author | paulson |
Fri, 17 Dec 2004 10:15:46 +0100 | |
changeset 15418 | e28853da5df5 |
parent 14981 | e73f8140af78 |
child 15459 | 16dd63c78049 |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/datatype_abs_proofs.ML |
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ID: $Id$ |
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Author: Stefan Berghofer, TU Muenchen |
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Proofs and defintions independent of concrete representation |
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of datatypes (i.e. requiring only abstract properties such as |
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injectivity / distinctness of constructors and induction) |
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- case distinction (exhaustion) theorems |
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- characteristic equations for primrec combinators |
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- characteristic equations for case combinators |
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- equations for splitting "P (case ...)" expressions |
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- datatype size function |
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- "nchotomy" and "case_cong" theorems for TFL |
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*) |
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signature DATATYPE_ABS_PROOFS = |
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sig |
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val prove_casedist_thms : string list -> |
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DatatypeAux.descr list -> (string * sort) list -> thm -> |
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theory attribute list -> theory -> theory * thm list |
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val prove_primrec_thms : bool -> string list -> |
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DatatypeAux.descr list -> (string * sort) list -> |
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DatatypeAux.datatype_info Symtab.table -> thm list list -> thm list list -> |
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simpset -> thm -> theory -> theory * (string list * thm list) |
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val prove_case_thms : bool -> string list -> |
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DatatypeAux.descr list -> (string * sort) list -> |
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string list -> thm list -> theory -> theory * (thm list list * string list) |
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val prove_split_thms : string list -> |
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DatatypeAux.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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theory * (thm * thm) list |
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val prove_size_thms : bool -> string list -> |
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DatatypeAux.descr list -> (string * sort) list -> |
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string list -> thm list -> theory -> theory * thm list |
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val prove_nchotomys : string list -> DatatypeAux.descr list -> |
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(string * sort) list -> thm list -> theory -> theory * thm list |
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val prove_weak_case_congs : string list -> DatatypeAux.descr list -> |
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(string * sort) list -> theory -> theory * thm list |
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val prove_case_congs : string list -> |
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DatatypeAux.descr list -> (string * sort) list -> |
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thm list -> thm list list -> theory -> theory * thm list |
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end; |
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structure DatatypeAbsProofs: DATATYPE_ABS_PROOFS = |
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struct |
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open DatatypeAux; |
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(************************ case distinction theorems ***************************) |
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fun prove_casedist_thms new_type_names descr sorts induct case_names_exhausts thy = |
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let |
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val _ = message "Proving case distinction theorems ..."; |
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val descr' = flat descr; |
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val recTs = get_rec_types descr' sorts; |
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val newTs = take (length (hd descr), recTs); |
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val {maxidx, ...} = rep_thm induct; |
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val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct))); |
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fun prove_casedist_thm ((i, t), T) = |
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let |
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val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) => |
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Abs ("z", T', Const ("True", T''))) induct_Ps; |
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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 (Theory.sign_of thy); |
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val insts' = (map cert induct_Ps) ~~ (map cert insts); |
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val induct' = refl RS ((nth_elem (i, |
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split_conj_thm (cterm_instantiate insts' induct))) RSN (2, rev_mp)) |
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in prove_goalw_cterm [] (cert t) (fn prems => |
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[rtac induct' 1, |
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REPEAT (rtac TrueI 1), |
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REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)), |
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REPEAT (rtac TrueI 1)]) |
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end; |
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val casedist_thms = map prove_casedist_thm ((0 upto (length newTs - 1)) ~~ |
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(DatatypeProp.make_casedists descr sorts) ~~ newTs) |
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in thy |> store_thms_atts "exhaust" new_type_names (map single case_names_exhausts) casedist_thms end; |
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(*************************** primrec combinators ******************************) |
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fun prove_primrec_thms flat_names new_type_names descr sorts |
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(dt_info : datatype_info Symtab.table) constr_inject dist_rewrites dist_ss induct thy = |
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let |
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val _ = message "Constructing primrec combinators ..."; |
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val big_name = space_implode "_" new_type_names; |
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val thy0 = add_path flat_names big_name thy; |
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val descr' = flat descr; |
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val recTs = get_rec_types descr' sorts; |
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val used = foldr add_typ_tfree_names (recTs, []); |
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val newTs = take (length (hd descr), recTs); |
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val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct))); |
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val big_rec_name' = big_name ^ "_rec_set"; |
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val rec_set_names = map (Sign.full_name (Theory.sign_of thy0)) |
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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_result_Ts = map TFree (variantlist (replicate (length descr') "'t", used) ~~ |
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replicate (length descr') HOLogic.typeS); |
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val reccomb_fn_Ts = flat (map (fn (i, (_, _, constrs)) => |
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map (fn (_, cargs) => |
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let |
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val Ts = map (typ_of_dtyp descr' sorts) cargs; |
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val recs = filter (is_rec_type o fst) (cargs ~~ Ts); |
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fun mk_argT (dt, T) = |
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binder_types T ---> nth_elem (body_index dt, rec_result_Ts); |
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val argTs = Ts @ map mk_argT recs |
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in argTs ---> nth_elem (i, rec_result_Ts) |
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end) constrs) descr'); |
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val rec_set_Ts = map (fn (T1, T2) => reccomb_fn_Ts ---> HOLogic.mk_setT |
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(HOLogic.mk_prodT (T1, T2))) (recTs ~~ rec_result_Ts); |
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val rec_fns = map (uncurry (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 (Const c, rec_fns)) |
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(rec_set_names ~~ rec_set_Ts); |
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(* introduction rules for graph of primrec function *) |
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fun make_rec_intr T set_name ((rec_intr_ts, l), (cname, cargs)) = |
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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 = mk_Free "x" U j |
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in (case (strip_dtyp dt, strip_type U) of |
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((_, DtRec m), (Us, _)) => |
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let |
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val free2 = mk_Free "y" (Us ---> nth_elem (m, rec_result_Ts)) 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, HOLogic.mk_mem (HOLogic.mk_prod |
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(app_bnds free1 i, app_bnds free2 i), |
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nth_elem (m, rec_sets)))) :: 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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end; |
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val Ts = map (typ_of_dtyp descr' sorts) cargs; |
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val (_, _, prems, t1s, t2s) = foldr mk_prem (cargs ~~ Ts, (1, 1, [], [], [])) |
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in (rec_intr_ts @ [Logic.list_implies (prems, HOLogic.mk_Trueprop (HOLogic.mk_mem |
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(HOLogic.mk_prod (list_comb (Const (cname, Ts ---> T), t1s), |
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list_comb (nth_elem (l, rec_fns), t1s @ t2s)), set_name)))], l + 1) |
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end; |
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val (rec_intr_ts, _) = foldl (fn (x, ((d, T), set_name)) => |
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foldl (make_rec_intr T set_name) (x, #3 (snd d))) |
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(([], 0), descr' ~~ recTs ~~ rec_sets); |
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val (thy1, {intrs = rec_intrs, elims = rec_elims, ...}) = |
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setmp InductivePackage.quiet_mode (!quiet_mode) |
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(InductivePackage.add_inductive_i false true big_rec_name' false false true |
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rec_sets (map (fn x => (("", x), [])) rec_intr_ts) []) thy0; |
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(* prove uniqueness and termination of primrec combinators *) |
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val _ = message "Proving termination and uniqueness of primrec functions ..."; |
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fun mk_unique_tac ((tac, intrs), ((((i, (tname, _, constrs)), elim), T), T')) = |
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let |
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val distinct_tac = (etac Pair_inject 1) THEN |
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(if i < length newTs then |
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full_simp_tac (HOL_ss addsimps (nth_elem (i, dist_rewrites))) 1 |
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else full_simp_tac dist_ss 1); |
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val inject = map (fn r => r RS iffD1) |
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(if i < length newTs then nth_elem (i, constr_inject) |
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else #inject (the (Symtab.lookup (dt_info, tname)))); |
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fun mk_unique_constr_tac n ((tac, intr::intrs, j), (cname, cargs)) = |
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let |
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val k = length (filter is_rec_type cargs) |
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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, |
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REPEAT_DETERM_N j distinct_tac, |
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etac Pair_inject 1, TRY (dresolve_tac inject 1), |
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REPEAT (etac conjE 1), hyp_subst_tac 1, |
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REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]), |
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TRY (hyp_subst_tac 1), |
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rtac refl 1, |
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REPEAT_DETERM_N (n - j - 1) distinct_tac], |
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intrs, j + 1) |
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end; |
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val (tac', intrs', _) = foldl (mk_unique_constr_tac (length constrs)) |
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((tac, intrs, 0), constrs); |
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in (tac', intrs') end; |
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val rec_unique_thms = |
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212 |
let |
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val rec_unique_ts = map (fn (((set_t, T1), T2), i) => |
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Const ("Ex1", (T2 --> HOLogic.boolT) --> HOLogic.boolT) $ |
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absfree ("y", T2, HOLogic.mk_mem (HOLogic.mk_prod |
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(mk_Free "x" T1 i, Free ("y", T2)), set_t))) |
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(rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs)); |
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val cert = cterm_of (Theory.sign_of thy1) |
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val insts = map (fn ((i, T), t) => absfree ("x" ^ (string_of_int i), T, t)) |
220 |
((1 upto length recTs) ~~ recTs ~~ rec_unique_ts); |
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val induct' = cterm_instantiate ((map cert induct_Ps) ~~ |
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(map cert insts)) induct; |
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val (tac, _) = foldl mk_unique_tac |
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(((rtac induct' THEN_ALL_NEW ObjectLogic.atomize_tac) 1 |
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THEN rewtac (mk_meta_eq choice_eq), rec_intrs), |
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descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts); |
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in split_conj_thm (prove_goalw_cterm [] |
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(cert (HOLogic.mk_Trueprop (mk_conj rec_unique_ts))) (K [tac])) |
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230 |
end; |
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val rec_total_thms = map (fn r => r RS theI') rec_unique_thms; |
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(* define primrec combinators *) |
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val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec"; |
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val reccomb_names = map (Sign.full_name (Theory.sign_of thy1)) |
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(if length descr' = 1 then [big_reccomb_name] else |
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(map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int) |
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(1 upto (length descr')))); |
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val reccombs = map (fn ((name, T), T') => list_comb |
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(Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns)) |
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(reccomb_names ~~ recTs ~~ rec_result_Ts); |
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val (thy2, reccomb_defs) = thy1 |> |
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Theory.add_consts_i (map (fn ((name, T), T') => |
247 |
(Sign.base_name name, reccomb_fn_Ts @ [T] ---> T', NoSyn)) |
|
248 |
(reccomb_names ~~ recTs ~~ rec_result_Ts)) |> |
|
9315 | 249 |
(PureThy.add_defs_i false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') => |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
250 |
((Sign.base_name name) ^ "_def", Logic.mk_equals (comb, absfree ("x", T, |
11435 | 251 |
Const ("The", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T', |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
252 |
HOLogic.mk_mem (HOLogic.mk_prod (Free ("x", T), Free ("y", T')), set)))))) |
8436 | 253 |
(reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts)) |>> |
5661 | 254 |
parent_path flat_names; |
5177 | 255 |
|
256 |
||
257 |
(* prove characteristic equations for primrec combinators *) |
|
258 |
||
6427 | 259 |
val _ = message "Proving characteristic theorems for primrec combinators ..." |
5177 | 260 |
|
261 |
val rec_thms = map (fn t => prove_goalw_cterm reccomb_defs |
|
6394 | 262 |
(cterm_of (Theory.sign_of thy2) t) (fn _ => |
11435 | 263 |
[rtac the1_equality 1, |
5177 | 264 |
resolve_tac rec_unique_thms 1, |
265 |
resolve_tac rec_intrs 1, |
|
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
12910
diff
changeset
|
266 |
REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)])) |
5177 | 267 |
(DatatypeProp.make_primrecs new_type_names descr sorts thy2) |
268 |
||
269 |
in |
|
8477
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
270 |
thy2 |> Theory.add_path (space_implode "_" new_type_names) |> |
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
271 |
PureThy.add_thmss [(("recs", rec_thms), [])] |>> |
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
272 |
Theory.parent_path |> apsnd (pair reccomb_names o flat) |
5177 | 273 |
end; |
274 |
||
8477
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
275 |
|
5177 | 276 |
(***************************** case combinators *******************************) |
277 |
||
5661 | 278 |
fun prove_case_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy = |
5177 | 279 |
let |
6427 | 280 |
val _ = message "Proving characteristic theorems for case combinators ..."; |
5661 | 281 |
|
282 |
val thy1 = add_path flat_names (space_implode "_" new_type_names) thy; |
|
5177 | 283 |
|
284 |
val descr' = flat descr; |
|
285 |
val recTs = get_rec_types descr' sorts; |
|
5578
7de426cf179c
Package now chooses type variable names more carefully to
berghofe
parents:
5553
diff
changeset
|
286 |
val used = foldr add_typ_tfree_names (recTs, []); |
5177 | 287 |
val newTs = take (length (hd descr), recTs); |
12338
de0f4a63baa5
renamed class "term" to "type" (actually "HOL.type");
wenzelm
parents:
12180
diff
changeset
|
288 |
val T' = TFree (variant used "'t", HOLogic.typeS); |
5177 | 289 |
|
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
12910
diff
changeset
|
290 |
fun mk_dummyT dt = binder_types (typ_of_dtyp descr' sorts dt) ---> T'; |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
291 |
|
5177 | 292 |
val case_dummy_fns = map (fn (_, (_, _, constrs)) => map (fn (_, cargs) => |
293 |
let |
|
294 |
val Ts = map (typ_of_dtyp descr' sorts) cargs; |
|
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
295 |
val Ts' = map mk_dummyT (filter is_rec_type cargs) |
5578
7de426cf179c
Package now chooses type variable names more carefully to
berghofe
parents:
5553
diff
changeset
|
296 |
in Const ("arbitrary", Ts @ Ts' ---> T') |
5177 | 297 |
end) constrs) descr'; |
298 |
||
299 |
val case_names = map (fn s => |
|
6394 | 300 |
Sign.full_name (Theory.sign_of thy1) (s ^ "_case")) new_type_names; |
5177 | 301 |
|
302 |
(* define case combinators via primrec combinators *) |
|
303 |
||
304 |
val (case_defs, thy2) = foldl (fn ((defs, thy), |
|
305 |
((((i, (_, _, constrs)), T), name), recname)) => |
|
306 |
let |
|
307 |
val (fns1, fns2) = ListPair.unzip (map (fn ((_, cargs), j) => |
|
308 |
let |
|
309 |
val Ts = map (typ_of_dtyp descr' sorts) cargs; |
|
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
310 |
val Ts' = Ts @ map mk_dummyT (filter is_rec_type cargs); |
5177 | 311 |
val frees' = map (uncurry (mk_Free "x")) (Ts' ~~ (1 upto length Ts')); |
312 |
val frees = take (length cargs, frees'); |
|
313 |
val free = mk_Free "f" (Ts ---> T') j |
|
314 |
in |
|
315 |
(free, list_abs_free (map dest_Free frees', |
|
316 |
list_comb (free, frees))) |
|
317 |
end) (constrs ~~ (1 upto length constrs))); |
|
318 |
||
319 |
val caseT = (map (snd o dest_Free) fns1) @ [T] ---> T'; |
|
320 |
val fns = (flat (take (i, case_dummy_fns))) @ |
|
321 |
fns2 @ (flat (drop (i + 1, case_dummy_fns))); |
|
322 |
val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T'); |
|
323 |
val decl = (Sign.base_name name, caseT, NoSyn); |
|
324 |
val def = ((Sign.base_name name) ^ "_def", |
|
325 |
Logic.mk_equals (list_comb (Const (name, caseT), fns1), |
|
326 |
list_comb (reccomb, (flat (take (i, case_dummy_fns))) @ |
|
327 |
fns2 @ (flat (drop (i + 1, case_dummy_fns))) ))); |
|
8436 | 328 |
val (thy', [def_thm]) = thy |> |
9315 | 329 |
Theory.add_consts_i [decl] |> (PureThy.add_defs_i false o map Thm.no_attributes) [def]; |
5177 | 330 |
|
8436 | 331 |
in (defs @ [def_thm], thy') |
5661 | 332 |
end) (([], thy1), (hd descr) ~~ newTs ~~ case_names ~~ |
5177 | 333 |
(take (length newTs, reccomb_names))); |
334 |
||
335 |
val case_thms = map (map (fn t => prove_goalw_cterm (case_defs @ |
|
6394 | 336 |
(map mk_meta_eq primrec_thms)) (cterm_of (Theory.sign_of thy2) t) |
5177 | 337 |
(fn _ => [rtac refl 1]))) |
8477
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
338 |
(DatatypeProp.make_cases new_type_names descr sorts thy2) |
5177 | 339 |
|
8477
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
340 |
in |
14799
a405aadff16c
Added more flexible parse / print translations for case expressions.
berghofe
parents:
13641
diff
changeset
|
341 |
thy2 |> |
8477
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
342 |
parent_path flat_names |> |
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
343 |
store_thmss "cases" new_type_names case_thms |> |
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
344 |
apsnd (rpair case_names) |
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
345 |
end; |
5177 | 346 |
|
347 |
||
348 |
(******************************* case splitting *******************************) |
|
349 |
||
350 |
fun prove_split_thms new_type_names descr sorts constr_inject dist_rewrites |
|
351 |
casedist_thms case_thms thy = |
|
352 |
let |
|
6427 | 353 |
val _ = message "Proving equations for case splitting ..."; |
5177 | 354 |
|
355 |
val descr' = flat descr; |
|
356 |
val recTs = get_rec_types descr' sorts; |
|
357 |
val newTs = take (length (hd descr), recTs); |
|
358 |
||
359 |
fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'), |
|
360 |
exhaustion), case_thms'), T) = |
|
361 |
let |
|
6394 | 362 |
val cert = cterm_of (Theory.sign_of thy); |
5177 | 363 |
val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion))); |
364 |
val exhaustion' = cterm_instantiate |
|
365 |
[(cert lhs, cert (Free ("x", T)))] exhaustion; |
|
366 |
val tacsf = K [rtac exhaustion' 1, ALLGOALS (asm_simp_tac |
|
367 |
(HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))] |
|
368 |
in |
|
369 |
(prove_goalw_cterm [] (cert t1) tacsf, |
|
370 |
prove_goalw_cterm [] (cert t2) tacsf) |
|
371 |
end; |
|
372 |
||
373 |
val split_thm_pairs = map prove_split_thms |
|
374 |
((DatatypeProp.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~ |
|
375 |
dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs); |
|
376 |
||
377 |
val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs |
|
378 |
||
379 |
in |
|
8436 | 380 |
thy |> store_thms "split" new_type_names split_thms |>>> |
381 |
store_thms "split_asm" new_type_names split_asm_thms |> apsnd ListPair.zip |
|
5177 | 382 |
end; |
383 |
||
384 |
(******************************* size functions *******************************) |
|
385 |
||
5661 | 386 |
fun prove_size_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy = |
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
12910
diff
changeset
|
387 |
if exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists (fn dt => |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
12910
diff
changeset
|
388 |
is_rec_type dt andalso not (null (fst (strip_dtyp dt)))) cargs) constrs) |
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
12910
diff
changeset
|
389 |
(flat descr) |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
390 |
then |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
391 |
(thy, []) |
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
392 |
else |
5177 | 393 |
let |
6427 | 394 |
val _ = message "Proving equations for size function ..."; |
5661 | 395 |
|
396 |
val big_name = space_implode "_" new_type_names; |
|
397 |
val thy1 = add_path flat_names big_name thy; |
|
5177 | 398 |
|
399 |
val descr' = flat descr; |
|
400 |
val recTs = get_rec_types descr' sorts; |
|
401 |
||
11957 | 402 |
val size_name = "Nat.size"; |
5177 | 403 |
val size_names = replicate (length (hd descr)) size_name @ |
9739 | 404 |
map (Sign.full_name (Theory.sign_of thy1)) (DatatypeProp.indexify_names |
405 |
(map (fn T => name_of_typ T ^ "_size") (drop (length (hd descr), recTs)))); |
|
406 |
val def_names = map (fn s => s ^ "_def") (DatatypeProp.indexify_names |
|
407 |
(map (fn T => name_of_typ T ^ "_size") recTs)); |
|
5177 | 408 |
|
7704 | 409 |
fun plus (t1, t2) = Const ("op +", [HOLogic.natT, HOLogic.natT] ---> HOLogic.natT) $ t1 $ t2; |
5177 | 410 |
|
411 |
fun make_sizefun (_, cargs) = |
|
412 |
let |
|
413 |
val Ts = map (typ_of_dtyp descr' sorts) cargs; |
|
414 |
val k = length (filter is_rec_type cargs); |
|
415 |
val t = if k = 0 then HOLogic.zero else |
|
7704 | 416 |
foldl1 plus (map Bound (k - 1 downto 0) @ [HOLogic.mk_nat 1]) |
5177 | 417 |
in |
418 |
foldr (fn (T, t') => Abs ("x", T, t')) (Ts @ replicate k HOLogic.natT, t) |
|
419 |
end; |
|
420 |
||
421 |
val fs = flat (map (fn (_, (_, _, constrs)) => map make_sizefun constrs) descr'); |
|
422 |
val fTs = map fastype_of fs; |
|
423 |
||
8436 | 424 |
val (thy', size_def_thms) = thy1 |> |
5177 | 425 |
Theory.add_consts_i (map (fn (s, T) => |
426 |
(Sign.base_name s, T --> HOLogic.natT, NoSyn)) |
|
427 |
(drop (length (hd descr), size_names ~~ recTs))) |> |
|
9315 | 428 |
(PureThy.add_defs_i true o map Thm.no_attributes) (map (fn (((s, T), def_name), rec_name) => |
5177 | 429 |
(def_name, Logic.mk_equals (Const (s, T --> HOLogic.natT), |
430 |
list_comb (Const (rec_name, fTs @ [T] ---> HOLogic.natT), fs)))) |
|
8436 | 431 |
(size_names ~~ recTs ~~ def_names ~~ reccomb_names)) |>> |
5661 | 432 |
parent_path flat_names; |
5177 | 433 |
|
5553 | 434 |
val rewrites = size_def_thms @ map mk_meta_eq primrec_thms; |
5177 | 435 |
|
436 |
val size_thms = map (fn t => prove_goalw_cterm rewrites |
|
6394 | 437 |
(cterm_of (Theory.sign_of thy') t) (fn _ => [rtac refl 1])) |
9739 | 438 |
(DatatypeProp.make_size descr sorts thy') |
5177 | 439 |
|
440 |
in |
|
8477
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
441 |
thy' |> Theory.add_path big_name |> |
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
442 |
PureThy.add_thmss [(("size", size_thms), [])] |>> |
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
443 |
Theory.parent_path |> apsnd flat |
5177 | 444 |
end; |
445 |
||
8601 | 446 |
fun prove_weak_case_congs new_type_names descr sorts thy = |
447 |
let |
|
448 |
fun prove_weak_case_cong t = |
|
449 |
prove_goalw_cterm [] (cterm_of (Theory.sign_of thy) t) |
|
450 |
(fn prems => [rtac ((hd prems) RS arg_cong) 1]) |
|
451 |
||
452 |
val weak_case_congs = map prove_weak_case_cong (DatatypeProp.make_weak_case_congs |
|
453 |
new_type_names descr sorts thy) |
|
454 |
||
455 |
in thy |> 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
|
456 |
|
5177 | 457 |
(************************* additional theorems for TFL ************************) |
458 |
||
459 |
fun prove_nchotomys new_type_names descr sorts casedist_thms thy = |
|
460 |
let |
|
6427 | 461 |
val _ = message "Proving additional theorems for TFL ..."; |
5177 | 462 |
|
463 |
fun prove_nchotomy (t, exhaustion) = |
|
464 |
let |
|
465 |
(* For goal i, select the correct disjunct to attack, then prove it *) |
|
466 |
fun tac i 0 = EVERY [TRY (rtac disjI1 i), |
|
467 |
hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i] |
|
468 |
| tac i n = rtac disjI2 i THEN tac i (n - 1) |
|
469 |
in |
|
6394 | 470 |
prove_goalw_cterm [] (cterm_of (Theory.sign_of thy) t) (fn _ => |
5177 | 471 |
[rtac allI 1, |
472 |
exh_tac (K exhaustion) 1, |
|
473 |
ALLGOALS (fn i => tac i (i-1))]) |
|
474 |
end; |
|
475 |
||
476 |
val nchotomys = |
|
477 |
map prove_nchotomy (DatatypeProp.make_nchotomys descr sorts ~~ casedist_thms) |
|
478 |
||
8436 | 479 |
in thy |> store_thms "nchotomy" new_type_names nchotomys end; |
5177 | 480 |
|
481 |
fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy = |
|
482 |
let |
|
483 |
fun prove_case_cong ((t, nchotomy), case_rewrites) = |
|
484 |
let |
|
485 |
val (Const ("==>", _) $ tm $ _) = t; |
|
486 |
val (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ Ma)) = tm; |
|
6394 | 487 |
val cert = cterm_of (Theory.sign_of thy); |
5177 | 488 |
val nchotomy' = nchotomy RS spec; |
489 |
val nchotomy'' = cterm_instantiate |
|
490 |
[(cert (hd (add_term_vars (concl_of nchotomy', []))), cert Ma)] nchotomy' |
|
491 |
in |
|
492 |
prove_goalw_cterm [] (cert t) (fn prems => |
|
493 |
let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites)) |
|
494 |
in [simp_tac (HOL_ss addsimps [hd prems]) 1, |
|
495 |
cut_facts_tac [nchotomy''] 1, |
|
496 |
REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1), |
|
497 |
REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)] |
|
498 |
end) |
|
499 |
end; |
|
500 |
||
501 |
val case_congs = map prove_case_cong (DatatypeProp.make_case_congs |
|
502 |
new_type_names descr sorts thy ~~ nchotomys ~~ case_thms) |
|
503 |
||
8436 | 504 |
in thy |> store_thms "case_cong" new_type_names case_congs end; |
5177 | 505 |
|
506 |
end; |