author | wenzelm |
Sun, 15 Apr 2007 14:31:49 +0200 | |
changeset 22692 | 1e057a3f087d |
parent 22578 | b0eb5652f210 |
child 22776 | 292dbccd8755 |
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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attribute list -> theory -> thm list * theory |
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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 -> (string list * thm list) * theory |
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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 -> (thm list list * string list) * theory |
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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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(thm * thm) list * theory |
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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 -> thm list * theory |
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val prove_nchotomys : string list -> DatatypeAux.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 -> DatatypeAux.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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DatatypeAux.descr list -> (string * sort) list -> |
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thm list -> thm list list -> theory -> thm list * theory |
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end; |
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||
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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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||
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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' = List.concat descr; |
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val recTs = get_rec_types descr' sorts; |
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val newTs = Library.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 = Library.take (i, dummyPs) @ (P::(Library.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 ((List.nth |
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(split_conj_thm (cterm_instantiate insts' induct), i)) RSN (2, rev_mp)) |
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in |
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Goal.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, |
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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 |
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thy |
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|> store_thms_atts "exhaust" new_type_names (map single case_names_exhausts) casedist_thms |
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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' = List.concat 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 = Library.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' = |
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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_name thy0) rec_set_names'; |
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val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used; |
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val rec_set_Ts = map (fn (T1, T2) => |
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reccomb_fn_Ts @ [T1, T2] ---> HOLogic.boolT) (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 (Free c, rec_fns)) |
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(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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(* introduction rules for graph of primrec function *) |
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fun make_rec_intr T rec_set ((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 ---> List.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, List.nth (rec_sets', m) $ |
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app_bnds free1 i $ 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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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 (1, 1, [], [], []) (cargs ~~ Ts) |
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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 (List.nth (rec_fns, l), t1s @ t2s)))], l + 1) |
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end; |
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val (rec_intr_ts, _) = Library.foldl (fn (x, ((d, T), set_name)) => |
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Library.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 ({intrs = rec_intrs, elims = rec_elims, ...}, thy1) = |
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setmp InductivePackage.quiet_mode (!quiet_mode) |
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(InductivePackage.add_inductive_global false big_rec_name' false false true |
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(map (fn (s, T) => (s, SOME T, NoSyn)) (rec_set_names' ~~ rec_set_Ts)) |
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(map (apsnd SOME o dest_Free) rec_fns) |
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(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 = |
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(if i < length newTs then |
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full_simp_tac (HOL_ss addsimps (List.nth (dist_rewrites, i))) 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 List.nth (constr_inject, i) |
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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 (List.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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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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||
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val (tac', intrs', _) = Library.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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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, set_t $ 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); |
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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, _) = Library.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 (Goal.prove_global thy1 [] [] |
223 |
(HOLogic.mk_Trueprop (mk_conj rec_unique_ts)) (K tac)) |
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end; |
225 |
||
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val rec_total_thms = map (fn r => r RS theI') rec_unique_thms; |
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228 |
(* define primrec combinators *) |
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229 |
||
230 |
val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec"; |
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val reccomb_names = map (Sign.full_name thy1) |
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(if length descr' = 1 then [big_reccomb_name] else |
233 |
(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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237 |
(reccomb_names ~~ recTs ~~ rec_result_Ts); |
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238 |
||
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val (reccomb_defs, thy2) = |
240 |
thy1 |
|
241 |
|> Theory.add_consts_i (map (fn ((name, T), T') => |
|
242 |
(Sign.base_name name, reccomb_fn_Ts @ [T] ---> T', NoSyn)) |
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(reccomb_names ~~ recTs ~~ rec_result_Ts)) |
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|> (PureThy.add_defs_i false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') => |
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((Sign.base_name name) ^ "_def", Logic.mk_equals (comb, absfree ("x", T, |
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Const ("The", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T', |
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set $ Free ("x", T) $ Free ("y", T')))))) |
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(reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts)) |
249 |
||> parent_path flat_names; |
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5177 | 250 |
|
251 |
||
252 |
(* prove characteristic equations for primrec combinators *) |
|
253 |
||
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val _ = message "Proving characteristic theorems for primrec combinators ..." |
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|
20046 | 256 |
val rec_thms = map (fn t => Goal.prove_global thy2 [] [] t |
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(fn _ => EVERY |
258 |
[rewrite_goals_tac reccomb_defs, |
|
259 |
rtac the1_equality 1, |
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resolve_tac rec_unique_thms 1, |
261 |
resolve_tac rec_intrs 1, |
|
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REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)])) |
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(DatatypeProp.make_primrecs new_type_names descr sorts thy2) |
264 |
||
265 |
in |
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thy2 |
267 |
|> Theory.add_path (space_implode "_" new_type_names) |
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|> PureThy.add_thmss [(("recs", rec_thms), [])] |
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||> Theory.parent_path |
270 |
|-> (fn thms => pair (reccomb_names, Library.flat thms)) |
|
5177 | 271 |
end; |
272 |
||
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(***************************** case combinators *******************************) |
275 |
||
5661 | 276 |
fun prove_case_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy = |
5177 | 277 |
let |
6427 | 278 |
val _ = message "Proving characteristic theorems for case combinators ..."; |
5661 | 279 |
|
280 |
val thy1 = add_path flat_names (space_implode "_" new_type_names) thy; |
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|
15570 | 282 |
val descr' = List.concat descr; |
5177 | 283 |
val recTs = get_rec_types descr' sorts; |
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
284 |
val used = foldr add_typ_tfree_names [] recTs; |
15570 | 285 |
val newTs = Library.take (length (hd descr), recTs); |
20071
8f3e1ddb50e6
replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents:
20046
diff
changeset
|
286 |
val T' = TFree (Name.variant used "'t", HOLogic.typeS); |
5177 | 287 |
|
13641
63d1790a43ed
Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents:
12910
diff
changeset
|
288 |
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
|
289 |
|
5177 | 290 |
val case_dummy_fns = map (fn (_, (_, _, constrs)) => map (fn (_, cargs) => |
291 |
let |
|
292 |
val Ts = map (typ_of_dtyp descr' sorts) cargs; |
|
15570 | 293 |
val Ts' = map mk_dummyT (List.filter is_rec_type cargs) |
5578
7de426cf179c
Package now chooses type variable names more carefully to
berghofe
parents:
5553
diff
changeset
|
294 |
in Const ("arbitrary", Ts @ Ts' ---> T') |
5177 | 295 |
end) constrs) descr'; |
296 |
||
22578 | 297 |
val case_names = map (fn s => Sign.full_name thy1 (s ^ "_case")) new_type_names; |
5177 | 298 |
|
299 |
(* define case combinators via primrec combinators *) |
|
300 |
||
15570 | 301 |
val (case_defs, thy2) = Library.foldl (fn ((defs, thy), |
5177 | 302 |
((((i, (_, _, constrs)), T), name), recname)) => |
303 |
let |
|
304 |
val (fns1, fns2) = ListPair.unzip (map (fn ((_, cargs), j) => |
|
305 |
let |
|
306 |
val Ts = map (typ_of_dtyp descr' sorts) cargs; |
|
15570 | 307 |
val Ts' = Ts @ map mk_dummyT (List.filter is_rec_type cargs); |
5177 | 308 |
val frees' = map (uncurry (mk_Free "x")) (Ts' ~~ (1 upto length Ts')); |
15570 | 309 |
val frees = Library.take (length cargs, frees'); |
5177 | 310 |
val free = mk_Free "f" (Ts ---> T') j |
311 |
in |
|
312 |
(free, list_abs_free (map dest_Free frees', |
|
313 |
list_comb (free, frees))) |
|
314 |
end) (constrs ~~ (1 upto length constrs))); |
|
315 |
||
316 |
val caseT = (map (snd o dest_Free) fns1) @ [T] ---> T'; |
|
15570 | 317 |
val fns = (List.concat (Library.take (i, case_dummy_fns))) @ |
318 |
fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns))); |
|
5177 | 319 |
val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T'); |
320 |
val decl = (Sign.base_name name, caseT, NoSyn); |
|
321 |
val def = ((Sign.base_name name) ^ "_def", |
|
322 |
Logic.mk_equals (list_comb (Const (name, caseT), fns1), |
|
15570 | 323 |
list_comb (reccomb, (List.concat (Library.take (i, case_dummy_fns))) @ |
324 |
fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns))) ))); |
|
18358 | 325 |
val ([def_thm], thy') = |
326 |
thy |
|
327 |
|> Theory.add_consts_i [decl] |
|
328 |
|> (PureThy.add_defs_i false o map Thm.no_attributes) [def]; |
|
5177 | 329 |
|
8436 | 330 |
in (defs @ [def_thm], thy') |
5661 | 331 |
end) (([], thy1), (hd descr) ~~ newTs ~~ case_names ~~ |
15570 | 332 |
(Library.take (length newTs, reccomb_names))); |
5177 | 333 |
|
20046 | 334 |
val case_thms = map (map (fn t => Goal.prove_global thy2 [] [] t |
335 |
(fn _ => EVERY [rewrite_goals_tac (case_defs @ map mk_meta_eq primrec_thms), rtac refl 1]))) |
|
8477
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
336 |
(DatatypeProp.make_cases new_type_names descr sorts thy2) |
5177 | 337 |
|
8477
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
338 |
in |
18314 | 339 |
thy2 |
340 |
|> parent_path flat_names |
|
341 |
|> store_thmss "cases" new_type_names case_thms |
|
342 |
|-> (fn thmss => pair (thmss, case_names)) |
|
8477
17231d71171a
- Fixed bug in prove_casedist_thms (proof failed because of
berghofe
parents:
8436
diff
changeset
|
343 |
end; |
5177 | 344 |
|
345 |
||
346 |
(******************************* case splitting *******************************) |
|
347 |
||
348 |
fun prove_split_thms new_type_names descr sorts constr_inject dist_rewrites |
|
349 |
casedist_thms case_thms thy = |
|
350 |
let |
|
6427 | 351 |
val _ = message "Proving equations for case splitting ..."; |
5177 | 352 |
|
15570 | 353 |
val descr' = List.concat descr; |
5177 | 354 |
val recTs = get_rec_types descr' sorts; |
15570 | 355 |
val newTs = Library.take (length (hd descr), recTs); |
5177 | 356 |
|
357 |
fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'), |
|
358 |
exhaustion), case_thms'), T) = |
|
359 |
let |
|
17985 | 360 |
val cert = cterm_of thy; |
5177 | 361 |
val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion))); |
362 |
val exhaustion' = cterm_instantiate |
|
363 |
[(cert lhs, cert (Free ("x", T)))] exhaustion; |
|
17985 | 364 |
val tacf = K (EVERY [rtac exhaustion' 1, ALLGOALS (asm_simp_tac |
365 |
(HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))]) |
|
5177 | 366 |
in |
20046 | 367 |
(Goal.prove_global thy [] [] t1 tacf, |
368 |
Goal.prove_global thy [] [] t2 tacf) |
|
5177 | 369 |
end; |
370 |
||
371 |
val split_thm_pairs = map prove_split_thms |
|
372 |
((DatatypeProp.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~ |
|
373 |
dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs); |
|
374 |
||
375 |
val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs |
|
376 |
||
377 |
in |
|
18314 | 378 |
thy |
379 |
|> store_thms "split" new_type_names split_thms |
|
380 |
||>> store_thms "split_asm" new_type_names split_asm_thms |
|
381 |
|-> (fn (thms1, thms2) => pair (thms1 ~~ thms2)) |
|
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) |
15570 | 389 |
(List.concat descr) |
7015
85be09eb136c
- Datatype package now also supports arbitrarily branching datatypes
berghofe
parents:
6522
diff
changeset
|
390 |
then |
18314 | 391 |
([], thy) |
7015
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 |
|
21419 | 399 |
val descr' = flat descr; |
5177 | 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 @ |
22578 | 404 |
map (Sign.full_name thy1) (DatatypeProp.indexify_names |
15570 | 405 |
(map (fn T => name_of_typ T ^ "_size") (Library.drop (length (hd descr), recTs)))); |
9739 | 406 |
val def_names = map (fn s => s ^ "_def") (DatatypeProp.indexify_names |
407 |
(map (fn T => name_of_typ T ^ "_size") recTs)); |
|
5177 | 408 |
|
19233
77ca20b0ed77
renamed HOL + - * etc. to HOL.plus HOL.minus HOL.times etc.
haftmann
parents:
18728
diff
changeset
|
409 |
fun plus (t1, t2) = Const ("HOL.plus", [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; |
|
21419 | 414 |
val k = length (filter is_rec_type cargs); |
5177 | 415 |
val t = if k = 0 then HOLogic.zero else |
21621 | 416 |
foldl1 plus (map Bound (k - 1 downto 0) @ [HOLogic.Suc_zero]) |
5177 | 417 |
in |
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
418 |
foldr (fn (T, t') => Abs ("x", T, t')) t (Ts @ replicate k HOLogic.natT) |
5177 | 419 |
end; |
420 |
||
21419 | 421 |
val fs = maps (fn (_, (_, _, constrs)) => map make_sizefun constrs) descr'; |
5177 | 422 |
val fTs = map fastype_of fs; |
423 |
||
21419 | 424 |
fun instance_size_class tyco thy = |
425 |
let |
|
426 |
val size_sort = ["Nat.size"]; |
|
427 |
val n = Sign.arity_number thy tyco; |
|
428 |
in |
|
429 |
thy |
|
430 |
|> AxClass.prove_arity (tyco, replicate n HOLogic.typeS, size_sort) |
|
431 |
(ClassPackage.intro_classes_tac []) |
|
432 |
end |
|
433 |
||
18358 | 434 |
val (size_def_thms, thy') = |
435 |
thy1 |
|
436 |
|> Theory.add_consts_i (map (fn (s, T) => |
|
437 |
(Sign.base_name s, T --> HOLogic.natT, NoSyn)) |
|
438 |
(Library.drop (length (hd descr), size_names ~~ recTs))) |
|
21419 | 439 |
|> fold (fn (_, (name, _, _)) => instance_size_class name) descr' |
440 |
|> PureThy.add_defs_i true (map (Thm.no_attributes o (fn (((s, T), def_name), rec_name) => |
|
18358 | 441 |
(def_name, Logic.mk_equals (Const (s, T --> HOLogic.natT), |
21419 | 442 |
list_comb (Const (rec_name, fTs @ [T] ---> HOLogic.natT), fs))))) |
18358 | 443 |
(size_names ~~ recTs ~~ def_names ~~ reccomb_names)) |
444 |
||> parent_path flat_names; |
|
5177 | 445 |
|
5553 | 446 |
val rewrites = size_def_thms @ map mk_meta_eq primrec_thms; |
5177 | 447 |
|
20046 | 448 |
val size_thms = map (fn t => Goal.prove_global thy' [] [] t |
449 |
(fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1])) |
|
9739 | 450 |
(DatatypeProp.make_size descr sorts thy') |
5177 | 451 |
|
452 |
in |
|
18314 | 453 |
thy' |
454 |
|> Theory.add_path big_name |
|
18377 | 455 |
|> PureThy.add_thmss [(("size", size_thms), [])] |
18314 | 456 |
||> Theory.parent_path |
21419 | 457 |
|-> (fn thmss => pair (flat thmss)) |
5177 | 458 |
end; |
459 |
||
8601 | 460 |
fun prove_weak_case_congs new_type_names descr sorts thy = |
461 |
let |
|
462 |
fun prove_weak_case_cong t = |
|
20046 | 463 |
Goal.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t) |
464 |
(fn prems => EVERY [rtac ((hd prems) RS arg_cong) 1]) |
|
8601 | 465 |
|
466 |
val weak_case_congs = map prove_weak_case_cong (DatatypeProp.make_weak_case_congs |
|
467 |
new_type_names descr sorts thy) |
|
468 |
||
469 |
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
|
470 |
|
5177 | 471 |
(************************* additional theorems for TFL ************************) |
472 |
||
473 |
fun prove_nchotomys new_type_names descr sorts casedist_thms thy = |
|
474 |
let |
|
6427 | 475 |
val _ = message "Proving additional theorems for TFL ..."; |
5177 | 476 |
|
477 |
fun prove_nchotomy (t, exhaustion) = |
|
478 |
let |
|
479 |
(* For goal i, select the correct disjunct to attack, then prove it *) |
|
480 |
fun tac i 0 = EVERY [TRY (rtac disjI1 i), |
|
481 |
hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i] |
|
482 |
| tac i n = rtac disjI2 i THEN tac i (n - 1) |
|
483 |
in |
|
20046 | 484 |
Goal.prove_global thy [] [] t (fn _ => |
17985 | 485 |
EVERY [rtac allI 1, |
5177 | 486 |
exh_tac (K exhaustion) 1, |
20046 | 487 |
ALLGOALS (fn i => tac i (i-1))]) |
5177 | 488 |
end; |
489 |
||
490 |
val nchotomys = |
|
491 |
map prove_nchotomy (DatatypeProp.make_nchotomys descr sorts ~~ casedist_thms) |
|
492 |
||
8436 | 493 |
in thy |> store_thms "nchotomy" new_type_names nchotomys end; |
5177 | 494 |
|
495 |
fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy = |
|
496 |
let |
|
497 |
fun prove_case_cong ((t, nchotomy), case_rewrites) = |
|
498 |
let |
|
499 |
val (Const ("==>", _) $ tm $ _) = t; |
|
500 |
val (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ Ma)) = tm; |
|
22578 | 501 |
val cert = cterm_of thy; |
5177 | 502 |
val nchotomy' = nchotomy RS spec; |
503 |
val nchotomy'' = cterm_instantiate |
|
504 |
[(cert (hd (add_term_vars (concl_of nchotomy', []))), cert Ma)] nchotomy' |
|
505 |
in |
|
20046 | 506 |
Goal.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t) |
17985 | 507 |
(fn prems => |
508 |
let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites)) |
|
509 |
in EVERY [simp_tac (HOL_ss addsimps [hd prems]) 1, |
|
510 |
cut_facts_tac [nchotomy''] 1, |
|
511 |
REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1), |
|
512 |
REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)] |
|
20046 | 513 |
end) |
5177 | 514 |
end; |
515 |
||
516 |
val case_congs = map prove_case_cong (DatatypeProp.make_case_congs |
|
517 |
new_type_names descr sorts thy ~~ nchotomys ~~ case_thms) |
|
518 |
||
8436 | 519 |
in thy |> store_thms "case_cong" new_type_names case_congs end; |
5177 | 520 |
|
521 |
end; |