src/Pure/defs.ML

clarified signature;

(*  Title:      Pure/defs.ML
    Author:     Makarius

Global well-formedness checks for overloaded definitions (mixed constants and
types). Recall that constant definitions may be explained syntactically within
Pure, but type definitions require particular set-theoretic semantics.
*)

signature DEFS =
sig
  datatype item_kind = Const | Type
  type item = item_kind * string
  type entry = item * typ list
  val item_kind_ord: item_kind ord
  val plain_args: typ list -> bool
  type context = Proof.context * (Name_Space.T * Name_Space.T)
  val global_context: theory -> context
  val space: context -> item_kind -> Name_Space.T
  val pretty_item: context -> item -> Pretty.T
  val pretty_args: Proof.context -> typ list -> Pretty.T list
  val pretty_entry: context -> entry -> Pretty.T
  type T
  type spec =
   {def: string option,
    description: string,
    pos: Position.T,
    lhs: typ list,
    rhs: entry list}
  val all_specifications_of: T -> (item * spec list) list
  val specifications_of: T -> item -> spec list
  val dest: T ->
   {restricts: (entry * string) list,
    reducts: (entry * entry list) list}
  val dest_constdefs: T list -> T -> (string * string) list
  val empty: T
  val merge: context -> T * T -> T
  val define: context -> bool -> string option -> string -> entry -> entry list -> T -> T
  val get_deps: T -> item -> (typ list * entry list) list
end;

structure Defs: DEFS =
struct

(* specification items *)

datatype item_kind = Const | Type;
type item = item_kind * string;
type entry = item * typ list;

fun item_kind_ord (Const, Type) = LESS
  | item_kind_ord (Type, Const) = GREATER
  | item_kind_ord _ = EQUAL;

structure Itemtab = Table(type key = item val ord = prod_ord item_kind_ord fast_string_ord);


(* pretty printing *)

type context = Proof.context * (Name_Space.T * Name_Space.T);

fun global_context thy =
  (Syntax.init_pretty_global thy, (Sign.const_space thy, Sign.type_space thy));

fun space ((_, spaces): context) kind =
  if kind = Const then #1 spaces else #2 spaces;

fun pretty_item (context as (ctxt, _)) (kind, name) =
  let val prt_name = Name_Space.pretty ctxt (space context kind) name in
    if kind = Const then prt_name
    else Pretty.block [Pretty.keyword1 "type", Pretty.brk 1, prt_name]
  end;

fun pretty_args ctxt args =
  if null args then []
  else [Pretty.list "(" ")" (map (Syntax.pretty_typ ctxt o Logic.unvarifyT_global) args)];

fun pretty_entry context (c, args) =
  Pretty.block (pretty_item context c :: pretty_args (#1 context) args);


(* type arguments *)

fun plain_args args =
  forall Term.is_TVar args andalso not (has_duplicates (op =) args);

fun disjoint_args (Ts, Us) =
  not (Type.could_unifys (Ts, Us)) orelse
    ((Vartab.build (Type.raw_unifys (Ts, map (Logic.incr_tvar (maxidx_of_typs Ts + 1)) Us)); false)
      handle Type.TUNIFY => true);

fun match_args (Ts, Us) =
  if Type.could_matches (Ts, Us) then
    Option.map Envir.subst_type
      (SOME (Vartab.build (Type.raw_matches (Ts, Us))) handle Type.TYPE_MATCH => NONE)
  else NONE;


(* datatype defs *)

type spec =
 {def: string option,
  description: string,
  pos: Position.T,
  lhs: typ list,
  rhs: entry list};

type def =
 {specs: spec Inttab.table,  (*source specifications*)
  restricts: (typ list * string) list,  (*global restrictions imposed by incomplete patterns*)
  reducts: (typ list * entry list) list};  (*specifications as reduction system*)

fun make_def (specs, restricts, reducts) =
  {specs = specs, restricts = restricts, reducts = reducts}: def;

fun map_def c f =
  Itemtab.default (c, make_def (Inttab.empty, [], [])) #>
  Itemtab.map_entry c (fn {specs, restricts, reducts}: def =>
    make_def (f (specs, restricts, reducts)));


datatype T = Defs of def Itemtab.table;

fun lookup_list which defs c =
  (case Itemtab.lookup defs c of
    SOME (def: def) => which def
  | NONE => []);

fun all_specifications_of (Defs defs) =
  (map o apsnd) (map snd o Inttab.dest o #specs) (Itemtab.dest defs);

fun specifications_of (Defs defs) = lookup_list (map snd o Inttab.dest o #specs) defs;

val restricts_of = lookup_list #restricts;
val reducts_of = lookup_list #reducts;

fun dest (Defs defs) =
  let
    val restricts = Itemtab.fold (fn (c, {restricts, ...}) =>
      fold (fn (args, description) => cons ((c, args), description)) restricts) defs [];
    val reducts = Itemtab.fold (fn (c, {reducts, ...}) =>
      fold (fn (args, deps) => cons ((c, args), deps)) reducts) defs [];
  in {restricts = restricts, reducts = reducts} end;

fun dest_constdefs prevs (Defs defs) =
  let
    fun prev_spec c i = prevs |> exists (fn Defs prev_defs =>
      (case Itemtab.lookup prev_defs c of
        NONE => false
      | SOME {specs, ...} => Inttab.defined specs i));
  in
    build (defs |> Itemtab.fold (fn (c, {specs, ...}) =>
      specs |> Inttab.fold (fn (i, spec) =>
        if #1 c = Const andalso is_some (#def spec) andalso not (prev_spec c i)
        then cons (#2 c, the (#def spec)) else I)))
  end;

val empty = Defs Itemtab.empty;


(* specifications *)

fun disjoint_specs context c (i, {description = a, pos = pos_a, lhs = Ts, ...}: spec) =
  Inttab.forall (fn (j, {description = b, pos = pos_b, lhs = Us, ...}: spec) =>
    i = j orelse disjoint_args (Ts, Us) orelse
      error ("Clash of specifications for " ^
        Pretty.unformatted_string_of (pretty_item context c) ^ ":\n" ^
        "  " ^ quote a ^ Position.here pos_a ^ "\n" ^
        "  " ^ quote b ^ Position.here pos_b));

fun join_specs context c ({specs = specs1, restricts, reducts}, {specs = specs2, ...}: def) =
  let
    val specs' =
      Inttab.fold (fn spec2 => (disjoint_specs context c spec2 specs1; Inttab.update spec2))
        specs2 specs1;
  in make_def (specs', restricts, reducts) end;

fun update_specs context c spec = map_def c (fn (specs, restricts, reducts) =>
  (disjoint_specs context c spec specs; (Inttab.update spec specs, restricts, reducts)));


(* normalized dependencies: reduction with well-formedness check *)

local

val prt = Pretty.string_of oo pretty_entry;

fun err context (c, Ts) (d, Us) s1 s2 =
  error (s1 ^ " dependency of " ^ prt context (c, Ts) ^ " -> " ^ prt context (d, Us) ^ s2);

fun acyclic context (c, Ts) (d, Us) =
  c <> d orelse
  is_none (match_args (Ts, Us)) orelse
  err context (c, Ts) (d, Us) "Circular" "";

fun reduction context defs const deps =
  let
    fun reduct Us (Ts, rhs) =
      (case match_args (Ts, Us) of
        NONE => NONE
      | SOME subst => SOME (map (apsnd (map subst)) rhs));
    fun reducts (d, Us) = get_first (reduct Us) (reducts_of defs d);

    val reds = map (`reducts) deps;
    val deps' =
      if forall (is_none o #1) reds then NONE
      else SOME (fold_rev
        (fn (NONE, dp) => insert (op =) dp | (SOME dps, _) => fold (insert (op =)) dps) reds []);
    val _ = forall (acyclic context const) (the_default deps deps');
  in deps' end;

fun restriction context defs (c, Ts) (d, Us) =
  plain_args Us orelse
  (case find_first (fn (Rs, _) => not (disjoint_args (Rs, Us))) (restricts_of defs d) of
    SOME (Rs, description) =>
      err context (c, Ts) (d, Us) "Malformed"
        ("\n(restriction " ^ prt context (d, Rs) ^ " from " ^ quote description ^ ")")
  | NONE => true);

in

fun normalize context =
  let
    fun check_def defs (c, {reducts, ...}: def) =
      reducts |> forall (fn (Ts, deps) => forall (restriction context defs (c, Ts)) deps);
    fun check_defs defs = Itemtab.forall (check_def defs) defs;

    fun norm_update (c, {reducts, ...}: def) (changed, defs) =
      let
        val reducts' = reducts |> map (fn (Ts, deps) =>
          (Ts, perhaps (reduction context defs (c, Ts)) deps));
      in
        if reducts = reducts' then (changed, defs)
        else (true, defs |> map_def c (fn (specs, restricts, _) => (specs, restricts, reducts')))
      end;
    fun norm_loop defs =
      (case Itemtab.fold norm_update defs (false, defs) of
        (true, defs') => norm_loop defs'
      | (false, _) => defs);
  in norm_loop #> tap check_defs end;

fun dependencies context (c, args) restr deps =
  map_def c (fn (specs, restricts, reducts) =>
    let
      val restricts' = Library.merge (op =) (restricts, restr);
      val reducts' = insert (op =) (args, deps) reducts;
    in (specs, restricts', reducts') end)
  #> normalize context;

end;


(* merge *)

fun merge context (Defs defs1, Defs defs2) =
  let
    fun add_deps (c, args) restr deps defs =
      if AList.defined (op =) (reducts_of defs c) args then defs
      else dependencies context (c, args) restr deps defs;
    fun add_def (c, {restricts, reducts, ...}: def) =
      fold (fn (args, deps) => add_deps (c, args) restricts deps) reducts;
  in
    Defs (Itemtab.join (join_specs context) (defs1, defs2)
      |> normalize context |> Itemtab.fold add_def defs2)
  end;


(* define *)

fun define context unchecked def description (c, args) deps (Defs defs) =
  let
    val pos = Position.thread_data ();
    val restr =
      if plain_args args orelse
        (case args of [Term.Type (_, rec_args)] => plain_args rec_args | _ => false)
      then [] else [(args, description)];
    val spec =
      (serial (), {def = def, description = description, pos = pos, lhs = args, rhs = deps});
    val defs' = defs |> update_specs context c spec;
  in Defs (defs' |> (if unchecked then I else dependencies context (c, args) restr deps)) end;

fun get_deps (Defs defs) c = reducts_of defs c;

end;