author | blanchet |
Sat, 08 Sep 2012 21:21:27 +0200 | |
changeset 49221 | 6d8d5fe9f3a2 |
parent 49220 | a6260b4fb410 |
child 49224 | 60a0394d98f7 |
permissions | -rw-r--r-- |
49112 | 1 |
(* Title: HOL/Codatatype/Tools/bnf_fp_sugar.ML |
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Author: Jasmin Blanchette, TU Muenchen |
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Copyright 2012 |
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Sugar for constructing LFPs and GFPs. |
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*) |
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signature BNF_FP_SUGAR = |
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sig |
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49205 | 10 |
(* TODO: programmatic interface *) |
49112 | 11 |
end; |
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structure BNF_FP_Sugar : BNF_FP_SUGAR = |
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struct |
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49119 | 16 |
open BNF_Util |
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open BNF_Wrap |
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open BNF_Def |
49119 | 19 |
open BNF_FP_Util |
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open BNF_LFP |
|
21 |
open BNF_GFP |
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22 |
open BNF_FP_Sugar_Tactics |
49119 | 23 |
|
49129 | 24 |
val caseN = "case"; |
49213 | 25 |
val coitersN = "coiters"; |
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val corecsN = "corecs"; |
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val itersN = "iters"; |
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val recsN = "recs"; |
49129 | 29 |
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fun split_list8 xs = |
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(map #1 xs, map #2 xs, map #3 xs, map #4 xs, map #5 xs, map #6 xs, map #7 xs, map #8 xs); |
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49217 | 33 |
fun strip_map_type (Type (@{type_name fun}, [T as Type _, T'])) = strip_map_type T' |>> cons T |
34 |
| strip_map_type T = ([], T); |
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35 |
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fun typ_subst inst (T as Type (s, Ts)) = |
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(case AList.lookup (op =) inst T of |
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NONE => Type (s, map (typ_subst inst) Ts) |
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| SOME T' => T') |
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| typ_subst inst T = the_default T (AList.lookup (op =) inst T); |
49205 | 41 |
|
49199 | 42 |
fun retype_free (Free (s, _)) T = Free (s, T); |
43 |
||
49212 | 44 |
val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs)) |
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49200 | 46 |
fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs)); |
47 |
fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs; |
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fun mk_uncurried2_fun f xss = |
49200 | 49 |
mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss); |
50 |
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fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v)) |
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49124 | 53 |
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters"; |
49119 | 54 |
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55 |
fun merge_type_arg_constrained ctxt (T, c) (T', c') = |
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56 |
if T = T' then |
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(case (c, c') of |
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58 |
(_, NONE) => (T, c) |
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| (NONE, _) => (T, c') |
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60 |
| _ => |
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if c = c' then |
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62 |
(T, c) |
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63 |
else |
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error ("Inconsistent sort constraints for type variable " ^ |
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65 |
quote (Syntax.string_of_typ ctxt T))) |
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66 |
else |
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67 |
cannot_merge_types (); |
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68 |
||
69 |
fun merge_type_args_constrained ctxt (cAs, cAs') = |
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if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs' |
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71 |
else cannot_merge_types (); |
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||
49121 | 73 |
fun type_args_constrained_of (((cAs, _), _), _) = cAs; |
74 |
val type_args_of = map fst o type_args_constrained_of; |
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49129 | 75 |
fun type_binder_of (((_, b), _), _) = b; |
49181 | 76 |
fun mixfix_of ((_, mx), _) = mx; |
49121 | 77 |
fun ctr_specs_of (_, ctr_specs) = ctr_specs; |
49119 | 78 |
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49121 | 79 |
fun disc_of (((disc, _), _), _) = disc; |
80 |
fun ctr_of (((_, ctr), _), _) = ctr; |
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81 |
fun args_of ((_, args), _) = args; |
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49181 | 82 |
fun ctr_mixfix_of (_, mx) = mx; |
49119 | 83 |
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49208 | 84 |
fun prepare_datatype prepare_typ lfp specs fake_lthy no_defs_lthy = |
49112 | 85 |
let |
49121 | 86 |
val constrained_As = |
87 |
map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs |
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49204 | 88 |
|> Library.foldr1 (merge_type_args_constrained no_defs_lthy); |
49121 | 89 |
val As = map fst constrained_As; |
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val As' = map dest_TFree As; |
49119 | 91 |
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49121 | 92 |
val _ = (case duplicates (op =) As of [] => () |
49204 | 93 |
| A :: _ => error ("Duplicate type parameter " ^ |
94 |
quote (Syntax.string_of_typ no_defs_lthy A))); |
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49119 | 95 |
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96 |
(* TODO: use sort constraints on type args *) |
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97 |
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98 |
val N = length specs; |
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99 |
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100 |
fun mk_fake_T b = |
49121 | 101 |
Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))), |
102 |
As); |
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103 |
||
49129 | 104 |
val bs = map type_binder_of specs; |
49204 | 105 |
val fakeTs = map mk_fake_T bs; |
49121 | 106 |
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49181 | 107 |
val mixfixes = map mixfix_of specs; |
49119 | 108 |
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val _ = (case duplicates Binding.eq_name bs of [] => () |
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| b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b))); |
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49121 | 112 |
val ctr_specss = map ctr_specs_of specs; |
49119 | 113 |
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49129 | 114 |
val disc_binderss = map (map disc_of) ctr_specss; |
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val ctr_binderss = map (map ctr_of) ctr_specss; |
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49121 | 116 |
val ctr_argsss = map (map args_of) ctr_specss; |
49181 | 117 |
val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss; |
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49129 | 119 |
val sel_bindersss = map (map (map fst)) ctr_argsss; |
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val fake_ctr_Tsss = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss; |
49121 | 121 |
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val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss []; |
49167 | 123 |
val _ = (case subtract (op =) As' rhs_As' of |
49165 | 124 |
[] => () |
125 |
| A' :: _ => error ("Extra type variables on rhs: " ^ |
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49204 | 126 |
quote (Syntax.string_of_typ no_defs_lthy (TFree A')))); |
49165 | 127 |
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49176 | 128 |
val ((Cs, Xs), _) = |
49204 | 129 |
no_defs_lthy |
49121 | 130 |
|> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs |
131 |
|> mk_TFrees N |
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49176 | 132 |
||>> mk_TFrees N; |
49119 | 133 |
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49204 | 134 |
fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) = |
49146 | 135 |
s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^ |
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quote (Syntax.string_of_typ fake_lthy T))) |
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49204 | 137 |
| eq_fpT _ _ = false; |
49146 | 138 |
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fun freeze_fp (T as Type (s, Us)) = |
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(case find_index (eq_fpT T) fakeTs of ~1 => Type (s, map freeze_fp Us) | j => nth Xs j) |
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| freeze_fp T = T; |
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49121 | 142 |
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49204 | 143 |
val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss; |
49176 | 144 |
val sum_prod_TsXs = map (mk_sumTN o map HOLogic.mk_tupleT) ctr_TsssXs; |
49119 | 145 |
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49176 | 146 |
val eqs = map dest_TFree Xs ~~ sum_prod_TsXs; |
49121 | 147 |
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49207 | 148 |
val (pre_map_defs, ((unfs0, flds0, fp_iters0, fp_recs0, unf_flds, fld_unfs, fld_injects, |
149 |
fp_iter_thms, fp_rec_thms), lthy)) = |
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49208 | 150 |
fp_bnf (if lfp then bnf_lfp else bnf_gfp) bs mixfixes As' eqs no_defs_lthy; |
49121 | 151 |
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49167 | 152 |
val timer = time (Timer.startRealTimer ()); |
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||
49176 | 154 |
fun mk_unf_or_fld get_T Ts t = |
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let val Type (_, Ts0) = get_T (fastype_of t) in |
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49124 | 156 |
Term.subst_atomic_types (Ts0 ~~ Ts) t |
49121 | 157 |
end; |
49119 | 158 |
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49126 | 159 |
val mk_unf = mk_unf_or_fld domain_type; |
160 |
val mk_fld = mk_unf_or_fld range_type; |
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49121 | 161 |
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49203 | 162 |
val unfs = map (mk_unf As) unfs0; |
163 |
val flds = map (mk_fld As) flds0; |
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49124 | 164 |
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49201 | 165 |
val fpTs = map (domain_type o fastype_of) unfs; |
49204 | 166 |
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49201 | 167 |
val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs; |
49203 | 168 |
val ns = map length ctr_Tsss; |
49212 | 169 |
val kss = map (fn n => 1 upto n) ns; |
49203 | 170 |
val mss = map (map length) ctr_Tsss; |
171 |
val Css = map2 replicate ns Cs; |
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172 |
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fun mk_iter_like Ts Us t = |
49121 | 174 |
let |
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175 |
val (binders, body) = strip_type (fastype_of t); |
49220 | 176 |
val _ = tracing ("mk_iter_like: " ^ PolyML.makestring (binders, body, t)) (*###*) |
49210 | 177 |
val (f_Us, prebody) = split_last binders; |
178 |
val Type (_, Ts0) = if lfp then prebody else body; |
|
179 |
val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us); |
|
49220 | 180 |
val _ = tracing (" Ts0 @ Us0 ...: " ^ PolyML.makestring (Ts0, Us0, Ts, Us)) (*###*) |
49176 | 181 |
in |
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182 |
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t |
49176 | 183 |
end; |
184 |
||
49210 | 185 |
val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0; |
186 |
val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0; |
|
187 |
||
49212 | 188 |
val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1))); |
189 |
val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1))); |
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49204 | 190 |
|
191 |
fun dest_rec_pair (T as Type (@{type_name prod}, Us as [_, U])) = |
|
192 |
if member (op =) Cs U then Us else [T] |
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193 |
| dest_rec_pair T = [T]; |
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194 |
||
49215 | 195 |
val ((iter_only as (gss, g_Tss, yssss), rec_only as (hss, h_Tss, zssss)), |
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(cs, cpss, p_Tss, coiter_only as ((pgss, cgsss), g_sum_prod_Ts, g_prod_Tss, g_Tsss), |
|
197 |
corec_only as ((phss, chsss), h_sum_prod_Ts, h_prod_Tss, h_Tsss))) = |
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49208 | 198 |
if lfp then |
199 |
let |
|
200 |
val y_Tsss = |
|
49210 | 201 |
map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN n o domain_type) |
49212 | 202 |
ns mss fp_iter_fun_Ts; |
49208 | 203 |
val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css; |
204 |
||
205 |
val ((gss, ysss), _) = |
|
206 |
lthy |
|
207 |
|> mk_Freess "f" g_Tss |
|
208 |
||>> mk_Freesss "x" y_Tsss; |
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49204 | 209 |
|
49208 | 210 |
val z_Tssss = |
49210 | 211 |
map3 (fn n => fn ms => map2 (map dest_rec_pair oo dest_tupleT) ms o dest_sumTN n |
49212 | 212 |
o domain_type) ns mss fp_rec_fun_Ts; |
49208 | 213 |
val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css; |
49204 | 214 |
|
49208 | 215 |
val hss = map2 (map2 retype_free) gss h_Tss; |
216 |
val (zssss, _) = |
|
217 |
lthy |
|
218 |
|> mk_Freessss "x" z_Tssss; |
|
49210 | 219 |
in |
49215 | 220 |
(((gss, g_Tss, map (map (map single)) ysss), (hss, h_Tss, zssss)), |
49212 | 221 |
([], [], [], (([], []), [], [], []), (([], []), [], [], []))) |
49210 | 222 |
end |
49208 | 223 |
else |
49210 | 224 |
let |
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225 |
(*avoid "'a itself" arguments in coiterators and corecursors*) |
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val mss' = map (fn [0] => [1] | ms => ms) mss; |
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227 |
|
49211 | 228 |
val p_Tss = |
49210 | 229 |
map2 (fn C => fn n => replicate (Int.max (0, n - 1)) (C --> HOLogic.boolT)) Cs ns; |
49211 | 230 |
|
49215 | 231 |
fun popescu_zip [] [fs] = fs |
232 |
| popescu_zip (p :: ps) (fs :: fss) = p :: fs @ popescu_zip ps fss; |
|
233 |
||
49212 | 234 |
fun mk_types fun_Ts = |
235 |
let |
|
236 |
val f_sum_prod_Ts = map range_type fun_Ts; |
|
237 |
val f_prod_Tss = map2 dest_sumTN ns f_sum_prod_Ts; |
|
238 |
val f_Tsss = |
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|
239 |
map3 (fn C => map2 (map (curry (op -->) C) oo dest_tupleT)) Cs mss' f_prod_Tss; |
49212 | 240 |
val pf_Tss = map2 popescu_zip p_Tss f_Tsss |
241 |
in (f_sum_prod_Ts, f_prod_Tss, f_Tsss, pf_Tss) end; |
|
49176 | 242 |
|
49212 | 243 |
val (g_sum_prod_Ts, g_prod_Tss, g_Tsss, pg_Tss) = mk_types fp_iter_fun_Ts; |
244 |
val (h_sum_prod_Ts, h_prod_Tss, h_Tsss, ph_Tss) = mk_types fp_rec_fun_Ts; |
|
49211 | 245 |
|
246 |
val (((c, pss), gsss), _) = |
|
49210 | 247 |
lthy |
248 |
|> yield_singleton (mk_Frees "c") dummyT |
|
49211 | 249 |
||>> mk_Freess "p" p_Tss |
49210 | 250 |
||>> mk_Freesss "g" g_Tsss; |
251 |
||
49211 | 252 |
val hsss = map2 (map2 (map2 retype_free)) gsss h_Tsss; |
253 |
||
49210 | 254 |
val cs = map (retype_free c) Cs; |
49212 | 255 |
val cpss = map2 (fn c => map (fn p => p $ c)) cs pss; |
256 |
||
257 |
fun mk_terms fsss = |
|
258 |
let |
|
259 |
val pfss = map2 popescu_zip pss fsss; |
|
260 |
val cfsss = map2 (fn c => map (map (fn f => f $ c))) cs fsss |
|
261 |
in (pfss, cfsss) end; |
|
49210 | 262 |
in |
49212 | 263 |
((([], [], []), ([], [], [])), |
264 |
(cs, cpss, p_Tss, (mk_terms gsss, g_sum_prod_Ts, g_prod_Tss, pg_Tss), |
|
265 |
(mk_terms hsss, h_sum_prod_Ts, h_prod_Tss, ph_Tss))) |
|
49210 | 266 |
end; |
267 |
||
49212 | 268 |
fun pour_some_sugar_on_type (((((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec), |
269 |
fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_binders), ctr_mixfixes), ctr_Tss), |
|
270 |
disc_binders), sel_binderss) no_defs_lthy = |
|
49176 | 271 |
let |
49201 | 272 |
val unfT = domain_type (fastype_of fld); |
49210 | 273 |
val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss; |
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|
274 |
val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss; |
49119 | 275 |
|
49176 | 276 |
val ((((u, v), fs), xss), _) = |
49204 | 277 |
no_defs_lthy |
49201 | 278 |
|> yield_singleton (mk_Frees "u") unfT |
279 |
||>> yield_singleton (mk_Frees "v") fpT |
|
49176 | 280 |
||>> mk_Frees "f" case_Ts |
49124 | 281 |
||>> mk_Freess "x" ctr_Tss; |
49121 | 282 |
|
49129 | 283 |
val ctr_rhss = |
49121 | 284 |
map2 (fn k => fn xs => |
49210 | 285 |
fold_rev Term.lambda xs (fld $ mk_InN ctr_prod_Ts (HOLogic.mk_tuple xs) k)) ks xss; |
49121 | 286 |
|
49130
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|
287 |
val case_binder = Binding.suffix_name ("_" ^ caseN) b; |
49129 | 288 |
|
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|
289 |
val case_rhs = |
49176 | 290 |
fold_rev Term.lambda (fs @ [v]) (mk_sum_caseN (map2 mk_uncurried_fun fs xss) $ (unf $ v)); |
49129 | 291 |
|
49201 | 292 |
val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy |
49169 | 293 |
|> apfst split_list o fold_map3 (fn b => fn mx => fn rhs => |
294 |
Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd) |
|
49201 | 295 |
(case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss) |
49121 | 296 |
||> `Local_Theory.restore; |
297 |
||
298 |
(*transforms defined frees into consts (and more)*) |
|
299 |
val phi = Proof_Context.export_morphism lthy lthy'; |
|
300 |
||
301 |
val ctr_defs = map (Morphism.thm phi) raw_ctr_defs; |
|
49130
3c26e17b2849
implemented "mk_case_tac" -- and got rid of "cheat_tac"
blanchet
parents:
49129
diff
changeset
|
302 |
val case_def = Morphism.thm phi raw_case_def; |
3c26e17b2849
implemented "mk_case_tac" -- and got rid of "cheat_tac"
blanchet
parents:
49129
diff
changeset
|
303 |
|
49203 | 304 |
val ctrs0 = map (Morphism.term phi) raw_ctrs; |
305 |
val casex0 = Morphism.term phi raw_case; |
|
306 |
||
307 |
val ctrs = map (mk_ctr As) ctrs0; |
|
49121 | 308 |
|
49135 | 309 |
fun exhaust_tac {context = ctxt, ...} = |
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
49121
diff
changeset
|
310 |
let |
49135 | 311 |
val fld_iff_unf_thm = |
312 |
let |
|
313 |
val goal = |
|
314 |
fold_rev Logic.all [u, v] |
|
315 |
(mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u))); |
|
316 |
in |
|
317 |
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => |
|
49201 | 318 |
mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT]) |
49176 | 319 |
(certify lthy fld) (certify lthy unf) fld_unf unf_fld) |
49135 | 320 |
|> Thm.close_derivation |
321 |
|> Morphism.thm phi |
|
322 |
end; |
|
323 |
||
324 |
val sumEN_thm' = |
|
325 |
Local_Defs.unfold lthy @{thms all_unit_eq} |
|
49210 | 326 |
(Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) [] (mk_sumEN n)) |
49135 | 327 |
|> Morphism.thm phi; |
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
49121
diff
changeset
|
328 |
in |
49161
a8e74375d971
fixed (n + 1)st bug in "mk_exhaust_tac" -- arose with uncurried constructors
blanchet
parents:
49157
diff
changeset
|
329 |
mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm' |
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
49121
diff
changeset
|
330 |
end; |
49121 | 331 |
|
49126 | 332 |
val inject_tacss = |
49205 | 333 |
map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} => |
334 |
mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs; |
|
49126 | 335 |
|
49127 | 336 |
val half_distinct_tacss = |
337 |
map (map (fn (def, def') => fn {context = ctxt, ...} => |
|
338 |
mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs); |
|
339 |
||
49130
3c26e17b2849
implemented "mk_case_tac" -- and got rid of "cheat_tac"
blanchet
parents:
49129
diff
changeset
|
340 |
val case_tacs = |
3c26e17b2849
implemented "mk_case_tac" -- and got rid of "cheat_tac"
blanchet
parents:
49129
diff
changeset
|
341 |
map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} => |
3c26e17b2849
implemented "mk_case_tac" -- and got rid of "cheat_tac"
blanchet
parents:
49129
diff
changeset
|
342 |
mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs; |
49121 | 343 |
|
344 |
val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs]; |
|
49134
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset
|
345 |
|
49210 | 346 |
fun some_lfp_sugar no_defs_lthy = |
49134
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset
|
347 |
let |
49208 | 348 |
val fpT_to_C = fpT --> C; |
49199 | 349 |
|
49215 | 350 |
fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) = |
351 |
let |
|
352 |
val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C; |
|
353 |
||
354 |
val binder = Binding.suffix_name ("_" ^ suf) b; |
|
49199 | 355 |
|
49215 | 356 |
val spec = |
357 |
mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binder, res_T)), |
|
358 |
Term.list_comb (fp_iter_like, |
|
359 |
map2 (mk_sum_caseN oo map2 mk_uncurried2_fun) fss xssss)); |
|
360 |
in (binder, spec) end; |
|
49199 | 361 |
|
49215 | 362 |
val iter_likes = |
363 |
[(iterN, fp_iter, iter_only), |
|
364 |
(recN, fp_rec, rec_only)]; |
|
365 |
||
366 |
val (binders, specs) = map generate_iter_like iter_likes |> split_list; |
|
367 |
||
368 |
val ((csts, defs), (lthy', lthy)) = no_defs_lthy |
|
49201 | 369 |
|> apfst split_list o fold_map2 (fn b => fn spec => |
49199 | 370 |
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) |
49215 | 371 |
#>> apsnd snd) binders specs |
49199 | 372 |
||> `Local_Theory.restore; |
49201 | 373 |
|
374 |
(*transforms defined frees into consts (and more)*) |
|
375 |
val phi = Proof_Context.export_morphism lthy lthy'; |
|
376 |
||
49215 | 377 |
val [iter_def, rec_def] = map (Morphism.thm phi) defs; |
49201 | 378 |
|
49220 | 379 |
val _ = tracing ("LFP As Cs: " ^ PolyML.makestring (As, Cs)) (*###*) |
49215 | 380 |
val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts; |
49134
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset
|
381 |
in |
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
382 |
((ctrs, iter, recx, v, xss, ctr_defs, iter_def, rec_def), lthy) |
49134
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset
|
383 |
end; |
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset
|
384 |
|
49210 | 385 |
fun some_gfp_sugar no_defs_lthy = |
386 |
let |
|
387 |
val B_to_fpT = C --> fpT; |
|
49211 | 388 |
|
49212 | 389 |
fun generate_coiter_like (suf, fp_iter_like, ((pfss, cfsss), f_sum_prod_Ts, f_prod_Tss, |
390 |
pf_Tss)) = |
|
49211 | 391 |
let |
392 |
val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT; |
|
49210 | 393 |
|
49211 | 394 |
val binder = Binding.suffix_name ("_" ^ suf) b; |
49210 | 395 |
|
49215 | 396 |
fun mk_popescu_join c n cps sum_prod_T prod_Ts cfss = |
49211 | 397 |
Term.lambda c (mk_IfN sum_prod_T cps |
398 |
(map2 (mk_InN prod_Ts) (map HOLogic.mk_tuple cfss) (1 upto n))); |
|
49210 | 399 |
|
49211 | 400 |
val spec = |
49212 | 401 |
mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binder, res_T)), |
49211 | 402 |
Term.list_comb (fp_iter_like, |
49215 | 403 |
map6 mk_popescu_join cs ns cpss f_sum_prod_Ts f_prod_Tss cfsss)); |
49211 | 404 |
in (binder, spec) end; |
49210 | 405 |
|
49212 | 406 |
val coiter_likes = |
49215 | 407 |
[(coiterN, fp_iter, coiter_only), |
408 |
(corecN, fp_rec, corec_only)]; |
|
49212 | 409 |
|
49211 | 410 |
val (binders, specs) = map generate_coiter_like coiter_likes |> split_list; |
411 |
||
412 |
val ((csts, defs), (lthy', lthy)) = no_defs_lthy |
|
49210 | 413 |
|> apfst split_list o fold_map2 (fn b => fn spec => |
414 |
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) |
|
49211 | 415 |
#>> apsnd snd) binders specs |
49210 | 416 |
||> `Local_Theory.restore; |
417 |
||
418 |
(*transforms defined frees into consts (and more)*) |
|
419 |
val phi = Proof_Context.export_morphism lthy lthy'; |
|
420 |
||
49211 | 421 |
val [coiter_def, corec_def] = map (Morphism.thm phi) defs; |
49210 | 422 |
|
49220 | 423 |
val _ = tracing ("GFP As Cs: " ^ PolyML.makestring (As, Cs)) (*###*) |
49211 | 424 |
val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts; |
49210 | 425 |
in |
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
426 |
((ctrs, coiter, corec, v, xss, ctr_defs, coiter_def, corec_def), lthy) |
49210 | 427 |
end; |
49119 | 428 |
in |
49203 | 429 |
wrap_datatype tacss ((ctrs0, casex0), (disc_binders, sel_binderss)) lthy' |
49210 | 430 |
|> (if lfp then some_lfp_sugar else some_gfp_sugar) |
49119 | 431 |
end; |
49167 | 432 |
|
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
433 |
fun mk_map Ts Us t = |
49217 | 434 |
let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) |>> List.last in |
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
435 |
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
436 |
end; |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
437 |
|
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
438 |
fun pour_more_sugar_on_lfps ((ctrss, iters, recs, vs, xsss, ctr_defss, iter_defs, rec_defs), |
49205 | 439 |
lthy) = |
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset
|
440 |
let |
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset
|
441 |
val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss; |
49212 | 442 |
val giters = map (lists_bmoc gss) iters; |
443 |
val hrecs = map (lists_bmoc hss) recs; |
|
49201 | 444 |
|
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset
|
445 |
val (iter_thmss, rec_thmss) = |
49207 | 446 |
let |
49212 | 447 |
fun mk_goal_iter_like fss fiter_like xctr f xs fxs = |
49207 | 448 |
fold_rev (fold_rev Logic.all) (xs :: fss) |
49212 | 449 |
(mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs))); |
49204 | 450 |
|
49215 | 451 |
fun build_call fiter_likes maybe_tick = |
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
452 |
let |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
453 |
fun build (T, U) = |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
454 |
if T = U then |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
455 |
Const (@{const_name id}, T --> T) |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
456 |
else |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
457 |
(case (find_index (curry (op =) T) fpTs, (T, U)) of |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
458 |
(~1, (Type (s, Ts), Type (_, Us))) => |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
459 |
let |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
460 |
val map0 = map_of_bnf (the (bnf_of lthy (Long_Name.base_name s))); |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
461 |
val mapx = mk_map Ts Us map0; |
49217 | 462 |
val TUs = |
463 |
map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx))))); |
|
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
464 |
val args = map build TUs; |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
465 |
in Term.list_comb (mapx, args) end |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
466 |
| (j, _) => maybe_tick (nth vs j) (nth fiter_likes j)) |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
467 |
in build end; |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
468 |
|
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
469 |
fun mk_U maybe_prodT = |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
470 |
typ_subst (map2 (fn fpT => fn C => (fpT, maybe_prodT fpT C)) fpTs Cs); |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
471 |
|
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
472 |
fun repair_calls fiter_likes maybe_cons maybe_tick maybe_prodT (x as Free (_, T)) = |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
473 |
if member (op =) fpTs T then |
49215 | 474 |
maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x] |
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
475 |
else if exists_subtype (member (op =) fpTs) T then |
49215 | 476 |
[build_call fiter_likes maybe_tick (T, mk_U maybe_prodT T) $ x] |
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
477 |
else |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
478 |
[x]; |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
479 |
|
49212 | 480 |
fun repair_rec_call (x as Free (_, T)) = |
481 |
(case find_index (curry (op =) T) fpTs of ~1 => [x] | j => [x, nth hrecs j $ x]); |
|
49201 | 482 |
|
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
483 |
val gxsss = map (map (maps (repair_calls giters (K I) (K I) (K I)))) xsss; |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
484 |
val hxsss = |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
485 |
map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss; |
49204 | 486 |
|
49212 | 487 |
val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss; |
488 |
val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss; |
|
49204 | 489 |
|
49203 | 490 |
val iter_tacss = |
49211 | 491 |
map2 (map o mk_iter_like_tac pre_map_defs iter_defs) fp_iter_thms ctr_defss; |
49203 | 492 |
val rec_tacss = |
49211 | 493 |
map2 (map o mk_iter_like_tac pre_map_defs rec_defs) fp_rec_thms ctr_defss; |
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset
|
494 |
in |
49218 | 495 |
([], []) |
496 |
(* NOTYET |
|
49205 | 497 |
(map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context))) |
498 |
goal_iterss iter_tacss, |
|
499 |
map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context))) |
|
500 |
goal_recss rec_tacss) |
|
49218 | 501 |
*) |
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset
|
502 |
end; |
49201 | 503 |
|
49218 | 504 |
val notes = []; |
505 |
(* NOTYET |
|
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset
|
506 |
[(itersN, iter_thmss), |
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset
|
507 |
(recsN, rec_thmss)] |
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset
|
508 |
|> maps (fn (thmN, thmss) => |
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset
|
509 |
map2 (fn b => fn thms => |
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset
|
510 |
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])) |
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset
|
511 |
bs thmss); |
49218 | 512 |
*) |
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset
|
513 |
in |
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset
|
514 |
lthy |> Local_Theory.notes notes |> snd |
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset
|
515 |
end; |
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset
|
516 |
|
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
517 |
fun pour_more_sugar_on_gfps ((ctrss, coiters, corecs, vs, xsss, ctr_defss, coiter_defs, |
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
518 |
corec_defs), lthy) = |
49212 | 519 |
let |
49216 | 520 |
(* NOTYET |
49212 | 521 |
val gcoiters = map (lists_bmoc pgss) coiters; |
522 |
val hcorecs = map (lists_bmoc phss) corecs; |
|
523 |
||
524 |
val (coiter_thmss, corec_thmss) = |
|
525 |
let |
|
526 |
fun mk_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not); |
|
527 |
||
528 |
fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr cfs' = |
|
529 |
fold_rev (fold_rev Logic.all) ([c] :: pfss) |
|
530 |
(Logic.list_implies (seq_conds mk_cond n k cps, |
|
531 |
mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, cfs')))); |
|
532 |
||
49215 | 533 |
fun repair_call fcoiter_likes (cf as Free (_, Type (_, [_, T])) $ _) = |
49212 | 534 |
(case find_index (curry (op =) T) Cs of ~1 => cf | j => nth fcoiter_likes j $ cf); |
535 |
||
49215 | 536 |
val cgsss = map (map (map (repair_call gcoiters))) cgsss; |
537 |
val chsss = map (map (map (repair_call hcorecs))) chsss; |
|
49212 | 538 |
|
539 |
val goal_coiterss = |
|
540 |
map7 (map3 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss cgsss; |
|
541 |
val goal_corecss = |
|
542 |
map7 (map3 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss chsss; |
|
49213 | 543 |
|
544 |
val coiter_tacss = |
|
545 |
map3 (map oo mk_coiter_like_tac coiter_defs) fp_iter_thms pre_map_defs ctr_defss; |
|
49212 | 546 |
in |
49213 | 547 |
(map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context))) |
548 |
goal_coiterss coiter_tacss, |
|
549 |
map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context))) |
|
550 |
goal_coiterss coiter_tacss (* TODO: should be corecs *)) |
|
49212 | 551 |
end; |
552 |
||
553 |
val notes = |
|
554 |
[(coitersN, coiter_thmss), |
|
555 |
(corecsN, corec_thmss)] |
|
556 |
|> maps (fn (thmN, thmss) => |
|
557 |
map2 (fn b => fn thms => |
|
558 |
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])) |
|
559 |
bs thmss); |
|
49216 | 560 |
*) |
49212 | 561 |
in |
49216 | 562 |
lthy (* NOTYET |> Local_Theory.notes notes |> snd *) |
49212 | 563 |
end; |
564 |
||
49204 | 565 |
val lthy' = lthy |
49210 | 566 |
|> fold_map pour_some_sugar_on_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~ |
49212 | 567 |
fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_binderss ~~ |
568 |
ctr_mixfixess ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss) |
|
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset
|
569 |
|>> split_list8 |
49212 | 570 |
|> (if lfp then pour_more_sugar_on_lfps else pour_more_sugar_on_gfps); |
49167 | 571 |
|
572 |
val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^ |
|
49208 | 573 |
(if lfp then "" else "co") ^ "datatype")); |
49112 | 574 |
in |
49204 | 575 |
(timer; lthy') |
49112 | 576 |
end; |
577 |
||
49199 | 578 |
fun datatype_cmd info specs lthy = |
49121 | 579 |
let |
49209 | 580 |
(* TODO: cleaner handling of fake contexts, without "background_theory" *) |
49184
83fdea0c4779
gracefully handle shadowing case (fourth step of sugar localization)
blanchet
parents:
49183
diff
changeset
|
581 |
(*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a |
83fdea0c4779
gracefully handle shadowing case (fourth step of sugar localization)
blanchet
parents:
49183
diff
changeset
|
582 |
locale and shadows an existing global type*) |
49179
f9d48d479c84
don't throw away the context when hacking the theory (first step to localize the sugar code)
blanchet
parents:
49177
diff
changeset
|
583 |
val fake_thy = Theory.copy |
49184
83fdea0c4779
gracefully handle shadowing case (fourth step of sugar localization)
blanchet
parents:
49183
diff
changeset
|
584 |
#> fold (fn spec => perhaps (try (Sign.add_type lthy |
83fdea0c4779
gracefully handle shadowing case (fourth step of sugar localization)
blanchet
parents:
49183
diff
changeset
|
585 |
(type_binder_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs; |
49179
f9d48d479c84
don't throw away the context when hacking the theory (first step to localize the sugar code)
blanchet
parents:
49177
diff
changeset
|
586 |
val fake_lthy = Proof_Context.background_theory fake_thy lthy; |
49121 | 587 |
in |
49199 | 588 |
prepare_datatype Syntax.read_typ info specs fake_lthy lthy |
49121 | 589 |
end; |
49119 | 590 |
|
49129 | 591 |
val parse_opt_binding_colon = Scan.optional (Parse.binding --| Parse.$$$ ":") no_binder |
49119 | 592 |
|
49112 | 593 |
val parse_ctr_arg = |
49119 | 594 |
Parse.$$$ "(" |-- parse_opt_binding_colon -- Parse.typ --| Parse.$$$ ")" || |
49129 | 595 |
(Parse.typ >> pair no_binder); |
49112 | 596 |
|
597 |
val parse_single_spec = |
|
598 |
Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix -- |
|
49119 | 599 |
(@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding -- |
600 |
Scan.repeat parse_ctr_arg -- Parse.opt_mixfix)); |
|
49112 | 601 |
|
602 |
val _ = |
|
603 |
Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes" |
|
49208 | 604 |
(Parse.and_list1 parse_single_spec >> datatype_cmd true); |
49112 | 605 |
|
606 |
val _ = |
|
607 |
Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes" |
|
49208 | 608 |
(Parse.and_list1 parse_single_spec >> datatype_cmd false); |
49112 | 609 |
|
610 |
end; |