# HG changeset patch # User haftmann # Date 1244639073 -7200 # Node ID eb2f9d709296bbeb5e7343211132ce0efacb4430 # Parent fa30cd74d7d6c6ce1db80a9477f635a02780094d separate directory for datatype package diff -r fa30cd74d7d6 -r eb2f9d709296 src/HOL/Fun.thy --- a/src/HOL/Fun.thy Wed Jun 10 15:04:32 2009 +0200 +++ b/src/HOL/Fun.thy Wed Jun 10 15:04:33 2009 +0200 @@ -133,7 +133,7 @@ shows "inj f" using assms unfolding inj_on_def by auto -text{*For Proofs in @{text "Tools/datatype_rep_proofs"}*} +text{*For Proofs in @{text "Tools/datatype_package/datatype_rep_proofs"}*} lemma datatype_injI: "(!! x. ALL y. f(x) = f(y) --> x=y) ==> inj(f)" by (simp add: inj_on_def) diff -r fa30cd74d7d6 -r eb2f9d709296 src/HOL/Inductive.thy --- a/src/HOL/Inductive.thy Wed Jun 10 15:04:32 2009 +0200 +++ b/src/HOL/Inductive.thy Wed Jun 10 15:04:33 2009 +0200 @@ -10,15 +10,15 @@ ("Tools/inductive_package.ML") "Tools/dseq.ML" ("Tools/inductive_codegen.ML") - ("Tools/datatype_aux.ML") - ("Tools/datatype_prop.ML") - ("Tools/datatype_rep_proofs.ML") - ("Tools/datatype_abs_proofs.ML") - ("Tools/datatype_case.ML") - ("Tools/datatype_package.ML") + ("Tools/datatype_package/datatype_aux.ML") + ("Tools/datatype_package/datatype_prop.ML") + ("Tools/datatype_package/datatype_rep_proofs.ML") + ("Tools/datatype_package/datatype_abs_proofs.ML") + ("Tools/datatype_package/datatype_case.ML") + ("Tools/datatype_package/datatype_package.ML") ("Tools/old_primrec_package.ML") ("Tools/primrec_package.ML") - ("Tools/datatype_codegen.ML") + ("Tools/datatype_package/datatype_codegen.ML") begin subsection {* Least and greatest fixed points *} @@ -335,17 +335,18 @@ text {* Package setup. *} -use "Tools/datatype_aux.ML" -use "Tools/datatype_prop.ML" -use "Tools/datatype_rep_proofs.ML" -use "Tools/datatype_abs_proofs.ML" -use "Tools/datatype_case.ML" -use "Tools/datatype_package.ML" +use "Tools/datatype_package/datatype_aux.ML" +use "Tools/datatype_package/datatype_prop.ML" +use "Tools/datatype_package/datatype_rep_proofs.ML" +use "Tools/datatype_package/datatype_abs_proofs.ML" +use "Tools/datatype_package/datatype_case.ML" +use "Tools/datatype_package/datatype_package.ML" setup DatatypePackage.setup + use "Tools/old_primrec_package.ML" use "Tools/primrec_package.ML" -use "Tools/datatype_codegen.ML" +use "Tools/datatype_package/datatype_codegen.ML" setup DatatypeCodegen.setup use "Tools/inductive_codegen.ML" diff -r fa30cd74d7d6 -r eb2f9d709296 src/HOL/IsaMakefile --- a/src/HOL/IsaMakefile Wed Jun 10 15:04:32 2009 +0200 +++ b/src/HOL/IsaMakefile Wed Jun 10 15:04:33 2009 +0200 @@ -141,14 +141,14 @@ Sum_Type.thy \ Tools/arith_data.ML \ Tools/cnf_funcs.ML \ - Tools/datatype_abs_proofs.ML \ - Tools/datatype_aux.ML \ - Tools/datatype_case.ML \ - Tools/datatype_codegen.ML \ - Tools/datatype_package.ML \ - Tools/datatype_prop.ML \ - Tools/datatype_realizer.ML \ - Tools/datatype_rep_proofs.ML \ + Tools/datatype_package/datatype_abs_proofs.ML \ + Tools/datatype_package/datatype_aux.ML \ + Tools/datatype_package/datatype_case.ML \ + Tools/datatype_package/datatype_codegen.ML \ + Tools/datatype_package/datatype_package.ML \ + Tools/datatype_package/datatype_prop.ML \ + Tools/datatype_package/datatype_realizer.ML \ + Tools/datatype_package/datatype_rep_proofs.ML \ Tools/dseq.ML \ Tools/function_package/auto_term.ML \ Tools/function_package/context_tree.ML \ diff -r fa30cd74d7d6 -r eb2f9d709296 src/HOL/Product_Type.thy --- a/src/HOL/Product_Type.thy Wed Jun 10 15:04:32 2009 +0200 +++ b/src/HOL/Product_Type.thy Wed Jun 10 15:04:33 2009 +0200 @@ -12,7 +12,7 @@ ("Tools/split_rule.ML") ("Tools/inductive_set_package.ML") ("Tools/inductive_realizer.ML") - ("Tools/datatype_realizer.ML") + ("Tools/datatype_package/datatype_realizer.ML") begin subsection {* @{typ bool} is a datatype *} @@ -1155,7 +1155,7 @@ use "Tools/inductive_set_package.ML" setup InductiveSetPackage.setup -use "Tools/datatype_realizer.ML" +use "Tools/datatype_package/datatype_realizer.ML" setup DatatypeRealizer.setup end diff -r fa30cd74d7d6 -r eb2f9d709296 src/HOL/Tools/datatype_package/datatype_abs_proofs.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Tools/datatype_package/datatype_abs_proofs.ML Wed Jun 10 15:04:33 2009 +0200 @@ -0,0 +1,446 @@ +(* Title: HOL/Tools/datatype_abs_proofs.ML + Author: Stefan Berghofer, TU Muenchen + +Proofs and defintions independent of concrete representation +of datatypes (i.e. requiring only abstract properties such as +injectivity / distinctness of constructors and induction) + + - case distinction (exhaustion) theorems + - characteristic equations for primrec combinators + - characteristic equations for case combinators + - equations for splitting "P (case ...)" expressions + - "nchotomy" and "case_cong" theorems for TFL +*) + +signature DATATYPE_ABS_PROOFS = +sig + val prove_casedist_thms : string list -> + DatatypeAux.descr list -> (string * sort) list -> thm -> + attribute list -> theory -> thm list * theory + val prove_primrec_thms : bool -> string list -> + DatatypeAux.descr list -> (string * sort) list -> + DatatypeAux.datatype_info Symtab.table -> thm list list -> thm list list -> + simpset -> thm -> theory -> (string list * thm list) * theory + val prove_case_thms : bool -> string list -> + DatatypeAux.descr list -> (string * sort) list -> + string list -> thm list -> theory -> (thm list list * string list) * theory + val prove_split_thms : string list -> + DatatypeAux.descr list -> (string * sort) list -> + thm list list -> thm list list -> thm list -> thm list list -> theory -> + (thm * thm) list * theory + val prove_nchotomys : string list -> DatatypeAux.descr list -> + (string * sort) list -> thm list -> theory -> thm list * theory + val prove_weak_case_congs : string list -> DatatypeAux.descr list -> + (string * sort) list -> theory -> thm list * theory + val prove_case_congs : string list -> + DatatypeAux.descr list -> (string * sort) list -> + thm list -> thm list list -> theory -> thm list * theory +end; + +structure DatatypeAbsProofs: DATATYPE_ABS_PROOFS = +struct + +open DatatypeAux; + +(************************ case distinction theorems ***************************) + +fun prove_casedist_thms new_type_names descr sorts induct case_names_exhausts thy = + let + val _ = message "Proving case distinction theorems ..."; + + val descr' = List.concat descr; + val recTs = get_rec_types descr' sorts; + val newTs = Library.take (length (hd descr), recTs); + + val {maxidx, ...} = rep_thm induct; + val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct))); + + fun prove_casedist_thm ((i, t), T) = + let + val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) => + Abs ("z", T', Const ("True", T''))) induct_Ps; + val P = Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx+1), T), Bound 0) $ + Var (("P", 0), HOLogic.boolT)) + val insts = Library.take (i, dummyPs) @ (P::(Library.drop (i + 1, dummyPs))); + val cert = cterm_of thy; + val insts' = (map cert induct_Ps) ~~ (map cert insts); + val induct' = refl RS ((List.nth + (split_conj_thm (cterm_instantiate insts' induct), i)) RSN (2, rev_mp)) + + in + SkipProof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t) + (fn {prems, ...} => EVERY + [rtac induct' 1, + REPEAT (rtac TrueI 1), + REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)), + REPEAT (rtac TrueI 1)]) + end; + + val casedist_thms = map prove_casedist_thm ((0 upto (length newTs - 1)) ~~ + (DatatypeProp.make_casedists descr sorts) ~~ newTs) + in + thy + |> store_thms_atts "exhaust" new_type_names (map single case_names_exhausts) casedist_thms + end; + + +(*************************** primrec combinators ******************************) + +fun prove_primrec_thms flat_names new_type_names descr sorts + (dt_info : datatype_info Symtab.table) constr_inject dist_rewrites dist_ss induct thy = + let + val _ = message "Constructing primrec combinators ..."; + + val big_name = space_implode "_" new_type_names; + val thy0 = add_path flat_names big_name thy; + + val descr' = List.concat descr; + val recTs = get_rec_types descr' sorts; + val used = List.foldr OldTerm.add_typ_tfree_names [] recTs; + val newTs = Library.take (length (hd descr), recTs); + + val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct))); + + val big_rec_name' = big_name ^ "_rec_set"; + val rec_set_names' = + if length descr' = 1 then [big_rec_name'] else + map ((curry (op ^) (big_rec_name' ^ "_")) o string_of_int) + (1 upto (length descr')); + val rec_set_names = map (Sign.full_bname thy0) rec_set_names'; + + val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used; + + val rec_set_Ts = map (fn (T1, T2) => + reccomb_fn_Ts @ [T1, T2] ---> HOLogic.boolT) (recTs ~~ rec_result_Ts); + + val rec_fns = map (uncurry (mk_Free "f")) + (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts))); + val rec_sets' = map (fn c => list_comb (Free c, rec_fns)) + (rec_set_names' ~~ rec_set_Ts); + val rec_sets = map (fn c => list_comb (Const c, rec_fns)) + (rec_set_names ~~ rec_set_Ts); + + (* introduction rules for graph of primrec function *) + + fun make_rec_intr T rec_set ((rec_intr_ts, l), (cname, cargs)) = + let + fun mk_prem ((dt, U), (j, k, prems, t1s, t2s)) = + let val free1 = mk_Free "x" U j + in (case (strip_dtyp dt, strip_type U) of + ((_, DtRec m), (Us, _)) => + let + val free2 = mk_Free "y" (Us ---> List.nth (rec_result_Ts, m)) k; + val i = length Us + in (j + 1, k + 1, HOLogic.mk_Trueprop (HOLogic.list_all + (map (pair "x") Us, List.nth (rec_sets', m) $ + app_bnds free1 i $ app_bnds free2 i)) :: prems, + free1::t1s, free2::t2s) + end + | _ => (j + 1, k, prems, free1::t1s, t2s)) + end; + + val Ts = map (typ_of_dtyp descr' sorts) cargs; + val (_, _, prems, t1s, t2s) = List.foldr mk_prem (1, 1, [], [], []) (cargs ~~ Ts) + + in (rec_intr_ts @ [Logic.list_implies (prems, HOLogic.mk_Trueprop + (rec_set $ list_comb (Const (cname, Ts ---> T), t1s) $ + list_comb (List.nth (rec_fns, l), t1s @ t2s)))], l + 1) + end; + + val (rec_intr_ts, _) = Library.foldl (fn (x, ((d, T), set_name)) => + Library.foldl (make_rec_intr T set_name) (x, #3 (snd d))) + (([], 0), descr' ~~ recTs ~~ rec_sets'); + + val ({intrs = rec_intrs, elims = rec_elims, ...}, thy1) = + InductivePackage.add_inductive_global (serial_string ()) + {quiet_mode = ! quiet_mode, verbose = false, kind = Thm.internalK, + alt_name = Binding.name big_rec_name', coind = false, no_elim = false, no_ind = true, + skip_mono = true, fork_mono = false} + (map (fn (s, T) => ((Binding.name s, T), NoSyn)) (rec_set_names' ~~ rec_set_Ts)) + (map dest_Free rec_fns) + (map (fn x => (Attrib.empty_binding, x)) rec_intr_ts) [] thy0; + + (* prove uniqueness and termination of primrec combinators *) + + val _ = message "Proving termination and uniqueness of primrec functions ..."; + + fun mk_unique_tac ((tac, intrs), ((((i, (tname, _, constrs)), elim), T), T')) = + let + val distinct_tac = + (if i < length newTs then + full_simp_tac (HOL_ss addsimps (List.nth (dist_rewrites, i))) 1 + else full_simp_tac dist_ss 1); + + val inject = map (fn r => r RS iffD1) + (if i < length newTs then List.nth (constr_inject, i) + else #inject (the (Symtab.lookup dt_info tname))); + + fun mk_unique_constr_tac n ((tac, intr::intrs, j), (cname, cargs)) = + let + val k = length (List.filter is_rec_type cargs) + + in (EVERY [DETERM tac, + REPEAT (etac ex1E 1), rtac ex1I 1, + DEPTH_SOLVE_1 (ares_tac [intr] 1), + REPEAT_DETERM_N k (etac thin_rl 1 THEN rotate_tac 1 1), + etac elim 1, + REPEAT_DETERM_N j distinct_tac, + TRY (dresolve_tac inject 1), + REPEAT (etac conjE 1), hyp_subst_tac 1, + REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]), + TRY (hyp_subst_tac 1), + rtac refl 1, + REPEAT_DETERM_N (n - j - 1) distinct_tac], + intrs, j + 1) + end; + + val (tac', intrs', _) = Library.foldl (mk_unique_constr_tac (length constrs)) + ((tac, intrs, 0), constrs); + + in (tac', intrs') end; + + val rec_unique_thms = + let + val rec_unique_ts = map (fn (((set_t, T1), T2), i) => + Const ("Ex1", (T2 --> HOLogic.boolT) --> HOLogic.boolT) $ + absfree ("y", T2, set_t $ mk_Free "x" T1 i $ Free ("y", T2))) + (rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs)); + val cert = cterm_of thy1 + val insts = map (fn ((i, T), t) => absfree ("x" ^ (string_of_int i), T, t)) + ((1 upto length recTs) ~~ recTs ~~ rec_unique_ts); + val induct' = cterm_instantiate ((map cert induct_Ps) ~~ + (map cert insts)) induct; + val (tac, _) = Library.foldl mk_unique_tac + (((rtac induct' THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1 + THEN rewrite_goals_tac [mk_meta_eq choice_eq], rec_intrs), + descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts); + + in split_conj_thm (SkipProof.prove_global thy1 [] [] + (HOLogic.mk_Trueprop (mk_conj rec_unique_ts)) (K tac)) + end; + + val rec_total_thms = map (fn r => r RS theI') rec_unique_thms; + + (* define primrec combinators *) + + val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec"; + val reccomb_names = map (Sign.full_bname thy1) + (if length descr' = 1 then [big_reccomb_name] else + (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int) + (1 upto (length descr')))); + val reccombs = map (fn ((name, T), T') => list_comb + (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns)) + (reccomb_names ~~ recTs ~~ rec_result_Ts); + + val (reccomb_defs, thy2) = + thy1 + |> Sign.add_consts_i (map (fn ((name, T), T') => + (Binding.name (Long_Name.base_name name), reccomb_fn_Ts @ [T] ---> T', NoSyn)) + (reccomb_names ~~ recTs ~~ rec_result_Ts)) + |> (PureThy.add_defs false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') => + (Binding.name (Long_Name.base_name name ^ "_def"), Logic.mk_equals (comb, absfree ("x", T, + Const ("The", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T', + set $ Free ("x", T) $ Free ("y", T')))))) + (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts)) + ||> parent_path flat_names + ||> Theory.checkpoint; + + + (* prove characteristic equations for primrec combinators *) + + val _ = message "Proving characteristic theorems for primrec combinators ..." + + val rec_thms = map (fn t => SkipProof.prove_global thy2 [] [] t + (fn _ => EVERY + [rewrite_goals_tac reccomb_defs, + rtac the1_equality 1, + resolve_tac rec_unique_thms 1, + resolve_tac rec_intrs 1, + REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)])) + (DatatypeProp.make_primrecs new_type_names descr sorts thy2) + + in + thy2 + |> Sign.add_path (space_implode "_" new_type_names) + |> PureThy.add_thmss [((Binding.name "recs", rec_thms), + [Nitpick_Const_Simp_Thms.add])] + ||> Sign.parent_path + ||> Theory.checkpoint + |-> (fn thms => pair (reccomb_names, Library.flat thms)) + end; + + +(***************************** case combinators *******************************) + +fun prove_case_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy = + let + val _ = message "Proving characteristic theorems for case combinators ..."; + + val thy1 = add_path flat_names (space_implode "_" new_type_names) thy; + + val descr' = List.concat descr; + val recTs = get_rec_types descr' sorts; + val used = List.foldr OldTerm.add_typ_tfree_names [] recTs; + val newTs = Library.take (length (hd descr), recTs); + val T' = TFree (Name.variant used "'t", HOLogic.typeS); + + fun mk_dummyT dt = binder_types (typ_of_dtyp descr' sorts dt) ---> T'; + + val case_dummy_fns = map (fn (_, (_, _, constrs)) => map (fn (_, cargs) => + let + val Ts = map (typ_of_dtyp descr' sorts) cargs; + val Ts' = map mk_dummyT (List.filter is_rec_type cargs) + in Const (@{const_name undefined}, Ts @ Ts' ---> T') + end) constrs) descr'; + + val case_names = map (fn s => Sign.full_bname thy1 (s ^ "_case")) new_type_names; + + (* define case combinators via primrec combinators *) + + val (case_defs, thy2) = Library.foldl (fn ((defs, thy), + ((((i, (_, _, constrs)), T), name), recname)) => + let + val (fns1, fns2) = ListPair.unzip (map (fn ((_, cargs), j) => + let + val Ts = map (typ_of_dtyp descr' sorts) cargs; + val Ts' = Ts @ map mk_dummyT (List.filter is_rec_type cargs); + val frees' = map (uncurry (mk_Free "x")) (Ts' ~~ (1 upto length Ts')); + val frees = Library.take (length cargs, frees'); + val free = mk_Free "f" (Ts ---> T') j + in + (free, list_abs_free (map dest_Free frees', + list_comb (free, frees))) + end) (constrs ~~ (1 upto length constrs))); + + val caseT = (map (snd o dest_Free) fns1) @ [T] ---> T'; + val fns = (List.concat (Library.take (i, case_dummy_fns))) @ + fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns))); + val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T'); + val decl = ((Binding.name (Long_Name.base_name name), caseT), NoSyn); + val def = (Binding.name (Long_Name.base_name name ^ "_def"), + Logic.mk_equals (list_comb (Const (name, caseT), fns1), + list_comb (reccomb, (List.concat (Library.take (i, case_dummy_fns))) @ + fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns))) ))); + val ([def_thm], thy') = + thy + |> Sign.declare_const [] decl |> snd + |> (PureThy.add_defs false o map Thm.no_attributes) [def]; + + in (defs @ [def_thm], thy') + end) (([], thy1), (hd descr) ~~ newTs ~~ case_names ~~ + (Library.take (length newTs, reccomb_names))) + ||> Theory.checkpoint; + + val case_thms = map (map (fn t => SkipProof.prove_global thy2 [] [] t + (fn _ => EVERY [rewrite_goals_tac (case_defs @ map mk_meta_eq primrec_thms), rtac refl 1]))) + (DatatypeProp.make_cases new_type_names descr sorts thy2) + in + thy2 + |> Context.the_theory o fold (fold Nitpick_Const_Simp_Thms.add_thm) case_thms + o Context.Theory + |> parent_path flat_names + |> store_thmss "cases" new_type_names case_thms + |-> (fn thmss => pair (thmss, case_names)) + end; + + +(******************************* case splitting *******************************) + +fun prove_split_thms new_type_names descr sorts constr_inject dist_rewrites + casedist_thms case_thms thy = + let + val _ = message "Proving equations for case splitting ..."; + + val descr' = List.concat descr; + val recTs = get_rec_types descr' sorts; + val newTs = Library.take (length (hd descr), recTs); + + fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'), + exhaustion), case_thms'), T) = + let + val cert = cterm_of thy; + val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion))); + val exhaustion' = cterm_instantiate + [(cert lhs, cert (Free ("x", T)))] exhaustion; + val tacf = K (EVERY [rtac exhaustion' 1, ALLGOALS (asm_simp_tac + (HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))]) + in + (SkipProof.prove_global thy [] [] t1 tacf, + SkipProof.prove_global thy [] [] t2 tacf) + end; + + val split_thm_pairs = map prove_split_thms + ((DatatypeProp.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~ + dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs); + + val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs + + in + thy + |> store_thms "split" new_type_names split_thms + ||>> store_thms "split_asm" new_type_names split_asm_thms + |-> (fn (thms1, thms2) => pair (thms1 ~~ thms2)) + end; + +fun prove_weak_case_congs new_type_names descr sorts thy = + let + fun prove_weak_case_cong t = + SkipProof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t) + (fn {prems, ...} => EVERY [rtac ((hd prems) RS arg_cong) 1]) + + val weak_case_congs = map prove_weak_case_cong (DatatypeProp.make_weak_case_congs + new_type_names descr sorts thy) + + in thy |> store_thms "weak_case_cong" new_type_names weak_case_congs end; + +(************************* additional theorems for TFL ************************) + +fun prove_nchotomys new_type_names descr sorts casedist_thms thy = + let + val _ = message "Proving additional theorems for TFL ..."; + + fun prove_nchotomy (t, exhaustion) = + let + (* For goal i, select the correct disjunct to attack, then prove it *) + fun tac i 0 = EVERY [TRY (rtac disjI1 i), + hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i] + | tac i n = rtac disjI2 i THEN tac i (n - 1) + in + SkipProof.prove_global thy [] [] t (fn _ => + EVERY [rtac allI 1, + exh_tac (K exhaustion) 1, + ALLGOALS (fn i => tac i (i-1))]) + end; + + val nchotomys = + map prove_nchotomy (DatatypeProp.make_nchotomys descr sorts ~~ casedist_thms) + + in thy |> store_thms "nchotomy" new_type_names nchotomys end; + +fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy = + let + fun prove_case_cong ((t, nchotomy), case_rewrites) = + let + val (Const ("==>", _) $ tm $ _) = t; + val (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ Ma)) = tm; + val cert = cterm_of thy; + val nchotomy' = nchotomy RS spec; + val [v] = Term.add_vars (concl_of nchotomy') []; + val nchotomy'' = cterm_instantiate [(cert (Var v), cert Ma)] nchotomy' + in + SkipProof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t) + (fn {prems, ...} => + let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites)) + in EVERY [simp_tac (HOL_ss addsimps [hd prems]) 1, + cut_facts_tac [nchotomy''] 1, + REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1), + REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)] + end) + end; + + val case_congs = map prove_case_cong (DatatypeProp.make_case_congs + new_type_names descr sorts thy ~~ nchotomys ~~ case_thms) + + in thy |> store_thms "case_cong" new_type_names case_congs end; + +end; diff -r fa30cd74d7d6 -r eb2f9d709296 src/HOL/Tools/datatype_package/datatype_case.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Tools/datatype_package/datatype_case.ML Wed Jun 10 15:04:33 2009 +0200 @@ -0,0 +1,469 @@ +(* Title: HOL/Tools/datatype_case.ML + Author: Konrad Slind, Cambridge University Computer Laboratory + Author: Stefan Berghofer, TU Muenchen + +Nested case expressions on datatypes. +*) + +signature DATATYPE_CASE = +sig + val make_case: (string -> DatatypeAux.datatype_info option) -> + Proof.context -> bool -> string list -> term -> (term * term) list -> + term * (term * (int * bool)) list + val dest_case: (string -> DatatypeAux.datatype_info option) -> bool -> + string list -> term -> (term * (term * term) list) option + val strip_case: (string -> DatatypeAux.datatype_info option) -> bool -> + term -> (term * (term * term) list) option + val case_tr: bool -> (theory -> string -> DatatypeAux.datatype_info option) + -> Proof.context -> term list -> term + val case_tr': (theory -> string -> DatatypeAux.datatype_info option) -> + string -> Proof.context -> term list -> term +end; + +structure DatatypeCase : DATATYPE_CASE = +struct + +exception CASE_ERROR of string * int; + +fun match_type thy pat ob = Sign.typ_match thy (pat, ob) Vartab.empty; + +(*--------------------------------------------------------------------------- + * Get information about datatypes + *---------------------------------------------------------------------------*) + +fun ty_info (tab : string -> DatatypeAux.datatype_info option) s = + case tab s of + SOME {descr, case_name, index, sorts, ...} => + let + val (_, (tname, dts, constrs)) = nth descr index; + val mk_ty = DatatypeAux.typ_of_dtyp descr sorts; + val T = Type (tname, map mk_ty dts) + in + SOME {case_name = case_name, + constructors = map (fn (cname, dts') => + Const (cname, Logic.varifyT (map mk_ty dts' ---> T))) constrs} + end + | NONE => NONE; + + +(*--------------------------------------------------------------------------- + * Each pattern carries with it a tag (i,b) where + * i is the clause it came from and + * b=true indicates that clause was given by the user + * (or is an instantiation of a user supplied pattern) + * b=false --> i = ~1 + *---------------------------------------------------------------------------*) + +fun pattern_subst theta (tm, x) = (subst_free theta tm, x); + +fun row_of_pat x = fst (snd x); + +fun add_row_used ((prfx, pats), (tm, tag)) = + fold Term.add_free_names (tm :: pats @ prfx); + +(* try to preserve names given by user *) +fun default_names names ts = + map (fn ("", Free (name', _)) => name' | (name, _) => name) (names ~~ ts); + +fun strip_constraints (Const ("_constrain", _) $ t $ tT) = + strip_constraints t ||> cons tT + | strip_constraints t = (t, []); + +fun mk_fun_constrain tT t = Syntax.const "_constrain" $ t $ + (Syntax.free "fun" $ tT $ Syntax.free "dummy"); + + +(*--------------------------------------------------------------------------- + * Produce an instance of a constructor, plus genvars for its arguments. + *---------------------------------------------------------------------------*) +fun fresh_constr ty_match ty_inst colty used c = + let + val (_, Ty) = dest_Const c + val Ts = binder_types Ty; + val names = Name.variant_list used + (DatatypeProp.make_tnames (map Logic.unvarifyT Ts)); + val ty = body_type Ty; + val ty_theta = ty_match ty colty handle Type.TYPE_MATCH => + raise CASE_ERROR ("type mismatch", ~1) + val c' = ty_inst ty_theta c + val gvars = map (ty_inst ty_theta o Free) (names ~~ Ts) + in (c', gvars) + end; + + +(*--------------------------------------------------------------------------- + * Goes through a list of rows and picks out the ones beginning with a + * pattern with constructor = name. + *---------------------------------------------------------------------------*) +fun mk_group (name, T) rows = + let val k = length (binder_types T) + in fold (fn (row as ((prfx, p :: rst), rhs as (_, (i, _)))) => + fn ((in_group, not_in_group), (names, cnstrts)) => (case strip_comb p of + (Const (name', _), args) => + if name = name' then + if length args = k then + let val (args', cnstrts') = split_list (map strip_constraints args) + in + ((((prfx, args' @ rst), rhs) :: in_group, not_in_group), + (default_names names args', map2 append cnstrts cnstrts')) + end + else raise CASE_ERROR + ("Wrong number of arguments for constructor " ^ name, i) + else ((in_group, row :: not_in_group), (names, cnstrts)) + | _ => raise CASE_ERROR ("Not a constructor pattern", i))) + rows (([], []), (replicate k "", replicate k [])) |>> pairself rev + end; + +(*--------------------------------------------------------------------------- + * Partition the rows. Not efficient: we should use hashing. + *---------------------------------------------------------------------------*) +fun partition _ _ _ _ _ _ _ [] = raise CASE_ERROR ("partition: no rows", ~1) + | partition ty_match ty_inst type_of used constructors colty res_ty + (rows as (((prfx, _ :: rstp), _) :: _)) = + let + fun part {constrs = [], rows = [], A} = rev A + | part {constrs = [], rows = (_, (_, (i, _))) :: _, A} = + raise CASE_ERROR ("Not a constructor pattern", i) + | part {constrs = c :: crst, rows, A} = + let + val ((in_group, not_in_group), (names, cnstrts)) = + mk_group (dest_Const c) rows; + val used' = fold add_row_used in_group used; + val (c', gvars) = fresh_constr ty_match ty_inst colty used' c; + val in_group' = + if null in_group (* Constructor not given *) + then + let + val Ts = map type_of rstp; + val xs = Name.variant_list + (fold Term.add_free_names gvars used') + (replicate (length rstp) "x") + in + [((prfx, gvars @ map Free (xs ~~ Ts)), + (Const ("HOL.undefined", res_ty), (~1, false)))] + end + else in_group + in + part{constrs = crst, + rows = not_in_group, + A = {constructor = c', + new_formals = gvars, + names = names, + constraints = cnstrts, + group = in_group'} :: A} + end + in part {constrs = constructors, rows = rows, A = []} + end; + +(*--------------------------------------------------------------------------- + * Misc. routines used in mk_case + *---------------------------------------------------------------------------*) + +fun mk_pat ((c, c'), l) = + let + val L = length (binder_types (fastype_of c)) + fun build (prfx, tag, plist) = + let val (args, plist') = chop L plist + in (prfx, tag, list_comb (c', args) :: plist') end + in map build l end; + +fun v_to_prfx (prfx, v::pats) = (v::prfx,pats) + | v_to_prfx _ = raise CASE_ERROR ("mk_case: v_to_prfx", ~1); + +fun v_to_pats (v::prfx,tag, pats) = (prfx, tag, v::pats) + | v_to_pats _ = raise CASE_ERROR ("mk_case: v_to_pats", ~1); + + +(*---------------------------------------------------------------------------- + * Translation of pattern terms into nested case expressions. + * + * This performs the translation and also builds the full set of patterns. + * Thus it supports the construction of induction theorems even when an + * incomplete set of patterns is given. + *---------------------------------------------------------------------------*) + +fun mk_case tab ctxt ty_match ty_inst type_of used range_ty = + let + val name = Name.variant used "a"; + fun expand constructors used ty ((_, []), _) = + raise CASE_ERROR ("mk_case: expand_var_row", ~1) + | expand constructors used ty (row as ((prfx, p :: rst), rhs)) = + if is_Free p then + let + val used' = add_row_used row used; + fun expnd c = + let val capp = + list_comb (fresh_constr ty_match ty_inst ty used' c) + in ((prfx, capp :: rst), pattern_subst [(p, capp)] rhs) + end + in map expnd constructors end + else [row] + fun mk {rows = [], ...} = raise CASE_ERROR ("no rows", ~1) + | mk {path = [], rows = ((prfx, []), (tm, tag)) :: _} = (* Done *) + ([(prfx, tag, [])], tm) + | mk {path, rows as ((row as ((_, [Free _]), _)) :: _ :: _)} = + mk {path = path, rows = [row]} + | mk {path = u :: rstp, rows as ((_, _ :: _), _) :: _} = + let val col0 = map (fn ((_, p :: _), (_, (i, _))) => (p, i)) rows + in case Option.map (apfst head_of) + (find_first (not o is_Free o fst) col0) of + NONE => + let + val rows' = map (fn ((v, _), row) => row ||> + pattern_subst [(v, u)] |>> v_to_prfx) (col0 ~~ rows); + val (pref_patl, tm) = mk {path = rstp, rows = rows'} + in (map v_to_pats pref_patl, tm) end + | SOME (Const (cname, cT), i) => (case ty_info tab cname of + NONE => raise CASE_ERROR ("Not a datatype constructor: " ^ cname, i) + | SOME {case_name, constructors} => + let + val pty = body_type cT; + val used' = fold Term.add_free_names rstp used; + val nrows = maps (expand constructors used' pty) rows; + val subproblems = partition ty_match ty_inst type_of used' + constructors pty range_ty nrows; + val new_formals = map #new_formals subproblems + val constructors' = map #constructor subproblems + val news = map (fn {new_formals, group, ...} => + {path = new_formals @ rstp, rows = group}) subproblems; + val (pat_rect, dtrees) = split_list (map mk news); + val case_functions = map2 + (fn {new_formals, names, constraints, ...} => + fold_rev (fn ((x as Free (_, T), s), cnstrts) => fn t => + Abs (if s = "" then name else s, T, + abstract_over (x, t)) |> + fold mk_fun_constrain cnstrts) + (new_formals ~~ names ~~ constraints)) + subproblems dtrees; + val types = map type_of (case_functions @ [u]); + val case_const = Const (case_name, types ---> range_ty) + val tree = list_comb (case_const, case_functions @ [u]) + val pat_rect1 = flat (map mk_pat + (constructors ~~ constructors' ~~ pat_rect)) + in (pat_rect1, tree) + end) + | SOME (t, i) => raise CASE_ERROR ("Not a datatype constructor: " ^ + Syntax.string_of_term ctxt t, i) + end + | mk _ = raise CASE_ERROR ("Malformed row matrix", ~1) + in mk + end; + +fun case_error s = error ("Error in case expression:\n" ^ s); + +(* Repeated variable occurrences in a pattern are not allowed. *) +fun no_repeat_vars ctxt pat = fold_aterms + (fn x as Free (s, _) => (fn xs => + if member op aconv xs x then + case_error (quote s ^ " occurs repeatedly in the pattern " ^ + quote (Syntax.string_of_term ctxt pat)) + else x :: xs) + | _ => I) pat []; + +fun gen_make_case ty_match ty_inst type_of tab ctxt err used x clauses = + let + fun string_of_clause (pat, rhs) = Syntax.string_of_term ctxt + (Syntax.const "_case1" $ pat $ rhs); + val _ = map (no_repeat_vars ctxt o fst) clauses; + val rows = map_index (fn (i, (pat, rhs)) => + (([], [pat]), (rhs, (i, true)))) clauses; + val rangeT = (case distinct op = (map (type_of o snd) clauses) of + [] => case_error "no clauses given" + | [T] => T + | _ => case_error "all cases must have the same result type"); + val used' = fold add_row_used rows used; + val (patts, case_tm) = mk_case tab ctxt ty_match ty_inst type_of + used' rangeT {path = [x], rows = rows} + handle CASE_ERROR (msg, i) => case_error (msg ^ + (if i < 0 then "" + else "\nIn clause\n" ^ string_of_clause (nth clauses i))); + val patts1 = map + (fn (_, tag, [pat]) => (pat, tag) + | _ => case_error "error in pattern-match translation") patts; + val patts2 = Library.sort (Library.int_ord o Library.pairself row_of_pat) patts1 + val finals = map row_of_pat patts2 + val originals = map (row_of_pat o #2) rows + val _ = case originals \\ finals of + [] => () + | is => (if err then case_error else warning) + ("The following clauses are redundant (covered by preceding clauses):\n" ^ + cat_lines (map (string_of_clause o nth clauses) is)); + in + (case_tm, patts2) + end; + +fun make_case tab ctxt = gen_make_case + (match_type (ProofContext.theory_of ctxt)) Envir.subst_TVars fastype_of tab ctxt; +val make_case_untyped = gen_make_case (K (K Vartab.empty)) + (K (Term.map_types (K dummyT))) (K dummyT); + + +(* parse translation *) + +fun case_tr err tab_of ctxt [t, u] = + let + val thy = ProofContext.theory_of ctxt; + (* replace occurrences of dummy_pattern by distinct variables *) + (* internalize constant names *) + fun prep_pat ((c as Const ("_constrain", _)) $ t $ tT) used = + let val (t', used') = prep_pat t used + in (c $ t' $ tT, used') end + | prep_pat (Const ("dummy_pattern", T)) used = + let val x = Name.variant used "x" + in (Free (x, T), x :: used) end + | prep_pat (Const (s, T)) used = + (case try (unprefix Syntax.constN) s of + SOME c => (Const (c, T), used) + | NONE => (Const (Sign.intern_const thy s, T), used)) + | prep_pat (v as Free (s, T)) used = + let val s' = Sign.intern_const thy s + in + if Sign.declared_const thy s' then + (Const (s', T), used) + else (v, used) + end + | prep_pat (t $ u) used = + let + val (t', used') = prep_pat t used; + val (u', used'') = prep_pat u used' + in + (t' $ u', used'') + end + | prep_pat t used = case_error ("Bad pattern: " ^ Syntax.string_of_term ctxt t); + fun dest_case1 (t as Const ("_case1", _) $ l $ r) = + let val (l', cnstrts) = strip_constraints l + in ((fst (prep_pat l' (Term.add_free_names t [])), r), cnstrts) + end + | dest_case1 t = case_error "dest_case1"; + fun dest_case2 (Const ("_case2", _) $ t $ u) = t :: dest_case2 u + | dest_case2 t = [t]; + val (cases, cnstrts) = split_list (map dest_case1 (dest_case2 u)); + val (case_tm, _) = make_case_untyped (tab_of thy) ctxt err [] + (fold (fn tT => fn t => Syntax.const "_constrain" $ t $ tT) + (flat cnstrts) t) cases; + in case_tm end + | case_tr _ _ _ ts = case_error "case_tr"; + + +(*--------------------------------------------------------------------------- + * Pretty printing of nested case expressions + *---------------------------------------------------------------------------*) + +(* destruct one level of pattern matching *) + +fun gen_dest_case name_of type_of tab d used t = + case apfst name_of (strip_comb t) of + (SOME cname, ts as _ :: _) => + let + val (fs, x) = split_last ts; + fun strip_abs i t = + let + val zs = strip_abs_vars t; + val _ = if length zs < i then raise CASE_ERROR ("", 0) else (); + val (xs, ys) = chop i zs; + val u = list_abs (ys, strip_abs_body t); + val xs' = map Free (Name.variant_list (OldTerm.add_term_names (u, used)) + (map fst xs) ~~ map snd xs) + in (xs', subst_bounds (rev xs', u)) end; + fun is_dependent i t = + let val k = length (strip_abs_vars t) - i + in k < 0 orelse exists (fn j => j >= k) + (loose_bnos (strip_abs_body t)) + end; + fun count_cases (_, _, true) = I + | count_cases (c, (_, body), false) = + AList.map_default op aconv (body, []) (cons c); + val is_undefined = name_of #> equal (SOME "HOL.undefined"); + fun mk_case (c, (xs, body), _) = (list_comb (c, xs), body) + in case ty_info tab cname of + SOME {constructors, case_name} => + if length fs = length constructors then + let + val cases = map (fn (Const (s, U), t) => + let + val k = length (binder_types U); + val p as (xs, _) = strip_abs k t + in + (Const (s, map type_of xs ---> type_of x), + p, is_dependent k t) + end) (constructors ~~ fs); + val cases' = sort (int_ord o swap o pairself (length o snd)) + (fold_rev count_cases cases []); + val R = type_of t; + val dummy = if d then Const ("dummy_pattern", R) + else Free (Name.variant used "x", R) + in + SOME (x, map mk_case (case find_first (is_undefined o fst) cases' of + SOME (_, cs) => + if length cs = length constructors then [hd cases] + else filter_out (fn (_, (_, body), _) => is_undefined body) cases + | NONE => case cases' of + [] => cases + | (default, cs) :: _ => + if length cs = 1 then cases + else if length cs = length constructors then + [hd cases, (dummy, ([], default), false)] + else + filter_out (fn (c, _, _) => member op aconv cs c) cases @ + [(dummy, ([], default), false)])) + end handle CASE_ERROR _ => NONE + else NONE + | _ => NONE + end + | _ => NONE; + +val dest_case = gen_dest_case (try (dest_Const #> fst)) fastype_of; +val dest_case' = gen_dest_case + (try (dest_Const #> fst #> unprefix Syntax.constN)) (K dummyT); + + +(* destruct nested patterns *) + +fun strip_case'' dest (pat, rhs) = + case dest (Term.add_free_names pat []) rhs of + SOME (exp as Free _, clauses) => + if member op aconv (OldTerm.term_frees pat) exp andalso + not (exists (fn (_, rhs') => + member op aconv (OldTerm.term_frees rhs') exp) clauses) + then + maps (strip_case'' dest) (map (fn (pat', rhs') => + (subst_free [(exp, pat')] pat, rhs')) clauses) + else [(pat, rhs)] + | _ => [(pat, rhs)]; + +fun gen_strip_case dest t = case dest [] t of + SOME (x, clauses) => + SOME (x, maps (strip_case'' dest) clauses) + | NONE => NONE; + +val strip_case = gen_strip_case oo dest_case; +val strip_case' = gen_strip_case oo dest_case'; + + +(* print translation *) + +fun case_tr' tab_of cname ctxt ts = + let + val thy = ProofContext.theory_of ctxt; + val consts = ProofContext.consts_of ctxt; + fun mk_clause (pat, rhs) = + let val xs = Term.add_frees pat [] + in + Syntax.const "_case1" $ + map_aterms + (fn Free p => Syntax.mark_boundT p + | Const (s, _) => Const (Consts.extern_early consts s, dummyT) + | t => t) pat $ + map_aterms + (fn x as Free (s, T) => + if member (op =) xs (s, T) then Syntax.mark_bound s else x + | t => t) rhs + end + in case strip_case' (tab_of thy) true (list_comb (Syntax.const cname, ts)) of + SOME (x, clauses) => Syntax.const "_case_syntax" $ x $ + foldr1 (fn (t, u) => Syntax.const "_case2" $ t $ u) + (map mk_clause clauses) + | NONE => raise Match + end; + +end; diff -r fa30cd74d7d6 -r eb2f9d709296 src/HOL/Tools/datatype_package/datatype_codegen.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Tools/datatype_package/datatype_codegen.ML Wed Jun 10 15:04:33 2009 +0200 @@ -0,0 +1,451 @@ +(* Title: HOL/Tools/datatype_codegen.ML + Author: Stefan Berghofer and Florian Haftmann, TU Muenchen + +Code generator facilities for inductive datatypes. +*) + +signature DATATYPE_CODEGEN = +sig + val find_shortest_path: DatatypeAux.descr -> int -> (string * int) option + val mk_eq_eqns: theory -> string -> (thm * bool) list + val mk_case_cert: theory -> string -> thm + val setup: theory -> theory +end; + +structure DatatypeCodegen : DATATYPE_CODEGEN = +struct + +(** SML code generator **) + +open Codegen; + +(**** datatype definition ****) + +(* find shortest path to constructor with no recursive arguments *) + +fun find_nonempty (descr: DatatypeAux.descr) is i = + let + val (_, _, constrs) = the (AList.lookup (op =) descr i); + fun arg_nonempty (_, DatatypeAux.DtRec i) = if member (op =) is i + then NONE + else Option.map (curry op + 1 o snd) (find_nonempty descr (i::is) i) + | arg_nonempty _ = SOME 0; + fun max xs = Library.foldl + (fn (NONE, _) => NONE + | (SOME i, SOME j) => SOME (Int.max (i, j)) + | (_, NONE) => NONE) (SOME 0, xs); + val xs = sort (int_ord o pairself snd) + (map_filter (fn (s, dts) => Option.map (pair s) + (max (map (arg_nonempty o DatatypeAux.strip_dtyp) dts))) constrs) + in case xs of [] => NONE | x :: _ => SOME x end; + +fun find_shortest_path descr i = find_nonempty descr [i] i; + +fun add_dt_defs thy defs dep module (descr: DatatypeAux.descr) sorts gr = + let + val descr' = List.filter (can (map DatatypeAux.dest_DtTFree o #2 o snd)) descr; + val rtnames = map (#1 o snd) (List.filter (fn (_, (_, _, cs)) => + exists (exists DatatypeAux.is_rec_type o snd) cs) descr'); + + val (_, (tname, _, _)) :: _ = descr'; + val node_id = tname ^ " (type)"; + val module' = if_library (thyname_of_type thy tname) module; + + fun mk_dtdef prfx [] gr = ([], gr) + | mk_dtdef prfx ((_, (tname, dts, cs))::xs) gr = + let + val tvs = map DatatypeAux.dest_DtTFree dts; + val cs' = map (apsnd (map (DatatypeAux.typ_of_dtyp descr sorts))) cs; + val ((_, type_id), gr') = mk_type_id module' tname gr; + val (ps, gr'') = gr' |> + fold_map (fn (cname, cargs) => + fold_map (invoke_tycodegen thy defs node_id module' false) + cargs ##>> + mk_const_id module' cname) cs'; + val (rest, gr''') = mk_dtdef "and " xs gr'' + in + (Pretty.block (str prfx :: + (if null tvs then [] else + [mk_tuple (map str tvs), str " "]) @ + [str (type_id ^ " ="), Pretty.brk 1] @ + List.concat (separate [Pretty.brk 1, str "| "] + (map (fn (ps', (_, cname)) => [Pretty.block + (str cname :: + (if null ps' then [] else + List.concat ([str " of", Pretty.brk 1] :: + separate [str " *", Pretty.brk 1] + (map single ps'))))]) ps))) :: rest, gr''') + end; + + fun mk_constr_term cname Ts T ps = + List.concat (separate [str " $", Pretty.brk 1] + ([str ("Const (\"" ^ cname ^ "\","), Pretty.brk 1, + mk_type false (Ts ---> T), str ")"] :: ps)); + + fun mk_term_of_def gr prfx [] = [] + | mk_term_of_def gr prfx ((_, (tname, dts, cs)) :: xs) = + let + val cs' = map (apsnd (map (DatatypeAux.typ_of_dtyp descr sorts))) cs; + val dts' = map (DatatypeAux.typ_of_dtyp descr sorts) dts; + val T = Type (tname, dts'); + val rest = mk_term_of_def gr "and " xs; + val (eqs, _) = fold_map (fn (cname, Ts) => fn prfx => + let val args = map (fn i => + str ("x" ^ string_of_int i)) (1 upto length Ts) + in (Pretty.blk (4, + [str prfx, mk_term_of gr module' false T, Pretty.brk 1, + if null Ts then str (snd (get_const_id gr cname)) + else parens (Pretty.block + [str (snd (get_const_id gr cname)), + Pretty.brk 1, mk_tuple args]), + str " =", Pretty.brk 1] @ + mk_constr_term cname Ts T + (map2 (fn x => fn U => [Pretty.block [mk_term_of gr module' false U, + Pretty.brk 1, x]]) args Ts)), " | ") + end) cs' prfx + in eqs @ rest end; + + fun mk_gen_of_def gr prfx [] = [] + | mk_gen_of_def gr prfx ((i, (tname, dts, cs)) :: xs) = + let + val tvs = map DatatypeAux.dest_DtTFree dts; + val Us = map (DatatypeAux.typ_of_dtyp descr sorts) dts; + val T = Type (tname, Us); + val (cs1, cs2) = + List.partition (exists DatatypeAux.is_rec_type o snd) cs; + val SOME (cname, _) = find_shortest_path descr i; + + fun mk_delay p = Pretty.block + [str "fn () =>", Pretty.brk 1, p]; + + fun mk_force p = Pretty.block [p, Pretty.brk 1, str "()"]; + + fun mk_constr s b (cname, dts) = + let + val gs = map (fn dt => mk_app false (mk_gen gr module' false rtnames s + (DatatypeAux.typ_of_dtyp descr sorts dt)) + [str (if b andalso DatatypeAux.is_rec_type dt then "0" + else "j")]) dts; + val Ts = map (DatatypeAux.typ_of_dtyp descr sorts) dts; + val xs = map str + (DatatypeProp.indexify_names (replicate (length dts) "x")); + val ts = map str + (DatatypeProp.indexify_names (replicate (length dts) "t")); + val (_, id) = get_const_id gr cname + in + mk_let + (map2 (fn p => fn q => mk_tuple [p, q]) xs ts ~~ gs) + (mk_tuple + [case xs of + _ :: _ :: _ => Pretty.block + [str id, Pretty.brk 1, mk_tuple xs] + | _ => mk_app false (str id) xs, + mk_delay (Pretty.block (mk_constr_term cname Ts T + (map (single o mk_force) ts)))]) + end; + + fun mk_choice [c] = mk_constr "(i-1)" false c + | mk_choice cs = Pretty.block [str "one_of", + Pretty.brk 1, Pretty.blk (1, str "[" :: + List.concat (separate [str ",", Pretty.fbrk] + (map (single o mk_delay o mk_constr "(i-1)" false) cs)) @ + [str "]"]), Pretty.brk 1, str "()"]; + + val gs = maps (fn s => + let val s' = strip_tname s + in [str (s' ^ "G"), str (s' ^ "T")] end) tvs; + val gen_name = "gen_" ^ snd (get_type_id gr tname) + + in + Pretty.blk (4, separate (Pretty.brk 1) + (str (prfx ^ gen_name ^ + (if null cs1 then "" else "'")) :: gs @ + (if null cs1 then [] else [str "i"]) @ + [str "j"]) @ + [str " =", Pretty.brk 1] @ + (if not (null cs1) andalso not (null cs2) + then [str "frequency", Pretty.brk 1, + Pretty.blk (1, [str "[", + mk_tuple [str "i", mk_delay (mk_choice cs1)], + str ",", Pretty.fbrk, + mk_tuple [str "1", mk_delay (mk_choice cs2)], + str "]"]), Pretty.brk 1, str "()"] + else if null cs2 then + [Pretty.block [str "(case", Pretty.brk 1, + str "i", Pretty.brk 1, str "of", + Pretty.brk 1, str "0 =>", Pretty.brk 1, + mk_constr "0" true (cname, valOf (AList.lookup (op =) cs cname)), + Pretty.brk 1, str "| _ =>", Pretty.brk 1, + mk_choice cs1, str ")"]] + else [mk_choice cs2])) :: + (if null cs1 then [] + else [Pretty.blk (4, separate (Pretty.brk 1) + (str ("and " ^ gen_name) :: gs @ [str "i"]) @ + [str " =", Pretty.brk 1] @ + separate (Pretty.brk 1) (str (gen_name ^ "'") :: gs @ + [str "i", str "i"]))]) @ + mk_gen_of_def gr "and " xs + end + + in + (module', (add_edge_acyclic (node_id, dep) gr + handle Graph.CYCLES _ => gr) handle Graph.UNDEF _ => + let + val gr1 = add_edge (node_id, dep) + (new_node (node_id, (NONE, "", "")) gr); + val (dtdef, gr2) = mk_dtdef "datatype " descr' gr1 ; + in + map_node node_id (K (NONE, module', + string_of (Pretty.blk (0, separate Pretty.fbrk dtdef @ + [str ";"])) ^ "\n\n" ^ + (if "term_of" mem !mode then + string_of (Pretty.blk (0, separate Pretty.fbrk + (mk_term_of_def gr2 "fun " descr') @ [str ";"])) ^ "\n\n" + else "") ^ + (if "test" mem !mode then + string_of (Pretty.blk (0, separate Pretty.fbrk + (mk_gen_of_def gr2 "fun " descr') @ [str ";"])) ^ "\n\n" + else ""))) gr2 + end) + end; + + +(**** case expressions ****) + +fun pretty_case thy defs dep module brack constrs (c as Const (_, T)) ts gr = + let val i = length constrs + in if length ts <= i then + invoke_codegen thy defs dep module brack (eta_expand c ts (i+1)) gr + else + let + val ts1 = Library.take (i, ts); + val t :: ts2 = Library.drop (i, ts); + val names = List.foldr OldTerm.add_term_names + (map (fst o fst o dest_Var) (List.foldr OldTerm.add_term_vars [] ts1)) ts1; + val (Ts, dT) = split_last (Library.take (i+1, fst (strip_type T))); + + fun pcase [] [] [] gr = ([], gr) + | pcase ((cname, cargs)::cs) (t::ts) (U::Us) gr = + let + val j = length cargs; + val xs = Name.variant_list names (replicate j "x"); + val Us' = Library.take (j, fst (strip_type U)); + val frees = map Free (xs ~~ Us'); + val (cp, gr0) = invoke_codegen thy defs dep module false + (list_comb (Const (cname, Us' ---> dT), frees)) gr; + val t' = Envir.beta_norm (list_comb (t, frees)); + val (p, gr1) = invoke_codegen thy defs dep module false t' gr0; + val (ps, gr2) = pcase cs ts Us gr1; + in + ([Pretty.block [cp, str " =>", Pretty.brk 1, p]] :: ps, gr2) + end; + + val (ps1, gr1) = pcase constrs ts1 Ts gr ; + val ps = List.concat (separate [Pretty.brk 1, str "| "] ps1); + val (p, gr2) = invoke_codegen thy defs dep module false t gr1; + val (ps2, gr3) = fold_map (invoke_codegen thy defs dep module true) ts2 gr2; + in ((if not (null ts2) andalso brack then parens else I) + (Pretty.block (separate (Pretty.brk 1) + (Pretty.block ([str "(case ", p, str " of", + Pretty.brk 1] @ ps @ [str ")"]) :: ps2))), gr3) + end + end; + + +(**** constructors ****) + +fun pretty_constr thy defs dep module brack args (c as Const (s, T)) ts gr = + let val i = length args + in if i > 1 andalso length ts < i then + invoke_codegen thy defs dep module brack (eta_expand c ts i) gr + else + let + val id = mk_qual_id module (get_const_id gr s); + val (ps, gr') = fold_map + (invoke_codegen thy defs dep module (i = 1)) ts gr; + in (case args of + _ :: _ :: _ => (if brack then parens else I) + (Pretty.block [str id, Pretty.brk 1, mk_tuple ps]) + | _ => (mk_app brack (str id) ps), gr') + end + end; + + +(**** code generators for terms and types ****) + +fun datatype_codegen thy defs dep module brack t gr = (case strip_comb t of + (c as Const (s, T), ts) => + (case DatatypePackage.datatype_of_case thy s of + SOME {index, descr, ...} => + if is_some (get_assoc_code thy (s, T)) then NONE else + SOME (pretty_case thy defs dep module brack + (#3 (the (AList.lookup op = descr index))) c ts gr ) + | NONE => case (DatatypePackage.datatype_of_constr thy s, strip_type T) of + (SOME {index, descr, ...}, (_, U as Type (tyname, _))) => + if is_some (get_assoc_code thy (s, T)) then NONE else + let + val SOME (tyname', _, constrs) = AList.lookup op = descr index; + val SOME args = AList.lookup op = constrs s + in + if tyname <> tyname' then NONE + else SOME (pretty_constr thy defs + dep module brack args c ts (snd (invoke_tycodegen thy defs dep module false U gr))) + end + | _ => NONE) + | _ => NONE); + +fun datatype_tycodegen thy defs dep module brack (Type (s, Ts)) gr = + (case DatatypePackage.get_datatype thy s of + NONE => NONE + | SOME {descr, sorts, ...} => + if is_some (get_assoc_type thy s) then NONE else + let + val (ps, gr') = fold_map + (invoke_tycodegen thy defs dep module false) Ts gr; + val (module', gr'') = add_dt_defs thy defs dep module descr sorts gr' ; + val (tyid, gr''') = mk_type_id module' s gr'' + in SOME (Pretty.block ((if null Ts then [] else + [mk_tuple ps, str " "]) @ + [str (mk_qual_id module tyid)]), gr''') + end) + | datatype_tycodegen _ _ _ _ _ _ _ = NONE; + + +(** generic code generator **) + +(* case certificates *) + +fun mk_case_cert thy tyco = + let + val raw_thms = + (#case_rewrites o DatatypePackage.the_datatype thy) tyco; + val thms as hd_thm :: _ = raw_thms + |> Conjunction.intr_balanced + |> Thm.unvarify + |> Conjunction.elim_balanced (length raw_thms) + |> map Simpdata.mk_meta_eq + |> map Drule.zero_var_indexes + val params = fold_aterms (fn (Free (v, _)) => insert (op =) v + | _ => I) (Thm.prop_of hd_thm) []; + val rhs = hd_thm + |> Thm.prop_of + |> Logic.dest_equals + |> fst + |> Term.strip_comb + |> apsnd (fst o split_last) + |> list_comb; + val lhs = Free (Name.variant params "case", Term.fastype_of rhs); + val asm = (Thm.cterm_of thy o Logic.mk_equals) (lhs, rhs); + in + thms + |> Conjunction.intr_balanced + |> MetaSimplifier.rewrite_rule [(Thm.symmetric o Thm.assume) asm] + |> Thm.implies_intr asm + |> Thm.generalize ([], params) 0 + |> AxClass.unoverload thy + |> Thm.varifyT + end; + + +(* equality *) + +fun mk_eq_eqns thy dtco = + let + val (vs, cos) = DatatypePackage.the_datatype_spec thy dtco; + val { descr, index, inject = inject_thms, ... } = DatatypePackage.the_datatype thy dtco; + val ty = Type (dtco, map TFree vs); + fun mk_eq (t1, t2) = Const (@{const_name eq_class.eq}, ty --> ty --> HOLogic.boolT) + $ t1 $ t2; + fun true_eq t12 = HOLogic.mk_eq (mk_eq t12, HOLogic.true_const); + fun false_eq t12 = HOLogic.mk_eq (mk_eq t12, HOLogic.false_const); + val triv_injects = map_filter + (fn (c, []) => SOME (HOLogic.mk_Trueprop (true_eq (Const (c, ty), Const (c, ty)))) + | _ => NONE) cos; + fun prep_inject (trueprop $ (equiv $ (_ $ t1 $ t2) $ rhs)) = + trueprop $ (equiv $ mk_eq (t1, t2) $ rhs); + val injects = map prep_inject (nth (DatatypeProp.make_injs [descr] vs) index); + fun prep_distinct (trueprop $ (not $ (_ $ t1 $ t2))) = + [trueprop $ false_eq (t1, t2), trueprop $ false_eq (t2, t1)]; + val distincts = maps prep_distinct (snd (nth (DatatypeProp.make_distincts [descr] vs) index)); + val refl = HOLogic.mk_Trueprop (true_eq (Free ("x", ty), Free ("x", ty))); + val simpset = Simplifier.context (ProofContext.init thy) (HOL_basic_ss + addsimps (map Simpdata.mk_eq (@{thm eq} :: @{thm eq_True} :: inject_thms)) + addsimprocs [DatatypePackage.distinct_simproc]); + fun prove prop = Goal.prove_global thy [] [] prop (K (ALLGOALS (simp_tac simpset))) + |> Simpdata.mk_eq; + in map (rpair true o prove) (triv_injects @ injects @ distincts) @ [(prove refl, false)] end; + +fun add_equality vs dtcos thy = + let + fun add_def dtco lthy = + let + val ty = Type (dtco, map TFree vs); + fun mk_side const_name = Const (const_name, ty --> ty --> HOLogic.boolT) + $ Free ("x", ty) $ Free ("y", ty); + val def = HOLogic.mk_Trueprop (HOLogic.mk_eq + (mk_side @{const_name eq_class.eq}, mk_side @{const_name "op ="})); + val def' = Syntax.check_term lthy def; + val ((_, (_, thm)), lthy') = Specification.definition + (NONE, (Attrib.empty_binding, def')) lthy; + val ctxt_thy = ProofContext.init (ProofContext.theory_of lthy); + val thm' = singleton (ProofContext.export lthy' ctxt_thy) thm; + in (thm', lthy') end; + fun tac thms = Class.intro_classes_tac [] + THEN ALLGOALS (ProofContext.fact_tac thms); + fun add_eq_thms dtco thy = + let + val const = AxClass.param_of_inst thy (@{const_name eq_class.eq}, dtco); + val thy_ref = Theory.check_thy thy; + fun mk_thms () = rev ((mk_eq_eqns (Theory.deref thy_ref) dtco)); + in + Code.add_eqnl (const, Lazy.lazy mk_thms) thy + end; + in + thy + |> TheoryTarget.instantiation (dtcos, vs, [HOLogic.class_eq]) + |> fold_map add_def dtcos + |-> (fn def_thms => Class.prove_instantiation_exit_result (map o Morphism.thm) + (fn _ => fn def_thms => tac def_thms) def_thms) + |-> (fn def_thms => fold Code.del_eqn def_thms) + |> fold add_eq_thms dtcos + end; + + +(* liberal addition of code data for datatypes *) + +fun mk_constr_consts thy vs dtco cos = + let + val cs = map (fn (c, tys) => (c, tys ---> Type (dtco, map TFree vs))) cos; + val cs' = map (fn c_ty as (_, ty) => (AxClass.unoverload_const thy c_ty, ty)) cs; + in if is_some (try (Code.constrset_of_consts thy) cs') + then SOME cs + else NONE + end; + +fun add_all_code dtcos thy = + let + val (vs :: _, coss) = (split_list o map (DatatypePackage.the_datatype_spec thy)) dtcos; + val any_css = map2 (mk_constr_consts thy vs) dtcos coss; + val css = if exists is_none any_css then [] + else map_filter I any_css; + val case_rewrites = maps (#case_rewrites o DatatypePackage.the_datatype thy) dtcos; + val certs = map (mk_case_cert thy) dtcos; + in + if null css then thy + else thy + |> fold Code.add_datatype css + |> fold_rev Code.add_default_eqn case_rewrites + |> fold Code.add_case certs + |> add_equality vs dtcos + end; + + + +(** theory setup **) + +val setup = + add_codegen "datatype" datatype_codegen + #> add_tycodegen "datatype" datatype_tycodegen + #> DatatypePackage.interpretation add_all_code + +end; diff -r fa30cd74d7d6 -r eb2f9d709296 src/HOL/Tools/datatype_package/datatype_package.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Tools/datatype_package/datatype_package.ML Wed Jun 10 15:04:33 2009 +0200 @@ -0,0 +1,712 @@ +(* Title: HOL/Tools/datatype_package.ML + Author: Stefan Berghofer, TU Muenchen + +Datatype package for Isabelle/HOL. +*) + +signature DATATYPE_PACKAGE = +sig + type datatype_info = DatatypeAux.datatype_info + type descr = DatatypeAux.descr + val get_datatypes : theory -> datatype_info Symtab.table + val get_datatype : theory -> string -> datatype_info option + val the_datatype : theory -> string -> datatype_info + val datatype_of_constr : theory -> string -> datatype_info option + val datatype_of_case : theory -> string -> datatype_info option + val the_datatype_spec : theory -> string -> (string * sort) list * (string * typ list) list + val the_datatype_descr : theory -> string list + -> descr * (string * sort) list * string list + * (string list * string list) * (typ list * typ list) + val get_datatype_constrs : theory -> string -> (string * typ) list option + val distinct_simproc : simproc + val make_case : Proof.context -> bool -> string list -> term -> + (term * term) list -> term * (term * (int * bool)) list + val strip_case : Proof.context -> bool -> term -> (term * (term * term) list) option + val read_typ: theory -> + (typ list * (string * sort) list) * string -> typ list * (string * sort) list + val interpretation : (string list -> theory -> theory) -> theory -> theory + val rep_datatype : ({distinct : thm list list, + inject : thm list list, + exhaustion : thm list, + rec_thms : thm list, + case_thms : thm list list, + split_thms : (thm * thm) list, + induction : thm, + simps : thm list} -> Proof.context -> Proof.context) -> string list option -> term list + -> theory -> Proof.state; + val rep_datatype_cmd : string list option -> string list -> theory -> Proof.state; + val add_datatype : bool -> bool -> string list -> (string list * binding * mixfix * + (binding * typ list * mixfix) list) list -> theory -> + {distinct : thm list list, + inject : thm list list, + exhaustion : thm list, + rec_thms : thm list, + case_thms : thm list list, + split_thms : (thm * thm) list, + induction : thm, + simps : thm list} * theory + val add_datatype_cmd : bool -> string list -> (string list * binding * mixfix * + (binding * string list * mixfix) list) list -> theory -> + {distinct : thm list list, + inject : thm list list, + exhaustion : thm list, + rec_thms : thm list, + case_thms : thm list list, + split_thms : (thm * thm) list, + induction : thm, + simps : thm list} * theory + val setup: theory -> theory + val quiet_mode : bool ref + val print_datatypes : theory -> unit +end; + +structure DatatypePackage : DATATYPE_PACKAGE = +struct + +open DatatypeAux; + +val quiet_mode = quiet_mode; + + +(* theory data *) + +structure DatatypesData = TheoryDataFun +( + type T = + {types: datatype_info Symtab.table, + constrs: datatype_info Symtab.table, + cases: datatype_info Symtab.table}; + + val empty = + {types = Symtab.empty, constrs = Symtab.empty, cases = Symtab.empty}; + val copy = I; + val extend = I; + fun merge _ + ({types = types1, constrs = constrs1, cases = cases1}, + {types = types2, constrs = constrs2, cases = cases2}) = + {types = Symtab.merge (K true) (types1, types2), + constrs = Symtab.merge (K true) (constrs1, constrs2), + cases = Symtab.merge (K true) (cases1, cases2)}; +); + +val get_datatypes = #types o DatatypesData.get; +val map_datatypes = DatatypesData.map; + +fun print_datatypes thy = + Pretty.writeln (Pretty.strs ("datatypes:" :: + map #1 (NameSpace.extern_table (Sign.type_space thy, get_datatypes thy)))); + + +(** theory information about datatypes **) + +fun put_dt_infos (dt_infos : (string * datatype_info) list) = + map_datatypes (fn {types, constrs, cases} => + {types = fold Symtab.update dt_infos types, + constrs = fold Symtab.default (*conservative wrt. overloaded constructors*) + (maps (fn (_, info as {descr, index, ...}) => map (rpair info o fst) + (#3 (the (AList.lookup op = descr index)))) dt_infos) constrs, + cases = fold Symtab.update + (map (fn (_, info as {case_name, ...}) => (case_name, info)) dt_infos) + cases}); + +val get_datatype = Symtab.lookup o get_datatypes; + +fun the_datatype thy name = (case get_datatype thy name of + SOME info => info + | NONE => error ("Unknown datatype " ^ quote name)); + +val datatype_of_constr = Symtab.lookup o #constrs o DatatypesData.get; +val datatype_of_case = Symtab.lookup o #cases o DatatypesData.get; + +fun get_datatype_descr thy dtco = + get_datatype thy dtco + |> Option.map (fn info as { descr, index, ... } => + (info, (((fn SOME (_, dtys, cos) => (dtys, cos)) o AList.lookup (op =) descr) index))); + +fun the_datatype_spec thy dtco = + let + val info as { descr, index, sorts = raw_sorts, ... } = the_datatype thy dtco; + val SOME (_, dtys, raw_cos) = AList.lookup (op =) descr index; + val sorts = map ((fn v => (v, (the o AList.lookup (op =) raw_sorts) v)) + o DatatypeAux.dest_DtTFree) dtys; + val cos = map + (fn (co, tys) => (co, map (DatatypeAux.typ_of_dtyp descr sorts) tys)) raw_cos; + in (sorts, cos) end; + +fun the_datatype_descr thy (raw_tycos as raw_tyco :: _) = + let + val info = the_datatype thy raw_tyco; + val descr = #descr info; + + val SOME (_, dtys, raw_cos) = AList.lookup (op =) descr (#index info); + val vs = map ((fn v => (v, (the o AList.lookup (op =) (#sorts info)) v)) + o dest_DtTFree) dtys; + + fun is_DtTFree (DtTFree _) = true + | is_DtTFree _ = false + val k = find_index (fn (_, (_, dTs, _)) => not (forall is_DtTFree dTs)) descr; + val protoTs as (dataTs, _) = chop k descr + |> (pairself o map) (fn (_, (tyco, dTs, _)) => (tyco, map (typ_of_dtyp descr vs) dTs)); + + val tycos = map fst dataTs; + val _ = if gen_eq_set (op =) (tycos, raw_tycos) then () + else error ("Type constructors " ^ commas (map quote raw_tycos) + ^ "do not belong exhaustively to one mutual recursive datatype"); + + val (Ts, Us) = (pairself o map) Type protoTs; + + val names = map Long_Name.base_name (the_default tycos (#alt_names info)); + val (auxnames, _) = Name.make_context names + |> fold_map (yield_singleton Name.variants o name_of_typ) Us + + in (descr, vs, tycos, (names, auxnames), (Ts, Us)) end; + +fun get_datatype_constrs thy dtco = + case try (the_datatype_spec thy) dtco + of SOME (sorts, cos) => + let + fun subst (v, sort) = TVar ((v, 0), sort); + fun subst_ty (TFree v) = subst v + | subst_ty ty = ty; + val dty = Type (dtco, map subst sorts); + fun mk_co (co, tys) = (co, map (Term.map_atyps subst_ty) tys ---> dty); + in SOME (map mk_co cos) end + | NONE => NONE; + + +(** induct method setup **) + +(* case names *) + +local + +fun dt_recs (DtTFree _) = [] + | dt_recs (DtType (_, dts)) = maps dt_recs dts + | dt_recs (DtRec i) = [i]; + +fun dt_cases (descr: descr) (_, args, constrs) = + let + fun the_bname i = Long_Name.base_name (#1 (the (AList.lookup (op =) descr i))); + val bnames = map the_bname (distinct (op =) (maps dt_recs args)); + in map (fn (c, _) => space_implode "_" (Long_Name.base_name c :: bnames)) constrs end; + + +fun induct_cases descr = + DatatypeProp.indexify_names (maps (dt_cases descr) (map #2 descr)); + +fun exhaust_cases descr i = dt_cases descr (the (AList.lookup (op =) descr i)); + +in + +fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr); + +fun mk_case_names_exhausts descr new = + map (RuleCases.case_names o exhaust_cases descr o #1) + (filter (fn ((_, (name, _, _))) => member (op =) new name) descr); + +end; + +fun add_rules simps case_thms rec_thms inject distinct + weak_case_congs cong_att = + PureThy.add_thmss [((Binding.name "simps", simps), []), + ((Binding.empty, flat case_thms @ + flat distinct @ rec_thms), [Simplifier.simp_add]), + ((Binding.empty, rec_thms), [Code.add_default_eqn_attribute]), + ((Binding.empty, flat inject), [iff_add]), + ((Binding.empty, map (fn th => th RS notE) (flat distinct)), [Classical.safe_elim NONE]), + ((Binding.empty, weak_case_congs), [cong_att])] + #> snd; + + +(* add_cases_induct *) + +fun add_cases_induct infos induction thy = + let + val inducts = ProjectRule.projections (ProofContext.init thy) induction; + + fun named_rules (name, {index, exhaustion, ...}: datatype_info) = + [((Binding.empty, nth inducts index), [Induct.induct_type name]), + ((Binding.empty, exhaustion), [Induct.cases_type name])]; + fun unnamed_rule i = + ((Binding.empty, nth inducts i), [Thm.kind_internal, Induct.induct_type ""]); + in + thy |> PureThy.add_thms + (maps named_rules infos @ + map unnamed_rule (length infos upto length inducts - 1)) |> snd + |> PureThy.add_thmss [((Binding.name "inducts", inducts), [])] |> snd + end; + + + +(**** simplification procedure for showing distinctness of constructors ****) + +fun stripT (i, Type ("fun", [_, T])) = stripT (i + 1, T) + | stripT p = p; + +fun stripC (i, f $ x) = stripC (i + 1, f) + | stripC p = p; + +val distinctN = "constr_distinct"; + +fun distinct_rule thy ss tname eq_t = case #distinct (the_datatype thy tname) of + FewConstrs thms => Goal.prove (Simplifier.the_context ss) [] [] eq_t (K + (EVERY [rtac eq_reflection 1, rtac iffI 1, rtac notE 1, + atac 2, resolve_tac thms 1, etac FalseE 1])) + | ManyConstrs (thm, simpset) => + let + val [In0_inject, In1_inject, In0_not_In1, In1_not_In0] = + map (PureThy.get_thm (ThyInfo.the_theory "Datatype" thy)) + ["In0_inject", "In1_inject", "In0_not_In1", "In1_not_In0"]; + in + Goal.prove (Simplifier.the_context ss) [] [] eq_t (K + (EVERY [rtac eq_reflection 1, rtac iffI 1, dtac thm 1, + full_simp_tac (Simplifier.inherit_context ss simpset) 1, + REPEAT (dresolve_tac [In0_inject, In1_inject] 1), + eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1, + etac FalseE 1])) + end; + +fun distinct_proc thy ss (t as Const ("op =", _) $ t1 $ t2) = + (case (stripC (0, t1), stripC (0, t2)) of + ((i, Const (cname1, T1)), (j, Const (cname2, T2))) => + (case (stripT (0, T1), stripT (0, T2)) of + ((i', Type (tname1, _)), (j', Type (tname2, _))) => + if tname1 = tname2 andalso not (cname1 = cname2) andalso i = i' andalso j = j' then + (case (get_datatype_descr thy) tname1 of + SOME (_, (_, constrs)) => let val cnames = map fst constrs + in if cname1 mem cnames andalso cname2 mem cnames then + SOME (distinct_rule thy ss tname1 + (Logic.mk_equals (t, Const ("False", HOLogic.boolT)))) + else NONE + end + | NONE => NONE) + else NONE + | _ => NONE) + | _ => NONE) + | distinct_proc _ _ _ = NONE; + +val distinct_simproc = + Simplifier.simproc @{theory HOL} distinctN ["s = t"] distinct_proc; + +val dist_ss = HOL_ss addsimprocs [distinct_simproc]; + +val simproc_setup = + Simplifier.map_simpset (fn ss => ss addsimprocs [distinct_simproc]); + + +(**** translation rules for case ****) + +fun make_case ctxt = DatatypeCase.make_case + (datatype_of_constr (ProofContext.theory_of ctxt)) ctxt; + +fun strip_case ctxt = DatatypeCase.strip_case + (datatype_of_case (ProofContext.theory_of ctxt)); + +fun add_case_tr' case_names thy = + Sign.add_advanced_trfuns ([], [], + map (fn case_name => + let val case_name' = Sign.const_syntax_name thy case_name + in (case_name', DatatypeCase.case_tr' datatype_of_case case_name') + end) case_names, []) thy; + +val trfun_setup = + Sign.add_advanced_trfuns ([], + [("_case_syntax", DatatypeCase.case_tr true datatype_of_constr)], + [], []); + + +(* prepare types *) + +fun read_typ thy ((Ts, sorts), str) = + let + val ctxt = ProofContext.init thy + |> fold (Variable.declare_typ o TFree) sorts; + val T = Syntax.read_typ ctxt str; + in (Ts @ [T], Term.add_tfreesT T sorts) end; + +fun cert_typ sign ((Ts, sorts), raw_T) = + let + val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle + TYPE (msg, _, _) => error msg; + val sorts' = Term.add_tfreesT T sorts; + in (Ts @ [T], + case duplicates (op =) (map fst sorts') of + [] => sorts' + | dups => error ("Inconsistent sort constraints for " ^ commas dups)) + end; + + +(**** make datatype info ****) + +fun make_dt_info alt_names descr sorts induct reccomb_names rec_thms + (((((((((i, (_, (tname, _, _))), case_name), case_thms), + exhaustion_thm), distinct_thm), inject), nchotomy), case_cong), weak_case_cong) = + (tname, + {index = i, + alt_names = alt_names, + descr = descr, + sorts = sorts, + rec_names = reccomb_names, + rec_rewrites = rec_thms, + case_name = case_name, + case_rewrites = case_thms, + induction = induct, + exhaustion = exhaustion_thm, + distinct = distinct_thm, + inject = inject, + nchotomy = nchotomy, + case_cong = case_cong, + weak_case_cong = weak_case_cong}); + +structure DatatypeInterpretation = InterpretationFun(type T = string list val eq = op =); +val interpretation = DatatypeInterpretation.interpretation; + + +(******************* definitional introduction of datatypes *******************) + +fun add_datatype_def flat_names new_type_names descr sorts types_syntax constr_syntax dt_info + case_names_induct case_names_exhausts thy = + let + val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names); + + val ((inject, distinct, dist_rewrites, simproc_dists, induct), thy2) = thy |> + DatatypeRepProofs.representation_proofs flat_names dt_info new_type_names descr sorts + types_syntax constr_syntax case_names_induct; + + val (casedist_thms, thy3) = DatatypeAbsProofs.prove_casedist_thms new_type_names descr + sorts induct case_names_exhausts thy2; + val ((reccomb_names, rec_thms), thy4) = DatatypeAbsProofs.prove_primrec_thms + flat_names new_type_names descr sorts dt_info inject dist_rewrites + (Simplifier.theory_context thy3 dist_ss) induct thy3; + val ((case_thms, case_names), thy6) = DatatypeAbsProofs.prove_case_thms + flat_names new_type_names descr sorts reccomb_names rec_thms thy4; + val (split_thms, thy7) = DatatypeAbsProofs.prove_split_thms new_type_names + descr sorts inject dist_rewrites casedist_thms case_thms thy6; + val (nchotomys, thy8) = DatatypeAbsProofs.prove_nchotomys new_type_names + descr sorts casedist_thms thy7; + val (case_congs, thy9) = DatatypeAbsProofs.prove_case_congs new_type_names + descr sorts nchotomys case_thms thy8; + val (weak_case_congs, thy10) = DatatypeAbsProofs.prove_weak_case_congs new_type_names + descr sorts thy9; + + val dt_infos = map + (make_dt_info (SOME new_type_names) (flat descr) sorts induct reccomb_names rec_thms) + ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~ + casedist_thms ~~ simproc_dists ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs); + + val simps = flat (distinct @ inject @ case_thms) @ rec_thms; + + val thy12 = + thy10 + |> add_case_tr' case_names + |> Sign.add_path (space_implode "_" new_type_names) + |> add_rules simps case_thms rec_thms inject distinct + weak_case_congs (Simplifier.attrib (op addcongs)) + |> put_dt_infos dt_infos + |> add_cases_induct dt_infos induct + |> Sign.parent_path + |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |> snd + |> DatatypeInterpretation.data (map fst dt_infos); + in + ({distinct = distinct, + inject = inject, + exhaustion = casedist_thms, + rec_thms = rec_thms, + case_thms = case_thms, + split_thms = split_thms, + induction = induct, + simps = simps}, thy12) + end; + + +(*********************** declare existing type as datatype *********************) + +fun prove_rep_datatype alt_names new_type_names descr sorts induct inject half_distinct thy = + let + val ((_, [induct']), _) = + Variable.importT_thms [induct] (Variable.thm_context induct); + + fun err t = error ("Ill-formed predicate in induction rule: " ^ + Syntax.string_of_term_global thy t); + + fun get_typ (t as _ $ Var (_, Type (tname, Ts))) = + ((tname, map (fst o dest_TFree) Ts) handle TERM _ => err t) + | get_typ t = err t; + val dtnames = map get_typ (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induct'))); + + val dt_info = get_datatypes thy; + + val distinct = (map o maps) (fn thm => [thm, thm RS not_sym]) half_distinct; + val (case_names_induct, case_names_exhausts) = + (mk_case_names_induct descr, mk_case_names_exhausts descr (map #1 dtnames)); + + val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names); + + val (casedist_thms, thy2) = thy |> + DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induct + case_names_exhausts; + val ((reccomb_names, rec_thms), thy3) = DatatypeAbsProofs.prove_primrec_thms + false new_type_names [descr] sorts dt_info inject distinct + (Simplifier.theory_context thy2 dist_ss) induct thy2; + val ((case_thms, case_names), thy4) = DatatypeAbsProofs.prove_case_thms false + new_type_names [descr] sorts reccomb_names rec_thms thy3; + val (split_thms, thy5) = DatatypeAbsProofs.prove_split_thms + new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4; + val (nchotomys, thy6) = DatatypeAbsProofs.prove_nchotomys new_type_names + [descr] sorts casedist_thms thy5; + val (case_congs, thy7) = DatatypeAbsProofs.prove_case_congs new_type_names + [descr] sorts nchotomys case_thms thy6; + val (weak_case_congs, thy8) = DatatypeAbsProofs.prove_weak_case_congs new_type_names + [descr] sorts thy7; + + val ((_, [induct']), thy10) = + thy8 + |> store_thmss "inject" new_type_names inject + ||>> store_thmss "distinct" new_type_names distinct + ||> Sign.add_path (space_implode "_" new_type_names) + ||>> PureThy.add_thms [((Binding.name "induct", induct), [case_names_induct])]; + + val dt_infos = map (make_dt_info alt_names descr sorts induct' reccomb_names rec_thms) + ((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~ casedist_thms ~~ + map FewConstrs distinct ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs); + + val simps = flat (distinct @ inject @ case_thms) @ rec_thms; + + val thy11 = + thy10 + |> add_case_tr' case_names + |> add_rules simps case_thms rec_thms inject distinct + weak_case_congs (Simplifier.attrib (op addcongs)) + |> put_dt_infos dt_infos + |> add_cases_induct dt_infos induct' + |> Sign.parent_path + |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) + |> snd + |> DatatypeInterpretation.data (map fst dt_infos); + in + ({distinct = distinct, + inject = inject, + exhaustion = casedist_thms, + rec_thms = rec_thms, + case_thms = case_thms, + split_thms = split_thms, + induction = induct', + simps = simps}, thy11) + end; + +fun gen_rep_datatype prep_term after_qed alt_names raw_ts thy = + let + fun constr_of_term (Const (c, T)) = (c, T) + | constr_of_term t = + error ("Not a constant: " ^ Syntax.string_of_term_global thy t); + fun no_constr (c, T) = error ("Bad constructor: " + ^ Sign.extern_const thy c ^ "::" + ^ Syntax.string_of_typ_global thy T); + fun type_of_constr (cT as (_, T)) = + let + val frees = OldTerm.typ_tfrees T; + val (tyco, vs) = ((apsnd o map) (dest_TFree) o dest_Type o snd o strip_type) T + handle TYPE _ => no_constr cT + val _ = if has_duplicates (eq_fst (op =)) vs then no_constr cT else (); + val _ = if length frees <> length vs then no_constr cT else (); + in (tyco, (vs, cT)) end; + + val raw_cs = AList.group (op =) (map (type_of_constr o constr_of_term o prep_term thy) raw_ts); + val _ = case map_filter (fn (tyco, _) => + if Symtab.defined (get_datatypes thy) tyco then SOME tyco else NONE) raw_cs + of [] => () + | tycos => error ("Type(s) " ^ commas (map quote tycos) + ^ " already represented inductivly"); + val raw_vss = maps (map (map snd o fst) o snd) raw_cs; + val ms = case distinct (op =) (map length raw_vss) + of [n] => 0 upto n - 1 + | _ => error ("Different types in given constructors"); + fun inter_sort m = map (fn xs => nth xs m) raw_vss + |> Library.foldr1 (Sorts.inter_sort (Sign.classes_of thy)) + val sorts = map inter_sort ms; + val vs = Name.names Name.context Name.aT sorts; + + fun norm_constr (raw_vs, (c, T)) = (c, map_atyps + (TFree o (the o AList.lookup (op =) (map fst raw_vs ~~ vs)) o fst o dest_TFree) T); + + val cs = map (apsnd (map norm_constr)) raw_cs; + val dtyps_of_typ = map (dtyp_of_typ (map (rpair (map fst vs) o fst) cs)) + o fst o strip_type; + val new_type_names = map Long_Name.base_name (the_default (map fst cs) alt_names); + + fun mk_spec (i, (tyco, constr)) = (i, (tyco, + map (DtTFree o fst) vs, + (map o apsnd) dtyps_of_typ constr)) + val descr = map_index mk_spec cs; + val injs = DatatypeProp.make_injs [descr] vs; + val half_distincts = map snd (DatatypeProp.make_distincts [descr] vs); + val ind = DatatypeProp.make_ind [descr] vs; + val rules = (map o map o map) Logic.close_form [[[ind]], injs, half_distincts]; + + fun after_qed' raw_thms = + let + val [[[induct]], injs, half_distincts] = + unflat rules (map Drule.zero_var_indexes_list raw_thms); + (*FIXME somehow dubious*) + in + ProofContext.theory_result + (prove_rep_datatype alt_names new_type_names descr vs induct injs half_distincts) + #-> after_qed + end; + in + thy + |> ProofContext.init + |> Proof.theorem_i NONE after_qed' ((map o map) (rpair []) (flat rules)) + end; + +val rep_datatype = gen_rep_datatype Sign.cert_term; +val rep_datatype_cmd = gen_rep_datatype Syntax.read_term_global (K I); + + + +(******************************** add datatype ********************************) + +fun gen_add_datatype prep_typ err flat_names new_type_names dts thy = + let + val _ = Theory.requires thy "Datatype" "datatype definitions"; + + (* this theory is used just for parsing *) + + val tmp_thy = thy |> + Theory.copy |> + Sign.add_types (map (fn (tvs, tname, mx, _) => + (tname, length tvs, mx)) dts); + + val (tyvars, _, _, _)::_ = dts; + val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) => + let val full_tname = Sign.full_name tmp_thy (Binding.map_name (Syntax.type_name mx) tname) + in (case duplicates (op =) tvs of + [] => if eq_set (tyvars, tvs) then ((full_tname, tvs), (tname, mx)) + else error ("Mutually recursive datatypes must have same type parameters") + | dups => error ("Duplicate parameter(s) for datatype " ^ quote (Binding.str_of tname) ^ + " : " ^ commas dups)) + end) dts); + + val _ = (case duplicates (op =) (map fst new_dts) @ duplicates (op =) new_type_names of + [] => () | dups => error ("Duplicate datatypes: " ^ commas dups)); + + fun prep_dt_spec ((tvs, tname, mx, constrs), tname') (dts', constr_syntax, sorts, i) = + let + fun prep_constr (cname, cargs, mx') (constrs, constr_syntax', sorts') = + let + val (cargs', sorts'') = Library.foldl (prep_typ tmp_thy) (([], sorts'), cargs); + val _ = (case fold (curry OldTerm.add_typ_tfree_names) cargs' [] \\ tvs of + [] => () + | vs => error ("Extra type variables on rhs: " ^ commas vs)) + in (constrs @ [((if flat_names then Sign.full_name tmp_thy else + Sign.full_name_path tmp_thy tname') + (Binding.map_name (Syntax.const_name mx') cname), + map (dtyp_of_typ new_dts) cargs')], + constr_syntax' @ [(cname, mx')], sorts'') + end handle ERROR msg => cat_error msg + ("The error above occured in constructor " ^ quote (Binding.str_of cname) ^ + " of datatype " ^ quote (Binding.str_of tname)); + + val (constrs', constr_syntax', sorts') = + fold prep_constr constrs ([], [], sorts) + + in + case duplicates (op =) (map fst constrs') of + [] => + (dts' @ [(i, (Sign.full_name tmp_thy (Binding.map_name (Syntax.type_name mx) tname), + map DtTFree tvs, constrs'))], + constr_syntax @ [constr_syntax'], sorts', i + 1) + | dups => error ("Duplicate constructors " ^ commas dups ^ + " in datatype " ^ quote (Binding.str_of tname)) + end; + + val (dts', constr_syntax, sorts', i) = + fold prep_dt_spec (dts ~~ new_type_names) ([], [], [], 0); + val sorts = sorts' @ (map (rpair (Sign.defaultS tmp_thy)) (tyvars \\ map fst sorts')); + val dt_info = get_datatypes thy; + val (descr, _) = unfold_datatypes tmp_thy dts' sorts dt_info dts' i; + val _ = check_nonempty descr handle (exn as Datatype_Empty s) => + if err then error ("Nonemptiness check failed for datatype " ^ s) + else raise exn; + + val descr' = flat descr; + val case_names_induct = mk_case_names_induct descr'; + val case_names_exhausts = mk_case_names_exhausts descr' (map #1 new_dts); + in + add_datatype_def + flat_names new_type_names descr sorts types_syntax constr_syntax dt_info + case_names_induct case_names_exhausts thy + end; + +val add_datatype = gen_add_datatype cert_typ; +val add_datatype_cmd = gen_add_datatype read_typ true; + + + +(** package setup **) + +(* setup theory *) + +val setup = + DatatypeRepProofs.distinctness_limit_setup #> + simproc_setup #> + trfun_setup #> + DatatypeInterpretation.init; + + +(* outer syntax *) + +local structure P = OuterParse and K = OuterKeyword in + +val datatype_decl = + Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.binding -- P.opt_infix -- + (P.$$$ "=" |-- P.enum1 "|" (P.binding -- Scan.repeat P.typ -- P.opt_mixfix)); + +fun mk_datatype args = + let + val names = map + (fn ((((NONE, _), t), _), _) => Binding.name_of t | ((((SOME t, _), _), _), _) => t) args; + val specs = map (fn ((((_, vs), t), mx), cons) => + (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args; + in snd o add_datatype_cmd false names specs end; + +val _ = + OuterSyntax.command "datatype" "define inductive datatypes" K.thy_decl + (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype)); + +val _ = + OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_goal + (Scan.option (P.$$$ "(" |-- Scan.repeat1 P.name --| P.$$$ ")") -- Scan.repeat1 P.term + >> (fn (alt_names, ts) => Toplevel.print + o Toplevel.theory_to_proof (rep_datatype_cmd alt_names ts))); + +end; + + +(* document antiquotation *) + +val _ = ThyOutput.antiquotation "datatype" Args.tyname + (fn {source = src, context = ctxt, ...} => fn dtco => + let + val thy = ProofContext.theory_of ctxt; + val (vs, cos) = the_datatype_spec thy dtco; + val ty = Type (dtco, map TFree vs); + fun pretty_typ_bracket (ty as Type (_, _ :: _)) = + Pretty.enclose "(" ")" [Syntax.pretty_typ ctxt ty] + | pretty_typ_bracket ty = + Syntax.pretty_typ ctxt ty; + fun pretty_constr (co, tys) = + (Pretty.block o Pretty.breaks) + (Syntax.pretty_term ctxt (Const (co, tys ---> ty)) :: + map pretty_typ_bracket tys); + val pretty_datatype = + Pretty.block + (Pretty.command "datatype" :: Pretty.brk 1 :: + Syntax.pretty_typ ctxt ty :: + Pretty.str " =" :: Pretty.brk 1 :: + flat (separate [Pretty.brk 1, Pretty.str "| "] + (map (single o pretty_constr) cos))); + in ThyOutput.output (ThyOutput.maybe_pretty_source (K pretty_datatype) src [()]) end); + +end; + diff -r fa30cd74d7d6 -r eb2f9d709296 src/HOL/Tools/datatype_package/datatype_prop.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Tools/datatype_package/datatype_prop.ML Wed Jun 10 15:04:33 2009 +0200 @@ -0,0 +1,435 @@ +(* Title: HOL/Tools/datatype_prop.ML + Author: Stefan Berghofer, TU Muenchen + +Characteristic properties of datatypes. +*) + +signature DATATYPE_PROP = +sig + val indexify_names: string list -> string list + val make_tnames: typ list -> string list + val make_injs : DatatypeAux.descr list -> (string * sort) list -> term list list + val make_distincts : DatatypeAux.descr list -> + (string * sort) list -> (int * term list) list (*no symmetric inequalities*) + val make_ind : DatatypeAux.descr list -> (string * sort) list -> term + val make_casedists : DatatypeAux.descr list -> (string * sort) list -> term list + val make_primrec_Ts : DatatypeAux.descr list -> (string * sort) list -> + string list -> typ list * typ list + val make_primrecs : string list -> DatatypeAux.descr list -> + (string * sort) list -> theory -> term list + val make_cases : string list -> DatatypeAux.descr list -> + (string * sort) list -> theory -> term list list + val make_splits : string list -> DatatypeAux.descr list -> + (string * sort) list -> theory -> (term * term) list + val make_weak_case_congs : string list -> DatatypeAux.descr list -> + (string * sort) list -> theory -> term list + val make_case_congs : string list -> DatatypeAux.descr list -> + (string * sort) list -> theory -> term list + val make_nchotomys : DatatypeAux.descr list -> + (string * sort) list -> term list +end; + +structure DatatypeProp : DATATYPE_PROP = +struct + +open DatatypeAux; + +fun indexify_names names = + let + fun index (x :: xs) tab = + (case AList.lookup (op =) tab x of + NONE => if member (op =) xs x then (x ^ "1") :: index xs ((x, 2) :: tab) else x :: index xs tab + | SOME i => (x ^ string_of_int i) :: index xs ((x, i + 1) :: tab)) + | index [] _ = []; + in index names [] end; + +fun make_tnames Ts = + let + fun type_name (TFree (name, _)) = implode (tl (explode name)) + | type_name (Type (name, _)) = + let val name' = Long_Name.base_name name + in if Syntax.is_identifier name' then name' else "x" end; + in indexify_names (map type_name Ts) end; + + +(************************* injectivity of constructors ************************) + +fun make_injs descr sorts = + let + val descr' = flat descr; + fun make_inj T (cname, cargs) = + if null cargs then I else + let + val Ts = map (typ_of_dtyp descr' sorts) cargs; + val constr_t = Const (cname, Ts ---> T); + val tnames = make_tnames Ts; + val frees = map Free (tnames ~~ Ts); + val frees' = map Free ((map ((op ^) o (rpair "'")) tnames) ~~ Ts); + in cons (HOLogic.mk_Trueprop (HOLogic.mk_eq + (HOLogic.mk_eq (list_comb (constr_t, frees), list_comb (constr_t, frees')), + foldr1 (HOLogic.mk_binop "op &") + (map HOLogic.mk_eq (frees ~~ frees'))))) + end; + in + map2 (fn d => fn T => fold_rev (make_inj T) (#3 (snd d)) []) + (hd descr) (Library.take (length (hd descr), get_rec_types descr' sorts)) + end; + + +(************************* distinctness of constructors ***********************) + +fun make_distincts descr sorts = + let + val descr' = flat descr; + val recTs = get_rec_types descr' sorts; + val newTs = Library.take (length (hd descr), recTs); + + fun prep_constr (cname, cargs) = (cname, map (typ_of_dtyp descr' sorts) cargs); + + fun make_distincts' _ [] = [] + | make_distincts' T ((cname, cargs)::constrs) = + let + val frees = map Free ((make_tnames cargs) ~~ cargs); + val t = list_comb (Const (cname, cargs ---> T), frees); + + fun make_distincts'' (cname', cargs') = + let + val frees' = map Free ((map ((op ^) o (rpair "'")) + (make_tnames cargs')) ~~ cargs'); + val t' = list_comb (Const (cname', cargs' ---> T), frees') + in + HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.mk_eq (t, t')) + end + + in map make_distincts'' constrs @ make_distincts' T constrs end; + + in + map2 (fn ((_, (_, _, constrs))) => fn T => + (length constrs, make_distincts' T (map prep_constr constrs))) (hd descr) newTs + end; + + +(********************************* induction **********************************) + +fun make_ind descr sorts = + let + val descr' = List.concat descr; + val recTs = get_rec_types descr' sorts; + val pnames = if length descr' = 1 then ["P"] + else map (fn i => "P" ^ string_of_int i) (1 upto length descr'); + + fun make_pred i T = + let val T' = T --> HOLogic.boolT + in Free (List.nth (pnames, i), T') end; + + fun make_ind_prem k T (cname, cargs) = + let + fun mk_prem ((dt, s), T) = + let val (Us, U) = strip_type T + in list_all (map (pair "x") Us, HOLogic.mk_Trueprop + (make_pred (body_index dt) U $ app_bnds (Free (s, T)) (length Us))) + end; + + val recs = List.filter is_rec_type cargs; + val Ts = map (typ_of_dtyp descr' sorts) cargs; + val recTs' = map (typ_of_dtyp descr' sorts) recs; + val tnames = Name.variant_list pnames (make_tnames Ts); + val rec_tnames = map fst (List.filter (is_rec_type o snd) (tnames ~~ cargs)); + val frees = tnames ~~ Ts; + val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs'); + + in list_all_free (frees, Logic.list_implies (prems, + HOLogic.mk_Trueprop (make_pred k T $ + list_comb (Const (cname, Ts ---> T), map Free frees)))) + end; + + val prems = List.concat (map (fn ((i, (_, _, constrs)), T) => + map (make_ind_prem i T) constrs) (descr' ~~ recTs)); + val tnames = make_tnames recTs; + val concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &") + (map (fn (((i, _), T), tname) => make_pred i T $ Free (tname, T)) + (descr' ~~ recTs ~~ tnames))) + + in Logic.list_implies (prems, concl) end; + +(******************************* case distinction *****************************) + +fun make_casedists descr sorts = + let + val descr' = List.concat descr; + + fun make_casedist_prem T (cname, cargs) = + let + val Ts = map (typ_of_dtyp descr' sorts) cargs; + val frees = Name.variant_list ["P", "y"] (make_tnames Ts) ~~ Ts; + val free_ts = map Free frees + in list_all_free (frees, Logic.mk_implies (HOLogic.mk_Trueprop + (HOLogic.mk_eq (Free ("y", T), list_comb (Const (cname, Ts ---> T), free_ts))), + HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT)))) + end; + + fun make_casedist ((_, (_, _, constrs)), T) = + let val prems = map (make_casedist_prem T) constrs + in Logic.list_implies (prems, HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT))) + end + + in map make_casedist + ((hd descr) ~~ Library.take (length (hd descr), get_rec_types descr' sorts)) + end; + +(*************** characteristic equations for primrec combinator **************) + +fun make_primrec_Ts descr sorts used = + let + val descr' = List.concat descr; + + val rec_result_Ts = map TFree (Name.variant_list used (replicate (length descr') "'t") ~~ + replicate (length descr') HOLogic.typeS); + + val reccomb_fn_Ts = List.concat (map (fn (i, (_, _, constrs)) => + map (fn (_, cargs) => + let + val Ts = map (typ_of_dtyp descr' sorts) cargs; + val recs = List.filter (is_rec_type o fst) (cargs ~~ Ts); + + fun mk_argT (dt, T) = + binder_types T ---> List.nth (rec_result_Ts, body_index dt); + + val argTs = Ts @ map mk_argT recs + in argTs ---> List.nth (rec_result_Ts, i) + end) constrs) descr'); + + in (rec_result_Ts, reccomb_fn_Ts) end; + +fun make_primrecs new_type_names descr sorts thy = + let + val descr' = List.concat descr; + val recTs = get_rec_types descr' sorts; + val used = List.foldr OldTerm.add_typ_tfree_names [] recTs; + + val (rec_result_Ts, reccomb_fn_Ts) = make_primrec_Ts descr sorts used; + + val rec_fns = map (uncurry (mk_Free "f")) + (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts))); + + val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec"; + val reccomb_names = map (Sign.intern_const thy) + (if length descr' = 1 then [big_reccomb_name] else + (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int) + (1 upto (length descr')))); + val reccombs = map (fn ((name, T), T') => list_comb + (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns)) + (reccomb_names ~~ recTs ~~ rec_result_Ts); + + fun make_primrec T comb_t ((ts, f::fs), (cname, cargs)) = + let + val recs = List.filter is_rec_type cargs; + val Ts = map (typ_of_dtyp descr' sorts) cargs; + val recTs' = map (typ_of_dtyp descr' sorts) recs; + val tnames = make_tnames Ts; + val rec_tnames = map fst (List.filter (is_rec_type o snd) (tnames ~~ cargs)); + val frees = map Free (tnames ~~ Ts); + val frees' = map Free (rec_tnames ~~ recTs'); + + fun mk_reccomb ((dt, T), t) = + let val (Us, U) = strip_type T + in list_abs (map (pair "x") Us, + List.nth (reccombs, body_index dt) $ app_bnds t (length Us)) + end; + + val reccombs' = map mk_reccomb (recs ~~ recTs' ~~ frees') + + in (ts @ [HOLogic.mk_Trueprop (HOLogic.mk_eq + (comb_t $ list_comb (Const (cname, Ts ---> T), frees), + list_comb (f, frees @ reccombs')))], fs) + end + + in fst (Library.foldl (fn (x, ((dt, T), comb_t)) => + Library.foldl (make_primrec T comb_t) (x, #3 (snd dt))) + (([], rec_fns), descr' ~~ recTs ~~ reccombs)) + end; + +(****************** make terms of form t_case f1 ... fn *********************) + +fun make_case_combs new_type_names descr sorts thy fname = + let + val descr' = List.concat descr; + val recTs = get_rec_types descr' sorts; + val used = List.foldr OldTerm.add_typ_tfree_names [] recTs; + val newTs = Library.take (length (hd descr), recTs); + val T' = TFree (Name.variant used "'t", HOLogic.typeS); + + val case_fn_Ts = map (fn (i, (_, _, constrs)) => + map (fn (_, cargs) => + let val Ts = map (typ_of_dtyp descr' sorts) cargs + in Ts ---> T' end) constrs) (hd descr); + + val case_names = map (fn s => + Sign.intern_const thy (s ^ "_case")) new_type_names + in + map (fn ((name, Ts), T) => list_comb + (Const (name, Ts @ [T] ---> T'), + map (uncurry (mk_Free fname)) (Ts ~~ (1 upto length Ts)))) + (case_names ~~ case_fn_Ts ~~ newTs) + end; + +(**************** characteristic equations for case combinator ****************) + +fun make_cases new_type_names descr sorts thy = + let + val descr' = List.concat descr; + val recTs = get_rec_types descr' sorts; + val newTs = Library.take (length (hd descr), recTs); + + fun make_case T comb_t ((cname, cargs), f) = + let + val Ts = map (typ_of_dtyp descr' sorts) cargs; + val frees = map Free ((make_tnames Ts) ~~ Ts) + in HOLogic.mk_Trueprop (HOLogic.mk_eq + (comb_t $ list_comb (Const (cname, Ts ---> T), frees), + list_comb (f, frees))) + end + + in map (fn (((_, (_, _, constrs)), T), comb_t) => + map (make_case T comb_t) (constrs ~~ (snd (strip_comb comb_t)))) + ((hd descr) ~~ newTs ~~ (make_case_combs new_type_names descr sorts thy "f")) + end; + + +(*************************** the "split" - equations **************************) + +fun make_splits new_type_names descr sorts thy = + let + val descr' = List.concat descr; + val recTs = get_rec_types descr' sorts; + val used' = List.foldr OldTerm.add_typ_tfree_names [] recTs; + val newTs = Library.take (length (hd descr), recTs); + val T' = TFree (Name.variant used' "'t", HOLogic.typeS); + val P = Free ("P", T' --> HOLogic.boolT); + + fun make_split (((_, (_, _, constrs)), T), comb_t) = + let + val (_, fs) = strip_comb comb_t; + val used = ["P", "x"] @ (map (fst o dest_Free) fs); + + fun process_constr (((cname, cargs), f), (t1s, t2s)) = + let + val Ts = map (typ_of_dtyp descr' sorts) cargs; + val frees = map Free (Name.variant_list used (make_tnames Ts) ~~ Ts); + val eqn = HOLogic.mk_eq (Free ("x", T), + list_comb (Const (cname, Ts ---> T), frees)); + val P' = P $ list_comb (f, frees) + in ((List.foldr (fn (Free (s, T), t) => HOLogic.mk_all (s, T, t)) + (HOLogic.imp $ eqn $ P') frees)::t1s, + (List.foldr (fn (Free (s, T), t) => HOLogic.mk_exists (s, T, t)) + (HOLogic.conj $ eqn $ (HOLogic.Not $ P')) frees)::t2s) + end; + + val (t1s, t2s) = List.foldr process_constr ([], []) (constrs ~~ fs); + val lhs = P $ (comb_t $ Free ("x", T)) + in + (HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, mk_conj t1s)), + HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, HOLogic.Not $ mk_disj t2s))) + end + + in map make_split ((hd descr) ~~ newTs ~~ + (make_case_combs new_type_names descr sorts thy "f")) + end; + +(************************* additional rules for TFL ***************************) + +fun make_weak_case_congs new_type_names descr sorts thy = + let + val case_combs = make_case_combs new_type_names descr sorts thy "f"; + + fun mk_case_cong comb = + let + val Type ("fun", [T, _]) = fastype_of comb; + val M = Free ("M", T); + val M' = Free ("M'", T); + in + Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (M, M')), + HOLogic.mk_Trueprop (HOLogic.mk_eq (comb $ M, comb $ M'))) + end + in + map mk_case_cong case_combs + end; + + +(*--------------------------------------------------------------------------- + * Structure of case congruence theorem looks like this: + * + * (M = M') + * ==> (!!x1,...,xk. (M' = C1 x1..xk) ==> (f1 x1..xk = g1 x1..xk)) + * ==> ... + * ==> (!!x1,...,xj. (M' = Cn x1..xj) ==> (fn x1..xj = gn x1..xj)) + * ==> + * (ty_case f1..fn M = ty_case g1..gn M') + *---------------------------------------------------------------------------*) + +fun make_case_congs new_type_names descr sorts thy = + let + val case_combs = make_case_combs new_type_names descr sorts thy "f"; + val case_combs' = make_case_combs new_type_names descr sorts thy "g"; + + fun mk_case_cong ((comb, comb'), (_, (_, _, constrs))) = + let + val Type ("fun", [T, _]) = fastype_of comb; + val (_, fs) = strip_comb comb; + val (_, gs) = strip_comb comb'; + val used = ["M", "M'"] @ map (fst o dest_Free) (fs @ gs); + val M = Free ("M", T); + val M' = Free ("M'", T); + + fun mk_clause ((f, g), (cname, _)) = + let + val (Ts, _) = strip_type (fastype_of f); + val tnames = Name.variant_list used (make_tnames Ts); + val frees = map Free (tnames ~~ Ts) + in + list_all_free (tnames ~~ Ts, Logic.mk_implies + (HOLogic.mk_Trueprop + (HOLogic.mk_eq (M', list_comb (Const (cname, Ts ---> T), frees))), + HOLogic.mk_Trueprop + (HOLogic.mk_eq (list_comb (f, frees), list_comb (g, frees))))) + end + + in + Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (M, M')) :: + map mk_clause (fs ~~ gs ~~ constrs), + HOLogic.mk_Trueprop (HOLogic.mk_eq (comb $ M, comb' $ M'))) + end + + in + map mk_case_cong (case_combs ~~ case_combs' ~~ hd descr) + end; + +(*--------------------------------------------------------------------------- + * Structure of exhaustion theorem looks like this: + * + * !v. (? y1..yi. v = C1 y1..yi) | ... | (? y1..yj. v = Cn y1..yj) + *---------------------------------------------------------------------------*) + +fun make_nchotomys descr sorts = + let + val descr' = List.concat descr; + val recTs = get_rec_types descr' sorts; + val newTs = Library.take (length (hd descr), recTs); + + fun mk_eqn T (cname, cargs) = + let + val Ts = map (typ_of_dtyp descr' sorts) cargs; + val tnames = Name.variant_list ["v"] (make_tnames Ts); + val frees = tnames ~~ Ts + in + List.foldr (fn ((s, T'), t) => HOLogic.mk_exists (s, T', t)) + (HOLogic.mk_eq (Free ("v", T), + list_comb (Const (cname, Ts ---> T), map Free frees))) frees + end + + in map (fn ((_, (_, _, constrs)), T) => + HOLogic.mk_Trueprop (HOLogic.mk_all ("v", T, mk_disj (map (mk_eqn T) constrs)))) + (hd descr ~~ newTs) + end; + +end; diff -r fa30cd74d7d6 -r eb2f9d709296 src/HOL/Tools/datatype_package/datatype_realizer.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Tools/datatype_package/datatype_realizer.ML Wed Jun 10 15:04:33 2009 +0200 @@ -0,0 +1,230 @@ +(* Title: HOL/Tools/datatype_realizer.ML + Author: Stefan Berghofer, TU Muenchen + +Porgram extraction from proofs involving datatypes: +Realizers for induction and case analysis +*) + +signature DATATYPE_REALIZER = +sig + val add_dt_realizers: string list -> theory -> theory + val setup: theory -> theory +end; + +structure DatatypeRealizer : DATATYPE_REALIZER = +struct + +open DatatypeAux; + +fun subsets i j = if i <= j then + let val is = subsets (i+1) j + in map (fn ks => i::ks) is @ is end + else [[]]; + +fun forall_intr_prf (t, prf) = + let val (a, T) = (case t of Var ((a, _), T) => (a, T) | Free p => p) + in Abst (a, SOME T, Proofterm.prf_abstract_over t prf) end; + +fun prf_of thm = + Reconstruct.reconstruct_proof (Thm.theory_of_thm thm) (Thm.prop_of thm) (Thm.proof_of thm); + +fun prf_subst_vars inst = + Proofterm.map_proof_terms (subst_vars ([], inst)) I; + +fun is_unit t = snd (strip_type (fastype_of t)) = HOLogic.unitT; + +fun tname_of (Type (s, _)) = s + | tname_of _ = ""; + +fun mk_realizes T = Const ("realizes", T --> HOLogic.boolT --> HOLogic.boolT); + +fun make_ind sorts ({descr, rec_names, rec_rewrites, induction, ...} : datatype_info) is thy = + let + val recTs = get_rec_types descr sorts; + val pnames = if length descr = 1 then ["P"] + else map (fn i => "P" ^ string_of_int i) (1 upto length descr); + + val rec_result_Ts = map (fn ((i, _), P) => + if i mem is then TFree ("'" ^ P, HOLogic.typeS) else HOLogic.unitT) + (descr ~~ pnames); + + fun make_pred i T U r x = + if i mem is then + Free (List.nth (pnames, i), T --> U --> HOLogic.boolT) $ r $ x + else Free (List.nth (pnames, i), U --> HOLogic.boolT) $ x; + + fun mk_all i s T t = + if i mem is then list_all_free ([(s, T)], t) else t; + + val (prems, rec_fns) = split_list (flat (fst (fold_map + (fn ((i, (_, _, constrs)), T) => fold_map (fn (cname, cargs) => fn j => + let + val Ts = map (typ_of_dtyp descr sorts) cargs; + val tnames = Name.variant_list pnames (DatatypeProp.make_tnames Ts); + val recs = filter (is_rec_type o fst o fst) (cargs ~~ tnames ~~ Ts); + val frees = tnames ~~ Ts; + + fun mk_prems vs [] = + let + val rT = nth (rec_result_Ts) i; + val vs' = filter_out is_unit vs; + val f = mk_Free "f" (map fastype_of vs' ---> rT) j; + val f' = Envir.eta_contract (list_abs_free + (map dest_Free vs, if i mem is then list_comb (f, vs') + else HOLogic.unit)); + in (HOLogic.mk_Trueprop (make_pred i rT T (list_comb (f, vs')) + (list_comb (Const (cname, Ts ---> T), map Free frees))), f') + end + | mk_prems vs (((dt, s), T) :: ds) = + let + val k = body_index dt; + val (Us, U) = strip_type T; + val i = length Us; + val rT = nth (rec_result_Ts) k; + val r = Free ("r" ^ s, Us ---> rT); + val (p, f) = mk_prems (vs @ [r]) ds + in (mk_all k ("r" ^ s) (Us ---> rT) (Logic.mk_implies + (list_all (map (pair "x") Us, HOLogic.mk_Trueprop + (make_pred k rT U (app_bnds r i) + (app_bnds (Free (s, T)) i))), p)), f) + end + + in (apfst (curry list_all_free frees) (mk_prems (map Free frees) recs), j + 1) end) + constrs) (descr ~~ recTs) 1))); + + fun mk_proj j [] t = t + | mk_proj j (i :: is) t = if null is then t else + if (j: int) = i then HOLogic.mk_fst t + else mk_proj j is (HOLogic.mk_snd t); + + val tnames = DatatypeProp.make_tnames recTs; + val fTs = map fastype_of rec_fns; + val ps = map (fn ((((i, _), T), U), s) => Abs ("x", T, make_pred i U T + (list_comb (Const (s, fTs ---> T --> U), rec_fns) $ Bound 0) (Bound 0))) + (descr ~~ recTs ~~ rec_result_Ts ~~ rec_names); + val r = if null is then Extraction.nullt else + foldr1 HOLogic.mk_prod (List.mapPartial (fn (((((i, _), T), U), s), tname) => + if i mem is then SOME + (list_comb (Const (s, fTs ---> T --> U), rec_fns) $ Free (tname, T)) + else NONE) (descr ~~ recTs ~~ rec_result_Ts ~~ rec_names ~~ tnames)); + val concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &") + (map (fn ((((i, _), T), U), tname) => + make_pred i U T (mk_proj i is r) (Free (tname, T))) + (descr ~~ recTs ~~ rec_result_Ts ~~ tnames))); + val cert = cterm_of thy; + val inst = map (pairself cert) (map head_of (HOLogic.dest_conj + (HOLogic.dest_Trueprop (concl_of induction))) ~~ ps); + + val thm = OldGoals.simple_prove_goal_cterm (cert (Logic.list_implies (prems, concl))) + (fn prems => + [rewrite_goals_tac (map mk_meta_eq [fst_conv, snd_conv]), + rtac (cterm_instantiate inst induction) 1, + ALLGOALS ObjectLogic.atomize_prems_tac, + rewrite_goals_tac (@{thm o_def} :: map mk_meta_eq rec_rewrites), + REPEAT ((resolve_tac prems THEN_ALL_NEW (fn i => + REPEAT (etac allE i) THEN atac i)) 1)]); + + val ind_name = Thm.get_name induction; + val vs = map (fn i => List.nth (pnames, i)) is; + val (thm', thy') = thy + |> Sign.root_path + |> PureThy.store_thm + (Binding.qualified_name (space_implode "_" (ind_name :: vs @ ["correctness"])), thm) + ||> Sign.restore_naming thy; + + val ivs = rev (Term.add_vars (Logic.varify (DatatypeProp.make_ind [descr] sorts)) []); + val rvs = rev (Thm.fold_terms Term.add_vars thm' []); + val ivs1 = map Var (filter_out (fn (_, T) => + tname_of (body_type T) mem ["set", "bool"]) ivs); + val ivs2 = map (fn (ixn, _) => Var (ixn, valOf (AList.lookup (op =) rvs ixn))) ivs; + + val prf = List.foldr forall_intr_prf + (List.foldr (fn ((f, p), prf) => + (case head_of (strip_abs_body f) of + Free (s, T) => + let val T' = Logic.varifyT T + in Abst (s, SOME T', Proofterm.prf_abstract_over + (Var ((s, 0), T')) (AbsP ("H", SOME p, prf))) + end + | _ => AbsP ("H", SOME p, prf))) + (Proofterm.proof_combP + (prf_of thm', map PBound (length prems - 1 downto 0))) (rec_fns ~~ prems_of thm)) ivs2; + + val r' = if null is then r else Logic.varify (List.foldr (uncurry lambda) + r (map Logic.unvarify ivs1 @ filter_out is_unit + (map (head_of o strip_abs_body) rec_fns))); + + in Extraction.add_realizers_i [(ind_name, (vs, r', prf))] thy' end; + + +fun make_casedists sorts ({index, descr, case_name, case_rewrites, exhaustion, ...} : datatype_info) thy = + let + val cert = cterm_of thy; + val rT = TFree ("'P", HOLogic.typeS); + val rT' = TVar (("'P", 0), HOLogic.typeS); + + fun make_casedist_prem T (cname, cargs) = + let + val Ts = map (typ_of_dtyp descr sorts) cargs; + val frees = Name.variant_list ["P", "y"] (DatatypeProp.make_tnames Ts) ~~ Ts; + val free_ts = map Free frees; + val r = Free ("r" ^ Long_Name.base_name cname, Ts ---> rT) + in (r, list_all_free (frees, Logic.mk_implies (HOLogic.mk_Trueprop + (HOLogic.mk_eq (Free ("y", T), list_comb (Const (cname, Ts ---> T), free_ts))), + HOLogic.mk_Trueprop (Free ("P", rT --> HOLogic.boolT) $ + list_comb (r, free_ts))))) + end; + + val SOME (_, _, constrs) = AList.lookup (op =) descr index; + val T = List.nth (get_rec_types descr sorts, index); + val (rs, prems) = split_list (map (make_casedist_prem T) constrs); + val r = Const (case_name, map fastype_of rs ---> T --> rT); + + val y = Var (("y", 0), Logic.legacy_varifyT T); + val y' = Free ("y", T); + + val thm = OldGoals.prove_goalw_cterm [] (cert (Logic.list_implies (prems, + HOLogic.mk_Trueprop (Free ("P", rT --> HOLogic.boolT) $ + list_comb (r, rs @ [y']))))) + (fn prems => + [rtac (cterm_instantiate [(cert y, cert y')] exhaustion) 1, + ALLGOALS (EVERY' + [asm_simp_tac (HOL_basic_ss addsimps case_rewrites), + resolve_tac prems, asm_simp_tac HOL_basic_ss])]); + + val exh_name = Thm.get_name exhaustion; + val (thm', thy') = thy + |> Sign.root_path + |> PureThy.store_thm (Binding.qualified_name (exh_name ^ "_P_correctness"), thm) + ||> Sign.restore_naming thy; + + val P = Var (("P", 0), rT' --> HOLogic.boolT); + val prf = forall_intr_prf (y, forall_intr_prf (P, + List.foldr (fn ((p, r), prf) => + forall_intr_prf (Logic.legacy_varify r, AbsP ("H", SOME (Logic.varify p), + prf))) (Proofterm.proof_combP (prf_of thm', + map PBound (length prems - 1 downto 0))) (prems ~~ rs))); + val r' = Logic.legacy_varify (Abs ("y", Logic.legacy_varifyT T, + list_abs (map dest_Free rs, list_comb (r, + map Bound ((length rs - 1 downto 0) @ [length rs]))))); + + in Extraction.add_realizers_i + [(exh_name, (["P"], r', prf)), + (exh_name, ([], Extraction.nullt, prf_of exhaustion))] thy' + end; + +fun add_dt_realizers names thy = + if ! Proofterm.proofs < 2 then thy + else let + val _ = message "Adding realizers for induction and case analysis ..." + val infos = map (DatatypePackage.the_datatype thy) names; + val info :: _ = infos; + in + thy + |> fold_rev (make_ind (#sorts info) info) (subsets 0 (length (#descr info) - 1)) + |> fold_rev (make_casedists (#sorts info)) infos + end; + +val setup = DatatypePackage.interpretation add_dt_realizers; + +end; diff -r fa30cd74d7d6 -r eb2f9d709296 src/HOL/Tools/datatype_package/datatype_rep_proofs.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Tools/datatype_package/datatype_rep_proofs.ML Wed Jun 10 15:04:33 2009 +0200 @@ -0,0 +1,642 @@ +(* Title: HOL/Tools/datatype_rep_proofs.ML + Author: Stefan Berghofer, TU Muenchen + +Definitional introduction of datatypes +Proof of characteristic theorems: + + - injectivity of constructors + - distinctness of constructors + - induction theorem +*) + +signature DATATYPE_REP_PROOFS = +sig + val distinctness_limit : int Config.T + val distinctness_limit_setup : theory -> theory + val representation_proofs : bool -> DatatypeAux.datatype_info Symtab.table -> + string list -> DatatypeAux.descr list -> (string * sort) list -> + (binding * mixfix) list -> (binding * mixfix) list list -> attribute + -> theory -> (thm list list * thm list list * thm list list * + DatatypeAux.simproc_dist list * thm) * theory +end; + +structure DatatypeRepProofs : DATATYPE_REP_PROOFS = +struct + +open DatatypeAux; + +(*the kind of distinctiveness axioms depends on number of constructors*) +val (distinctness_limit, distinctness_limit_setup) = + Attrib.config_int "datatype_distinctness_limit" 7; + +val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma); + +val collect_simp = rewrite_rule [mk_meta_eq mem_Collect_eq]; + + +(** theory context references **) + +val f_myinv_f = thm "f_myinv_f"; +val myinv_f_f = thm "myinv_f_f"; + + +fun exh_thm_of (dt_info : datatype_info Symtab.table) tname = + #exhaustion (the (Symtab.lookup dt_info tname)); + +(******************************************************************************) + +fun representation_proofs flat_names (dt_info : datatype_info Symtab.table) + new_type_names descr sorts types_syntax constr_syntax case_names_induct thy = + let + val Datatype_thy = ThyInfo.the_theory "Datatype" thy; + val node_name = "Datatype.node"; + val In0_name = "Datatype.In0"; + val In1_name = "Datatype.In1"; + val Scons_name = "Datatype.Scons"; + val Leaf_name = "Datatype.Leaf"; + val Numb_name = "Datatype.Numb"; + val Lim_name = "Datatype.Lim"; + val Suml_name = "Datatype.Suml"; + val Sumr_name = "Datatype.Sumr"; + + val [In0_inject, In1_inject, Scons_inject, Leaf_inject, + In0_eq, In1_eq, In0_not_In1, In1_not_In0, + Lim_inject, Suml_inject, Sumr_inject] = map (PureThy.get_thm Datatype_thy) + ["In0_inject", "In1_inject", "Scons_inject", "Leaf_inject", + "In0_eq", "In1_eq", "In0_not_In1", "In1_not_In0", + "Lim_inject", "Suml_inject", "Sumr_inject"]; + + val descr' = flat descr; + + val big_name = space_implode "_" new_type_names; + val thy1 = add_path flat_names big_name thy; + val big_rec_name = big_name ^ "_rep_set"; + val rep_set_names' = + (if length descr' = 1 then [big_rec_name] else + (map ((curry (op ^) (big_rec_name ^ "_")) o string_of_int) + (1 upto (length descr')))); + val rep_set_names = map (Sign.full_bname thy1) rep_set_names'; + + val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr); + val leafTs' = get_nonrec_types descr' sorts; + val branchTs = get_branching_types descr' sorts; + val branchT = if null branchTs then HOLogic.unitT + else BalancedTree.make (fn (T, U) => Type ("+", [T, U])) branchTs; + val arities = get_arities descr' \ 0; + val unneeded_vars = hd tyvars \\ List.foldr OldTerm.add_typ_tfree_names [] (leafTs' @ branchTs); + val leafTs = leafTs' @ (map (fn n => TFree (n, (the o AList.lookup (op =) sorts) n)) unneeded_vars); + val recTs = get_rec_types descr' sorts; + val newTs = Library.take (length (hd descr), recTs); + val oldTs = Library.drop (length (hd descr), recTs); + val sumT = if null leafTs then HOLogic.unitT + else BalancedTree.make (fn (T, U) => Type ("+", [T, U])) leafTs; + val Univ_elT = HOLogic.mk_setT (Type (node_name, [sumT, branchT])); + val UnivT = HOLogic.mk_setT Univ_elT; + val UnivT' = Univ_elT --> HOLogic.boolT; + val Collect = Const ("Collect", UnivT' --> UnivT); + + val In0 = Const (In0_name, Univ_elT --> Univ_elT); + val In1 = Const (In1_name, Univ_elT --> Univ_elT); + val Leaf = Const (Leaf_name, sumT --> Univ_elT); + val Lim = Const (Lim_name, (branchT --> Univ_elT) --> Univ_elT); + + (* make injections needed for embedding types in leaves *) + + fun mk_inj T' x = + let + fun mk_inj' T n i = + if n = 1 then x else + let val n2 = n div 2; + val Type (_, [T1, T2]) = T + in + if i <= n2 then + Const ("Sum_Type.Inl", T1 --> T) $ (mk_inj' T1 n2 i) + else + Const ("Sum_Type.Inr", T2 --> T) $ (mk_inj' T2 (n - n2) (i - n2)) + end + in mk_inj' sumT (length leafTs) (1 + find_index_eq T' leafTs) + end; + + (* make injections for constructors *) + + fun mk_univ_inj ts = BalancedTree.access + {left = fn t => In0 $ t, + right = fn t => In1 $ t, + init = + if ts = [] then Const (@{const_name undefined}, Univ_elT) + else foldr1 (HOLogic.mk_binop Scons_name) ts}; + + (* function spaces *) + + fun mk_fun_inj T' x = + let + fun mk_inj T n i = + if n = 1 then x else + let + val n2 = n div 2; + val Type (_, [T1, T2]) = T; + fun mkT U = (U --> Univ_elT) --> T --> Univ_elT + in + if i <= n2 then Const (Suml_name, mkT T1) $ mk_inj T1 n2 i + else Const (Sumr_name, mkT T2) $ mk_inj T2 (n - n2) (i - n2) + end + in mk_inj branchT (length branchTs) (1 + find_index_eq T' branchTs) + end; + + val mk_lim = List.foldr (fn (T, t) => Lim $ mk_fun_inj T (Abs ("x", T, t))); + + (************** generate introduction rules for representing set **********) + + val _ = message "Constructing representing sets ..."; + + (* make introduction rule for a single constructor *) + + fun make_intr s n (i, (_, cargs)) = + let + fun mk_prem (dt, (j, prems, ts)) = (case strip_dtyp dt of + (dts, DtRec k) => + let + val Ts = map (typ_of_dtyp descr' sorts) dts; + val free_t = + app_bnds (mk_Free "x" (Ts ---> Univ_elT) j) (length Ts) + in (j + 1, list_all (map (pair "x") Ts, + HOLogic.mk_Trueprop + (Free (List.nth (rep_set_names', k), UnivT') $ free_t)) :: prems, + mk_lim free_t Ts :: ts) + end + | _ => + let val T = typ_of_dtyp descr' sorts dt + in (j + 1, prems, (Leaf $ mk_inj T (mk_Free "x" T j))::ts) + end); + + val (_, prems, ts) = List.foldr mk_prem (1, [], []) cargs; + val concl = HOLogic.mk_Trueprop + (Free (s, UnivT') $ mk_univ_inj ts n i) + in Logic.list_implies (prems, concl) + end; + + val intr_ts = maps (fn ((_, (_, _, constrs)), rep_set_name) => + map (make_intr rep_set_name (length constrs)) + ((1 upto (length constrs)) ~~ constrs)) (descr' ~~ rep_set_names'); + + val ({raw_induct = rep_induct, intrs = rep_intrs, ...}, thy2) = + InductivePackage.add_inductive_global (serial_string ()) + {quiet_mode = ! quiet_mode, verbose = false, kind = Thm.internalK, + alt_name = Binding.name big_rec_name, coind = false, no_elim = true, no_ind = false, + skip_mono = true, fork_mono = false} + (map (fn s => ((Binding.name s, UnivT'), NoSyn)) rep_set_names') [] + (map (fn x => (Attrib.empty_binding, x)) intr_ts) [] thy1; + + (********************************* typedef ********************************) + + val (typedefs, thy3) = thy2 |> + parent_path flat_names |> + fold_map (fn ((((name, mx), tvs), c), name') => + TypedefPackage.add_typedef false (SOME (Binding.name name')) (name, tvs, mx) + (Collect $ Const (c, UnivT')) NONE + (rtac exI 1 THEN rtac CollectI 1 THEN + QUIET_BREADTH_FIRST (has_fewer_prems 1) + (resolve_tac rep_intrs 1))) + (types_syntax ~~ tyvars ~~ + (Library.take (length newTs, rep_set_names)) ~~ new_type_names) ||> + add_path flat_names big_name; + + (*********************** definition of constructors ***********************) + + val big_rep_name = (space_implode "_" new_type_names) ^ "_Rep_"; + val rep_names = map (curry op ^ "Rep_") new_type_names; + val rep_names' = map (fn i => big_rep_name ^ (string_of_int i)) + (1 upto (length (flat (tl descr)))); + val all_rep_names = map (Sign.intern_const thy3) rep_names @ + map (Sign.full_bname thy3) rep_names'; + + (* isomorphism declarations *) + + val iso_decls = map (fn (T, s) => (Binding.name s, T --> Univ_elT, NoSyn)) + (oldTs ~~ rep_names'); + + (* constructor definitions *) + + fun make_constr_def tname T n ((thy, defs, eqns, i), ((cname, cargs), (cname', mx))) = + let + fun constr_arg (dt, (j, l_args, r_args)) = + let val T = typ_of_dtyp descr' sorts dt; + val free_t = mk_Free "x" T j + in (case (strip_dtyp dt, strip_type T) of + ((_, DtRec m), (Us, U)) => (j + 1, free_t :: l_args, mk_lim + (Const (List.nth (all_rep_names, m), U --> Univ_elT) $ + app_bnds free_t (length Us)) Us :: r_args) + | _ => (j + 1, free_t::l_args, (Leaf $ mk_inj T free_t)::r_args)) + end; + + val (_, l_args, r_args) = List.foldr constr_arg (1, [], []) cargs; + val constrT = (map (typ_of_dtyp descr' sorts) cargs) ---> T; + val abs_name = Sign.intern_const thy ("Abs_" ^ tname); + val rep_name = Sign.intern_const thy ("Rep_" ^ tname); + val lhs = list_comb (Const (cname, constrT), l_args); + val rhs = mk_univ_inj r_args n i; + val def = Logic.mk_equals (lhs, Const (abs_name, Univ_elT --> T) $ rhs); + val def_name = Long_Name.base_name cname ^ "_def"; + val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq + (Const (rep_name, T --> Univ_elT) $ lhs, rhs)); + val ([def_thm], thy') = + thy + |> Sign.add_consts_i [(cname', constrT, mx)] + |> (PureThy.add_defs false o map Thm.no_attributes) [(Binding.name def_name, def)]; + + in (thy', defs @ [def_thm], eqns @ [eqn], i + 1) end; + + (* constructor definitions for datatype *) + + fun dt_constr_defs ((thy, defs, eqns, rep_congs, dist_lemmas), + ((((_, (_, _, constrs)), tname), T), constr_syntax)) = + let + val _ $ (_ $ (cong_f $ _) $ _) = concl_of arg_cong; + val rep_const = cterm_of thy + (Const (Sign.intern_const thy ("Rep_" ^ tname), T --> Univ_elT)); + val cong' = standard (cterm_instantiate [(cterm_of thy cong_f, rep_const)] arg_cong); + val dist = standard (cterm_instantiate [(cterm_of thy distinct_f, rep_const)] distinct_lemma); + val (thy', defs', eqns', _) = Library.foldl ((make_constr_def tname T) (length constrs)) + ((add_path flat_names tname thy, defs, [], 1), constrs ~~ constr_syntax) + in + (parent_path flat_names thy', defs', eqns @ [eqns'], + rep_congs @ [cong'], dist_lemmas @ [dist]) + end; + + val (thy4, constr_defs, constr_rep_eqns, rep_congs, dist_lemmas) = Library.foldl dt_constr_defs + ((thy3 |> Sign.add_consts_i iso_decls |> parent_path flat_names, [], [], [], []), + hd descr ~~ new_type_names ~~ newTs ~~ constr_syntax); + + (*********** isomorphisms for new types (introduced by typedef) ***********) + + val _ = message "Proving isomorphism properties ..."; + + val newT_iso_axms = map (fn (_, td) => + (collect_simp (#Abs_inverse td), #Rep_inverse td, + collect_simp (#Rep td))) typedefs; + + val newT_iso_inj_thms = map (fn (_, td) => + (collect_simp (#Abs_inject td) RS iffD1, #Rep_inject td RS iffD1)) typedefs; + + (********* isomorphisms between existing types and "unfolded" types *******) + + (*---------------------------------------------------------------------*) + (* isomorphisms are defined using primrec-combinators: *) + (* generate appropriate functions for instantiating primrec-combinator *) + (* *) + (* e.g. dt_Rep_i = list_rec ... (%h t y. In1 (Scons (Leaf h) y)) *) + (* *) + (* also generate characteristic equations for isomorphisms *) + (* *) + (* e.g. dt_Rep_i (cons h t) = In1 (Scons (dt_Rep_j h) (dt_Rep_i t)) *) + (*---------------------------------------------------------------------*) + + fun make_iso_def k ks n ((fs, eqns, i), (cname, cargs)) = + let + val argTs = map (typ_of_dtyp descr' sorts) cargs; + val T = List.nth (recTs, k); + val rep_name = List.nth (all_rep_names, k); + val rep_const = Const (rep_name, T --> Univ_elT); + val constr = Const (cname, argTs ---> T); + + fun process_arg ks' ((i2, i2', ts, Ts), dt) = + let + val T' = typ_of_dtyp descr' sorts dt; + val (Us, U) = strip_type T' + in (case strip_dtyp dt of + (_, DtRec j) => if j mem ks' then + (i2 + 1, i2' + 1, ts @ [mk_lim (app_bnds + (mk_Free "y" (Us ---> Univ_elT) i2') (length Us)) Us], + Ts @ [Us ---> Univ_elT]) + else + (i2 + 1, i2', ts @ [mk_lim + (Const (List.nth (all_rep_names, j), U --> Univ_elT) $ + app_bnds (mk_Free "x" T' i2) (length Us)) Us], Ts) + | _ => (i2 + 1, i2', ts @ [Leaf $ mk_inj T' (mk_Free "x" T' i2)], Ts)) + end; + + val (i2, i2', ts, Ts) = Library.foldl (process_arg ks) ((1, 1, [], []), cargs); + val xs = map (uncurry (mk_Free "x")) (argTs ~~ (1 upto (i2 - 1))); + val ys = map (uncurry (mk_Free "y")) (Ts ~~ (1 upto (i2' - 1))); + val f = list_abs_free (map dest_Free (xs @ ys), mk_univ_inj ts n i); + + val (_, _, ts', _) = Library.foldl (process_arg []) ((1, 1, [], []), cargs); + val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq + (rep_const $ list_comb (constr, xs), mk_univ_inj ts' n i)) + + in (fs @ [f], eqns @ [eqn], i + 1) end; + + (* define isomorphisms for all mutually recursive datatypes in list ds *) + + fun make_iso_defs (ds, (thy, char_thms)) = + let + val ks = map fst ds; + val (_, (tname, _, _)) = hd ds; + val {rec_rewrites, rec_names, ...} = the (Symtab.lookup dt_info tname); + + fun process_dt ((fs, eqns, isos), (k, (tname, _, constrs))) = + let + val (fs', eqns', _) = Library.foldl (make_iso_def k ks (length constrs)) + ((fs, eqns, 1), constrs); + val iso = (List.nth (recTs, k), List.nth (all_rep_names, k)) + in (fs', eqns', isos @ [iso]) end; + + val (fs, eqns, isos) = Library.foldl process_dt (([], [], []), ds); + val fTs = map fastype_of fs; + val defs = map (fn (rec_name, (T, iso_name)) => (Binding.name (Long_Name.base_name iso_name ^ "_def"), + Logic.mk_equals (Const (iso_name, T --> Univ_elT), + list_comb (Const (rec_name, fTs @ [T] ---> Univ_elT), fs)))) (rec_names ~~ isos); + val (def_thms, thy') = + apsnd Theory.checkpoint ((PureThy.add_defs false o map Thm.no_attributes) defs thy); + + (* prove characteristic equations *) + + val rewrites = def_thms @ (map mk_meta_eq rec_rewrites); + val char_thms' = map (fn eqn => SkipProof.prove_global thy' [] [] eqn + (fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1])) eqns; + + in (thy', char_thms' @ char_thms) end; + + val (thy5, iso_char_thms) = apfst Theory.checkpoint (List.foldr make_iso_defs + (add_path flat_names big_name thy4, []) (tl descr)); + + (* prove isomorphism properties *) + + fun mk_funs_inv thy thm = + let + val prop = Thm.prop_of thm; + val _ $ (_ $ ((S as Const (_, Type (_, [U, _]))) $ _ )) $ + (_ $ (_ $ (r $ (a $ _)) $ _)) = Type.freeze prop; + val used = OldTerm.add_term_tfree_names (a, []); + + fun mk_thm i = + let + val Ts = map (TFree o rpair HOLogic.typeS) + (Name.variant_list used (replicate i "'t")); + val f = Free ("f", Ts ---> U) + in SkipProof.prove_global thy [] [] (Logic.mk_implies + (HOLogic.mk_Trueprop (HOLogic.list_all + (map (pair "x") Ts, S $ app_bnds f i)), + HOLogic.mk_Trueprop (HOLogic.mk_eq (list_abs (map (pair "x") Ts, + r $ (a $ app_bnds f i)), f)))) + (fn _ => EVERY [REPEAT_DETERM_N i (rtac ext 1), + REPEAT (etac allE 1), rtac thm 1, atac 1]) + end + in map (fn r => r RS subst) (thm :: map mk_thm arities) end; + + (* prove inj dt_Rep_i and dt_Rep_i x : dt_rep_set_i *) + + val fun_congs = map (fn T => make_elim (Drule.instantiate' + [SOME (ctyp_of thy5 T)] [] fun_cong)) branchTs; + + fun prove_iso_thms (ds, (inj_thms, elem_thms)) = + let + val (_, (tname, _, _)) = hd ds; + val {induction, ...} = the (Symtab.lookup dt_info tname); + + fun mk_ind_concl (i, _) = + let + val T = List.nth (recTs, i); + val Rep_t = Const (List.nth (all_rep_names, i), T --> Univ_elT); + val rep_set_name = List.nth (rep_set_names, i) + in (HOLogic.all_const T $ Abs ("y", T, HOLogic.imp $ + HOLogic.mk_eq (Rep_t $ mk_Free "x" T i, Rep_t $ Bound 0) $ + HOLogic.mk_eq (mk_Free "x" T i, Bound 0)), + Const (rep_set_name, UnivT') $ (Rep_t $ mk_Free "x" T i)) + end; + + val (ind_concl1, ind_concl2) = ListPair.unzip (map mk_ind_concl ds); + + val rewrites = map mk_meta_eq iso_char_thms; + val inj_thms' = map snd newT_iso_inj_thms @ + map (fn r => r RS @{thm injD}) inj_thms; + + val inj_thm = SkipProof.prove_global thy5 [] [] + (HOLogic.mk_Trueprop (mk_conj ind_concl1)) (fn _ => EVERY + [(indtac induction [] THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1, + REPEAT (EVERY + [rtac allI 1, rtac impI 1, + exh_tac (exh_thm_of dt_info) 1, + REPEAT (EVERY + [hyp_subst_tac 1, + rewrite_goals_tac rewrites, + REPEAT (dresolve_tac [In0_inject, In1_inject] 1), + (eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1) + ORELSE (EVERY + [REPEAT (eresolve_tac (Scons_inject :: + map make_elim [Leaf_inject, Inl_inject, Inr_inject]) 1), + REPEAT (cong_tac 1), rtac refl 1, + REPEAT (atac 1 ORELSE (EVERY + [REPEAT (rtac ext 1), + REPEAT (eresolve_tac (mp :: allE :: + map make_elim (Suml_inject :: Sumr_inject :: + Lim_inject :: inj_thms') @ fun_congs) 1), + atac 1]))])])])]); + + val inj_thms'' = map (fn r => r RS @{thm datatype_injI}) + (split_conj_thm inj_thm); + + val elem_thm = + SkipProof.prove_global thy5 [] [] (HOLogic.mk_Trueprop (mk_conj ind_concl2)) + (fn _ => + EVERY [(indtac induction [] THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1, + rewrite_goals_tac rewrites, + REPEAT ((resolve_tac rep_intrs THEN_ALL_NEW + ((REPEAT o etac allE) THEN' ares_tac elem_thms)) 1)]); + + in (inj_thms'' @ inj_thms, elem_thms @ (split_conj_thm elem_thm)) + end; + + val (iso_inj_thms_unfolded, iso_elem_thms) = List.foldr prove_iso_thms + ([], map #3 newT_iso_axms) (tl descr); + val iso_inj_thms = map snd newT_iso_inj_thms @ + map (fn r => r RS @{thm injD}) iso_inj_thms_unfolded; + + (* prove dt_rep_set_i x --> x : range dt_Rep_i *) + + fun mk_iso_t (((set_name, iso_name), i), T) = + let val isoT = T --> Univ_elT + in HOLogic.imp $ + (Const (set_name, UnivT') $ mk_Free "x" Univ_elT i) $ + (if i < length newTs then Const ("True", HOLogic.boolT) + else HOLogic.mk_mem (mk_Free "x" Univ_elT i, + Const ("image", [isoT, HOLogic.mk_setT T] ---> UnivT) $ + Const (iso_name, isoT) $ Const (@{const_name UNIV}, HOLogic.mk_setT T))) + end; + + val iso_t = HOLogic.mk_Trueprop (mk_conj (map mk_iso_t + (rep_set_names ~~ all_rep_names ~~ (0 upto (length descr' - 1)) ~~ recTs))); + + (* all the theorems are proved by one single simultaneous induction *) + + val range_eqs = map (fn r => mk_meta_eq (r RS @{thm range_ex1_eq})) + iso_inj_thms_unfolded; + + val iso_thms = if length descr = 1 then [] else + Library.drop (length newTs, split_conj_thm + (SkipProof.prove_global thy5 [] [] iso_t (fn _ => EVERY + [(indtac rep_induct [] THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1, + REPEAT (rtac TrueI 1), + rewrite_goals_tac (mk_meta_eq choice_eq :: + symmetric (mk_meta_eq @{thm expand_fun_eq}) :: range_eqs), + rewrite_goals_tac (map symmetric range_eqs), + REPEAT (EVERY + [REPEAT (eresolve_tac ([rangeE, ex1_implies_ex RS exE] @ + maps (mk_funs_inv thy5 o #1) newT_iso_axms) 1), + TRY (hyp_subst_tac 1), + rtac (sym RS range_eqI) 1, + resolve_tac iso_char_thms 1])]))); + + val Abs_inverse_thms' = + map #1 newT_iso_axms @ + map2 (fn r_inj => fn r => f_myinv_f OF [r_inj, r RS mp]) + iso_inj_thms_unfolded iso_thms; + + val Abs_inverse_thms = maps (mk_funs_inv thy5) Abs_inverse_thms'; + + (******************* freeness theorems for constructors *******************) + + val _ = message "Proving freeness of constructors ..."; + + (* prove theorem Rep_i (Constr_j ...) = Inj_j ... *) + + fun prove_constr_rep_thm eqn = + let + val inj_thms = map fst newT_iso_inj_thms; + val rewrites = @{thm o_def} :: constr_defs @ (map (mk_meta_eq o #2) newT_iso_axms) + in SkipProof.prove_global thy5 [] [] eqn (fn _ => EVERY + [resolve_tac inj_thms 1, + rewrite_goals_tac rewrites, + rtac refl 3, + resolve_tac rep_intrs 2, + REPEAT (resolve_tac iso_elem_thms 1)]) + end; + + (*--------------------------------------------------------------*) + (* constr_rep_thms and rep_congs are used to prove distinctness *) + (* of constructors. *) + (*--------------------------------------------------------------*) + + val constr_rep_thms = map (map prove_constr_rep_thm) constr_rep_eqns; + + val dist_rewrites = map (fn (rep_thms, dist_lemma) => + dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0])) + (constr_rep_thms ~~ dist_lemmas); + + fun prove_distinct_thms _ _ (_, []) = [] + | prove_distinct_thms lim dist_rewrites' (k, ts as _ :: _) = + if k >= lim then [] else let + (*number of constructors < distinctness_limit : C_i ... ~= C_j ...*) + fun prove [] = [] + | prove (t :: ts) = + let + val dist_thm = SkipProof.prove_global thy5 [] [] t (fn _ => + EVERY [simp_tac (HOL_ss addsimps dist_rewrites') 1]) + in dist_thm :: standard (dist_thm RS not_sym) :: prove ts end; + in prove ts end; + + val distinct_thms = DatatypeProp.make_distincts descr sorts + |> map2 (prove_distinct_thms + (Config.get_thy thy5 distinctness_limit)) dist_rewrites; + + val simproc_dists = map (fn ((((_, (_, _, constrs)), rep_thms), congr), dists) => + if length constrs < Config.get_thy thy5 distinctness_limit + then FewConstrs dists + else ManyConstrs (congr, HOL_basic_ss addsimps rep_thms)) (hd descr ~~ + constr_rep_thms ~~ rep_congs ~~ distinct_thms); + + (* prove injectivity of constructors *) + + fun prove_constr_inj_thm rep_thms t = + let val inj_thms = Scons_inject :: (map make_elim + (iso_inj_thms @ + [In0_inject, In1_inject, Leaf_inject, Inl_inject, Inr_inject, + Lim_inject, Suml_inject, Sumr_inject])) + in SkipProof.prove_global thy5 [] [] t (fn _ => EVERY + [rtac iffI 1, + REPEAT (etac conjE 2), hyp_subst_tac 2, rtac refl 2, + dresolve_tac rep_congs 1, dtac box_equals 1, + REPEAT (resolve_tac rep_thms 1), + REPEAT (eresolve_tac inj_thms 1), + REPEAT (ares_tac [conjI] 1 ORELSE (EVERY [REPEAT (rtac ext 1), + REPEAT (eresolve_tac (make_elim fun_cong :: inj_thms) 1), + atac 1]))]) + end; + + val constr_inject = map (fn (ts, thms) => map (prove_constr_inj_thm thms) ts) + ((DatatypeProp.make_injs descr sorts) ~~ constr_rep_thms); + + val ((constr_inject', distinct_thms'), thy6) = + thy5 + |> parent_path flat_names + |> store_thmss "inject" new_type_names constr_inject + ||>> store_thmss "distinct" new_type_names distinct_thms; + + (*************************** induction theorem ****************************) + + val _ = message "Proving induction rule for datatypes ..."; + + val Rep_inverse_thms = (map (fn (_, iso, _) => iso RS subst) newT_iso_axms) @ + (map (fn r => r RS myinv_f_f RS subst) iso_inj_thms_unfolded); + val Rep_inverse_thms' = map (fn r => r RS myinv_f_f) iso_inj_thms_unfolded; + + fun mk_indrule_lemma ((prems, concls), ((i, _), T)) = + let + val Rep_t = Const (List.nth (all_rep_names, i), T --> Univ_elT) $ + mk_Free "x" T i; + + val Abs_t = if i < length newTs then + Const (Sign.intern_const thy6 + ("Abs_" ^ (List.nth (new_type_names, i))), Univ_elT --> T) + else Const ("Inductive.myinv", [T --> Univ_elT, Univ_elT] ---> T) $ + Const (List.nth (all_rep_names, i), T --> Univ_elT) + + in (prems @ [HOLogic.imp $ + (Const (List.nth (rep_set_names, i), UnivT') $ Rep_t) $ + (mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))], + concls @ [mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ mk_Free "x" T i]) + end; + + val (indrule_lemma_prems, indrule_lemma_concls) = + Library.foldl mk_indrule_lemma (([], []), (descr' ~~ recTs)); + + val cert = cterm_of thy6; + + val indrule_lemma = SkipProof.prove_global thy6 [] [] + (Logic.mk_implies + (HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems), + HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls))) (fn _ => EVERY + [REPEAT (etac conjE 1), + REPEAT (EVERY + [TRY (rtac conjI 1), resolve_tac Rep_inverse_thms 1, + etac mp 1, resolve_tac iso_elem_thms 1])]); + + val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma))); + val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else + map (Free o apfst fst o dest_Var) Ps; + val indrule_lemma' = cterm_instantiate (map cert Ps ~~ map cert frees) indrule_lemma; + + val dt_induct_prop = DatatypeProp.make_ind descr sorts; + val dt_induct = SkipProof.prove_global thy6 [] + (Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop) + (fn {prems, ...} => EVERY + [rtac indrule_lemma' 1, + (indtac rep_induct [] THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1, + EVERY (map (fn (prem, r) => (EVERY + [REPEAT (eresolve_tac Abs_inverse_thms 1), + simp_tac (HOL_basic_ss addsimps ((symmetric r)::Rep_inverse_thms')) 1, + DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)])) + (prems ~~ (constr_defs @ (map mk_meta_eq iso_char_thms))))]); + + val ([dt_induct'], thy7) = + thy6 + |> Sign.add_path big_name + |> PureThy.add_thms [((Binding.name "induct", dt_induct), [case_names_induct])] + ||> Sign.parent_path + ||> Theory.checkpoint; + + in + ((constr_inject', distinct_thms', dist_rewrites, simproc_dists, dt_induct'), thy7) + end; + +end;