
wenzelm@256
   873
        | inf(Ts, Bound i, tye) = ((nth_elem(i, Ts) , tye)
clasohm@0
   874
          handle LIST _=> raise TYPE ("loose bound variable", [], [Bound i]))
wenzelm@256
   875
        | inf(Ts, Var (_, T), tye) = (T, tye)
wenzelm@256
   876
        | inf(Ts, Abs (_, T, body), tye) =
wenzelm@256
   877
            let val (U, tye') = inf(T::Ts, body, tye) in  (T-->U, tye')  end
clasohm@0
   878
        | inf(Ts, f$u, tye) =
wenzelm@256
   879
            let val (U, tyeU) = inf(Ts, u, tye);
wenzelm@256
   880
                val (T, tyeT) = inf(Ts, f, tyeU);
clasohm@0
   881
                fun err s =
clasohm@0
   882
                  raise TYPE(s, [inst_typ tyeT T, inst_typ tyeT U], [f$u])
wenzelm@256
   883
            in case T of
wenzelm@256
   884
                 Type("fun", [T1, T2]) =>
wenzelm@256
   885
                   ( (T2, unify tsig ((T1, U), tyeT))
clasohm@0
   886
                     handle TUNIFY => err"type mismatch in application" )
wenzelm@256
   887
               | TVar _ =>
clasohm@0
   888
                   let val T2 = gen_tyvar([])
clasohm@0
   889
                   in (T2, unify tsig ((T, U-->T2), tyeT))
clasohm@0
   890
                      handle TUNIFY => err"type mismatch in application"
clasohm@0
   891
                   end
clasohm@0
   892
               | _ => err"rator must have function type"
clasohm@0
   893
           end
clasohm@0
   894
  in inf end;
clasohm@0
   895
wenzelm@256
   896
fun freeze_vars(Type(a, Ts)) = Type(a, map freeze_vars Ts)
clasohm@0
   897
  | freeze_vars(T as TFree _) = T
wenzelm@256
   898
  | freeze_vars(TVar(v, S)) = TFree(Syntax.string_of_vname v, S);
clasohm@0
   899
clasohm@0
   900
(* Attach a type to a constant *)
wenzelm@256
   901
fun type_const (a, T) = Const(a, incr_tvar (new_tvar_inx()) T);
clasohm@0
   902
clasohm@0
   903
(*Find type of ident.  If not in table then use ident's name for tyvar
clasohm@0
   904
  to get consistent typing.*)
wenzelm@256
   905
fun new_id_type a = TVar(("'"^a, new_tvar_inx()), []);
wenzelm@256
   906
fun type_of_ixn(types, ixn as (a, _)) =
wenzelm@256
   907
        case types ixn of Some T => freeze_vars T | None => TVar(("'"^a, ~1), []);
clasohm@0
   908
wenzelm@256
   909
fun constrain(term, T) = Const(Syntax.constrainC, T-->T) $ term;
wenzelm@256
   910
fun constrainAbs(Abs(a, _, body), T) = Abs(a, T, body);
wenzelm@256
   911
clasohm@0
   912
clasohm@0
   913
(*
wenzelm@256
   914
  Attach types to a term. Input is a "parse tree" containing dummy types.
wenzelm@256
   915
  Type constraints are translated and checked for validity wrt tsig. TVars in
wenzelm@256
   916
  constraints are frozen.
clasohm@0
   917
wenzelm@256
   918
  The atoms in the resulting term satisfy the following spec:
clasohm@0
   919
wenzelm@256
   920
  Const (a, T):
wenzelm@256
   921
    T is a renamed copy of the generic type of a; renaming decreases index of
wenzelm@256
   922
    all TVars by new_tvar_inx(), which is less than ~1. The index of all
wenzelm@256
   923
    TVars in the generic type must be 0 for this to work!
clasohm@0
   924
wenzelm@256
   925
  Free (a, T), Var (ixn, T):
wenzelm@256
   926
    T is either the frozen default type of a or TVar (("'"^a, ~1), [])
clasohm@0
   927
wenzelm@256
   928
  Abs (a, T, _):
wenzelm@256
   929
    T is either a type constraint or TVar (("'" ^ a, i), []), where i is
wenzelm@256
   930
    generated by new_tvar_inx(). Thus different abstractions can have the
wenzelm@256
   931
    bound variables of the same name but different types.
clasohm@0
   932
*)
clasohm@0
   933
wenzelm@256
   934
(* FIXME replace const_tab by (const_typ: string -> typ option) (?) *)
wenzelm@256
   935
(* FIXME improve handling of sort constraints *)
wenzelm@256
   936
wenzelm@256
   937
fun add_types (tsig, const_tab, types, sorts) =
wenzelm@256
   938
  let
wenzelm@256
   939
    val S0 = defaultS tsig;
wenzelm@256
   940
    fun defS0 ixn = if_none (sorts ixn) S0;
wenzelm@256
   941
wenzelm@256
   942
    fun prepareT typ =
wenzelm@256
   943
      freeze_vars (cert_typ tsig (Syntax.typ_of_term defS0 typ));
wenzelm@256
   944
wenzelm@256
   945
    fun add (Const (a, _)) =
wenzelm@256
   946
          (case Symtab.lookup (const_tab, a) of
wenzelm@256
   947
            Some T => type_const (a, T)
wenzelm@256
   948
          | None => raise_type ("No such constant: " ^ quote a) [] [])
wenzelm@256
   949
      | add (Bound i) = Bound i
wenzelm@256
   950
      | add (Free (a, _)) =
wenzelm@256
   951
          (case Symtab.lookup (const_tab, a) of
wenzelm@256
   952
            Some T => type_const (a, T)
wenzelm@256
   953
          | None => Free (a, type_of_ixn (types, (a, ~1))))
wenzelm@256
   954
      | add (Var (ixn, _)) = Var (ixn, type_of_ixn (types, ixn))
wenzelm@256
   955
      | add (Abs (a, _, body)) = Abs (a, new_id_type a, add body)
wenzelm@256
   956
      | add ((f as Const (a, _) $ t1) $ t2) =
wenzelm@256
   957
          if a = Syntax.constrainC then
wenzelm@256
   958
            constrain (add t1, prepareT t2)
wenzelm@256
   959
          else if a = Syntax.constrainAbsC then
wenzelm@256
   960
            constrainAbs (add t1, prepareT t2)
wenzelm@256
   961
          else add f $ add t2
wenzelm@256
   962
      | add (f $ t) = add f $ add t;
wenzelm@256
   963
  in add end;
clasohm@0
   964
clasohm@0
   965
clasohm@0
   966
(* Post-Processing *)
clasohm@0
   967
clasohm@0
   968
clasohm@0
   969
(*Instantiation of type variables in terms*)
clasohm@0
   970
fun inst_types tye = map_term_types (inst_typ tye);
clasohm@0
   971
clasohm@0
   972
(*Delete explicit constraints -- occurrences of "_constrain" *)
wenzelm@256
   973
fun unconstrain (Abs(a, T, t)) = Abs(a, T, unconstrain t)
wenzelm@256
   974
  | unconstrain ((f as Const(a, _)) $ t) =
clasohm@0
   975
      if a=Syntax.constrainC then unconstrain t
clasohm@0
   976
      else unconstrain f $ unconstrain t
clasohm@0
   977
  | unconstrain (f$t) = unconstrain f $ unconstrain t
clasohm@0
   978
  | unconstrain (t) = t;
clasohm@0
   979
clasohm@0
   980
clasohm@0
   981
(* Turn all TVars which satisfy p into new TFrees *)
clasohm@0
   982
fun freeze p t =
wenzelm@256
   983
  let val fs = add_term_tfree_names(t, []);
wenzelm@256
   984
      val inxs = filter p (add_term_tvar_ixns(t, []));
clasohm@0
   985
      val vmap = inxs ~~ variantlist(map #1 inxs, fs);
wenzelm@256
   986
      fun free(Type(a, Ts)) = Type(a, map free Ts)
wenzelm@256
   987
        | free(T as TVar(v, S)) =
wenzelm@256
   988
            (case assoc(vmap, v) of None => T | Some(a) => TFree(a, S))
clasohm@0
   989
        | free(T as TFree _) = T
clasohm@0
   990
  in map_term_types free t end;
clasohm@0
   991
clasohm@0
   992
(* Thaw all TVars that were frozen in freeze_vars *)
wenzelm@256
   993
fun thaw_vars(Type(a, Ts)) = Type(a, map thaw_vars Ts)
wenzelm@256
   994
  | thaw_vars(T as TFree(a, S)) = (case explode a of
wenzelm@256
   995
          "?"::"'"::vn => let val ((b, i), _) = Syntax.scan_varname vn
wenzelm@256
   996
                          in TVar(("'"^b, i), S) end
wenzelm@256
   997
        | _ => T)
clasohm@0
   998
  | thaw_vars(T) = T;
clasohm@0
   999
clasohm@0
  1000
clasohm@0
  1001
fun restrict tye =
wenzelm@256
  1002
  let fun clean(tye1, ((a, i), T)) =
wenzelm@256
  1003
        if i < 0 then tye1 else ((a, i), inst_typ tye T) :: tye1
wenzelm@256
  1004
  in foldl clean ([], tye) end
clasohm@0
  1005
clasohm@0
  1006
clasohm@0
  1007
(*Infer types for term t using tables. Check that t's type and T unify *)
clasohm@0
  1008
wenzelm@256
  1009
fun infer_term (tsig, const_tab, types, sorts, T, t) =
wenzelm@256
  1010
  let val u = add_types (tsig, const_tab, types, sorts) t;
wenzelm@256
  1011
      val (U, tye) = infer tsig ([], u, []);
clasohm@0
  1012
      val uu = unconstrain u;
wenzelm@256
  1013
      val tye' = unify tsig ((T, U), tye) handle TUNIFY => raise TYPE
wenzelm@256
  1014
        ("Term does not have expected type", [T, U], [inst_types tye uu])
clasohm@0
  1015
      val Ttye = restrict tye' (* restriction to TVars in T *)
clasohm@0
  1016
      val all = Const("", Type("", map snd Ttye)) $ (inst_types tye' uu)
clasohm@0
  1017
        (* all is a dummy term which contains all exported TVars *)
wenzelm@256
  1018
      val Const(_, Type(_, Ts)) $ u'' =
wenzelm@256
  1019
            map_term_types thaw_vars (freeze (fn (_, i) => i<0) all)
clasohm@0
  1020
        (* turn all internally generated TVars into TFrees
clasohm@0
  1021
           and thaw all initially frozen TVars *)
clasohm@0
  1022
  in (u'', (map fst Ttye) ~~ Ts) end;
clasohm@0
  1023
clasohm@0
  1024
fun infer_types args = (tyinit(); infer_term args);
clasohm@0
  1025
clasohm@0
  1026
clasohm@0
  1027
(* Turn TFrees into TVars to allow types & axioms to be written without "?" *)
wenzelm@256
  1028
fun varifyT (Type (a, Ts)) = Type (a, map varifyT Ts)
wenzelm@256
  1029
  | varifyT (TFree (a, S)) = TVar ((a, 0), S)
wenzelm@256
  1030
  | varifyT T = T;
clasohm@0
  1031
clasohm@0
  1032
(* Turn TFrees except those in fixed into new TVars *)
wenzelm@256
  1033
fun varify (t, fixed) =
wenzelm@256
  1034
  let val fs = add_term_tfree_names(t, []) \\ fixed;
wenzelm@256
  1035
      val ixns = add_term_tvar_ixns(t, []);
clasohm@0
  1036
      val fmap = fs ~~ variantlist(fs, map #1 ixns)
wenzelm@256
  1037
      fun thaw(Type(a, Ts)) = Type(a, map thaw Ts)
clasohm@0
  1038
        | thaw(T as TVar _) = T
wenzelm@256
  1039
        | thaw(T as TFree(a, S)) =
wenzelm@256
  1040
            (case assoc(fmap, a) of None => T | Some b => TVar((b, 0), S))
clasohm@0
  1041
  in map_term_types thaw t end;
clasohm@0
  1042
clasohm@0
  1043
clasohm@0
  1044
end;
wenzelm@256
  1045