(* Title: HOL/BNF/Tools/bnf_ctr_sugar.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2012
Wrapping existing freely generated type's constructors.
*)
signature BNF_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_thmss: thm list list,
discIs: thm list,
sel_thmss: thm list list,
disc_exhausts: thm list,
collapses: thm list,
expands: thm list,
case_convs: thm list};
val morph_ctr_sugar: morphism -> ctr_sugar -> ctr_sugar
val rep_compat_prefix: string
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_disc_or_sel: typ list -> term -> term
val name_of_ctr: term -> string
val name_of_disc: term -> string
val wrap_free_constructors: ({prems: thm list, context: Proof.context} -> tactic) list list ->
(((bool * bool) * term list) * binding) *
(binding list * (binding list list * (binding * term) list list)) -> local_theory ->
ctr_sugar * local_theory
val parse_wrap_free_constructors_options: (bool * bool) parser
val parse_bound_term: (binding * string) parser
end;
structure BNF_Ctr_Sugar : BNF_CTR_SUGAR =
struct
open BNF_Util
open BNF_Ctr_Sugar_Tactics
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_thmss: thm list list,
discIs: thm list,
sel_thmss: thm list list,
disc_exhausts: thm list,
collapses: thm list,
expands: thm list,
case_convs: 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_thmss, discIs, sel_thmss,
disc_exhausts, collapses, expands, case_convs} =
{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_thmss = map (map (Morphism.thm phi)) disc_thmss,
discIs = map (Morphism.thm phi) discIs,
sel_thmss = map (map (Morphism.thm phi)) sel_thmss,
disc_exhausts = map (Morphism.thm phi) disc_exhausts,
collapses = map (Morphism.thm phi) collapses,
expands = map (Morphism.thm phi) expands,
case_convs = map (Morphism.thm phi) case_convs};
val rep_compat_prefix = "new";
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_convN = "case_conv";
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 splitN = "split";
val splitsN = "splits";
val split_asmN = "split_asm";
val weak_case_cong_thmsN = "weak_case_cong";
val cong_attrs = @{attributes [cong]};
val safe_elim_attrs = @{attributes [elim!]};
val iff_attrs = @{attributes [iff]};
val induct_simp_attrs = @{attributes [induct_simp]};
val simp_attrs = @{attributes [simp]};
fun unflat_lookup eq xs ys = map (fn xs' => permute_like 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 =
let
val xsss =
map2 (map2 append) (Library.chop_groups n half_xss)
(transpose (Library.chop_groups n other_half_xss))
val xs = splice (flat half_xss) (flat other_half_xss);
in (xs, xsss) end;
fun mk_undefined T = Const (@{const_name undefined}, T);
fun mk_ctr Ts t =
let val Type (_, Ts0) = body_type (fastype_of t) in
Term.subst_atomic_types (Ts0 ~~ Ts) t
end;
fun mk_disc_or_sel Ts t =
Term.subst_atomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
fun mk_case Ts T t =
let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in
Term.subst_atomic_types ((body, T) :: (Ts0 ~~ Ts)) t
end;
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 eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;
fun prepare_wrap_free_constructors prep_term ((((no_discs_sels, rep_compat), raw_ctrs),
raw_case_binding), (raw_disc_bindings, (raw_sel_bindingss, raw_sel_defaultss))) no_defs_lthy =
let
(* TODO: sanity checks on arguments *)
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 =
pad_list [] n (map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss);
val Type (dataT_name, As0) = body_type (fastype_of (hd ctrs0));
val data_b_name = Long_Name.base_name dataT_name;
val data_b = Binding.name data_b_name;
fun qualify mandatory =
Binding.qualify mandatory data_b_name o
(rep_compat ? Binding.qualify false rep_compat_prefix);
fun dest_TFree_or_TVar (TFree p) = p
| 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 dataT = Type (dataT_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;
val raw_disc_bindings' = pad_list Binding.empty n raw_disc_bindings;
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));
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 standard_disc_binding ctr
else if Binding.eq_name (disc, equal_binding) then
if m = 0 then disc
else error "Cannot use \"=\" syntax for discriminating nonnullary constructor"
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 =
pad_list [] n raw_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;
val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
val ((((((((xss, xss'), yss), fs), gs), [u', v']), [w]), (p, p')), names_lthy) = no_defs_lthy |>
mk_Freess' "x" ctr_Tss
||>> mk_Freess "y" ctr_Tss
||>> mk_Frees "f" case_Ts
||>> mk_Frees "g" case_Ts
||>> (apfst (map (rpair dataT)) oo Variable.variant_fixes) [data_b_name, data_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.suffix_name ("_" ^ caseN) data_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), ((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, udiscs, uselss, vdiscs, vselss, 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 dataT);
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, dataT --> 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;
val udiscs = map (rapp u) discs;
val uselss = map (map (rapp u)) selss;
val vdiscs = map (rapp v) discs;
val vselss = map (map (rapp v)) selss;
in
(all_sels_distinct, discs, selss, udiscs, uselss, vdiscs, vselss, 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 (u, xctr)]) in
fold_rev Logic.all [p, u] (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_thm], (inject_thmss, half_distinct_thmss)) = (hd thmss, chop n (tl thmss));
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 (all_sel_thms, sel_thmss, disc_thmss, disc_thms, discI_thms, disc_exclude_thms,
disc_exhaust_thms, collapse_thms, expand_thms, case_conv_thms) =
if no_discs_sels then
([], [], [], [], [], [], [], [], [], [])
else
let
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)))));
fun has_undefined_rhs thm =
(case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
Const (@{const_name undefined}, _) => true
| _ => false);
val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
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)
|> Thm.close_derivation
|> singleton (Proof_Context.export names_lthy lthy)
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)
|> Thm.close_derivation
|> singleton (Proof_Context.export names_lthy lthy)
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 disc_thms = flat (map2 (fn b => if is_disc_binding_valid b then I else K [])
disc_bindings disc_thmss);
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 (collapse_thms, collapse_thm_opts) =
let
fun mk_goal ctr udisc usels =
let
val prem = HOLogic.mk_Trueprop udisc;
val concl =
mk_Trueprop_eq ((null usels ? swap) (Term.list_comb (ctr, usels), u));
in
if prem aconv concl then NONE
else SOME (Logic.all u (Logic.mk_implies (prem, concl)))
end;
val goals = map3 mk_goal ctrs udiscs uselss;
in
map4 (fn m => fn discD => fn sel_thms => Option.map (fn goal =>
Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
mk_collapse_tac ctxt m discD sel_thms)
|> Thm.close_derivation
|> perhaps (try (fn thm => refl RS thm)))) ms discD_thms sel_thmss goals
|> `(map_filter I)
end;
val expand_thms =
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 NONE => K asm_rl | SOME thm => fn [] => thm | _ => thm RS sym)
collapse_thm_opts 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')]
|> map Thm.close_derivation
|> Proof_Context.export names_lthy lthy
end;
val case_conv_thms =
let
fun mk_body f usels = Term.list_comb (f, usels);
val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs (map2 mk_body fs uselss));
in
[Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
mk_case_conv_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)]
|> map Thm.close_derivation
|> Proof_Context.export names_lthy lthy
end;
in
(all_sel_thms, sel_thmss, disc_thmss, disc_thms, discI_thms, disc_exclude_thms,
[disc_exhaust_thm], collapse_thms, expand_thms, case_conv_thms)
end;
val nontriv_discI_thms = if n = 1 then [] else discI_thms;
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 (Thm.close_derivation #> singleton (Proof_Context.export names_lthy lthy))
end;
val (split_thm, split_asm_thm) =
let
fun mk_conjunct xctr xs f_xs =
list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
fun mk_disjunct xctr xs f_xs =
list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
HOLogic.mk_not (q $ f_xs)));
val lhs = q $ ufcase;
val goal =
mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs));
val asm_goal =
mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
(map3 mk_disjunct xctrs xss xfs)));
val split_thm =
Goal.prove_sorry lthy [] [] goal
(fn _ => mk_split_tac lthy uexhaust_thm case_thms inject_thmss distinct_thmsss)
|> Thm.close_derivation
|> singleton (Proof_Context.export names_lthy lthy);
val split_asm_thm =
Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
mk_split_asm_tac ctxt split_thm)
|> Thm.close_derivation
|> singleton (Proof_Context.export names_lthy lthy);
in
(split_thm, split_asm_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 dataT_name));
val notes =
[(caseN, case_thms, simp_attrs),
(case_congN, [case_cong_thm], []),
(case_convN, case_conv_thms, []),
(collapseN, collapse_thms, simp_attrs),
(discN, disc_thms, simp_attrs),
(discIN, nontriv_discI_thms, []),
(disc_excludeN, disc_exclude_thms, []),
(disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
(distinctN, distinct_thms, simp_attrs @ induct_simp_attrs),
(exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
(expandN, expand_thms, []),
(injectN, inject_thms, iff_attrs @ induct_simp_attrs),
(nchotomyN, [nchotomy_thm], []),
(selN, all_sel_thms, simp_attrs),
(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 notes' =
[(map (fn th => th RS notE) distinct_thms, safe_elim_attrs)]
|> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
in
({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_thmss = disc_thmss,
discIs = discI_thms, sel_thmss = sel_thmss, disc_exhausts = disc_exhaust_thms,
collapses = collapse_thms, expands = expand_thms, case_convs = case_conv_thms},
lthy
|> not rep_compat ?
(Local_Theory.declaration {syntax = false, pervasive = true}
(fn phi => Case_Translation.register
(Morphism.term phi casex) (map (Morphism.term phi) ctrs)))
|> Local_Theory.notes (notes' @ notes) |> snd)
end;
in
(goalss, after_qed, lthy')
end;
fun wrap_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_wrap_free_constructors (K I);
val wrap_free_constructors_cmd = (fn (goalss, after_qed, lthy) =>
Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
prepare_wrap_free_constructors Syntax.read_term;
fun parse_bracket_list parser = @{keyword "["} |-- Parse.list parser --| @{keyword "]"};
val parse_bindings = parse_bracket_list parse_binding;
val parse_bindingss = parse_bracket_list parse_bindings;
val parse_bound_term = (parse_binding --| @{keyword ":"}) -- Parse.term;
val parse_bound_terms = parse_bracket_list parse_bound_term;
val parse_bound_termss = parse_bracket_list parse_bound_terms;
val parse_wrap_free_constructors_options =
Scan.optional (@{keyword "("} |-- Parse.list1 ((@{keyword "no_discs_sels"} >> K (true, false)) ||
(@{keyword "rep_compat"} >> K (false, true))) --| @{keyword ")"}
>> (pairself (exists I) o split_list)) (false, false);
val _ =
Outer_Syntax.local_theory_to_proof @{command_spec "wrap_free_constructors"}
"wrap an existing freely generated type's constructors"
((parse_wrap_free_constructors_options -- (@{keyword "["} |-- Parse.list Parse.term --|
@{keyword "]"}) --
parse_binding -- Scan.optional (parse_bindings -- Scan.optional (parse_bindingss --
Scan.optional parse_bound_termss []) ([], [])) ([], ([], [])))
>> wrap_free_constructors_cmd);
end;