(* Title: HOLCF/Tools/Domain/domain_extender.ML
Author: David von Oheimb
Theory extender for domain command, including theory syntax.
*)
signature DOMAIN_EXTENDER =
sig
val add_domain_cmd:
string ->
((string * string option) list * binding * mixfix *
(binding * (bool * binding option * string) list * mixfix) list) list
-> theory -> theory
val add_domain:
string ->
((string * string option) list * binding * mixfix *
(binding * (bool * binding option * typ) list * mixfix) list) list
-> theory -> theory
val add_new_domain_cmd:
string ->
((string * string option) list * binding * mixfix *
(binding * (bool * binding option * string) list * mixfix) list) list
-> theory -> theory
val add_new_domain:
string ->
((string * string option) list * binding * mixfix *
(binding * (bool * binding option * typ) list * mixfix) list) list
-> theory -> theory
end;
structure Domain_Extender :> DOMAIN_EXTENDER =
struct
open Domain_Library;
(* ----- general testing and preprocessing of constructor list -------------- *)
fun check_and_sort_domain
(definitional : bool)
(dtnvs : (string * typ list) list)
(cons'' : (binding * (bool * binding option * typ) list * mixfix) list list)
(thy : theory)
: ((string * typ list) *
(binding * (bool * binding option * typ) list * mixfix) list) list =
let
val defaultS = Sign.defaultS thy;
val test_dupl_typs =
case duplicates (op =) (map fst dtnvs) of
[] => false | dups => error ("Duplicate types: " ^ commas_quote dups);
val all_cons = map (Binding.name_of o first) (flat cons'');
val test_dupl_cons =
case duplicates (op =) all_cons of
[] => false | dups => error ("Duplicate constructors: "
^ commas_quote dups);
val all_sels =
(map Binding.name_of o map_filter second o maps second) (flat cons'');
val test_dupl_sels =
case duplicates (op =) all_sels of
[] => false | dups => error("Duplicate selectors: "^commas_quote dups);
fun test_dupl_tvars s =
case duplicates (op =) (map(fst o dest_TFree)s) of
[] => false | dups => error("Duplicate type arguments: "
^commas_quote dups);
val test_dupl_tvars' = exists test_dupl_tvars (map snd dtnvs);
(* test for free type variables, illegal sort constraints on rhs,
non-pcpo-types and invalid use of recursive type;
replace sorts in type variables on rhs *)
fun analyse_equation ((dname,typevars),cons') =
let
val tvars = map dest_TFree typevars;
val distinct_typevars = map TFree tvars;
fun rm_sorts (TFree(s,_)) = TFree(s,[])
| rm_sorts (Type(s,ts)) = Type(s,remove_sorts ts)
| rm_sorts (TVar(s,_)) = TVar(s,[])
and remove_sorts l = map rm_sorts l;
val indirect_ok = ["*","Cfun.->","Ssum.++","Sprod.**","Up.u"]
fun analyse indirect (TFree(v,s)) =
(case AList.lookup (op =) tvars v of
NONE => error ("Free type variable " ^ quote v ^ " on rhs.")
| SOME sort => if eq_set (op =) (s, defaultS) orelse
eq_set (op =) (s, sort)
then TFree(v,sort)
else error ("Inconsistent sort constraint" ^
" for type variable " ^ quote v))
| analyse indirect (t as Type(s,typl)) =
(case AList.lookup (op =) dtnvs s of
NONE =>
if definitional orelse s mem indirect_ok
then Type(s,map (analyse false) typl)
else Type(s,map (analyse true) typl)
| SOME typevars =>
if indirect
then error ("Indirect recursion of type " ^
quote (string_of_typ thy t))
else if dname <> s orelse
(** BUG OR FEATURE?:
mutual recursion may use different arguments **)
remove_sorts typevars = remove_sorts typl
then Type(s,map (analyse true) typl)
else error ("Direct recursion of type " ^
quote (string_of_typ thy t) ^
" with different arguments"))
| analyse indirect (TVar _) = Imposs "extender:analyse";
fun check_pcpo lazy T =
let val ok = if lazy then cpo_type else pcpo_type
in if ok thy T then T
else error ("Constructor argument type is not of sort pcpo: " ^
string_of_typ thy T)
end;
fun analyse_arg (lazy, sel, T) =
(lazy, sel, check_pcpo lazy (analyse false T));
fun analyse_con (b, args, mx) = (b, map analyse_arg args, mx);
in ((dname,distinct_typevars), map analyse_con cons') end;
in ListPair.map analyse_equation (dtnvs,cons'')
end; (* let *)
(* ----- calls for building new thy and thms -------------------------------- *)
fun gen_add_domain
(prep_typ : theory -> 'a -> typ)
(comp_dnam : string)
(eqs''' : ((string * string option) list * binding * mixfix *
(binding * (bool * binding option * 'a) list * mixfix) list) list)
(thy''' : theory) =
let
fun readS (SOME s) = Syntax.read_sort_global thy''' s
| readS NONE = Sign.defaultS thy''';
fun readTFree (a, s) = TFree (a, readS s);
val dtnvs = map (fn (vs,dname:binding,mx,_) =>
(dname, map readTFree vs, mx)) eqs''';
val cons''' = map (fn (_,_,_,cons) => cons) eqs''';
fun thy_type (dname,tvars,mx) = (dname, length tvars, mx);
fun thy_arity (dname,tvars,mx) =
(Sign.full_name thy''' dname, map (snd o dest_TFree) tvars, pcpoS);
val thy'' =
thy'''
|> Sign.add_types (map thy_type dtnvs)
|> fold (AxClass.axiomatize_arity o thy_arity) dtnvs;
val cons'' =
map (map (upd_second (map (upd_third (prep_typ thy''))))) cons''';
val dtnvs' =
map (fn (dname,vs,mx) => (Sign.full_name thy''' dname,vs)) dtnvs;
val eqs' : ((string * typ list) *
(binding * (bool * binding option * typ) list * mixfix) list) list =
check_and_sort_domain false dtnvs' cons'' thy'';
val thy' = thy'' |> Domain_Syntax.add_syntax false comp_dnam eqs';
val dts = map (Type o fst) eqs';
val new_dts = map (fn ((s,Ts),_) => (s, map (fst o dest_TFree) Ts)) eqs';
fun strip ss = (uncurry drop) (find_index (fn s => s = "'") ss + 1, ss);
fun typid (Type (id,_)) =
let val c = hd (Symbol.explode (Long_Name.base_name id))
in if Symbol.is_letter c then c else "t" end
| typid (TFree (id,_) ) = hd (strip (tl (Symbol.explode id)))
| typid (TVar ((id,_),_)) = hd (tl (Symbol.explode id));
fun one_con (con,args,mx) =
((Syntax.const_name mx (Binding.name_of con)),
ListPair.map (fn ((lazy,sel,tp),vn) =>
mk_arg ((lazy, DatatypeAux.dtyp_of_typ new_dts tp),
Option.map Binding.name_of sel,vn))
(args,(mk_var_names(map (typid o third) args)))
) : cons;
val eqs : eq list =
map (fn (dtnvs,cons') => (dtnvs, map one_con cons')) eqs';
val thy = thy' |> Domain_Axioms.add_axioms false comp_dnam eqs;
val ((rewss, take_rews), theorems_thy) =
thy
|> fold_map (fn eq => Domain_Theorems.theorems (eq, eqs)) eqs
||>> Domain_Theorems.comp_theorems (comp_dnam, eqs);
in
theorems_thy
|> Sign.add_path (Long_Name.base_name comp_dnam)
|> PureThy.add_thmss
[((Binding.name "rews", flat rewss @ take_rews), [])]
|> snd
|> Sign.parent_path
end;
fun gen_add_new_domain
(prep_typ : theory -> 'a -> typ)
(comp_dnam : string)
(eqs''' : ((string * string option) list * binding * mixfix *
(binding * (bool * binding option * 'a) list * mixfix) list) list)
(thy''' : theory) =
let
fun readS (SOME s) = Syntax.read_sort_global thy''' s
| readS NONE = Sign.defaultS thy''';
fun readTFree (a, s) = TFree (a, readS s);
val dtnvs = map (fn (vs,dname:binding,mx,_) =>
(dname, map readTFree vs, mx)) eqs''';
val cons''' = map (fn (_,_,_,cons) => cons) eqs''';
fun thy_type (dname,tvars,mx) = (dname, length tvars, mx);
fun thy_arity (dname,tvars,mx) =
(Sign.full_name thy''' dname, map (snd o dest_TFree) tvars, @{sort rep});
(* this theory is used just for parsing and error checking *)
val tmp_thy = thy'''
|> Theory.copy
|> Sign.add_types (map thy_type dtnvs)
|> fold (AxClass.axiomatize_arity o thy_arity) dtnvs;
val cons'' : (binding * (bool * binding option * typ) list * mixfix) list list =
map (map (upd_second (map (upd_third (prep_typ tmp_thy))))) cons''';
val dtnvs' : (string * typ list) list =
map (fn (dname,vs,mx) => (Sign.full_name thy''' dname,vs)) dtnvs;
val eqs' : ((string * typ list) *
(binding * (bool * binding option * typ) list * mixfix) list) list =
check_and_sort_domain true dtnvs' cons'' tmp_thy;
fun mk_arg_typ (lazy, dest_opt, T) = if lazy then mk_uT T else T;
fun mk_con_typ (bind, args, mx) =
if null args then oneT else foldr1 mk_sprodT (map mk_arg_typ args);
fun mk_eq_typ (_, cons) = foldr1 mk_ssumT (map mk_con_typ cons);
val thy'' = thy''' |>
Domain_Isomorphism.domain_isomorphism
(map (fn ((vs, dname, mx, _), eq) =>
(map fst vs, dname, mx, mk_eq_typ eq))
(eqs''' ~~ eqs'))
val thy' = thy'' |> Domain_Syntax.add_syntax true comp_dnam eqs';
val dts = map (Type o fst) eqs';
val new_dts = map (fn ((s,Ts),_) => (s, map (fst o dest_TFree) Ts)) eqs';
fun strip ss = (uncurry drop) (find_index (fn s => s = "'") ss + 1, ss);
fun typid (Type (id,_)) =
let val c = hd (Symbol.explode (Long_Name.base_name id))
in if Symbol.is_letter c then c else "t" end
| typid (TFree (id,_) ) = hd (strip (tl (Symbol.explode id)))
| typid (TVar ((id,_),_)) = hd (tl (Symbol.explode id));
fun one_con (con,args,mx) =
((Syntax.const_name mx (Binding.name_of con)),
ListPair.map (fn ((lazy,sel,tp),vn) =>
mk_arg ((lazy, DatatypeAux.dtyp_of_typ new_dts tp),
Option.map Binding.name_of sel,vn))
(args,(mk_var_names(map (typid o third) args)))
) : cons;
val eqs : eq list =
map (fn (dtnvs,cons') => (dtnvs, map one_con cons')) eqs';
val thy = thy' |> Domain_Axioms.add_axioms true comp_dnam eqs;
val ((rewss, take_rews), theorems_thy) =
thy
|> fold_map (fn eq => Domain_Theorems.theorems (eq, eqs)) eqs
||>> Domain_Theorems.comp_theorems (comp_dnam, eqs);
in
theorems_thy
|> Sign.add_path (Long_Name.base_name comp_dnam)
|> PureThy.add_thmss
[((Binding.name "rews", flat rewss @ take_rews), [])]
|> snd
|> Sign.parent_path
end;
val add_domain = gen_add_domain Sign.certify_typ;
val add_domain_cmd = gen_add_domain Syntax.read_typ_global;
val add_new_domain = gen_add_new_domain Sign.certify_typ;
val add_new_domain_cmd = gen_add_new_domain Syntax.read_typ_global;
(** outer syntax **)
local structure P = OuterParse and K = OuterKeyword in
val _ = OuterKeyword.keyword "lazy";
val dest_decl : (bool * binding option * string) parser =
P.$$$ "(" |-- Scan.optional (P.$$$ "lazy" >> K true) false --
(P.binding >> SOME) -- (P.$$$ "::" |-- P.typ) --| P.$$$ ")" >> P.triple1
|| P.$$$ "(" |-- P.$$$ "lazy" |-- P.typ --| P.$$$ ")"
>> (fn t => (true,NONE,t))
|| P.typ >> (fn t => (false,NONE,t));
val cons_decl =
P.binding -- Scan.repeat dest_decl -- P.opt_mixfix;
val type_var' : (string * string option) parser =
(P.type_ident -- Scan.option (P.$$$ "::" |-- P.!!! P.sort));
val type_args' : (string * string option) list parser =
type_var' >> single
|| P.$$$ "(" |-- P.!!! (P.list1 type_var' --| P.$$$ ")")
|| Scan.succeed [];
val domain_decl =
(type_args' -- P.binding -- P.opt_infix) --
(P.$$$ "=" |-- P.enum1 "|" cons_decl);
val domains_decl =
Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") --
P.and_list1 domain_decl;
fun mk_domain
(definitional : bool)
(opt_name : string option,
doms : ((((string * string option) list * binding) * mixfix) *
((binding * (bool * binding option * string) list) * mixfix) list) list ) =
let
val names = map (fn (((_, t), _), _) => Binding.name_of t) doms;
val specs : ((string * string option) list * binding * mixfix *
(binding * (bool * binding option * string) list * mixfix) list) list =
map (fn (((vs, t), mx), cons) =>
(vs, t, mx, map (fn ((c, ds), mx) => (c, ds, mx)) cons)) doms;
val comp_dnam =
case opt_name of NONE => space_implode "_" names | SOME s => s;
in
if definitional
then add_new_domain_cmd comp_dnam specs
else add_domain_cmd comp_dnam specs
end;
val _ =
OuterSyntax.command "domain" "define recursive domains (HOLCF)"
K.thy_decl (domains_decl >> (Toplevel.theory o mk_domain false));
val _ =
OuterSyntax.command "new_domain" "define recursive domains (HOLCF)"
K.thy_decl (domains_decl >> (Toplevel.theory o mk_domain true));
end;
end;