(* Title: HOL/BNF/Tools/bnf_fp_rec_sugar.ML
Author: Lorenz Panny, TU Muenchen
Copyright 2013
Recursor and corecursor sugar.
*)
signature BNF_FP_REC_SUGAR =
sig
val add_primrec_cmd: (binding * string option * mixfix) list ->
(Attrib.binding * string) list -> local_theory -> local_theory;
val add_primcorec_cmd: bool ->
(binding * string option * mixfix) list * (Attrib.binding * string) list -> Proof.context ->
Proof.state
end;
structure BNF_FP_Rec_Sugar : BNF_FP_REC_SUGAR =
struct
open BNF_Util
open BNF_FP_Util
open BNF_FP_Rec_Sugar_Util
open BNF_FP_Rec_Sugar_Tactics
exception Primrec_Error of string * term list;
fun primrec_error str = raise Primrec_Error (str, []);
fun primrec_error_eqn str eqn = raise Primrec_Error (str, [eqn]);
fun primrec_error_eqns str eqns = raise Primrec_Error (str, eqns);
fun finds eq = fold_map (fn x => List.partition (curry eq x) #>> pair x);
val simp_attrs = @{attributes [simp]};
(* Primrec *)
type eqn_data = {
fun_name: string,
rec_type: typ,
ctr: term,
ctr_args: term list,
left_args: term list,
right_args: term list,
res_type: typ,
rhs_term: term,
user_eqn: term
};
fun permute_args n t = list_comb (t, map Bound (0 :: (n downto 1)))
|> fold (K (fn u => Abs (Name.uu, dummyT, u))) (0 upto n);
fun dissect_eqn lthy fun_names eqn' =
let
val eqn = subst_bounds (strip_qnt_vars @{const_name all} eqn' |> map Free |> rev,
strip_qnt_body @{const_name all} eqn') |> HOLogic.dest_Trueprop
handle TERM _ =>
primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn';
val (lhs, rhs) = HOLogic.dest_eq eqn
handle TERM _ =>
primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn';
val (fun_name, args) = strip_comb lhs
|>> (fn x => if is_Free x then fst (dest_Free x)
else primrec_error_eqn "malformed function equation (does not start with free)" eqn);
val (left_args, rest) = take_prefix is_Free args;
val (nonfrees, right_args) = take_suffix is_Free rest;
val _ = length nonfrees = 1 orelse if length nonfrees = 0 then
primrec_error_eqn "constructor pattern missing in left-hand side" eqn else
primrec_error_eqn "more than one non-variable argument in left-hand side" eqn;
val _ = member (op =) fun_names fun_name orelse
primrec_error_eqn "malformed function equation (does not start with function name)" eqn
val (ctr, ctr_args) = strip_comb (the_single nonfrees);
val _ = try (num_binder_types o fastype_of) ctr = SOME (length ctr_args) orelse
primrec_error_eqn "partially applied constructor in pattern" eqn;
val _ = let val d = duplicates (op =) (left_args @ ctr_args @ right_args) in null d orelse
primrec_error_eqn ("duplicate variable \"" ^ Syntax.string_of_term lthy (hd d) ^
"\" in left-hand side") eqn end;
val _ = forall is_Free ctr_args orelse
primrec_error_eqn "non-primitive pattern in left-hand side" eqn;
val _ =
let val b = fold_aterms (fn x as Free (v, _) =>
if (not (member (op =) (left_args @ ctr_args @ right_args) x) andalso
not (member (op =) fun_names v) andalso
not (Variable.is_fixed lthy v)) then cons x else I | _ => I) rhs []
in
null b orelse
primrec_error_eqn ("extra variable(s) in right-hand side: " ^
commas (map (Syntax.string_of_term lthy) b)) eqn
end;
in
{fun_name = fun_name,
rec_type = body_type (type_of ctr),
ctr = ctr,
ctr_args = ctr_args,
left_args = left_args,
right_args = right_args,
res_type = map fastype_of (left_args @ right_args) ---> fastype_of rhs,
rhs_term = rhs,
user_eqn = eqn'}
end;
(* substitutes (f ls x rs) by (y ls rs) for all f: get_idx f \<ge> 0, (x,y) \<in> substs *)
fun subst_direct_calls get_idx get_ctr_pos substs =
let
fun subst (Abs (v, T, b)) = Abs (v, T, subst b)
| subst t =
let
val (f, args) = strip_comb t;
val idx = get_idx f;
val ctr_pos = if idx >= 0 then get_ctr_pos idx else ~1;
in
if idx < 0 then
list_comb (f, map subst args)
else if ctr_pos >= length args then
primrec_error_eqn "too few arguments in recursive call" t
else
let
val (key, repl) = the (find_first (equal (nth args ctr_pos) o fst) substs)
handle Option.Option => primrec_error_eqn
"recursive call not directly applied to constructor argument" t;
in
remove (op =) key args |> map subst |> curry list_comb repl
end
end
in subst end;
(* FIXME get rid of funs_data or get_indices *)
fun rewrite_map_arg funs_data get_indices y rec_type res_type =
let
val pT = HOLogic.mk_prodT (rec_type, res_type);
val fstx = fst_const pT;
val sndx = snd_const pT;
val SOME ({fun_name, left_args, ...} :: _) =
find_first (equal rec_type o #rec_type o hd) funs_data;
val ctr_pos = length left_args;
fun subst _ d (t as Bound d') = t |> d = d' ? curry (op $) fstx
| subst l d (Abs (v, T, b)) = Abs (v, if d < 0 then pT else T, subst l (d + 1) b)
| subst l d t =
let val (u, vs) = strip_comb t in
if try (fst o dest_Free) u = SOME fun_name then
if l andalso length vs = ctr_pos then
list_comb (sndx |> permute_args ctr_pos, vs)
else if length vs <= ctr_pos then
primrec_error_eqn "too few arguments in recursive call" t
else if nth vs ctr_pos |> member (op =) [y, Bound d] then
list_comb (sndx $ nth vs ctr_pos, nth_drop ctr_pos vs |> map (subst false d))
else
primrec_error_eqn "recursive call not directly applied to constructor argument" t
else if try (fst o dest_Const) u = SOME @{const_name comp} then
(hd vs |> get_indices |> null orelse
primrec_error_eqn "recursive call not directly applied to constructor argument" t;
list_comb
(u |> map_types (strip_type #>> (fn Ts => Ts
|> nth_map (length Ts - 1) (K pT)
|> nth_map (length Ts - 2) (strip_type #>> nth_map 0 (K pT) #> (op --->)))
#> (op --->)),
nth_map 1 (subst l d) vs))
else
list_comb (u, map (subst false d) vs)
end
in
subst true ~1
end;
(* FIXME get rid of funs_data or get_indices *)
fun subst_indirect_call lthy funs_data get_indices (y, y') =
let
fun massage massage_map_arg bound_Ts =
massage_indirect_rec_call lthy (not o null o get_indices) massage_map_arg bound_Ts y y';
fun subst bound_Ts (t as _ $ _) =
let
val (f', args') = strip_comb t;
val fun_arg_idx = find_index (exists_subterm (not o null o get_indices)) args';
val arg_idx = find_index (exists_subterm (equal y)) args';
val (f, args) = chop (arg_idx + 1) args' |>> curry list_comb f';
val _ = fun_arg_idx < 0 orelse arg_idx >= 0 orelse
primrec_error_eqn "recursive call not applied to constructor argument" t;
in
if fun_arg_idx <> arg_idx andalso fun_arg_idx >= 0 then
if nth args' arg_idx = y then
list_comb (massage (rewrite_map_arg funs_data get_indices y) bound_Ts f, args)
else
primrec_error_eqn "recursive call not directly applied to constructor argument" f
else
list_comb (f', map (subst bound_Ts) args')
end
| subst bound_Ts (Abs (v, T, b)) = Abs (v, T, subst (T :: bound_Ts) b)
| subst bound_Ts t = t |> t = y ? massage (K I |> K) bound_Ts;
in subst [] end;
fun build_rec_arg lthy get_indices funs_data ctr_spec maybe_eqn_data =
if is_some maybe_eqn_data then
let
val eqn_data = the maybe_eqn_data;
val t = #rhs_term eqn_data;
val ctr_args = #ctr_args eqn_data;
val calls = #calls ctr_spec;
val n_args = fold (curry (op +) o (fn Direct_Rec _ => 2 | _ => 1)) calls 0;
val no_calls' = tag_list 0 calls
|> map_filter (try (apsnd (fn No_Rec n => n | Direct_Rec (n, _) => n)));
val direct_calls' = tag_list 0 calls
|> map_filter (try (apsnd (fn Direct_Rec (_, n) => n)));
val indirect_calls' = tag_list 0 calls
|> map_filter (try (apsnd (fn Indirect_Rec n => n)));
fun make_direct_type T = dummyT; (* FIXME? *)
val rec_res_type_list = map (fn (x :: _) => (#rec_type x, #res_type x)) funs_data;
fun make_indirect_type (Type (Tname, Ts)) = Type (Tname, Ts |> map (fn T =>
let val maybe_res_type = AList.lookup (op =) rec_res_type_list T in
if is_some maybe_res_type
then HOLogic.mk_prodT (T, the maybe_res_type)
else make_indirect_type T end))
| make_indirect_type T = T;
val args = replicate n_args ("", dummyT)
|> Term.rename_wrt_term t
|> map Free
|> fold (fn (ctr_arg_idx, arg_idx) =>
nth_map arg_idx (K (nth ctr_args ctr_arg_idx)))
no_calls'
|> fold (fn (ctr_arg_idx, arg_idx) =>
nth_map arg_idx (K (nth ctr_args ctr_arg_idx |> map_types make_direct_type)))
direct_calls'
|> fold (fn (ctr_arg_idx, arg_idx) =>
nth_map arg_idx (K (nth ctr_args ctr_arg_idx |> map_types make_indirect_type)))
indirect_calls';
val direct_calls = map (apfst (nth ctr_args) o apsnd (nth args)) direct_calls';
val indirect_calls = map (apfst (nth ctr_args) o apsnd (nth args)) indirect_calls';
val get_idx = (fn Free (v, _) => find_index (equal v o #fun_name o hd) funs_data | _ => ~1);
val t' = t
|> fold (subst_indirect_call lthy funs_data get_indices) indirect_calls
|> subst_direct_calls get_idx (length o #left_args o hd o nth funs_data) direct_calls;
val abstractions = map dest_Free (args @ #left_args eqn_data @ #right_args eqn_data);
in
t' |> fold_rev absfree abstractions
end
else Const (@{const_name undefined}, dummyT)
fun build_defs lthy bs funs_data rec_specs get_indices =
let
val n_funs = length funs_data;
val ctr_spec_eqn_data_list' =
(take n_funs rec_specs |> map #ctr_specs) ~~ funs_data
|> maps (uncurry (finds (fn (x, y) => #ctr x = #ctr y))
##> (fn x => null x orelse
primrec_error_eqns "excess equations in definition" (map #rhs_term x)) #> fst);
val _ = ctr_spec_eqn_data_list' |> map (fn (_, x) => length x <= 1 orelse
primrec_error_eqns ("multiple equations for constructor") (map #user_eqn x));
val ctr_spec_eqn_data_list =
ctr_spec_eqn_data_list' @ (drop n_funs rec_specs |> maps #ctr_specs |> map (rpair []));
val recs = take n_funs rec_specs |> map #recx;
val rec_args = ctr_spec_eqn_data_list
|> sort ((op <) o pairself (#offset o fst) |> make_ord)
|> map (uncurry (build_rec_arg lthy get_indices funs_data) o apsnd (try the_single));
val ctr_poss = map (fn x =>
if length (distinct ((op =) o pairself (length o #left_args)) x) <> 1 then
primrec_error ("inconstant constructor pattern position for function " ^
quote (#fun_name (hd x)))
else
hd x |> #left_args |> length) funs_data;
in
(recs, ctr_poss)
|-> map2 (fn recx => fn ctr_pos => list_comb (recx, rec_args) |> permute_args ctr_pos)
|> Syntax.check_terms lthy
|> map2 (fn b => fn t => ((b, NoSyn), ((Binding.map_name Thm.def_name b, []), t))) bs
end;
fun find_rec_calls get_indices eqn_data =
let
fun find (Abs (_, _, b)) ctr_arg = find b ctr_arg
| find (t as _ $ _) ctr_arg =
let
val (f', args') = strip_comb t;
val n = find_index (equal ctr_arg) args';
in
if n < 0 then
find f' ctr_arg @ maps (fn x => find x ctr_arg) args'
else
let val (f, args) = chop n args' |>> curry list_comb f' in
if exists_subterm (not o null o get_indices) f then
f :: maps (fn x => find x ctr_arg) args
else
find f ctr_arg @ maps (fn x => find x ctr_arg) args
end
end
| find _ _ = [];
in
map (find (#rhs_term eqn_data)) (#ctr_args eqn_data)
|> (fn [] => NONE | callss => SOME (#ctr eqn_data, callss))
end;
fun add_primrec fixes specs lthy =
let
val bs = map (fst o fst) fixes;
val fun_names = map Binding.name_of bs;
val eqns_data = map (snd #> dissect_eqn lthy fun_names) specs;
val funs_data = eqns_data
|> partition_eq ((op =) o pairself #fun_name)
|> finds (fn (x, y) => x = #fun_name (hd y)) fun_names |> fst
|> map (fn (x, y) => the_single y handle List.Empty =>
primrec_error ("missing equations for function " ^ quote x));
fun get_indices t = map (fst #>> Binding.name_of #> Free) fixes
|> map_index (fn (i, v) => if exists_subterm (equal v) t then SOME i else NONE)
|> map_filter I;
val arg_Ts = map (#rec_type o hd) funs_data;
val res_Ts = map (#res_type o hd) funs_data;
val callssss = funs_data
|> map (partition_eq ((op =) o pairself #ctr))
|> map (maps (map_filter (find_rec_calls get_indices)));
val ((nontriv, rec_specs, _, induct_thm, induct_thms), lthy') =
rec_specs_of bs arg_Ts res_Ts get_indices callssss lthy;
val actual_nn = length funs_data;
val _ = let val ctrs = (maps (map #ctr o #ctr_specs) rec_specs) in
map (fn {ctr, user_eqn, ...} => member (op =) ctrs ctr orelse
primrec_error_eqn ("argument " ^ quote (Syntax.string_of_term lthy' ctr) ^
" is not a constructor in left-hand side") user_eqn) eqns_data end;
val defs = build_defs lthy' bs funs_data rec_specs get_indices;
fun prove def_thms' {ctr_specs, nested_map_idents, nested_map_comps, ...} induct_thm fun_data
lthy =
let
val fun_name = #fun_name (hd fun_data);
val def_thms = map (snd o snd) def_thms';
val simp_thms = finds (fn (x, y) => #ctr x = #ctr y) fun_data ctr_specs
|> fst
|> map_filter (try (fn (x, [y]) =>
(#user_eqn x, length (#left_args x) + length (#right_args x), #rec_thm y)))
|> map (fn (user_eqn, num_extra_args, rec_thm) =>
mk_primrec_tac lthy num_extra_args nested_map_idents nested_map_comps def_thms rec_thm
|> K |> Goal.prove lthy [] [] user_eqn)
val notes =
[(inductN, if actual_nn > 1 then [induct_thm] else [], []),
(simpsN, simp_thms, simp_attrs)]
|> filter_out (null o #2)
|> map (fn (thmN, thms, attrs) =>
((Binding.qualify true fun_name (Binding.name thmN), attrs), [(thms, [])]));
in
lthy |> Local_Theory.notes notes
end;
val common_name = mk_common_name fun_names;
val common_notes =
[(inductN, if nontriv andalso actual_nn > 1 then [induct_thm] else [], [])]
|> filter_out (null o #2)
|> map (fn (thmN, thms, attrs) =>
((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
in
lthy'
|> fold_map Local_Theory.define defs
|-> (fn def_thms' => fold_map3 (prove def_thms') (take actual_nn rec_specs)
(take actual_nn induct_thms) funs_data)
|> snd
|> Local_Theory.notes common_notes |> snd
end;
fun add_primrec_cmd raw_fixes raw_specs lthy =
let
val _ = let val d = duplicates (op =) (map (Binding.name_of o #1) raw_fixes) in null d orelse
primrec_error ("duplicate function name(s): " ^ commas d) end;
val (fixes, specs) = fst (Specification.read_spec raw_fixes raw_specs lthy);
in
add_primrec fixes specs lthy
handle ERROR str => primrec_error str
end
handle Primrec_Error (str, eqns) =>
if null eqns
then error ("primrec_new error:\n " ^ str)
else error ("primrec_new error:\n " ^ str ^ "\nin\n " ^
space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns))
(* Primcorec *)
type co_eqn_data_dtr_disc = {
fun_name: string,
ctr_no: int,
cond: term,
user_eqn: term
};
type co_eqn_data_dtr_sel = {
fun_name: string,
ctr_no: int,
sel_no: int,
fun_args: term list,
rhs_term: term,
user_eqn: term
};
datatype co_eqn_data =
Dtr_Disc of co_eqn_data_dtr_disc |
Dtr_Sel of co_eqn_data_dtr_sel
fun co_dissect_eqn_disc sequential fun_name_corec_spec_list eqn' imp_lhs' imp_rhs matched_conds_ps =
let
fun find_subterm p = let (* FIXME \<exists>? *)
fun f (t as u $ v) =
fold_rev (curry merge_options) [if p t then SOME t else NONE, f u, f v] NONE
| f t = if p t then SOME t else NONE
in f end;
val fun_name = imp_rhs
|> perhaps (try HOLogic.dest_not)
|> `(try (fst o dest_Free o head_of o snd o dest_comb))
||> (try (fst o dest_Free o head_of o fst o HOLogic.dest_eq))
|> the o merge_options;
val corec_spec = the (AList.lookup (op =) fun_name_corec_spec_list fun_name)
handle Option.Option => primrec_error_eqn "malformed discriminator equation" imp_rhs;
val discs = #ctr_specs corec_spec |> map #disc;
val ctrs = #ctr_specs corec_spec |> map #ctr;
val n_ctrs = length ctrs;
val not_disc = head_of imp_rhs = @{term Not};
val _ = not_disc andalso n_ctrs <> 2 andalso
primrec_error_eqn "\<not>ed discriminator for a type with \<noteq> 2 constructors" imp_rhs;
val disc = find_subterm (member (op =) discs o head_of) imp_rhs;
val eq_ctr0 = imp_rhs |> perhaps (try (HOLogic.dest_not)) |> try (HOLogic.dest_eq #> snd)
|> (fn SOME t => let val n = find_index (equal t) ctrs in
if n >= 0 then SOME n else NONE end | _ => NONE);
val _ = is_some disc orelse is_some eq_ctr0 orelse
primrec_error_eqn "no discriminator in equation" imp_rhs;
val ctr_no' =
if is_none disc then the eq_ctr0 else find_index (equal (head_of (the disc))) discs;
val ctr_no = if not_disc then 1 - ctr_no' else ctr_no';
val fun_args = if is_none disc
then imp_rhs |> perhaps (try HOLogic.dest_not) |> HOLogic.dest_eq |> fst |> strip_comb |> snd
else the disc |> the_single o snd o strip_comb
|> (fn t => if try (fst o dest_Free o head_of) t = SOME fun_name
then snd (strip_comb t) else []);
val mk_conjs = try (foldr1 HOLogic.mk_conj) #> the_default @{const True};
val mk_disjs = try (foldr1 HOLogic.mk_disj) #> the_default @{const False};
val catch_all = try (fst o dest_Free o the_single) imp_lhs' = SOME Name.uu_;
val matched_conds = filter (equal fun_name o fst) matched_conds_ps |> map snd;
val imp_lhs = mk_conjs imp_lhs';
val cond =
if catch_all then
if null matched_conds then fold_rev absfree (map dest_Free fun_args) @{const True} else
(strip_abs_vars (hd matched_conds),
mk_disjs (map strip_abs_body matched_conds) |> HOLogic.mk_not)
|-> fold_rev (fn (v, T) => fn u => Abs (v, T, u))
else if sequential then
HOLogic.mk_conj (HOLogic.mk_not (mk_disjs (map strip_abs_body matched_conds)), imp_lhs)
|> fold_rev absfree (map dest_Free fun_args)
else
imp_lhs |> fold_rev absfree (map dest_Free fun_args);
val matched_cond =
if sequential then fold_rev absfree (map dest_Free fun_args) imp_lhs else cond;
val matched_conds_ps' = if catch_all
then (fun_name, cond) :: filter (not_equal fun_name o fst) matched_conds_ps
else (fun_name, matched_cond) :: matched_conds_ps;
in
(Dtr_Disc {
fun_name = fun_name,
ctr_no = ctr_no,
cond = cond,
user_eqn = eqn'
}, matched_conds_ps')
end;
fun co_dissect_eqn_sel fun_name_corec_spec_list eqn' eqn =
let
val (lhs, rhs) = HOLogic.dest_eq eqn
handle TERM _ =>
primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn;
val sel = head_of lhs;
val (fun_name, fun_args) = dest_comb lhs |> snd |> strip_comb |> apfst (fst o dest_Free)
handle TERM _ =>
primrec_error_eqn "malformed selector argument in left-hand side" eqn;
val corec_spec = the (AList.lookup (op =) fun_name_corec_spec_list fun_name)
handle Option.Option => primrec_error_eqn "malformed selector argument in left-hand side" eqn;
val ((ctr_spec, ctr_no), sel) = #ctr_specs corec_spec
|> the o get_index (try (the o find_first (equal sel) o #sels))
|>> `(nth (#ctr_specs corec_spec));
val sel_no = find_index (equal sel) (#sels ctr_spec);
in
Dtr_Sel {
fun_name = fun_name,
ctr_no = ctr_no,
sel_no = sel_no,
fun_args = fun_args,
rhs_term = rhs,
user_eqn = eqn'
}
end;
fun co_dissect_eqn_ctr sequential fun_name_corec_spec_list eqn' imp_lhs' imp_rhs matched_conds_ps =
let
val (lhs, rhs) = HOLogic.dest_eq imp_rhs;
val fun_name = head_of lhs |> fst o dest_Free;
val corec_spec = the (AList.lookup (op =) fun_name_corec_spec_list fun_name);
val (ctr, ctr_args) = strip_comb rhs;
val ctr_spec = the (find_first (equal ctr o #ctr) (#ctr_specs corec_spec))
handle Option.Option => primrec_error_eqn "not a constructor" ctr;
val disc_imp_rhs = betapply (#disc ctr_spec, lhs);
val (eqn_data_disc, matched_conds_ps') = co_dissect_eqn_disc
sequential fun_name_corec_spec_list eqn' imp_lhs' disc_imp_rhs matched_conds_ps;
val sel_imp_rhss = (#sels ctr_spec ~~ ctr_args)
|> map (fn (sel, ctr_arg) => HOLogic.mk_eq (betapply (sel, lhs), ctr_arg));
val _ = warning ("reduced\n " ^ Syntax.string_of_term @{context} imp_rhs ^ "\nto\n \<cdot> " ^
Syntax.string_of_term @{context} disc_imp_rhs ^ "\n \<cdot> " ^
space_implode "\n \<cdot> " (map (Syntax.string_of_term @{context}) sel_imp_rhss));
val eqns_data_sel =
map (co_dissect_eqn_sel fun_name_corec_spec_list @{const True}(*###*)) sel_imp_rhss;
in
(eqn_data_disc :: eqns_data_sel, matched_conds_ps')
end;
fun co_dissect_eqn sequential fun_name_corec_spec_list eqn' matched_conds_ps =
let
val eqn = subst_bounds (strip_qnt_vars @{const_name all} eqn' |> map Free |> rev,
strip_qnt_body @{const_name all} eqn')
handle TERM _ => primrec_error_eqn "malformed function equation" eqn';
val (imp_lhs', imp_rhs) =
(map HOLogic.dest_Trueprop (Logic.strip_imp_prems eqn),
HOLogic.dest_Trueprop (Logic.strip_imp_concl eqn));
val head = imp_rhs
|> perhaps (try HOLogic.dest_not) |> perhaps (try (fst o HOLogic.dest_eq))
|> head_of;
val maybe_rhs = imp_rhs |> perhaps (try (HOLogic.dest_not)) |> try (snd o HOLogic.dest_eq);
val fun_names = map fst fun_name_corec_spec_list;
val discs = maps (#ctr_specs o snd) fun_name_corec_spec_list |> map #disc;
val sels = maps (#ctr_specs o snd) fun_name_corec_spec_list |> maps #sels;
val ctrs = maps (#ctr_specs o snd) fun_name_corec_spec_list |> map #ctr;
in
if member (op =) discs head orelse
is_some maybe_rhs andalso
member (op =) (filter (null o binder_types o fastype_of) ctrs) (the maybe_rhs) then
co_dissect_eqn_disc sequential fun_name_corec_spec_list eqn' imp_lhs' imp_rhs matched_conds_ps
|>> single
else if member (op =) sels head then
([co_dissect_eqn_sel fun_name_corec_spec_list eqn' imp_rhs], matched_conds_ps)
else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) then
co_dissect_eqn_ctr sequential fun_name_corec_spec_list eqn' imp_lhs' imp_rhs matched_conds_ps
else
primrec_error_eqn "malformed function equation" eqn
end;
fun build_corec_args_discs ctr_specs disc_eqns =
let
val conds = map #cond disc_eqns;
val args =
if length ctr_specs = 1 then []
else if length disc_eqns = length ctr_specs then
fst (split_last conds)
else if length disc_eqns = length ctr_specs - 1 then
let val n = 0 upto length ctr_specs - 1
|> the o find_first (fn idx => not (exists (equal idx o #ctr_no) disc_eqns)) (*###*) in
if n = length ctr_specs - 1 then
conds
else
split_last conds
||> (fn t => fold_rev absfree (strip_abs_vars t) (strip_abs_body t |> HOLogic.mk_not))
|>> chop n
|> (fn ((l, r), x) => l @ (x :: r))
end
else
0 upto length ctr_specs - 1
|> map (fn idx => find_first (equal idx o #ctr_no) disc_eqns
|> Option.map #cond
|> the_default (Const (@{const_name undefined}, dummyT)))
|> fst o split_last;
fun finish t =
let val n = length (fastype_of t |> binder_types) in
if t = Const (@{const_name undefined}, dummyT) then t
else if n = 0 then Abs (Name.uu_, @{typ unit}, t)
else if n = 1 then t
else Const (@{const_name prod_case}, dummyT) $ t
end;
in
map finish args
end;
fun build_corec_args_sel sel_eqns ctr_spec =
let
(* FIXME *)
val n_args = fold (curry (op +)) (map (fn Direct_Corec _ => 3 | _ => 1) (#calls ctr_spec)) 0;
in
replicate n_args (Const (@{const_name undefined}, dummyT))
end;
fun co_build_defs lthy sequential bs arg_Tss fun_name_corec_spec_list eqns_data =
let
val fun_names = map Binding.name_of bs;
(* fun group _ [] = [] (* FIXME \<exists>? *)
| group eq (x :: xs) =
let val (xs', ys) = List.partition (eq x) xs in (x :: xs') :: group eq ys end;*)
val disc_eqnss = map_filter (try (fn Dtr_Disc x => x)) eqns_data
|> partition_eq ((op =) o pairself #fun_name)
|> finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names |> fst
|> map (sort ((op <) o pairself #ctr_no |> make_ord) o flat o snd);
val _ = disc_eqnss |> map (fn x =>
let val d = duplicates ((op =) o pairself #ctr_no) x in null d orelse
primrec_error_eqns "excess discriminator equations in definition"
(maps (fn t => filter (equal (#ctr_no t) o #ctr_no) x) d |> map #user_eqn) end);
val _ = warning ("disc_eqnss:\n \<cdot> " ^ space_implode "\n \<cdot> " (map @{make_string} disc_eqnss));
val sel_eqnss = map_filter (try (fn Dtr_Sel x => x)) eqns_data
|> partition_eq ((op =) o pairself #fun_name)
|> finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names |> fst
|> map (sort ((op <) o pairself #ctr_no |> make_ord) o flat o snd);
val _ = warning ("sel_eqnss:\n \<cdot> " ^ space_implode "\n \<cdot> " (map @{make_string} sel_eqnss));
fun splice (xs :: xss) (ys :: yss) = xs @ ys @ splice xss yss (* FIXME \<exists>? *)
| splice xss yss = flat xss @ flat yss;
val corecs = map (#corec o snd) fun_name_corec_spec_list;
val corec_args = (map snd fun_name_corec_spec_list ~~ disc_eqnss ~~ sel_eqnss)
|> maps (fn (({ctr_specs, ...}, disc_eqns), sel_eqns) =>
splice (build_corec_args_discs ctr_specs disc_eqns |> map single)
(map (build_corec_args_sel sel_eqns) ctr_specs));
val _ = warning ("corecursor arguments:\n \<cdot> " ^
space_implode "\n \<cdot> " (map (Syntax.string_of_term @{context}) corec_args));
fun uneq_pairs_rev xs = xs (* FIXME \<exists>? *)
|> these o try (split_last #> (fn (ys, y) => uneq_pairs_rev ys @ map (pair y) ys));
val proof_obligations = if sequential then [] else
maps (uneq_pairs_rev o map #cond) disc_eqnss
|> map (fn (x, y) => ((strip_abs_body x, strip_abs_body y), strip_abs_vars x))
|> map (apfst (apsnd HOLogic.mk_not #> pairself HOLogic.mk_Trueprop
#> apfst (curry (op $) @{const ==>}) #> (op $)))
|> map (fn (t, abs_vars) => fold_rev (fn (v, T) => fn u =>
Const (@{const_name all}, (T --> @{typ prop}) --> @{typ prop}) $
Abs (v, T, u)) abs_vars t);
fun currys Ts t = if length Ts <= 1 then t else
t $ foldr1 (fn (u, v) => HOLogic.pair_const dummyT dummyT $ u $ v)
(length Ts - 1 downto 0 |> map Bound)
|> fold_rev (fn T => fn u => Abs (Name.uu, T, u)) Ts;
in
map (list_comb o rpair corec_args) corecs
|> map2 (fn Ts => fn t => if length Ts = 0 then t $ HOLogic.unit else t) arg_Tss
|> map2 currys arg_Tss
|> Syntax.check_terms lthy
|> map2 (fn b => fn t => ((b, NoSyn), ((Binding.map_name Thm.def_name b, []), t))) bs
|> rpair proof_obligations
end;
fun add_primcorec sequential fixes specs lthy =
let
val bs = map (fst o fst) fixes;
val (arg_Ts, res_Ts) = map (strip_type o snd o fst #>> HOLogic.mk_tupleT) fixes |> split_list;
(* copied from primrec_new *)
fun get_indices t = map (fst #>> Binding.name_of #> Free) fixes
|> map_index (fn (i, v) => if exists_subterm (equal v) t then SOME i else NONE)
|> map_filter I;
val callssss = []; (* FIXME *)
val ((nontriv, corec_specs, _, coinduct_thm, strong_co_induct_thm, coinduct_thmss,
strong_coinduct_thmss), lthy') =
corec_specs_of bs arg_Ts res_Ts get_indices callssss lthy;
val fun_names = map Binding.name_of bs;
val fun_name_corec_spec_list = (fun_names ~~ res_Ts, corec_specs)
|> uncurry (finds (fn ((v, T), {corec, ...}) => T = body_type (fastype_of corec))) |> fst
|> map (apfst fst #> apsnd the_single); (*###*)
val (eqns_data, _) =
fold_map (co_dissect_eqn sequential fun_name_corec_spec_list) (map snd specs) []
|>> flat;
val (defs, proof_obligations) =
co_build_defs lthy' sequential bs (map (binder_types o snd o fst) fixes)
fun_name_corec_spec_list eqns_data;
in
lthy'
|> fold_map Local_Theory.define defs |> snd
|> Proof.theorem NONE (K I) [map (rpair []) proof_obligations]
|> Proof.refine (Method.primitive_text I)
|> Seq.hd
end
fun add_primcorec_cmd seq (raw_fixes, raw_specs) lthy =
let
val (fixes, specs) = fst (Specification.read_spec raw_fixes raw_specs lthy);
in
add_primcorec seq fixes specs lthy
handle ERROR str => primrec_error str
end
handle Primrec_Error (str, eqns) =>
if null eqns
then error ("primcorec error:\n " ^ str)
else error ("primcorec error:\n " ^ str ^ "\nin\n " ^
space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns))
end;