use '%x. x = C' as default discriminator for nullary constructor C, instead of relying on odd '=:' syntax
(* Title: HOL/Tools/Ctr_Sugar/ctr_sugar.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2012, 2013
Wrapping existing freely generated type's constructors.
*)
signature CTR_SUGAR =
sig
type ctr_sugar =
{ctrs: term list,
casex: term,
discs: term list,
selss: term list list,
exhaust: thm,
nchotomy: thm,
injects: thm list,
distincts: thm list,
case_thms: thm list,
case_cong: thm,
weak_case_cong: thm,
split: thm,
split_asm: thm,
disc_defs: thm list,
disc_thmss: thm list list,
discIs: thm list,
sel_defs: thm list,
sel_thmss: thm list list,
disc_excludesss: thm list list list,
disc_exhausts: thm list,
sel_exhausts: thm list,
collapses: thm list,
expands: thm list,
sel_splits: thm list,
sel_split_asms: thm list,
case_eq_ifs: thm list};
val morph_ctr_sugar: morphism -> ctr_sugar -> ctr_sugar
val transfer_ctr_sugar: Proof.context -> ctr_sugar -> ctr_sugar
val ctr_sugar_of: Proof.context -> string -> ctr_sugar option
val ctr_sugars_of: Proof.context -> ctr_sugar list
val ctr_sugar_of_case: Proof.context -> string -> ctr_sugar option
val ctr_sugar_interpretation: (ctr_sugar -> theory -> theory) -> theory -> theory
val register_ctr_sugar: string -> ctr_sugar -> local_theory -> local_theory
val default_register_ctr_sugar_global: string -> ctr_sugar -> theory -> theory
val mk_half_pairss: 'a list * 'a list -> ('a * 'a) list list
val join_halves: int -> 'a list list -> 'a list list -> 'a list * 'a list list list
val mk_ctr: typ list -> term -> term
val mk_case: typ list -> typ -> term -> term
val mk_disc_or_sel: typ list -> term -> term
val name_of_ctr: term -> string
val name_of_disc: term -> string
val dest_ctr: Proof.context -> string -> term -> term * term list
val dest_case: Proof.context -> string -> typ list -> term ->
(ctr_sugar * term list * term list) option
type ('c, 'a, 'v) ctr_spec = ((binding * 'c) * 'a list) * (binding * 'v) list
val disc_of_ctr_spec: ('c, 'a, 'v) ctr_spec -> binding
val ctr_of_ctr_spec: ('c, 'a, 'v) ctr_spec -> 'c
val args_of_ctr_spec: ('c, 'a, 'v) ctr_spec -> 'a list
val sel_defaults_of_ctr_spec: ('c, 'a, 'v) ctr_spec -> (binding * 'v) list
val free_constructors: ({prems: thm list, context: Proof.context} -> tactic) list list ->
((bool * bool) * binding) * (term, binding, term) ctr_spec list -> local_theory ->
ctr_sugar * local_theory
val parse_bound_term: (binding * string) parser
val parse_ctr_options: (bool * bool) parser
val parse_ctr_spec: 'c parser -> 'a parser -> ('c, 'a, string) ctr_spec parser
end;
structure Ctr_Sugar : CTR_SUGAR =
struct
open Ctr_Sugar_Util
open Ctr_Sugar_Tactics
open Ctr_Sugar_Code
type ctr_sugar =
{ctrs: term list,
casex: term,
discs: term list,
selss: term list list,
exhaust: thm,
nchotomy: thm,
injects: thm list,
distincts: thm list,
case_thms: thm list,
case_cong: thm,
weak_case_cong: thm,
split: thm,
split_asm: thm,
disc_defs: thm list,
disc_thmss: thm list list,
discIs: thm list,
sel_defs: thm list,
sel_thmss: thm list list,
disc_excludesss: thm list list list,
disc_exhausts: thm list,
sel_exhausts: thm list,
collapses: thm list,
expands: thm list,
sel_splits: thm list,
sel_split_asms: thm list,
case_eq_ifs: thm list};
fun morph_ctr_sugar phi {ctrs, casex, discs, selss, exhaust, nchotomy, injects, distincts,
case_thms, case_cong, weak_case_cong, split, split_asm, disc_defs, disc_thmss, discIs, sel_defs,
sel_thmss, disc_excludesss, disc_exhausts, sel_exhausts, collapses, expands, sel_splits,
sel_split_asms, case_eq_ifs} =
{ctrs = map (Morphism.term phi) ctrs,
casex = Morphism.term phi casex,
discs = map (Morphism.term phi) discs,
selss = map (map (Morphism.term phi)) selss,
exhaust = Morphism.thm phi exhaust,
nchotomy = Morphism.thm phi nchotomy,
injects = map (Morphism.thm phi) injects,
distincts = map (Morphism.thm phi) distincts,
case_thms = map (Morphism.thm phi) case_thms,
case_cong = Morphism.thm phi case_cong,
weak_case_cong = Morphism.thm phi weak_case_cong,
split = Morphism.thm phi split,
split_asm = Morphism.thm phi split_asm,
disc_defs = map (Morphism.thm phi) disc_defs,
disc_thmss = map (map (Morphism.thm phi)) disc_thmss,
discIs = map (Morphism.thm phi) discIs,
sel_defs = map (Morphism.thm phi) sel_defs,
sel_thmss = map (map (Morphism.thm phi)) sel_thmss,
disc_excludesss = map (map (map (Morphism.thm phi))) disc_excludesss,
disc_exhausts = map (Morphism.thm phi) disc_exhausts,
sel_exhausts = map (Morphism.thm phi) sel_exhausts,
collapses = map (Morphism.thm phi) collapses,
expands = map (Morphism.thm phi) expands,
sel_splits = map (Morphism.thm phi) sel_splits,
sel_split_asms = map (Morphism.thm phi) sel_split_asms,
case_eq_ifs = map (Morphism.thm phi) case_eq_ifs};
val transfer_ctr_sugar =
morph_ctr_sugar o Morphism.transfer_morphism o Proof_Context.theory_of;
structure Data = Generic_Data
(
type T = ctr_sugar Symtab.table;
val empty = Symtab.empty;
val extend = I;
fun merge data : T = Symtab.merge (K true) data;
);
fun ctr_sugar_of ctxt =
Symtab.lookup (Data.get (Context.Proof ctxt))
#> Option.map (transfer_ctr_sugar ctxt);
fun ctr_sugars_of ctxt =
Symtab.fold (cons o transfer_ctr_sugar ctxt o snd) (Data.get (Context.Proof ctxt)) [];
fun ctr_sugar_of_case ctxt s =
find_first (fn {casex = Const (s', _), ...} => s' = s | _ => false) (ctr_sugars_of ctxt);
structure Ctr_Sugar_Interpretation = Interpretation
(
type T = ctr_sugar;
val eq: T * T -> bool = op = o pairself #ctrs;
);
fun with_repaired_path f (ctr_sugar as {ctrs = ctr1 :: _, ...} : ctr_sugar) thy =
thy
|> Sign.root_path
|> Sign.add_path (Long_Name.qualifier (fst (dest_Type (body_type (fastype_of ctr1)))))
|> (fn thy => f (morph_ctr_sugar (Morphism.transfer_morphism thy) ctr_sugar) thy)
|> Sign.restore_naming thy;
fun ctr_sugar_interpretation f = Ctr_Sugar_Interpretation.interpretation (with_repaired_path f);
fun register_ctr_sugar key ctr_sugar =
Local_Theory.declaration {syntax = false, pervasive = true}
(fn phi => Data.map (Symtab.update (key, morph_ctr_sugar phi ctr_sugar)))
#> Local_Theory.background_theory (Ctr_Sugar_Interpretation.data ctr_sugar);
fun default_register_ctr_sugar_global key ctr_sugar thy =
let val tab = Data.get (Context.Theory thy) in
if Symtab.defined tab key then
thy
else
thy
|> Context.theory_map (Data.put (Symtab.update_new (key, ctr_sugar) tab))
|> Ctr_Sugar_Interpretation.data ctr_sugar
end;
val isN = "is_";
val unN = "un_";
fun mk_unN 1 1 suf = unN ^ suf
| mk_unN _ l suf = unN ^ suf ^ string_of_int l;
val caseN = "case";
val case_congN = "case_cong";
val case_eq_ifN = "case_eq_if";
val collapseN = "collapse";
val disc_excludeN = "disc_exclude";
val disc_exhaustN = "disc_exhaust";
val discN = "disc";
val discIN = "discI";
val distinctN = "distinct";
val exhaustN = "exhaust";
val expandN = "expand";
val injectN = "inject";
val nchotomyN = "nchotomy";
val selN = "sel";
val sel_exhaustN = "sel_exhaust";
val sel_splitN = "sel_split";
val sel_split_asmN = "sel_split_asm";
val splitN = "split";
val splitsN = "splits";
val split_asmN = "split_asm";
val weak_case_cong_thmsN = "weak_case_cong";
val cong_attrs = @{attributes [cong]};
val dest_attrs = @{attributes [dest]};
val safe_elim_attrs = @{attributes [elim!]};
val iff_attrs = @{attributes [iff]};
val inductsimp_attrs = @{attributes [induct_simp]};
val nitpicksimp_attrs = @{attributes [nitpick_simp]};
val simp_attrs = @{attributes [simp]};
val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
val code_nitpicksimp_simp_attrs = code_nitpicksimp_attrs @ simp_attrs;
fun unflat_lookup eq xs ys = map (fn xs' => permute_like_unique eq xs xs' ys);
fun mk_half_pairss' _ ([], []) = []
| mk_half_pairss' indent (x :: xs, _ :: ys) =
indent @ fold_rev (cons o single o pair x) ys (mk_half_pairss' ([] :: indent) (xs, ys));
fun mk_half_pairss p = mk_half_pairss' [[]] p;
fun join_halves n half_xss other_half_xss =
(splice (flat half_xss) (flat other_half_xss),
map2 (map2 append) (Library.chop_groups n half_xss)
(transpose (Library.chop_groups n other_half_xss)));
fun mk_undefined T = Const (@{const_name undefined}, T);
fun mk_ctr Ts t =
let val Type (_, Ts0) = body_type (fastype_of t) in
subst_nonatomic_types (Ts0 ~~ Ts) t
end;
fun mk_case Ts T t =
let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in
subst_nonatomic_types ((body, T) :: (Ts0 ~~ Ts)) t
end;
fun mk_disc_or_sel Ts t =
subst_nonatomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
fun name_of_const what t =
(case head_of t of
Const (s, _) => s
| Free (s, _) => s
| _ => error ("Cannot extract name of " ^ what));
val name_of_ctr = name_of_const "constructor";
val notN = "not_";
val eqN = "eq_";
val neqN = "neq_";
fun name_of_disc t =
(case head_of t of
Abs (_, _, @{const Not} $ (t' $ Bound 0)) =>
Long_Name.map_base_name (prefix notN) (name_of_disc t')
| Abs (_, _, Const (@{const_name HOL.eq}, _) $ Bound 0 $ t') =>
Long_Name.map_base_name (prefix eqN) (name_of_disc t')
| Abs (_, _, @{const Not} $ (Const (@{const_name HOL.eq}, _) $ Bound 0 $ t')) =>
Long_Name.map_base_name (prefix neqN) (name_of_disc t')
| t' => name_of_const "destructor" t');
val base_name_of_ctr = Long_Name.base_name o name_of_ctr;
fun dest_ctr ctxt s t =
let val (f, args) = Term.strip_comb t in
(case ctr_sugar_of ctxt s of
SOME {ctrs, ...} =>
(case find_first (can (fo_match ctxt f)) ctrs of
SOME f' => (f', args)
| NONE => raise Fail "dest_ctr")
| NONE => raise Fail "dest_ctr")
end;
fun dest_case ctxt s Ts t =
(case Term.strip_comb t of
(Const (c, _), args as _ :: _) =>
(case ctr_sugar_of ctxt s of
SOME (ctr_sugar as {casex = Const (case_name, _), discs = discs0, selss = selss0, ...}) =>
if case_name = c then
let val n = length discs0 in
if n < length args then
let
val (branches, obj :: leftovers) = chop n args;
val discs = map (mk_disc_or_sel Ts) discs0;
val selss = map (map (mk_disc_or_sel Ts)) selss0;
val conds = map (rapp obj) discs;
val branch_argss = map (fn sels => map (rapp obj) sels @ leftovers) selss;
val branches' = map2 (curry Term.betapplys) branches branch_argss;
in
SOME (ctr_sugar, conds, branches')
end
else
NONE
end
else
NONE
| _ => NONE)
| _ => NONE);
fun eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;
type ('c, 'a, 'v) ctr_spec = ((binding * 'c) * 'a list) * (binding * 'v) list;
fun disc_of_ctr_spec (((disc, _), _), _) = disc;
fun ctr_of_ctr_spec (((_, ctr), _), _) = ctr;
fun args_of_ctr_spec ((_, args), _) = args;
fun sel_defaults_of_ctr_spec (_, ds) = ds;
fun prepare_free_constructors prep_term (((no_discs_sels, no_code), raw_case_binding), ctr_specs)
no_defs_lthy =
let
(* TODO: sanity checks on arguments *)
val raw_ctrs = map ctr_of_ctr_spec ctr_specs;
val raw_disc_bindings = map disc_of_ctr_spec ctr_specs;
val raw_sel_bindingss = map args_of_ctr_spec ctr_specs;
val raw_sel_defaultss = map sel_defaults_of_ctr_spec ctr_specs;
val n = length raw_ctrs;
val ks = 1 upto n;
val _ = if n > 0 then () else error "No constructors specified";
val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
val sel_defaultss = map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss;
val Type (fcT_name, As0) = body_type (fastype_of (hd ctrs0));
val fc_b_name = Long_Name.base_name fcT_name;
val fc_b = Binding.name fc_b_name;
fun qualify mandatory = Binding.qualify mandatory fc_b_name;
fun dest_TFree_or_TVar (TFree sS) = sS
| dest_TFree_or_TVar (TVar ((s, _), S)) = (s, S)
| dest_TFree_or_TVar _ = error "Invalid type argument";
val (unsorted_As, B) =
no_defs_lthy
|> variant_tfrees (map (fst o dest_TFree_or_TVar) As0)
||> the_single o fst o mk_TFrees 1;
val As = map2 (resort_tfree o snd o dest_TFree_or_TVar) As0 unsorted_As;
val fcT = Type (fcT_name, As);
val ctrs = map (mk_ctr As) ctrs0;
val ctr_Tss = map (binder_types o fastype_of) ctrs;
val ms = map length ctr_Tss;
fun can_definitely_rely_on_disc k = not (Binding.is_empty (nth raw_disc_bindings (k - 1)));
fun can_rely_on_disc k =
can_definitely_rely_on_disc k orelse (k = 1 andalso not (can_definitely_rely_on_disc 2));
fun should_omit_disc_binding k = n = 1 orelse (n = 2 andalso can_rely_on_disc (3 - k));
val equal_binding = @{binding "="};
fun is_disc_binding_valid b =
not (Binding.is_empty b orelse Binding.eq_name (b, equal_binding));
val standard_disc_binding = Binding.name o prefix isN o base_name_of_ctr;
val disc_bindings =
raw_disc_bindings
|> map4 (fn k => fn m => fn ctr => fn disc =>
qualify false
(if Binding.is_empty disc then
if should_omit_disc_binding k then disc
else if m = 0 then equal_binding
else standard_disc_binding ctr
else if Binding.eq_name (disc, standard_binding) then
standard_disc_binding ctr
else
disc)) ks ms ctrs0;
fun standard_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
val sel_bindingss =
map3 (fn ctr => fn m => map2 (fn l => fn sel =>
qualify false
(if Binding.is_empty sel orelse Binding.eq_name (sel, standard_binding) then
standard_sel_binding m l ctr
else
sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms raw_sel_bindingss;
val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
val (((((((([exh_y], (xss, xss')), yss), fs), gs), [u', v']), [w]), (p, p')), names_lthy) =
no_defs_lthy
|> mk_Frees "y" [fcT] (* for compatibility with "datatype_realizer.ML" *)
||>> mk_Freess' "x" ctr_Tss
||>> mk_Freess "y" ctr_Tss
||>> mk_Frees "f" case_Ts
||>> mk_Frees "g" case_Ts
||>> (apfst (map (rpair fcT)) oo Variable.variant_fixes) [fc_b_name, fc_b_name ^ "'"]
||>> mk_Frees "z" [B]
||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
val u = Free u';
val v = Free v';
val q = Free (fst p', mk_pred1T B);
val xctrs = map2 (curry Term.list_comb) ctrs xss;
val yctrs = map2 (curry Term.list_comb) ctrs yss;
val xfs = map2 (curry Term.list_comb) fs xss;
val xgs = map2 (curry Term.list_comb) gs xss;
(* TODO: Eta-expension is for compatibility with the old datatype package (but it also provides
nicer names). Consider removing. *)
val eta_fs = map2 eta_expand_arg xss xfs;
val eta_gs = map2 eta_expand_arg xss xgs;
val case_binding =
qualify false
(if Binding.is_empty raw_case_binding orelse
Binding.eq_name (raw_case_binding, standard_binding) then
Binding.prefix_name (caseN ^ "_") fc_b
else
raw_case_binding);
fun mk_case_disj xctr xf xs =
list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr), HOLogic.mk_eq (w, xf)));
val case_rhs = fold_rev (fold_rev Term.lambda) [fs, [u]]
(Const (@{const_name The}, (B --> HOLogic.boolT) --> B) $
Term.lambda w (Library.foldr1 HOLogic.mk_disj (map3 mk_case_disj xctrs xfs xss)));
val ((raw_case, (_, raw_case_def)), (lthy', lthy)) = no_defs_lthy
|> Local_Theory.define ((case_binding, NoSyn),
((Binding.conceal (Thm.def_binding case_binding), []), case_rhs))
||> `Local_Theory.restore;
val phi = Proof_Context.export_morphism lthy lthy';
val case_def = Morphism.thm phi raw_case_def;
val case0 = Morphism.term phi raw_case;
val casex = mk_case As B case0;
val fcase = Term.list_comb (casex, fs);
val ufcase = fcase $ u;
val vfcase = fcase $ v;
val eta_fcase = Term.list_comb (casex, eta_fs);
val eta_gcase = Term.list_comb (casex, eta_gs);
val eta_ufcase = eta_fcase $ u;
val eta_vgcase = eta_gcase $ v;
fun mk_uu_eq () = HOLogic.mk_eq (u, u);
val uv_eq = mk_Trueprop_eq (u, v);
val exist_xs_u_eq_ctrs =
map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
val unique_disc_no_def = TrueI; (*arbitrary marker*)
val alternate_disc_no_def = FalseE; (*arbitrary marker*)
fun alternate_disc_lhs get_udisc k =
HOLogic.mk_not
(let val b = nth disc_bindings (k - 1) in
if is_disc_binding_valid b then get_udisc b (k - 1) else nth exist_xs_u_eq_ctrs (k - 1)
end);
val (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy') =
if no_discs_sels then
(true, [], [], [], [], [], lthy')
else
let
fun disc_free b = Free (Binding.name_of b, mk_pred1T fcT);
fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
fun alternate_disc k =
Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
fun mk_sel_case_args b proto_sels T =
map2 (fn Ts => fn k =>
(case AList.lookup (op =) proto_sels k of
NONE =>
(case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
| SOME t => t |> Type.constraint (Ts ---> T) |> Syntax.check_term lthy)
| SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
fun sel_spec b proto_sels =
let
val _ =
(case duplicates (op =) (map fst proto_sels) of
k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
" for constructor " ^
quote (Syntax.string_of_term lthy (nth ctrs (k - 1))))
| [] => ())
val T =
(case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
[T] => T
| T :: T' :: _ => error ("Inconsistent range type for selector " ^
quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ lthy T) ^ " vs. "
^ quote (Syntax.string_of_typ lthy T')));
in
mk_Trueprop_eq (Free (Binding.name_of b, fcT --> T) $ u,
Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
end;
val sel_bindings = flat sel_bindingss;
val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
val sel_binding_index =
if all_sels_distinct then 1 upto length sel_bindings
else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
val sel_infos =
AList.group (op =) (sel_binding_index ~~ proto_sels)
|> sort (int_ord o pairself fst)
|> map snd |> curry (op ~~) uniq_sel_bindings;
val sel_bindings = map fst sel_infos;
fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
lthy
|> apfst split_list o fold_map3 (fn k => fn exist_xs_u_eq_ctr => fn b =>
if Binding.is_empty b then
if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
else pair (alternate_disc k, alternate_disc_no_def)
else if Binding.eq_name (b, equal_binding) then
pair (Term.lambda u exist_xs_u_eq_ctr, refl)
else
Specification.definition (SOME (b, NONE, NoSyn),
((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
ks exist_xs_u_eq_ctrs disc_bindings
||>> apfst split_list o fold_map (fn (b, proto_sels) =>
Specification.definition (SOME (b, NONE, NoSyn),
((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
||> `Local_Theory.restore;
val phi = Proof_Context.export_morphism lthy lthy';
val disc_defs = map (Morphism.thm phi) raw_disc_defs;
val sel_defs = map (Morphism.thm phi) raw_sel_defs;
val sel_defss = unflat_selss sel_defs;
val discs0 = map (Morphism.term phi) raw_discs;
val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
val discs = map (mk_disc_or_sel As) discs0;
val selss = map (map (mk_disc_or_sel As)) selss0;
in
(all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy')
end;
fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
val exhaust_goal =
let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (exh_y, xctr)]) in
fold_rev Logic.all [p, exh_y] (mk_imp_p (map2 mk_prem xctrs xss))
end;
val inject_goalss =
let
fun mk_goal _ _ [] [] = []
| mk_goal xctr yctr xs ys =
[fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
in
map4 mk_goal xctrs yctrs xss yss
end;
val half_distinct_goalss =
let
fun mk_goal ((xs, xc), (xs', xc')) =
fold_rev Logic.all (xs @ xs')
(HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
in
map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
end;
val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss;
fun after_qed thmss lthy =
let
val ([exhaust_thm0], (inject_thmss, half_distinct_thmss)) = (hd thmss, chop n (tl thmss));
(* for "datatype_realizer.ML": *)
val exhaust_thm =
Thm.name_derivation (fcT_name ^ Long_Name.separator ^ exhaustN) exhaust_thm0;
val inject_thms = flat inject_thmss;
val rho_As = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
fun inst_thm t thm =
Drule.instantiate' [] [SOME (certify lthy t)]
(Thm.instantiate (rho_As, []) (Drule.zero_var_indexes thm));
val uexhaust_thm = inst_thm u exhaust_thm;
val exhaust_cases = map base_name_of_ctr ctrs;
val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
val nchotomy_thm =
let
val goal =
HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
in
Goal.prove_sorry lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
|> Thm.close_derivation
end;
val case_thms =
let
val goals =
map3 (fn xctr => fn xf => fn xs =>
fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xctrs xfs xss;
in
map4 (fn k => fn goal => fn injects => fn distinctss =>
Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
mk_case_tac ctxt n k case_def injects distinctss)
|> Thm.close_derivation)
ks goals inject_thmss distinct_thmsss
end;
val (case_cong_thm, weak_case_cong_thm) =
let
fun mk_prem xctr xs xf xg =
fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
mk_Trueprop_eq (xf, xg)));
val goal =
Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss xfs xgs,
mk_Trueprop_eq (eta_ufcase, eta_vgcase));
val weak_goal = Logic.mk_implies (uv_eq, mk_Trueprop_eq (ufcase, vfcase));
in
(Goal.prove_sorry lthy [] [] goal (fn _ => mk_case_cong_tac lthy uexhaust_thm case_thms),
Goal.prove_sorry lthy [] [] weak_goal (K (etac arg_cong 1)))
|> pairself (singleton (Proof_Context.export names_lthy lthy) #>
Thm.close_derivation)
end;
val split_lhs = q $ ufcase;
fun mk_split_conjunct xctr xs f_xs =
list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
fun mk_split_disjunct xctr xs f_xs =
list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
HOLogic.mk_not (q $ f_xs)));
fun mk_split_goal xctrs xss xfs =
mk_Trueprop_eq (split_lhs, Library.foldr1 HOLogic.mk_conj
(map3 mk_split_conjunct xctrs xss xfs));
fun mk_split_asm_goal xctrs xss xfs =
mk_Trueprop_eq (split_lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
(map3 mk_split_disjunct xctrs xss xfs)));
fun prove_split selss goal =
Goal.prove_sorry lthy [] [] goal (fn _ =>
mk_split_tac lthy uexhaust_thm case_thms selss inject_thmss distinct_thmsss)
|> singleton (Proof_Context.export names_lthy lthy)
|> Thm.close_derivation;
fun prove_split_asm asm_goal split_thm =
Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
mk_split_asm_tac ctxt split_thm)
|> singleton (Proof_Context.export names_lthy lthy)
|> Thm.close_derivation;
val (split_thm, split_asm_thm) =
let
val goal = mk_split_goal xctrs xss xfs;
val asm_goal = mk_split_asm_goal xctrs xss xfs;
val thm = prove_split (replicate n []) goal;
val asm_thm = prove_split_asm asm_goal thm;
in
(thm, asm_thm)
end;
val (sel_defs, all_sel_thms, sel_thmss, disc_defs, disc_thmss, nontriv_disc_thmss,
discI_thms, nontriv_discI_thms, disc_exclude_thms, disc_exclude_thmsss,
disc_exhaust_thms, sel_exhaust_thms, all_collapse_thms, safe_collapse_thms,
expand_thms, sel_split_thms, sel_split_asm_thms, case_eq_if_thms) =
if no_discs_sels then
([], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [])
else
let
val udiscs = map (rapp u) discs;
val uselss = map (map (rapp u)) selss;
val usel_ctrs = map2 (curry Term.list_comb) ctrs uselss;
val usel_fs = map2 (curry Term.list_comb) fs uselss;
val vdiscs = map (rapp v) discs;
val vselss = map (map (rapp v)) selss;
fun make_sel_thm xs' case_thm sel_def =
zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
(Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
fun has_undefined_rhs thm =
(case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
Const (@{const_name undefined}, _) => true
| _ => false);
val all_sel_thms =
(if all_sels_distinct andalso forall null sel_defaultss then
flat sel_thmss
else
map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
(xss' ~~ case_thms))
|> filter_out has_undefined_rhs;
fun mk_unique_disc_def () =
let
val m = the_single ms;
val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
in
Goal.prove_sorry lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
|> singleton (Proof_Context.export names_lthy lthy)
|> Thm.close_derivation
end;
fun mk_alternate_disc_def k =
let
val goal =
mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
nth exist_xs_u_eq_ctrs (k - 1));
in
Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
(nth distinct_thms (2 - k)) uexhaust_thm)
|> singleton (Proof_Context.export names_lthy lthy)
|> Thm.close_derivation
end;
val has_alternate_disc_def =
exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
val disc_defs' =
map2 (fn k => fn def =>
if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
else def) ks disc_defs;
val discD_thms = map (fn def => def RS iffD1) disc_defs';
val discI_thms =
map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
disc_defs';
val not_discI_thms =
map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
(unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
ms disc_defs';
val (disc_thmss', disc_thmss) =
let
fun mk_thm discI _ [] = refl RS discI
| mk_thm _ not_discI [distinct] = distinct RS not_discI;
fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
in
map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
end;
val nontriv_disc_thmss =
map2 (fn b => if is_disc_binding_valid b then I else K []) disc_bindings disc_thmss;
fun is_discI_boring b =
(n = 1 andalso Binding.is_empty b) orelse Binding.eq_name (b, equal_binding);
val nontriv_discI_thms =
flat (map2 (fn b => if is_discI_boring b then K [] else single) disc_bindings
discI_thms);
val (disc_exclude_thms, (disc_exclude_thmsss', disc_exclude_thmsss)) =
let
fun mk_goal [] = []
| mk_goal [((_, udisc), (_, udisc'))] =
[Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
fun prove tac goal =
Goal.prove_sorry lthy [] [] goal (K tac)
|> Thm.close_derivation;
val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
val half_goalss = map mk_goal half_pairss;
val half_thmss =
map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
fn disc_thm => [prove (mk_half_disc_exclude_tac lthy m discD disc_thm) goal])
half_goalss half_pairss (flat disc_thmss');
val other_half_goalss = map (mk_goal o map swap) half_pairss;
val other_half_thmss =
map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
other_half_goalss;
in
join_halves n half_thmss other_half_thmss ||> `transpose
|>> has_alternate_disc_def ? K []
end;
val disc_exhaust_thm =
let
fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
in
Goal.prove_sorry lthy [] [] goal (fn _ =>
mk_disc_exhaust_tac n exhaust_thm discI_thms)
|> Thm.close_derivation
end;
val (safe_collapse_thms, all_collapse_thms) =
let
fun mk_goal m udisc usel_ctr =
let
val prem = HOLogic.mk_Trueprop udisc;
val concl = mk_Trueprop_eq ((usel_ctr, u) |> m = 0 ? swap);
in
(prem aconv concl, Logic.all u (Logic.mk_implies (prem, concl)))
end;
val (trivs, goals) = map3 mk_goal ms udiscs usel_ctrs |> split_list;
val thms =
map5 (fn m => fn discD => fn sel_thms => fn triv => fn goal =>
Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
mk_collapse_tac ctxt m discD sel_thms ORELSE HEADGOAL atac)
|> Thm.close_derivation
|> not triv ? perhaps (try (fn thm => refl RS thm)))
ms discD_thms sel_thmss trivs goals;
in
(map_filter (fn (true, _) => NONE | (false, thm) => SOME thm) (trivs ~~ thms),
thms)
end;
val swapped_all_collapse_thms =
map2 (fn m => fn thm => if m = 0 then thm else thm RS sym) ms all_collapse_thms;
val sel_exhaust_thm =
let
fun mk_prem usel_ctr = mk_imp_p [mk_Trueprop_eq (u, usel_ctr)];
val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem usel_ctrs));
in
Goal.prove_sorry lthy [] [] goal (fn _ =>
mk_sel_exhaust_tac n disc_exhaust_thm swapped_all_collapse_thms)
|> Thm.close_derivation
end;
val expand_thm =
let
fun mk_prems k udisc usels vdisc vsels =
(if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
(if null usels then
[]
else
[Logic.list_implies
(if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
(map2 (curry HOLogic.mk_eq) usels vsels)))]);
val goal =
Library.foldr Logic.list_implies
(map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
val uncollapse_thms =
map2 (fn thm => fn [] => thm | _ => thm RS sym) all_collapse_thms uselss;
in
Goal.prove_sorry lthy [] [] goal (fn _ =>
mk_expand_tac lthy n ms (inst_thm u disc_exhaust_thm)
(inst_thm v disc_exhaust_thm) uncollapse_thms disc_exclude_thmsss
disc_exclude_thmsss')
|> singleton (Proof_Context.export names_lthy lthy)
|> Thm.close_derivation
end;
val (sel_split_thm, sel_split_asm_thm) =
let
val zss = map (K []) xss;
val goal = mk_split_goal usel_ctrs zss usel_fs;
val asm_goal = mk_split_asm_goal usel_ctrs zss usel_fs;
val thm = prove_split sel_thmss goal;
val asm_thm = prove_split_asm asm_goal thm;
in
(thm, asm_thm)
end;
val case_eq_if_thm =
let
val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs usel_fs);
in
Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
mk_case_eq_if_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)
|> singleton (Proof_Context.export names_lthy lthy)
|> Thm.close_derivation
end;
in
(sel_defs, all_sel_thms, sel_thmss, disc_defs, disc_thmss, nontriv_disc_thmss,
discI_thms, nontriv_discI_thms, disc_exclude_thms, disc_exclude_thmsss,
[disc_exhaust_thm], [sel_exhaust_thm], all_collapse_thms, safe_collapse_thms,
[expand_thm], [sel_split_thm], [sel_split_asm_thm], [case_eq_if_thm])
end;
val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
val cases_type_attr = Attrib.internal (K (Induct.cases_type fcT_name));
val nontriv_disc_eq_thmss =
map (map (fn th => th RS @{thm eq_False[THEN iffD2]}
handle THM _ => th RS @{thm eq_True[THEN iffD2]})) nontriv_disc_thmss;
val anonymous_notes =
[(map (fn th => th RS notE) distinct_thms, safe_elim_attrs),
(flat nontriv_disc_eq_thmss, code_nitpicksimp_attrs)]
|> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
(* "exhaust" is deliberately put first to avoid apparent circular dependencies in the proof
objects, which would confuse MaSh. *)
val notes =
[(exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
(caseN, case_thms, code_nitpicksimp_simp_attrs),
(case_congN, [case_cong_thm], []),
(case_eq_ifN, case_eq_if_thms, []),
(collapseN, safe_collapse_thms, simp_attrs),
(discN, flat nontriv_disc_thmss, simp_attrs),
(discIN, nontriv_discI_thms, []),
(disc_excludeN, disc_exclude_thms, dest_attrs),
(disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
(distinctN, distinct_thms, simp_attrs @ inductsimp_attrs),
(expandN, expand_thms, []),
(injectN, inject_thms, iff_attrs @ inductsimp_attrs),
(nchotomyN, [nchotomy_thm], []),
(selN, all_sel_thms, code_nitpicksimp_simp_attrs),
(sel_exhaustN, sel_exhaust_thms, [exhaust_case_names_attr]),
(sel_splitN, sel_split_thms, []),
(sel_split_asmN, sel_split_asm_thms, []),
(splitN, [split_thm], []),
(split_asmN, [split_asm_thm], []),
(splitsN, [split_thm, split_asm_thm], []),
(weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]
|> filter_out (null o #2)
|> map (fn (thmN, thms, attrs) =>
((qualify true (Binding.name thmN), attrs), [(thms, [])]));
val ctr_sugar =
{ctrs = ctrs, casex = casex, discs = discs, selss = selss, exhaust = exhaust_thm,
nchotomy = nchotomy_thm, injects = inject_thms, distincts = distinct_thms,
case_thms = case_thms, case_cong = case_cong_thm, weak_case_cong = weak_case_cong_thm,
split = split_thm, split_asm = split_asm_thm, disc_defs = disc_defs,
disc_thmss = disc_thmss, discIs = discI_thms, sel_defs = sel_defs, sel_thmss = sel_thmss,
disc_excludesss = disc_exclude_thmsss, disc_exhausts = disc_exhaust_thms,
sel_exhausts = sel_exhaust_thms, collapses = all_collapse_thms, expands = expand_thms,
sel_splits = sel_split_thms, sel_split_asms = sel_split_asm_thms,
case_eq_ifs = case_eq_if_thms};
in
(ctr_sugar,
lthy
|> Spec_Rules.add Spec_Rules.Equational ([casex], case_thms)
|> fold (Spec_Rules.add Spec_Rules.Equational)
(AList.group (eq_list (op aconv)) (map (`(single o lhs_head_of)) all_sel_thms))
|> fold (Spec_Rules.add Spec_Rules.Equational)
(filter_out (null o snd) (map single discs ~~ nontriv_disc_eq_thmss))
|> Local_Theory.declaration {syntax = false, pervasive = true}
(fn phi => Case_Translation.register
(Morphism.term phi casex) (map (Morphism.term phi) ctrs))
|> Local_Theory.background_theory (fold (fold Code.del_eqn) [disc_defs, sel_defs])
|> not no_code ?
Local_Theory.declaration {syntax = false, pervasive = false}
(fn phi => Context.mapping
(add_ctr_code fcT_name (map (Morphism.typ phi) As)
(map (dest_Const o Morphism.term phi) ctrs) (Morphism.fact phi inject_thms)
(Morphism.fact phi distinct_thms) (Morphism.fact phi case_thms))
I)
|> Local_Theory.notes (anonymous_notes @ notes) |> snd
|> register_ctr_sugar fcT_name ctr_sugar)
end;
in
(goalss, after_qed, lthy')
end;
fun free_constructors tacss = (fn (goalss, after_qed, lthy) =>
map2 (map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])) goalss tacss
|> (fn thms => after_qed thms lthy)) oo prepare_free_constructors (K I);
val free_constructors_cmd = (fn (goalss, after_qed, lthy) =>
Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
prepare_free_constructors Syntax.read_term;
val parse_bound_term = parse_binding --| @{keyword ":"} -- Parse.term;
val parse_ctr_options =
Scan.optional (@{keyword "("} |-- Parse.list1
(Parse.reserved "no_discs_sels" >> K 0 || Parse.reserved "no_code" >> K 1) --|
@{keyword ")"}
>> (fn js => (member (op =) js 0, member (op =) js 1)))
(false, false);
val parse_defaults =
@{keyword "("} |-- Parse.reserved "defaults" |-- Scan.repeat parse_bound_term --| @{keyword ")"};
fun parse_ctr_spec parse_ctr parse_arg =
parse_opt_binding_colon -- parse_ctr -- Scan.repeat parse_arg --
Scan.optional parse_defaults [];
val parse_ctr_specs = Parse.enum1 "|" (parse_ctr_spec Parse.term parse_binding);
val _ =
Outer_Syntax.local_theory_to_proof @{command_spec "free_constructors"}
"register an existing freely generated type's constructors"
(parse_ctr_options -- parse_binding --| @{keyword "for"} -- parse_ctr_specs
>> free_constructors_cmd);
val _ = Context.>> (Context.map_theory Ctr_Sugar_Interpretation.init);
end;