author | wenzelm |
Wed, 17 Aug 2011 18:05:31 +0200 | |
changeset 44241 | 7943b69f0188 |
parent 44121 | 44adaa6db327 |
child 45700 | 9dcbf6a1829c |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/Datatype/datatype_abs_proofs.ML |
11539 | 2 |
Author: Stefan Berghofer, TU Muenchen |
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|
33968
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modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
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changeset
|
4 |
Datatype package: proofs and defintions independent of concrete |
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
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5 |
representation of datatypes (i.e. requiring only abstract |
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
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parents:
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properties: injectivity / distinctness of constructors and induction). |
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*) |
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||
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signature DATATYPE_ABS_PROOFS = |
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sig |
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include DATATYPE_COMMON |
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val prove_casedist_thms : config -> string list -> |
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descr list -> (string * sort) list -> thm -> |
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attribute list -> theory -> thm list * theory |
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val prove_primrec_thms : config -> string list -> |
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descr list -> (string * sort) list -> |
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(string -> thm list) -> thm list list -> thm list list * thm list list -> |
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thm -> theory -> (string list * thm list) * theory |
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val prove_case_thms : config -> string list -> |
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descr list -> (string * sort) list -> |
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string list -> thm list -> theory -> (thm list list * string list) * theory |
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val prove_split_thms : config -> string list -> |
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descr list -> (string * sort) list -> |
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thm list list -> thm list list -> thm list -> thm list list -> theory -> |
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(thm * thm) list * theory |
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val prove_nchotomys : config -> string list -> descr list -> |
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(string * sort) list -> thm list -> theory -> thm list * theory |
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val prove_weak_case_congs : string list -> descr list -> |
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(string * sort) list -> theory -> thm list * theory |
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val prove_case_congs : string list -> |
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descr list -> (string * sort) list -> |
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thm list -> thm list list -> theory -> thm list * theory |
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end; |
34 |
||
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structure Datatype_Abs_Proofs: DATATYPE_ABS_PROOFS = |
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struct |
37 |
||
38 |
(************************ case distinction theorems ***************************) |
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39 |
||
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fun prove_casedist_thms (config : Datatype_Aux.config) |
41 |
new_type_names descr sorts induct case_names_exhausts thy = |
|
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let |
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val _ = Datatype_Aux.message config "Proving case distinction theorems ..."; |
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|
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val descr' = flat descr; |
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val recTs = Datatype_Aux.get_rec_types descr' sorts; |
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val newTs = take (length (hd descr)) recTs; |
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|
44058 | 49 |
val maxidx = Thm.maxidx_of induct; |
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val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct))); |
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|
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fun prove_casedist_thm (i, (T, t)) = |
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let |
54 |
val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) => |
|
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Abs ("z", T', Const (@{const_name True}, T''))) induct_Ps; |
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56 |
val P = Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx+1), T), Bound 0) $ |
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Var (("P", 0), HOLogic.boolT)) |
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val insts = take i dummyPs @ (P::(drop (i + 1) dummyPs)); |
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val cert = cterm_of thy; |
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val insts' = (map cert induct_Ps) ~~ (map cert insts); |
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val induct' = refl RS ((nth |
41423 | 62 |
(Datatype_Aux.split_conj_thm (cterm_instantiate insts' induct)) i) RSN (2, rev_mp)) |
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|
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in |
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Skip_Proof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t) |
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(fn {prems, ...} => EVERY |
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[rtac induct' 1, |
68 |
REPEAT (rtac TrueI 1), |
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69 |
REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)), |
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REPEAT (rtac TrueI 1)]) |
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end; |
72 |
||
33063 | 73 |
val casedist_thms = map_index prove_casedist_thm |
33968
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modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
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changeset
|
74 |
(newTs ~~ Datatype_Prop.make_casedists descr sorts) |
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in |
76 |
thy |
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|> Datatype_Aux.store_thms_atts "exhaust" new_type_names |
78 |
(map single case_names_exhausts) casedist_thms |
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end; |
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81 |
||
82 |
(*************************** primrec combinators ******************************) |
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83 |
||
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fun prove_primrec_thms (config : Datatype_Aux.config) new_type_names descr sorts |
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injects_of constr_inject (dist_rewrites, other_dist_rewrites) induct thy = |
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let |
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val _ = Datatype_Aux.message config "Constructing primrec combinators ..."; |
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|
89 |
val big_name = space_implode "_" new_type_names; |
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32124 | 90 |
val thy0 = Sign.add_path big_name thy; |
5177 | 91 |
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val descr' = flat descr; |
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val recTs = Datatype_Aux.get_rec_types descr' sorts; |
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val used = List.foldr Misc_Legacy.add_typ_tfree_names [] recTs; |
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val newTs = take (length (hd descr)) recTs; |
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|
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val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct))); |
5177 | 98 |
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val big_rec_name' = big_name ^ "_rec_set"; |
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val rec_set_names' = |
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if length descr' = 1 then [big_rec_name'] else |
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map ((curry (op ^) (big_rec_name' ^ "_")) o string_of_int) |
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(1 upto (length descr')); |
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val rec_set_names = map (Sign.full_bname thy0) rec_set_names'; |
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33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
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106 |
val (rec_result_Ts, reccomb_fn_Ts) = Datatype_Prop.make_primrec_Ts descr sorts used; |
5177 | 107 |
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21021 | 108 |
val rec_set_Ts = map (fn (T1, T2) => |
109 |
reccomb_fn_Ts @ [T1, T2] ---> HOLogic.boolT) (recTs ~~ rec_result_Ts); |
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5177 | 110 |
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val rec_fns = map (uncurry (Datatype_Aux.mk_Free "f")) |
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(reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts))); |
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val rec_sets' = map (fn c => list_comb (Free c, rec_fns)) |
114 |
(rec_set_names' ~~ rec_set_Ts); |
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val rec_sets = map (fn c => list_comb (Const c, rec_fns)) |
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(rec_set_names ~~ rec_set_Ts); |
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117 |
||
118 |
(* introduction rules for graph of primrec function *) |
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119 |
||
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fun make_rec_intr T rec_set (cname, cargs) (rec_intr_ts, l) = |
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let |
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fun mk_prem (dt, U) (j, k, prems, t1s, t2s) = |
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let val free1 = Datatype_Aux.mk_Free "x" U j |
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in (case (Datatype_Aux.strip_dtyp dt, strip_type U) of |
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((_, Datatype_Aux.DtRec m), (Us, _)) => |
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let |
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val free2 = Datatype_Aux.mk_Free "y" (Us ---> nth rec_result_Ts m) k; |
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val i = length Us |
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in (j + 1, k + 1, HOLogic.mk_Trueprop (HOLogic.list_all |
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(map (pair "x") Us, nth rec_sets' m $ |
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Datatype_Aux.app_bnds free1 i $ Datatype_Aux.app_bnds free2 i)) :: prems, |
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free1::t1s, free2::t2s) |
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end |
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| _ => (j + 1, k, prems, free1::t1s, t2s)) |
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135 |
end; |
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136 |
||
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val Ts = map (Datatype_Aux.typ_of_dtyp descr' sorts) cargs; |
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val (_, _, prems, t1s, t2s) = fold_rev mk_prem (cargs ~~ Ts) (1, 1, [], [], []) |
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|
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in (rec_intr_ts @ [Logic.list_implies (prems, HOLogic.mk_Trueprop |
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(rec_set $ list_comb (Const (cname, Ts ---> T), t1s) $ |
|
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list_comb (nth rec_fns l, t1s @ t2s)))], l + 1) |
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end; |
144 |
||
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val (rec_intr_ts, _) = fold (fn ((d, T), set_name) => |
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fold (make_rec_intr T set_name) (#3 (snd d))) |
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(descr' ~~ recTs ~~ rec_sets') ([], 0); |
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val ({intrs = rec_intrs, elims = rec_elims, ...}, thy1) = |
33278 | 150 |
thy0 |
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|> Sign.map_naming Name_Space.conceal |
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|> Inductive.add_inductive_global |
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{quiet_mode = #quiet config, verbose = false, alt_name = Binding.name big_rec_name', |
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coind = false, no_elim = false, no_ind = true, skip_mono = true, fork_mono = false} |
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(map (fn (s, T) => ((Binding.name s, T), NoSyn)) (rec_set_names' ~~ rec_set_Ts)) |
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(map dest_Free rec_fns) |
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(map (fn x => (Attrib.empty_binding, x)) rec_intr_ts) [] |
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||> Sign.restore_naming thy0 |
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||> Theory.checkpoint; |
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(* prove uniqueness and termination of primrec combinators *) |
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||
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val _ = Datatype_Aux.message config "Proving termination and uniqueness of primrec functions ..."; |
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fun mk_unique_tac ((((i, (tname, _, constrs)), elim), T), T') (tac, intrs) = |
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let |
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val distinct_tac = |
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(if i < length newTs then |
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full_simp_tac (HOL_ss addsimps (nth dist_rewrites i)) 1 |
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else full_simp_tac (HOL_ss addsimps (flat other_dist_rewrites)) 1); |
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172 |
val inject = map (fn r => r RS iffD1) |
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32905 | 173 |
(if i < length newTs then nth constr_inject i |
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else injects_of tname); |
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|
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fun mk_unique_constr_tac n (cname, cargs) (tac, intr::intrs, j) = |
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let |
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val k = length (filter Datatype_Aux.is_rec_type cargs) |
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|
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in (EVERY [DETERM tac, |
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REPEAT (etac ex1E 1), rtac ex1I 1, |
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DEPTH_SOLVE_1 (ares_tac [intr] 1), |
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REPEAT_DETERM_N k (etac thin_rl 1 THEN rotate_tac 1 1), |
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etac elim 1, |
185 |
REPEAT_DETERM_N j distinct_tac, |
|
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TRY (dresolve_tac inject 1), |
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REPEAT (etac conjE 1), hyp_subst_tac 1, |
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188 |
REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]), |
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TRY (hyp_subst_tac 1), |
190 |
rtac refl 1, |
|
191 |
REPEAT_DETERM_N (n - j - 1) distinct_tac], |
|
192 |
intrs, j + 1) |
|
193 |
end; |
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||
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val (tac', intrs', _) = fold (mk_unique_constr_tac (length constrs)) |
196 |
constrs (tac, intrs, 0); |
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5177 | 197 |
|
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in (tac', intrs') end; |
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199 |
||
200 |
val rec_unique_thms = |
|
201 |
let |
|
202 |
val rec_unique_ts = map (fn (((set_t, T1), T2), i) => |
|
35364 | 203 |
Const (@{const_name Ex1}, (T2 --> HOLogic.boolT) --> HOLogic.boolT) $ |
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absfree ("y", T2) (set_t $ Datatype_Aux.mk_Free "x" T1 i $ Free ("y", T2))) |
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(rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs)); |
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val cert = cterm_of thy1 |
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val insts = map (fn ((i, T), t) => absfree ("x" ^ string_of_int i, T) t) |
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((1 upto length recTs) ~~ recTs ~~ rec_unique_ts); |
209 |
val induct' = cterm_instantiate ((map cert induct_Ps) ~~ |
|
210 |
(map cert insts)) induct; |
|
32906 | 211 |
val (tac, _) = fold mk_unique_tac (descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts) |
35625 | 212 |
(((rtac induct' THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1 |
35410 | 213 |
THEN rewrite_goals_tac [mk_meta_eq @{thm choice_eq}], rec_intrs)); |
5177 | 214 |
|
41423 | 215 |
in |
216 |
Datatype_Aux.split_conj_thm (Skip_Proof.prove_global thy1 [] [] |
|
217 |
(HOLogic.mk_Trueprop (Datatype_Aux.mk_conj rec_unique_ts)) (K tac)) |
|
5177 | 218 |
end; |
219 |
||
35410 | 220 |
val rec_total_thms = map (fn r => r RS @{thm theI'}) rec_unique_thms; |
5177 | 221 |
|
222 |
(* define primrec combinators *) |
|
223 |
||
224 |
val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec"; |
|
28965 | 225 |
val reccomb_names = map (Sign.full_bname thy1) |
5177 | 226 |
(if length descr' = 1 then [big_reccomb_name] else |
227 |
(map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int) |
|
228 |
(1 upto (length descr')))); |
|
229 |
val reccombs = map (fn ((name, T), T') => list_comb |
|
230 |
(Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns)) |
|
231 |
(reccomb_names ~~ recTs ~~ rec_result_Ts); |
|
232 |
||
18358 | 233 |
val (reccomb_defs, thy2) = |
234 |
thy1 |
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|> Sign.add_consts_i (map (fn ((name, T), T') => |
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(Binding.name (Long_Name.base_name name), reccomb_fn_Ts @ [T] ---> T', NoSyn)) |
18358 | 237 |
(reccomb_names ~~ recTs ~~ rec_result_Ts)) |
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238 |
|> (Global_Theory.add_defs false o map Thm.no_attributes) |
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239 |
(map (fn ((((name, comb), set), T), T') => |
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renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
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parents:
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diff
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|
240 |
(Binding.name (Long_Name.base_name name ^ "_def"), |
44241 | 241 |
Logic.mk_equals (comb, absfree ("x", T) |
242 |
(Const (@{const_name The}, (T' --> HOLogic.boolT) --> T') $ absfree ("y", T') |
|
243 |
(set $ Free ("x", T) $ Free ("y", T')))))) |
|
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
38864
diff
changeset
|
244 |
(reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts)) |
32124 | 245 |
||> Sign.parent_path |
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|
246 |
||> Theory.checkpoint; |
5177 | 247 |
|
248 |
||
249 |
(* prove characteristic equations for primrec combinators *) |
|
250 |
||
41423 | 251 |
val _ = Datatype_Aux.message config "Proving characteristic theorems for primrec combinators ..."; |
5177 | 252 |
|
32970
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operations of structure Skip_Proof (formerly SkipProof) no longer require quick_and_dirty mode;
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parents:
32952
diff
changeset
|
253 |
val rec_thms = map (fn t => Skip_Proof.prove_global thy2 [] [] t |
17985 | 254 |
(fn _ => EVERY |
255 |
[rewrite_goals_tac reccomb_defs, |
|
35410 | 256 |
rtac @{thm the1_equality} 1, |
5177 | 257 |
resolve_tac rec_unique_thms 1, |
258 |
resolve_tac rec_intrs 1, |
|
20046 | 259 |
REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)])) |
41423 | 260 |
(Datatype_Prop.make_primrecs new_type_names descr sorts thy2); |
5177 | 261 |
in |
18314 | 262 |
thy2 |
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|
263 |
|> Sign.add_path (space_implode "_" new_type_names) |
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
38864
diff
changeset
|
264 |
|> Global_Theory.add_thmss [((Binding.name "recs", rec_thms), [Nitpick_Simps.add])] |
24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24699
diff
changeset
|
265 |
||> Sign.parent_path |
28361
232fcbba2e4e
explicit checkpoint for low-level (global) theory operations, admits concurrent proofs;
wenzelm
parents:
28110
diff
changeset
|
266 |
||> Theory.checkpoint |
32906 | 267 |
|-> (fn thms => pair (reccomb_names, flat thms)) |
5177 | 268 |
end; |
269 |
||
8477
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
270 |
|
5177 | 271 |
(***************************** case combinators *******************************) |
272 |
||
41423 | 273 |
fun prove_case_thms (config : Datatype_Aux.config) |
274 |
new_type_names descr sorts reccomb_names primrec_thms thy = |
|
5177 | 275 |
let |
41423 | 276 |
val _ = Datatype_Aux.message config "Proving characteristic theorems for case combinators ..."; |
5661 | 277 |
|
32124 | 278 |
val thy1 = Sign.add_path (space_implode "_" new_type_names) thy; |
5177 | 279 |
|
32952 | 280 |
val descr' = flat descr; |
41423 | 281 |
val recTs = Datatype_Aux.get_rec_types descr' sorts; |
44121 | 282 |
val used = List.foldr Misc_Legacy.add_typ_tfree_names [] recTs; |
33957 | 283 |
val newTs = take (length (hd descr)) recTs; |
43324
2b47822868e4
discontinued Name.variant to emphasize that this is old-style / indirect;
wenzelm
parents:
42375
diff
changeset
|
284 |
val T' = TFree (singleton (Name.variant_list used) "'t", HOLogic.typeS); |
5177 | 285 |
|
41423 | 286 |
fun mk_dummyT dt = binder_types (Datatype_Aux.typ_of_dtyp descr' sorts dt) ---> T'; |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
287 |
|
5177 | 288 |
val case_dummy_fns = map (fn (_, (_, _, constrs)) => map (fn (_, cargs) => |
289 |
let |
|
41423 | 290 |
val Ts = map (Datatype_Aux.typ_of_dtyp descr' sorts) cargs; |
291 |
val Ts' = map mk_dummyT (filter Datatype_Aux.is_rec_type cargs) |
|
28524 | 292 |
in Const (@{const_name undefined}, Ts @ Ts' ---> T') |
5177 | 293 |
end) constrs) descr'; |
294 |
||
28965 | 295 |
val case_names = map (fn s => Sign.full_bname thy1 (s ^ "_case")) new_type_names; |
5177 | 296 |
|
297 |
(* define case combinators via primrec combinators *) |
|
298 |
||
32906 | 299 |
val (case_defs, thy2) = fold (fn ((((i, (_, _, constrs)), T), name), recname) => fn (defs, thy) => |
5177 | 300 |
let |
32906 | 301 |
val (fns1, fns2) = split_list (map (fn ((_, cargs), j) => |
5177 | 302 |
let |
41423 | 303 |
val Ts = map (Datatype_Aux.typ_of_dtyp descr' sorts) cargs; |
304 |
val Ts' = Ts @ map mk_dummyT (filter Datatype_Aux.is_rec_type cargs); |
|
305 |
val frees' = map2 (Datatype_Aux.mk_Free "x") Ts' (1 upto length Ts'); |
|
33957 | 306 |
val frees = take (length cargs) frees'; |
41423 | 307 |
val free = Datatype_Aux.mk_Free "f" (Ts ---> T') j |
5177 | 308 |
in |
44241 | 309 |
(free, fold_rev (absfree o dest_Free) frees' (list_comb (free, frees))) |
5177 | 310 |
end) (constrs ~~ (1 upto length constrs))); |
311 |
||
312 |
val caseT = (map (snd o dest_Free) fns1) @ [T] ---> T'; |
|
33957 | 313 |
val fns = flat (take i case_dummy_fns) @ |
314 |
fns2 @ flat (drop (i + 1) case_dummy_fns); |
|
5177 | 315 |
val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T'); |
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset
|
316 |
val decl = ((Binding.name (Long_Name.base_name name), caseT), NoSyn); |
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset
|
317 |
val def = (Binding.name (Long_Name.base_name name ^ "_def"), |
5177 | 318 |
Logic.mk_equals (list_comb (Const (name, caseT), fns1), |
33957 | 319 |
list_comb (reccomb, (flat (take i case_dummy_fns)) @ |
320 |
fns2 @ (flat (drop (i + 1) case_dummy_fns))))); |
|
18358 | 321 |
val ([def_thm], thy') = |
322 |
thy |
|
42375
774df7c59508
report Name_Space.declare/define, relatively to context;
wenzelm
parents:
41423
diff
changeset
|
323 |
|> Sign.declare_const_global decl |> snd |
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
38864
diff
changeset
|
324 |
|> (Global_Theory.add_defs false o map Thm.no_attributes) [def]; |
5177 | 325 |
|
8436 | 326 |
in (defs @ [def_thm], thy') |
32906 | 327 |
end) (hd descr ~~ newTs ~~ case_names ~~ |
33957 | 328 |
take (length newTs) reccomb_names) ([], thy1) |
28361
232fcbba2e4e
explicit checkpoint for low-level (global) theory operations, admits concurrent proofs;
wenzelm
parents:
28110
diff
changeset
|
329 |
||> Theory.checkpoint; |
5177 | 330 |
|
32970
fbd2bb2489a8
operations of structure Skip_Proof (formerly SkipProof) no longer require quick_and_dirty mode;
wenzelm
parents:
32952
diff
changeset
|
331 |
val case_thms = map (map (fn t => Skip_Proof.prove_global thy2 [] [] t |
20046 | 332 |
(fn _ => EVERY [rewrite_goals_tac (case_defs @ map mk_meta_eq primrec_thms), rtac refl 1]))) |
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
333 |
(Datatype_Prop.make_cases new_type_names descr sorts thy2) |
8477
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
334 |
in |
18314 | 335 |
thy2 |
33459 | 336 |
|> Context.theory_map ((fold o fold) Nitpick_Simps.add_thm case_thms) |
32124 | 337 |
|> Sign.parent_path |
41423 | 338 |
|> Datatype_Aux.store_thmss "cases" new_type_names case_thms |
18314 | 339 |
|-> (fn thmss => pair (thmss, case_names)) |
8477
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
340 |
end; |
5177 | 341 |
|
342 |
||
343 |
(******************************* case splitting *******************************) |
|
344 |
||
41423 | 345 |
fun prove_split_thms (config : Datatype_Aux.config) |
346 |
new_type_names descr sorts constr_inject dist_rewrites casedist_thms case_thms thy = |
|
5177 | 347 |
let |
41423 | 348 |
val _ = Datatype_Aux.message config "Proving equations for case splitting ..."; |
5177 | 349 |
|
31668
a616e56a5ec8
datatype packages: record datatype_config for configuration flags; less verbose signatures
haftmann
parents:
31604
diff
changeset
|
350 |
val descr' = flat descr; |
41423 | 351 |
val recTs = Datatype_Aux.get_rec_types descr' sorts; |
33957 | 352 |
val newTs = take (length (hd descr)) recTs; |
5177 | 353 |
|
354 |
fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'), |
|
355 |
exhaustion), case_thms'), T) = |
|
356 |
let |
|
17985 | 357 |
val cert = cterm_of thy; |
5177 | 358 |
val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion))); |
359 |
val exhaustion' = cterm_instantiate |
|
360 |
[(cert lhs, cert (Free ("x", T)))] exhaustion; |
|
17985 | 361 |
val tacf = K (EVERY [rtac exhaustion' 1, ALLGOALS (asm_simp_tac |
362 |
(HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))]) |
|
5177 | 363 |
in |
32970
fbd2bb2489a8
operations of structure Skip_Proof (formerly SkipProof) no longer require quick_and_dirty mode;
wenzelm
parents:
32952
diff
changeset
|
364 |
(Skip_Proof.prove_global thy [] [] t1 tacf, |
fbd2bb2489a8
operations of structure Skip_Proof (formerly SkipProof) no longer require quick_and_dirty mode;
wenzelm
parents:
32952
diff
changeset
|
365 |
Skip_Proof.prove_global thy [] [] t2 tacf) |
5177 | 366 |
end; |
367 |
||
368 |
val split_thm_pairs = map prove_split_thms |
|
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
369 |
((Datatype_Prop.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~ |
5177 | 370 |
dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs); |
371 |
||
372 |
val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs |
|
373 |
||
374 |
in |
|
18314 | 375 |
thy |
41423 | 376 |
|> Datatype_Aux.store_thms "split" new_type_names split_thms |
377 |
||>> Datatype_Aux.store_thms "split_asm" new_type_names split_asm_thms |
|
18314 | 378 |
|-> (fn (thms1, thms2) => pair (thms1 ~~ thms2)) |
5177 | 379 |
end; |
380 |
||
8601 | 381 |
fun prove_weak_case_congs new_type_names descr sorts thy = |
382 |
let |
|
383 |
fun prove_weak_case_cong t = |
|
32970
fbd2bb2489a8
operations of structure Skip_Proof (formerly SkipProof) no longer require quick_and_dirty mode;
wenzelm
parents:
32952
diff
changeset
|
384 |
Skip_Proof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t) |
26711 | 385 |
(fn {prems, ...} => EVERY [rtac ((hd prems) RS arg_cong) 1]) |
8601 | 386 |
|
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
387 |
val weak_case_congs = map prove_weak_case_cong (Datatype_Prop.make_weak_case_congs |
8601 | 388 |
new_type_names descr sorts thy) |
389 |
||
41423 | 390 |
in thy |> Datatype_Aux.store_thms "weak_case_cong" new_type_names weak_case_congs end; |
8477
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
391 |
|
5177 | 392 |
(************************* additional theorems for TFL ************************) |
393 |
||
41423 | 394 |
fun prove_nchotomys (config : Datatype_Aux.config) |
395 |
new_type_names descr sorts casedist_thms thy = |
|
5177 | 396 |
let |
41423 | 397 |
val _ = Datatype_Aux.message config "Proving additional theorems for TFL ..."; |
5177 | 398 |
|
399 |
fun prove_nchotomy (t, exhaustion) = |
|
400 |
let |
|
401 |
(* For goal i, select the correct disjunct to attack, then prove it *) |
|
402 |
fun tac i 0 = EVERY [TRY (rtac disjI1 i), |
|
403 |
hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i] |
|
404 |
| tac i n = rtac disjI2 i THEN tac i (n - 1) |
|
405 |
in |
|
32970
fbd2bb2489a8
operations of structure Skip_Proof (formerly SkipProof) no longer require quick_and_dirty mode;
wenzelm
parents:
32952
diff
changeset
|
406 |
Skip_Proof.prove_global thy [] [] t (fn _ => |
17985 | 407 |
EVERY [rtac allI 1, |
41423 | 408 |
Datatype_Aux.exh_tac (K exhaustion) 1, |
20046 | 409 |
ALLGOALS (fn i => tac i (i-1))]) |
5177 | 410 |
end; |
411 |
||
412 |
val nchotomys = |
|
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
413 |
map prove_nchotomy (Datatype_Prop.make_nchotomys descr sorts ~~ casedist_thms) |
5177 | 414 |
|
41423 | 415 |
in thy |> Datatype_Aux.store_thms "nchotomy" new_type_names nchotomys end; |
5177 | 416 |
|
417 |
fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy = |
|
418 |
let |
|
419 |
fun prove_case_cong ((t, nchotomy), case_rewrites) = |
|
420 |
let |
|
421 |
val (Const ("==>", _) $ tm $ _) = t; |
|
38864
4abe644fcea5
formerly unnamed infix equality now named HOL.eq
haftmann
parents:
35625
diff
changeset
|
422 |
val (Const (@{const_name Trueprop}, _) $ (Const (@{const_name HOL.eq}, _) $ _ $ Ma)) = tm; |
22578 | 423 |
val cert = cterm_of thy; |
5177 | 424 |
val nchotomy' = nchotomy RS spec; |
29264 | 425 |
val [v] = Term.add_vars (concl_of nchotomy') []; |
426 |
val nchotomy'' = cterm_instantiate [(cert (Var v), cert Ma)] nchotomy' |
|
5177 | 427 |
in |
32970
fbd2bb2489a8
operations of structure Skip_Proof (formerly SkipProof) no longer require quick_and_dirty mode;
wenzelm
parents:
32952
diff
changeset
|
428 |
Skip_Proof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t) |
26711 | 429 |
(fn {prems, ...} => |
17985 | 430 |
let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites)) |
431 |
in EVERY [simp_tac (HOL_ss addsimps [hd prems]) 1, |
|
432 |
cut_facts_tac [nchotomy''] 1, |
|
433 |
REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1), |
|
434 |
REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)] |
|
20046 | 435 |
end) |
5177 | 436 |
end; |
437 |
||
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
438 |
val case_congs = map prove_case_cong (Datatype_Prop.make_case_congs |
5177 | 439 |
new_type_names descr sorts thy ~~ nchotomys ~~ case_thms) |
440 |
||
41423 | 441 |
in thy |> Datatype_Aux.store_thms "case_cong" new_type_names case_congs end; |
442 |
||
443 |
||
444 |
open Datatype_Aux; |
|
5177 | 445 |
|
446 |
end; |