(* Title: Pure/defs.ML
Author: Makarius
Global well-formedness checks for constant definitions. Covers plain
definitions and simple sub-structural overloading.
*)
signature DEFS =
sig
val pretty_const: Proof.context -> string * typ list -> Pretty.T
val plain_args: typ list -> bool
type T
type spec =
{def: string option, description: string, lhs: typ list, rhs: (string * typ list) list}
val all_specifications_of: T -> (string * spec list) list
val specifications_of: T -> string -> spec list
val dest: T ->
{restricts: ((string * typ list) * string) list,
reducts: ((string * typ list) * (string * typ list) list) list}
val empty: T
val merge: Proof.context -> T * T -> T
val define: Proof.context -> bool -> string option -> string ->
string * typ list -> (string * typ list) list -> T -> T
end
structure Defs: DEFS =
struct
(* type arguments *)
type args = typ list;
fun pretty_const ctxt (c, args) =
let
val prt_args =
if null args then []
else [Pretty.list "(" ")" (map (Syntax.pretty_typ ctxt o Logic.unvarifyT_global) args)];
in Pretty.block (Pretty.str c :: prt_args) end;
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
((Type.raw_unifys (Ts, map (Logic.incr_tvar (maxidx_of_typs Ts + 1)) Us) Vartab.empty; false)
handle Type.TUNIFY => true);
fun match_args (Ts, Us) =
Option.map Envir.subst_type
(SOME (Type.raw_matches (Ts, Us) Vartab.empty) handle Type.TYPE_MATCH => NONE);
(* datatype defs *)
type spec =
{def: string option, description: string, lhs: args, rhs: (string * args) list};
type def =
{specs: spec Inttab.table, (*source specifications*)
restricts: (args * string) list, (*global restrictions imposed by incomplete patterns*)
reducts: (args * (string * args) list) list}; (*specifications as reduction system*)
fun make_def (specs, restricts, reducts) =
{specs = specs, restricts = restricts, reducts = reducts}: def;
fun map_def c f =
Symtab.default (c, make_def (Inttab.empty, [], [])) #>
Symtab.map_entry c (fn {specs, restricts, reducts}: def =>
make_def (f (specs, restricts, reducts)));
datatype T = Defs of def Symtab.table;
fun lookup_list which defs c =
(case Symtab.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) (Symtab.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 = Symtab.fold (fn (c, {restricts, ...}) =>
fold (fn (args, description) => cons ((c, args), description)) restricts) defs [];
val reducts = Symtab.fold (fn (c, {reducts, ...}) =>
fold (fn (args, deps) => cons ((c, args), deps)) reducts) defs [];
in {restricts = restricts, reducts = reducts} end;
val empty = Defs Symtab.empty;
(* specifications *)
fun disjoint_specs c (i, {lhs = Ts, description = a, ...}: spec) =
Inttab.forall (fn (j, {lhs = Us, description = b, ...}: spec) =>
i = j orelse disjoint_args (Ts, Us) orelse
error ("Clash of specifications " ^ quote a ^ " and " ^ quote b ^
" for constant " ^ quote c));
fun join_specs c ({specs = specs1, restricts, reducts}, {specs = specs2, ...}: def) =
let
val specs' =
Inttab.fold (fn spec2 => (disjoint_specs c spec2 specs1; Inttab.update spec2)) specs2 specs1;
in make_def (specs', restricts, reducts) end;
fun update_specs c spec = map_def c (fn (specs, restricts, reducts) =>
(disjoint_specs c spec specs; (Inttab.update spec specs, restricts, reducts)));
(* normalized dependencies: reduction with well-formedness check *)
local
val prt = Pretty.string_of oo pretty_const;
fun err ctxt (c, args) (d, Us) s1 s2 =
error (s1 ^ " dependency of constant " ^ prt ctxt (c, args) ^ " -> " ^ prt ctxt (d, Us) ^ s2);
fun contained (U as TVar _) (Type (_, Ts)) = exists (fn T => T = U orelse contained U T) Ts
| contained _ _ = false;
fun acyclic ctxt (c, args) (d, Us) =
c <> d orelse
exists (fn U => exists (contained U) args) Us orelse
is_none (match_args (args, Us)) orelse
err ctxt (c, args) (d, Us) "Circular" "";
fun wellformed ctxt defs (c, args) (d, Us) =
forall is_TVar Us orelse
(case find_first (fn (Ts, _) => not (disjoint_args (Ts, Us))) (restricts_of defs d) of
SOME (Ts, description) =>
err ctxt (c, args) (d, Us) "Malformed"
("\n(restriction " ^ prt ctxt (d, Ts) ^ " from " ^ quote description ^ ")")
| NONE => true);
fun reduction ctxt 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 ctxt const) (the_default deps deps');
in deps' end;
in
fun normalize ctxt =
let
fun norm_update (c, {reducts, ...}: def) (changed, defs) =
let
val reducts' = reducts |> map (fn (args, deps) =>
(args, perhaps (reduction ctxt defs (c, args)) deps));
in
if reducts = reducts' then (changed, defs)
else (true, defs |> map_def c (fn (specs, restricts, _) => (specs, restricts, reducts')))
end;
fun norm_all defs =
(case Symtab.fold norm_update defs (false, defs) of
(true, defs') => norm_all defs'
| (false, _) => defs);
fun check defs (c, {reducts, ...}: def) =
reducts |> forall (fn (args, deps) => forall (wellformed ctxt defs (c, args)) deps);
in norm_all #> (fn defs => tap (Symtab.forall (check defs)) defs) end;
fun dependencies ctxt (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 ctxt;
end;
(* merge *)
fun merge ctxt (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 ctxt (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 (Symtab.join join_specs (defs1, defs2)
|> normalize ctxt |> Symtab.fold add_def defs2)
end;
(* define *)
fun define ctxt unchecked def description (c, args) deps (Defs defs) =
let
val restr =
if plain_args args orelse
(case args of [Type (_, rec_args)] => plain_args rec_args | _ => false)
then [] else [(args, description)];
val spec =
(serial (), {def = def, description = description, lhs = args, rhs = deps});
val defs' = defs |> update_specs c spec;
in Defs (defs' |> (if unchecked then I else dependencies ctxt (c, args) restr deps)) end;
end;