(* Title: HOL/Tools/datatype_aux.ML
ID: $Id$
Author: Stefan Berghofer, TU Muenchen
License: GPL (GNU GENERAL PUBLIC LICENSE)
Auxiliary functions for defining datatypes.
*)
signature DATATYPE_AUX =
sig
val quiet_mode : bool ref
val message : string -> unit
val foldl1 : ('a * 'a -> 'a) -> 'a list -> 'a
val add_path : bool -> string -> theory -> theory
val parent_path : bool -> theory -> theory
val store_thmss : string -> string list -> thm list list -> theory -> theory * thm list list
val store_thms_atts : string -> string list -> theory attribute list list -> thm list
-> theory -> theory * thm list
val store_thms : string -> string list -> thm list -> theory -> theory * thm list
val split_conj_thm : thm -> thm list
val mk_conj : term list -> term
val mk_disj : term list -> term
val indtac : thm -> int -> tactic
val exh_tac : (string -> thm) -> int -> tactic
datatype simproc_dist = QuickAndDirty
| FewConstrs of thm list
| ManyConstrs of thm * simpset;
datatype dtyp =
DtTFree of string
| DtType of string * (dtyp list)
| DtRec of int;
type descr
type datatype_info
exception Datatype
val name_of_typ : typ -> string
val dtyp_of_typ : (string * string list) list -> typ -> dtyp
val mk_Free : string -> typ -> int -> term
val is_rec_type : dtyp -> bool
val typ_of_dtyp : (int * (string * dtyp list *
(string * dtyp list) list)) list -> (string * sort) list -> dtyp -> typ
val dest_DtTFree : dtyp -> string
val dest_DtRec : dtyp -> int
val dest_TFree : typ -> string
val get_nonrec_types : (int * (string * dtyp list *
(string * dtyp list) list)) list -> (string * sort) list -> typ list
val get_branching_types : (int * (string * dtyp list *
(string * dtyp list) list)) list -> (string * sort) list -> typ list
val get_rec_types : (int * (string * dtyp list *
(string * dtyp list) list)) list -> (string * sort) list -> typ list
val check_nonempty : (int * (string * dtyp list *
(string * dtyp list) list)) list list -> unit
val unfold_datatypes :
Sign.sg -> (int * (string * dtyp list * (string * dtyp list) list)) list ->
(string * sort) list -> datatype_info Symtab.table ->
(int * (string * dtyp list * (string * dtyp list) list)) list -> int ->
(int * (string * dtyp list *
(string * dtyp list) list)) list list * int
end;
structure DatatypeAux : DATATYPE_AUX =
struct
val quiet_mode = ref false;
fun message s = if !quiet_mode then () else writeln s;
(* FIXME: move to library ? *)
fun foldl1 f (x::xs) = foldl f (x, xs);
fun add_path flat_names s = if flat_names then I else Theory.add_path s;
fun parent_path flat_names = if flat_names then I else Theory.parent_path;
(* store theorems in theory *)
fun store_thmss label tnames thmss thy =
(thy, tnames ~~ thmss) |>
foldl_map (fn (thy', (tname, thms)) => thy' |>
Theory.add_path tname |>
(apsnd hd o PureThy.add_thmss [((label, thms), [])]) |>>
Theory.parent_path);
fun store_thms_atts label tnames attss thms thy =
(thy, tnames ~~ attss ~~ thms) |>
foldl_map (fn (thy', ((tname, atts), thm)) => thy' |>
Theory.add_path tname |>
(apsnd hd o PureThy.add_thms [((label, thm), atts)]) |>>
Theory.parent_path);
fun store_thms label tnames = store_thms_atts label tnames (replicate (length tnames) []);
(* split theorem thm_1 & ... & thm_n into n theorems *)
fun split_conj_thm th =
((th RS conjunct1)::(split_conj_thm (th RS conjunct2))) handle THM _ => [th];
val mk_conj = foldr1 (HOLogic.mk_binop "op &");
val mk_disj = foldr1 (HOLogic.mk_binop "op |");
(* instantiate induction rule *)
fun indtac indrule i st =
let
val ts = HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule));
val ts' = HOLogic.dest_conj (HOLogic.dest_Trueprop
(Logic.strip_imp_concl (nth_elem (i - 1, prems_of st))));
val getP = if can HOLogic.dest_imp (hd ts) then
(apfst Some) o HOLogic.dest_imp else pair None;
fun abstr (t1, t2) = (case t1 of
None => let val [Free (s, T)] = add_term_frees (t2, [])
in absfree (s, T, t2) end
| Some (_ $ t' $ _) => Abs ("x", fastype_of t', abstract_over (t', t2)))
val cert = cterm_of (Thm.sign_of_thm st);
val Ps = map (cert o head_of o snd o getP) ts;
val indrule' = cterm_instantiate (Ps ~~
(map (cert o abstr o getP) ts')) indrule
in
rtac indrule' i st
end;
(* perform exhaustive case analysis on last parameter of subgoal i *)
fun exh_tac exh_thm_of i state =
let
val sg = Thm.sign_of_thm state;
val prem = nth_elem (i - 1, prems_of state);
val params = Logic.strip_params prem;
val (_, Type (tname, _)) = hd (rev params);
val exhaustion = lift_rule (state, i) (exh_thm_of tname);
val prem' = hd (prems_of exhaustion);
val _ $ (_ $ lhs $ _) = hd (rev (Logic.strip_assums_hyp prem'));
val exhaustion' = cterm_instantiate [(cterm_of sg (head_of lhs),
cterm_of sg (foldr (fn ((_, T), t) => Abs ("z", T, t))
(params, Bound 0)))] exhaustion
in compose_tac (false, exhaustion', nprems_of exhaustion) i state
end;
(* handling of distinctness theorems *)
datatype simproc_dist = QuickAndDirty
| FewConstrs of thm list
| ManyConstrs of thm * simpset;
(********************** Internal description of datatypes *********************)
datatype dtyp =
DtTFree of string
| DtType of string * (dtyp list)
| DtRec of int;
(* information about datatypes *)
type descr = (int * (string * dtyp list * (string * dtyp list) list)) list;
type datatype_info =
{index : int,
descr : descr,
rec_names : string list,
rec_rewrites : thm list,
case_name : string,
case_rewrites : thm list,
induction : thm,
exhaustion : thm,
distinct : simproc_dist,
inject : thm list,
nchotomy : thm,
case_cong : thm,
weak_case_cong : thm};
fun mk_Free s T i = Free (s ^ (string_of_int i), T);
fun subst_DtTFree _ substs (T as (DtTFree name)) =
(case assoc (substs, name) of
None => T
| Some U => U)
| subst_DtTFree i substs (DtType (name, ts)) =
DtType (name, map (subst_DtTFree i substs) ts)
| subst_DtTFree i _ (DtRec j) = DtRec (i + j);
exception Datatype;
fun dest_DtTFree (DtTFree a) = a
| dest_DtTFree _ = raise Datatype;
fun dest_DtRec (DtRec i) = i
| dest_DtRec _ = raise Datatype;
fun is_rec_type (DtType (_, dts)) = exists is_rec_type dts
| is_rec_type (DtRec _) = true
| is_rec_type _ = false;
fun dest_TFree (TFree (n, _)) = n;
fun name_of_typ (Type (s, Ts)) = space_implode "_"
(filter (not o equal "") (map name_of_typ Ts) @ [Sign.base_name s])
| name_of_typ _ = "";
fun dtyp_of_typ _ (TFree (n, _)) = DtTFree n
| dtyp_of_typ _ (TVar _) = error "Illegal schematic type variable(s)"
| dtyp_of_typ new_dts (Type (tname, Ts)) =
(case assoc (new_dts, tname) of
None => DtType (tname, map (dtyp_of_typ new_dts) Ts)
| Some vs => if map (try dest_TFree) Ts = map Some vs then
DtRec (find_index (curry op = tname o fst) new_dts)
else error ("Illegal occurence of recursive type " ^ tname));
fun typ_of_dtyp descr sorts (DtTFree a) = TFree (a, the (assoc (sorts, a)))
| typ_of_dtyp descr sorts (DtRec i) =
let val (s, ds, _) = the (assoc (descr, i))
in Type (s, map (typ_of_dtyp descr sorts) ds) end
| typ_of_dtyp descr sorts (DtType (s, ds)) =
Type (s, map (typ_of_dtyp descr sorts) ds);
(* find all non-recursive types in datatype description *)
fun get_nonrec_types descr sorts =
let fun add (Ts, T as DtTFree _) = T ins Ts
| add (Ts, T as DtType ("fun", [_, DtRec _])) = Ts
| add (Ts, T as DtType _) = T ins Ts
| add (Ts, _) = Ts
in map (typ_of_dtyp descr sorts) (foldl (fn (Ts, (_, (_, _, constrs))) =>
foldl (fn (Ts', (_, cargs)) =>
foldl add (Ts', cargs)) (Ts, constrs)) ([], descr))
end;
(* get all recursive types in datatype description *)
fun get_rec_types descr sorts = map (fn (_ , (s, ds, _)) =>
Type (s, map (typ_of_dtyp descr sorts) ds)) descr;
(* get all branching types *)
fun get_branching_types descr sorts =
let fun add (Ts, DtType ("fun", [T, DtRec _])) = T ins Ts
| add (Ts, _) = Ts
in map (typ_of_dtyp descr sorts) (foldl (fn (Ts, (_, (_, _, constrs))) =>
foldl (fn (Ts', (_, cargs)) =>
foldl add (Ts', cargs)) (Ts, constrs)) ([], descr))
end;
(* nonemptiness check for datatypes *)
fun check_nonempty descr =
let
val descr' = flat descr;
fun is_nonempty_dt is i =
let
val (_, _, constrs) = the (assoc (descr', i));
fun arg_nonempty (DtRec i) = if i mem is then false
else is_nonempty_dt (i::is) i
| arg_nonempty (DtType ("fun", [_, T])) = arg_nonempty T
| arg_nonempty _ = true;
in exists ((forall arg_nonempty) o snd) constrs
end
in assert_all (fn (i, _) => is_nonempty_dt [i] i) (hd descr)
(fn (_, (s, _, _)) => "Nonemptiness check failed for datatype " ^ s)
end;
(* unfold a list of mutually recursive datatype specifications *)
(* all types of the form DtType (dt_name, [..., DtRec _, ...]) *)
(* need to be unfolded *)
fun unfold_datatypes sign orig_descr sorts (dt_info : datatype_info Symtab.table) descr i =
let
fun typ_error T msg = error ("Non-admissible type expression\n" ^
Sign.string_of_typ sign (typ_of_dtyp (orig_descr @ descr) sorts T) ^ "\n" ^ msg);
fun get_dt_descr T i tname dts =
(case Symtab.lookup (dt_info, tname) of
None => typ_error T (tname ^ " is not a datatype - can't use it in\
\ nested recursion")
| (Some {index, descr, ...}) =>
let val (_, vars, _) = the (assoc (descr, index));
val subst = ((map dest_DtTFree vars) ~~ dts) handle LIST _ =>
typ_error T ("Type constructor " ^ tname ^ " used with wrong\
\ number of arguments")
in (i + index, map (fn (j, (tn, args, cs)) => (i + j,
(tn, map (subst_DtTFree i subst) args,
map (apsnd (map (subst_DtTFree i subst))) cs))) descr)
end);
(* unfold a single constructor argument *)
fun unfold_arg ((i, Ts, descrs), T as (DtType (tname, dts))) =
if is_rec_type T then
if tname = "fun" then
if is_rec_type (hd dts) then
typ_error T "Non-strictly positive recursive occurrence of type"
else
(case hd (tl dts) of
DtType ("fun", _) => typ_error T "Curried function types not allowed"
| T' => let val (i', [T''], descrs') = unfold_arg ((i, [], descrs), T')
in (i', Ts @ [DtType (tname, [hd dts, T''])], descrs') end)
else
let val (index, descr) = get_dt_descr T i tname dts;
val (descr', i') = unfold_datatypes sign orig_descr sorts dt_info descr (i + length descr)
in (i', Ts @ [DtRec index], descrs @ descr') end
else (i, Ts @ [T], descrs)
| unfold_arg ((i, Ts, descrs), T) = (i, Ts @ [T], descrs);
(* unfold a constructor *)
fun unfold_constr ((i, constrs, descrs), (cname, cargs)) =
let val (i', cargs', descrs') = foldl unfold_arg ((i, [], descrs), cargs)
in (i', constrs @ [(cname, cargs')], descrs') end;
(* unfold a single datatype *)
fun unfold_datatype ((i, dtypes, descrs), (j, (tname, tvars, constrs))) =
let val (i', constrs', descrs') =
foldl unfold_constr ((i, [], descrs), constrs)
in (i', dtypes @ [(j, (tname, tvars, constrs'))], descrs')
end;
val (i', descr', descrs) = foldl unfold_datatype ((i, [],[]), descr);
in (descr' :: descrs, i') end;
end;