author | blanchet |
Sat, 08 Sep 2012 21:04:26 +0200 | |
changeset 49203 | 262ab1ac38b9 |
parent 49201 | c69c2c18dccb |
child 49210 | 656fb50d33f0 |
permissions | -rw-r--r-- |
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(* Title: HOL/Codatatype/Tools/bnf_wrap.ML |
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Author: Jasmin Blanchette, TU Muenchen |
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Copyright 2012 |
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Wrapping existing datatypes. |
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*) |
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signature BNF_WRAP = |
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sig |
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val no_binder: binding |
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val mk_half_pairss: 'a list -> ('a * 'a) list list |
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val mk_ctr: typ list -> term -> term |
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val wrap_datatype: ({prems: thm list, context: Proof.context} -> tactic) list list -> |
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(term list * term) * (binding list * binding list list) -> local_theory -> local_theory |
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end; |
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structure BNF_Wrap : BNF_WRAP = |
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struct |
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open BNF_Util |
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open BNF_Wrap_Tactics |
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val is_N = "is_"; |
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val un_N = "un_"; |
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fun mk_un_N 1 1 suf = un_N ^ suf |
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| mk_un_N _ l suf = un_N ^ suf ^ string_of_int l; |
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val case_congN = "case_cong"; |
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val case_eqN = "case_eq"; |
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val casesN = "cases"; |
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val collapseN = "collapse"; |
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val disc_excludeN = "disc_exclude"; |
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val disc_exhaustN = "disc_exhaust"; |
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val discsN = "discs"; |
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val distinctN = "distinct"; |
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val exhaustN = "exhaust"; |
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val injectN = "inject"; |
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val nchotomyN = "nchotomy"; |
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val selsN = "sels"; |
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val splitN = "split"; |
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val split_asmN = "split_asm"; |
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val weak_case_cong_thmsN = "weak_case_cong"; |
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val no_binder = @{binding ""}; |
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val fallback_binder = @{binding _}; |
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fun pad_list x n xs = xs @ replicate (n - length xs) x; |
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fun mk_half_pairss' _ [] = [] |
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| mk_half_pairss' indent (y :: ys) = |
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indent @ fold_rev (cons o single o pair y) ys (mk_half_pairss' ([] :: indent) ys); |
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fun mk_half_pairss ys = mk_half_pairss' [[]] ys; |
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(* TODO: provide a way to have a different default value, e.g. "tl Nil = Nil" *) |
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fun mk_undef T Ts = Const (@{const_name undefined}, Ts ---> T); |
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fun mk_ctr Ts ctr = |
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let val Type (_, Ts0) = body_type (fastype_of ctr) in |
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Term.subst_atomic_types (Ts0 ~~ Ts) ctr |
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end; |
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||
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fun eta_expand_case_arg xs f_xs = fold_rev Term.lambda xs f_xs; |
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fun name_of_ctr c = |
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case head_of c of |
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Const (s, _) => s |
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| Free (s, _) => s |
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| _ => error "Cannot extract name of constructor"; |
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fun prepare_wrap_datatype prep_term ((raw_ctrs, raw_case), (raw_disc_binders, raw_sel_binderss)) |
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no_defs_lthy = |
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let |
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(* TODO: sanity checks on arguments *) |
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(* TODO: attributes (simp, case_names, etc.) *) |
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(* TODO: case syntax *) |
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(* TODO: integration with function package ("size") *) |
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val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs; |
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val case0 = prep_term no_defs_lthy raw_case; |
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val n = length ctrs0; |
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val ks = 1 upto n; |
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val _ = if n > 0 then () else error "No constructors specified"; |
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val Type (T_name, As0) = body_type (fastype_of (hd ctrs0)); |
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val b = Binding.qualified_name T_name; |
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||
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val (As, B) = |
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no_defs_lthy |
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|> mk_TFrees (length As0) |
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||> the_single o fst o mk_TFrees 1; |
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||
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val T = Type (T_name, As); |
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val ctrs = map (mk_ctr As) ctrs0; |
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val ctr_Tss = map (binder_types o fastype_of) ctrs; |
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||
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val ms = map length ctr_Tss; |
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||
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val raw_disc_binders' = pad_list no_binder n raw_disc_binders; |
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fun can_really_rely_on_disc k = |
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not (Binding.eq_name (nth raw_disc_binders' (k - 1), no_binder)) orelse nth ms (k - 1) = 0; |
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fun can_rely_on_disc k = |
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can_really_rely_on_disc k orelse (k = 1 andalso not (can_really_rely_on_disc 2)); |
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fun can_omit_disc_binder k m = |
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n = 1 orelse m = 0 orelse (n = 2 andalso can_rely_on_disc (3 - k)); |
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val fallback_disc_binder = Binding.name o prefix is_N o Long_Name.base_name o name_of_ctr; |
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val disc_binders = |
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raw_disc_binders' |
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|> map4 (fn k => fn m => fn ctr => fn disc => |
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if Binding.eq_name (disc, no_binder) then |
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if can_omit_disc_binder k m then NONE else SOME (fallback_disc_binder ctr) |
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else if Binding.eq_name (disc, fallback_binder) then |
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SOME (fallback_disc_binder ctr) |
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else |
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SOME disc) ks ms ctrs0; |
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val no_discs = map is_none disc_binders; |
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val no_discs_at_all = forall I no_discs; |
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fun fallback_sel_binder m l = Binding.name o mk_un_N m l o Long_Name.base_name o name_of_ctr; |
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val sel_binderss = |
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pad_list [] n raw_sel_binderss |
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|> map3 (fn ctr => fn m => map2 (fn l => fn sel => |
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if Binding.eq_name (sel, no_binder) orelse Binding.eq_name (sel, fallback_binder) then |
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fallback_sel_binder m l ctr |
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else |
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sel) (1 upto m) o pad_list no_binder m) ctrs0 ms; |
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fun mk_case Ts T = |
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let |
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val (binders, body) = strip_type (fastype_of case0) |
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val Type (_, Ts0) = List.last binders |
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in Term.subst_atomic_types ((body, T) :: (Ts0 ~~ Ts)) case0 end; |
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val casex = mk_case As B; |
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val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss; |
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val (((((((xss, yss), fs), gs), (v, v')), w), (p, p')), names_lthy) = no_defs_lthy |> |
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mk_Freess "x" ctr_Tss |
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||>> mk_Freess "y" ctr_Tss |
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||>> mk_Frees "f" case_Ts |
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||>> mk_Frees "g" case_Ts |
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||>> yield_singleton (apfst (op ~~) oo mk_Frees' "v") T |
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||>> yield_singleton (mk_Frees "w") T |
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||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT; |
152 |
||
153 |
val q = Free (fst p', B --> HOLogic.boolT); |
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fun mk_v_eq_v () = HOLogic.mk_eq (v, v); |
156 |
||
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val xctrs = map2 (curry Term.list_comb) ctrs xss; |
158 |
val yctrs = map2 (curry Term.list_comb) ctrs yss; |
|
49032 | 159 |
|
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val xfs = map2 (curry Term.list_comb) fs xss; |
161 |
val xgs = map2 (curry Term.list_comb) gs xss; |
|
162 |
||
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val eta_fs = map2 eta_expand_case_arg xss xfs; |
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val eta_gs = map2 eta_expand_case_arg xss xgs; |
49043 | 165 |
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49201 | 166 |
val fcase = Term.list_comb (casex, eta_fs); |
167 |
val gcase = Term.list_comb (casex, eta_gs); |
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168 |
|
49025 | 169 |
val exist_xs_v_eq_ctrs = |
170 |
map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (v, xctr))) xctrs xss; |
|
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172 |
fun mk_sel_case_args k xs x T = |
49025 | 173 |
map2 (fn Ts => fn i => if i = k then fold_rev Term.lambda xs x else mk_undef T Ts) ctr_Tss ks; |
174 |
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fun disc_free b = Free (Binding.name_of b, T --> HOLogic.boolT); |
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fun disc_spec b exist_xs_v_eq_ctr = mk_Trueprop_eq (disc_free b $ v, exist_xs_v_eq_ctr); |
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fun alternate_disc_lhs k = |
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180 |
HOLogic.mk_not |
49152 | 181 |
(case nth disc_binders (k - 1) of |
182 |
NONE => nth exist_xs_v_eq_ctrs (k - 1) |
|
183 |
| SOME b => disc_free b $ v); |
|
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184 |
|
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fun alternate_disc k = |
49152 | 186 |
if n = 2 then Term.lambda v (alternate_disc_lhs (3 - k)) else error "Cannot use \"*\" here" |
49025 | 187 |
|
49028 | 188 |
fun sel_spec b x xs k = |
49025 | 189 |
let val T' = fastype_of x in |
49032 | 190 |
mk_Trueprop_eq (Free (Binding.name_of b, T --> T') $ v, |
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191 |
Term.list_comb (mk_case As T', mk_sel_case_args k xs x T') $ v) |
49022 | 192 |
end; |
193 |
||
49137 | 194 |
val missing_unique_disc_def = TrueI; (*arbitrary marker*) |
195 |
val missing_alternate_disc_def = FalseE; (*arbitrary marker*) |
|
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(* TODO: Allow use of same selector for several constructors *) |
198 |
(* TODO: Allow use of same name for datatype and for constructor, e.g. "data L = L" *) |
|
199 |
||
49114 | 200 |
val (((raw_discs, raw_disc_defs), (raw_selss, raw_sel_defss)), (lthy', lthy)) = |
49022 | 201 |
no_defs_lthy |
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202 |
|> apfst split_list o fold_map4 (fn k => fn m => fn exist_xs_v_eq_ctr => |
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203 |
fn NONE => |
49137 | 204 |
if n = 1 then pair (Term.lambda v (mk_v_eq_v ()), missing_unique_disc_def) |
49136 | 205 |
else if m = 0 then pair (Term.lambda v exist_xs_v_eq_ctr, refl) |
49137 | 206 |
else pair (alternate_disc k, missing_alternate_disc_def) |
49114 | 207 |
| SOME b => Specification.definition (SOME (b, NONE, NoSyn), |
208 |
((Thm.def_binding b, []), disc_spec b exist_xs_v_eq_ctr)) #>> apsnd snd) |
|
49129 | 209 |
ks ms exist_xs_v_eq_ctrs disc_binders |
49114 | 210 |
||>> apfst split_list o fold_map3 (fn bs => fn xs => fn k => apfst split_list o |
211 |
fold_map2 (fn b => fn x => Specification.definition (SOME (b, NONE, NoSyn), |
|
49129 | 212 |
((Thm.def_binding b, []), sel_spec b x xs k)) #>> apsnd snd) bs xs) sel_binderss xss ks |
49022 | 213 |
||> `Local_Theory.restore; |
214 |
||
49025 | 215 |
(*transforms defined frees into consts (and more)*) |
216 |
val phi = Proof_Context.export_morphism lthy lthy'; |
|
217 |
||
49028 | 218 |
val disc_defs = map (Morphism.thm phi) raw_disc_defs; |
219 |
val sel_defss = map (map (Morphism.thm phi)) raw_sel_defss; |
|
220 |
||
221 |
val discs0 = map (Morphism.term phi) raw_discs; |
|
222 |
val selss0 = map (map (Morphism.term phi)) raw_selss; |
|
49025 | 223 |
|
49203 | 224 |
fun mk_disc_or_sel Ts c = |
225 |
Term.subst_atomic_types (snd (Term.dest_Type (domain_type (fastype_of c))) ~~ Ts) c; |
|
49028 | 226 |
|
227 |
val discs = map (mk_disc_or_sel As) discs0; |
|
228 |
val selss = map (map (mk_disc_or_sel As)) selss0; |
|
49025 | 229 |
|
49032 | 230 |
fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p); |
49029 | 231 |
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232 |
val goal_exhaust = |
49032 | 233 |
let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (v, xctr)]) in |
49121 | 234 |
fold_rev Logic.all [p, v] (mk_imp_p (map2 mk_prem xctrs xss)) |
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235 |
end; |
49019 | 236 |
|
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237 |
val goal_injectss = |
49017 | 238 |
let |
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|
239 |
fun mk_goal _ _ [] [] = [] |
49025 | 240 |
| mk_goal xctr yctr xs ys = |
49121 | 241 |
[fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr), |
242 |
Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))]; |
|
49017 | 243 |
in |
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244 |
map4 mk_goal xctrs yctrs xss yss |
49017 | 245 |
end; |
246 |
||
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diff
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|
247 |
val goal_half_distinctss = |
49121 | 248 |
let |
49203 | 249 |
fun mk_goal ((xs, xc), (xs', xc')) = |
49121 | 250 |
fold_rev Logic.all (xs @ xs') |
49203 | 251 |
(HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc')))); |
49121 | 252 |
in |
253 |
map (map mk_goal) (mk_half_pairss (xss ~~ xctrs)) |
|
254 |
end; |
|
49019 | 255 |
|
49121 | 256 |
val goal_cases = |
257 |
map3 (fn xs => fn xctr => fn xf => |
|
49201 | 258 |
fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xss xctrs xfs; |
49025 | 259 |
|
49121 | 260 |
val goalss = [goal_exhaust] :: goal_injectss @ goal_half_distinctss @ [goal_cases]; |
49019 | 261 |
|
262 |
fun after_qed thmss lthy = |
|
263 |
let |
|
49048
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49046
diff
changeset
|
264 |
val ([exhaust_thm], (inject_thmss, (half_distinct_thmss, [case_thms]))) = |
4e0f0f98be02
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parents:
49046
diff
changeset
|
265 |
(hd thmss, apsnd (chop (n * n)) (chop n (tl thmss))); |
49019 | 266 |
|
49032 | 267 |
val exhaust_thm' = |
268 |
let val Tinst = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As) in |
|
269 |
Drule.instantiate' [] [SOME (certify lthy v)] |
|
270 |
(Thm.instantiate (Tinst, []) (Drule.zero_var_indexes exhaust_thm)) |
|
271 |
end; |
|
272 |
||
49048
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|
273 |
val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss; |
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|
274 |
|
49052 | 275 |
val (distinct_thmsss', distinct_thmsss) = |
49048
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changeset
|
276 |
map2 (map2 append) (Library.chop_groups n half_distinct_thmss) |
49052 | 277 |
(transpose (Library.chop_groups n other_half_distinct_thmss)) |
278 |
|> `transpose; |
|
49048
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diff
changeset
|
279 |
val distinct_thms = interleave (flat half_distinct_thmss) (flat other_half_distinct_thmss); |
49019 | 280 |
|
49020
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
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49019
diff
changeset
|
281 |
val nchotomy_thm = |
f379cf5d71bd
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diff
changeset
|
282 |
let |
f379cf5d71bd
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parents:
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diff
changeset
|
283 |
val goal = |
49022 | 284 |
HOLogic.mk_Trueprop (HOLogic.mk_all (fst v', snd v', |
49029 | 285 |
Library.foldr1 HOLogic.mk_disj exist_xs_v_eq_ctrs)); |
49020
f379cf5d71bd
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parents:
49019
diff
changeset
|
286 |
in |
f379cf5d71bd
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blanchet
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49019
diff
changeset
|
287 |
Skip_Proof.prove lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm) |
f379cf5d71bd
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49019
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|
288 |
end; |
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parents:
49019
diff
changeset
|
289 |
|
49030 | 290 |
val sel_thmss = |
49025 | 291 |
let |
49028 | 292 |
fun mk_thm k xs goal_case case_thm x sel_def = |
49025 | 293 |
let |
294 |
val T = fastype_of x; |
|
295 |
val cTs = |
|
296 |
map ((fn T' => certifyT lthy (if T' = B then T else T')) o TFree) |
|
297 |
(rev (Term.add_tfrees goal_case [])); |
|
49130
3c26e17b2849
implemented "mk_case_tac" -- and got rid of "cheat_tac"
blanchet
parents:
49129
diff
changeset
|
298 |
val cxs = map (certify lthy) (mk_sel_case_args k xs x T); |
49025 | 299 |
in |
300 |
Local_Defs.fold lthy [sel_def] |
|
301 |
(Drule.instantiate' (map SOME cTs) (map SOME cxs) case_thm) |
|
302 |
end; |
|
49028 | 303 |
fun mk_thms k xs goal_case case_thm sel_defs = |
49140 | 304 |
map2 (mk_thm k xs (strip_all_body goal_case) case_thm) xs sel_defs; |
49025 | 305 |
in |
49030 | 306 |
map5 mk_thms ks xss goal_cases case_thms sel_defss |
49025 | 307 |
end; |
308 |
||
49157 | 309 |
fun mk_unique_disc_def () = |
49137 | 310 |
let |
311 |
val m = the_single ms; |
|
312 |
val goal = mk_Trueprop_eq (mk_v_eq_v (), the_single exist_xs_v_eq_ctrs); |
|
313 |
in |
|
314 |
Skip_Proof.prove lthy [] [] goal (fn _ => mk_unique_disc_def_tac m exhaust_thm') |
|
315 |
|> singleton (Proof_Context.export names_lthy lthy) |
|
316 |
|> Thm.close_derivation |
|
317 |
end; |
|
318 |
||
319 |
fun mk_alternate_disc_def k = |
|
49116
3d520eec2746
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parents:
49114
diff
changeset
|
320 |
let |
3d520eec2746
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blanchet
parents:
49114
diff
changeset
|
321 |
val goal = |
49152 | 322 |
mk_Trueprop_eq (Morphism.term phi (alternate_disc_lhs (3 - k)), |
49116
3d520eec2746
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blanchet
parents:
49114
diff
changeset
|
323 |
nth exist_xs_v_eq_ctrs (k - 1)); |
3d520eec2746
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blanchet
parents:
49114
diff
changeset
|
324 |
in |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
325 |
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => |
49148
93f281430e77
fixed "mk_alternate_disc_def_tac" in the case where the constructors are swapped compared with the common Nil/Cons case
blanchet
parents:
49140
diff
changeset
|
326 |
mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k)) (nth distinct_thms (2 - k)) |
49116
3d520eec2746
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blanchet
parents:
49114
diff
changeset
|
327 |
exhaust_thm') |
3d520eec2746
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blanchet
parents:
49114
diff
changeset
|
328 |
|> singleton (Proof_Context.export names_lthy lthy) |
49125 | 329 |
|> Thm.close_derivation |
49116
3d520eec2746
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parents:
49114
diff
changeset
|
330 |
end; |
3d520eec2746
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blanchet
parents:
49114
diff
changeset
|
331 |
|
49137 | 332 |
val has_alternate_disc_def = |
333 |
exists (fn def => Thm.eq_thm_prop (def, missing_alternate_disc_def)) disc_defs; |
|
49116
3d520eec2746
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blanchet
parents:
49114
diff
changeset
|
334 |
|
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
335 |
val disc_defs' = |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
336 |
map2 (fn k => fn def => |
49157 | 337 |
if Thm.eq_thm_prop (def, missing_unique_disc_def) then mk_unique_disc_def () |
49137 | 338 |
else if Thm.eq_thm_prop (def, missing_alternate_disc_def) then mk_alternate_disc_def k |
339 |
else def) |
|
49116
3d520eec2746
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blanchet
parents:
49114
diff
changeset
|
340 |
ks disc_defs; |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
341 |
|
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
342 |
val discD_thms = map (fn def => def RS iffD1) disc_defs'; |
49028 | 343 |
val discI_thms = |
49116
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
344 |
map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms disc_defs'; |
49137 | 345 |
val not_discI_thms = |
49030 | 346 |
map2 (fn m => fn def => funpow m (fn thm => allI RS thm) |
49116
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
347 |
(Local_Defs.unfold lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]}))) |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
348 |
ms disc_defs'; |
49028 | 349 |
|
49050 | 350 |
val (disc_thmss', disc_thmss) = |
49027 | 351 |
let |
49048
4e0f0f98be02
rationalized data structure for distinctness theorems
blanchet
parents:
49046
diff
changeset
|
352 |
fun mk_thm discI _ [] = refl RS discI |
49137 | 353 |
| mk_thm _ not_discI [distinct] = distinct RS not_discI; |
354 |
fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss; |
|
49027 | 355 |
in |
49137 | 356 |
map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose |
49027 | 357 |
end; |
49025 | 358 |
|
49116
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
359 |
val disc_thms = flat (map2 (fn true => K [] | false => I) no_discs disc_thmss); |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
360 |
|
49122 | 361 |
val disc_exclude_thms = |
49137 | 362 |
if has_alternate_disc_def then |
49116
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
363 |
[] |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
364 |
else |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
365 |
let |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
366 |
fun mk_goal [] = [] |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
367 |
| mk_goal [((_, true), (_, true))] = [] |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
368 |
| mk_goal [(((_, disc), _), ((_, disc'), _))] = |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
369 |
[Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (betapply (disc, v)), |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
370 |
HOLogic.mk_Trueprop (HOLogic.mk_not (betapply (disc', v)))))]; |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
371 |
fun prove tac goal = Skip_Proof.prove lthy [] [] goal (K tac); |
49028 | 372 |
|
49116
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
373 |
val bundles = ms ~~ discD_thms ~~ discs ~~ no_discs; |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
374 |
val half_pairss = mk_half_pairss bundles; |
49028 | 375 |
|
49116
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
376 |
val goal_halvess = map mk_goal half_pairss; |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
377 |
val half_thmss = |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
378 |
map3 (fn [] => K (K []) | [goal] => fn [((((m, discD), _), _), _)] => fn disc_thm => |
49122 | 379 |
[prove (mk_half_disc_exclude_tac m discD disc_thm) goal]) |
49116
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
380 |
goal_halvess half_pairss (flat disc_thmss'); |
49028 | 381 |
|
49116
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
382 |
val goal_other_halvess = map (mk_goal o map swap) half_pairss; |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
383 |
val other_half_thmss = |
49122 | 384 |
map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss goal_other_halvess; |
49116
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
385 |
in |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
386 |
interleave (flat half_thmss) (flat other_half_thmss) |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
387 |
end; |
49025 | 388 |
|
49116
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
389 |
val disc_exhaust_thms = |
49137 | 390 |
if has_alternate_disc_def orelse no_discs_at_all then |
49116
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
391 |
[] |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
392 |
else |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
393 |
let |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
394 |
fun mk_prem disc = mk_imp_p [HOLogic.mk_Trueprop (betapply (disc, v))]; |
49121 | 395 |
val goal = fold_rev Logic.all [p, v] (mk_imp_p (map mk_prem discs)); |
49116
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
396 |
in |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
397 |
[Skip_Proof.prove lthy [] [] goal (fn _ => |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
398 |
mk_disc_exhaust_tac n exhaust_thm discI_thms)] |
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
399 |
end; |
49025 | 400 |
|
49118 | 401 |
val collapse_thms = |
49030 | 402 |
let |
403 |
fun mk_goal ctr disc sels = |
|
49114 | 404 |
let |
405 |
val prem = HOLogic.mk_Trueprop (betapply (disc, v)); |
|
406 |
val concl = |
|
407 |
mk_Trueprop_eq ((null sels ? swap) |
|
408 |
(Term.list_comb (ctr, map (fn sel => sel $ v) sels), v)); |
|
409 |
in |
|
410 |
if prem aconv concl then NONE |
|
411 |
else SOME (Logic.all v (Logic.mk_implies (prem, concl))) |
|
412 |
end; |
|
49030 | 413 |
val goals = map3 mk_goal ctrs discs selss; |
414 |
in |
|
49114 | 415 |
map4 (fn m => fn discD => fn sel_thms => Option.map (fn goal => |
49030 | 416 |
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => |
49137 | 417 |
mk_collapse_tac ctxt m discD sel_thms) |
418 |
|> perhaps (try (fn thm => refl RS thm)))) ms discD_thms sel_thmss goals |
|
49114 | 419 |
|> map_filter I |
49030 | 420 |
end; |
49025 | 421 |
|
49116
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
422 |
val case_eq_thm = |
49031 | 423 |
let |
424 |
fun mk_core f sels = Term.list_comb (f, map (fn sel => sel $ v) sels); |
|
425 |
fun mk_rhs _ [f] [sels] = mk_core f sels |
|
426 |
| mk_rhs (disc :: discs) (f :: fs) (sels :: selss) = |
|
427 |
Const (@{const_name If}, HOLogic.boolT --> B --> B --> B) $ |
|
49114 | 428 |
betapply (disc, v) $ mk_core f sels $ mk_rhs discs fs selss; |
49201 | 429 |
val goal = mk_Trueprop_eq (fcase $ v, mk_rhs discs fs selss); |
49031 | 430 |
in |
431 |
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => |
|
49153
c15a7123605c
made "mk_case_eq_tac" work in the case where the first constructor is an "alternate" constructor (in which case its discriminator paradoxically starts with a negation)
blanchet
parents:
49152
diff
changeset
|
432 |
mk_case_eq_tac ctxt n exhaust_thm' case_thms disc_thmss' sel_thmss) |
49031 | 433 |
|> singleton (Proof_Context.export names_lthy lthy) |
434 |
end; |
|
49025 | 435 |
|
49033 | 436 |
val (case_cong_thm, weak_case_cong_thm) = |
49032 | 437 |
let |
438 |
fun mk_prem xctr xs f g = |
|
49045
7d9631754bba
minor fixes (for compatibility with existing datatype package)
blanchet
parents:
49044
diff
changeset
|
439 |
fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (w, xctr), |
49032 | 440 |
mk_Trueprop_eq (f, g))); |
49033 | 441 |
|
442 |
val v_eq_w = mk_Trueprop_eq (v, w); |
|
49032 | 443 |
|
444 |
val goal = |
|
49033 | 445 |
Logic.list_implies (v_eq_w :: map4 mk_prem xctrs xss fs gs, |
49201 | 446 |
mk_Trueprop_eq (fcase $ v, gcase $ w)); |
447 |
val goal_weak = Logic.mk_implies (v_eq_w, mk_Trueprop_eq (fcase $ v, fcase $ w)); |
|
49032 | 448 |
in |
49049 | 449 |
(Skip_Proof.prove lthy [] [] goal (fn _ => mk_case_cong_tac exhaust_thm' case_thms), |
49033 | 450 |
Skip_Proof.prove lthy [] [] goal_weak (K (etac arg_cong 1))) |
451 |
|> pairself (singleton (Proof_Context.export names_lthy lthy)) |
|
49032 | 452 |
end; |
49025 | 453 |
|
49044 | 454 |
val (split_thm, split_asm_thm) = |
49043 | 455 |
let |
49044 | 456 |
fun mk_conjunct xctr xs f_xs = |
49043 | 457 |
list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (v, xctr), q $ f_xs)); |
49044 | 458 |
fun mk_disjunct xctr xs f_xs = |
459 |
list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (v, xctr), |
|
460 |
HOLogic.mk_not (q $ f_xs))); |
|
461 |
||
49201 | 462 |
val lhs = q $ (fcase $ v); |
49044 | 463 |
|
49043 | 464 |
val goal = |
49044 | 465 |
mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs)); |
466 |
val goal_asm = |
|
467 |
mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj |
|
468 |
(map3 mk_disjunct xctrs xss xfs))); |
|
469 |
||
470 |
val split_thm = |
|
49049 | 471 |
Skip_Proof.prove lthy [] [] goal |
49052 | 472 |
(fn _ => mk_split_tac exhaust_thm' case_thms inject_thmss distinct_thmsss) |
49044 | 473 |
|> singleton (Proof_Context.export names_lthy lthy) |
474 |
val split_asm_thm = |
|
475 |
Skip_Proof.prove lthy [] [] goal_asm (fn {context = ctxt, ...} => |
|
476 |
mk_split_asm_tac ctxt split_thm) |
|
477 |
|> singleton (Proof_Context.export names_lthy lthy) |
|
49043 | 478 |
in |
49044 | 479 |
(split_thm, split_asm_thm) |
49043 | 480 |
end; |
49025 | 481 |
|
49052 | 482 |
val notes = |
483 |
[(case_congN, [case_cong_thm]), |
|
49116
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
484 |
(case_eqN, [case_eq_thm]), |
49052 | 485 |
(casesN, case_thms), |
49118 | 486 |
(collapseN, collapse_thms), |
49116
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
487 |
(discsN, disc_thms), |
49122 | 488 |
(disc_excludeN, disc_exclude_thms), |
49116
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
489 |
(disc_exhaustN, disc_exhaust_thms), |
49052 | 490 |
(distinctN, distinct_thms), |
491 |
(exhaustN, [exhaust_thm]), |
|
49121 | 492 |
(injectN, flat inject_thmss), |
49052 | 493 |
(nchotomyN, [nchotomy_thm]), |
49121 | 494 |
(selsN, flat sel_thmss), |
49052 | 495 |
(splitN, [split_thm]), |
496 |
(split_asmN, [split_asm_thm]), |
|
497 |
(weak_case_cong_thmsN, [weak_case_cong_thm])] |
|
49116
3d520eec2746
allow pseudo-definition of is_Cons in terms of is_Nil (and similarly for other two-constructor datatypes)
blanchet
parents:
49114
diff
changeset
|
498 |
|> filter_out (null o snd) |
49052 | 499 |
|> map (fn (thmN, thms) => |
500 |
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])); |
|
49019 | 501 |
in |
49052 | 502 |
lthy |> Local_Theory.notes notes |> snd |
49019 | 503 |
end; |
49017 | 504 |
in |
49121 | 505 |
(goalss, after_qed, lthy') |
49017 | 506 |
end; |
507 |
||
49199 | 508 |
fun wrap_datatype tacss = (fn (goalss, after_qed, lthy) => |
49111 | 509 |
map2 (map2 (Skip_Proof.prove lthy [] [])) goalss tacss |
510 |
|> (fn thms => after_qed thms lthy)) oo |
|
49199 | 511 |
prepare_wrap_datatype (K I) (* FIXME? (singleton o Type_Infer_Context.infer_types) *) |
49111 | 512 |
|
49114 | 513 |
val parse_bindings = Parse.$$$ "[" |-- Parse.list Parse.binding --| Parse.$$$ "]"; |
49057 | 514 |
val parse_bindingss = Parse.$$$ "[" |-- Parse.list parse_bindings --| Parse.$$$ "]"; |
49017 | 515 |
|
49199 | 516 |
val wrap_datatype_cmd = (fn (goalss, after_qed, lthy) => |
49019 | 517 |
Proof.theorem NONE after_qed (map (map (rpair [])) goalss) lthy) oo |
49199 | 518 |
prepare_wrap_datatype Syntax.read_term; |
49017 | 519 |
|
520 |
val _ = |
|
49074 | 521 |
Outer_Syntax.local_theory_to_proof @{command_spec "wrap_data"} "wraps an existing datatype" |
49023 | 522 |
(((Parse.$$$ "[" |-- Parse.list Parse.term --| Parse.$$$ "]") -- Parse.term -- |
49057 | 523 |
Scan.optional (parse_bindings -- Scan.optional parse_bindingss []) ([], [])) |
49199 | 524 |
>> wrap_datatype_cmd); |
49017 | 525 |
|
526 |
end; |