--- a/src/HOL/HOLCF/Tools/Domain/domain_induction.ML Tue Nov 30 14:01:49 2010 -0800
+++ b/src/HOL/HOLCF/Tools/Domain/domain_induction.ML Tue Nov 30 14:21:57 2010 -0800
@@ -13,20 +13,20 @@
Domain_Constructors.constr_info list ->
theory -> thm list * theory
- val quiet_mode: bool Unsynchronized.ref;
- val trace_domain: bool Unsynchronized.ref;
-end;
+ val quiet_mode: bool Unsynchronized.ref
+ val trace_domain: bool Unsynchronized.ref
+end
structure Domain_Induction :> DOMAIN_INDUCTION =
struct
-val quiet_mode = Unsynchronized.ref false;
-val trace_domain = Unsynchronized.ref false;
+val quiet_mode = Unsynchronized.ref false
+val trace_domain = Unsynchronized.ref false
-fun message s = if !quiet_mode then () else writeln s;
-fun trace s = if !trace_domain then tracing s else ();
+fun message s = if !quiet_mode then () else writeln s
+fun trace s = if !trace_domain then tracing s else ()
-open HOLCF_Library;
+open HOLCF_Library
(******************************************************************************)
(***************************** proofs about take ******************************)
@@ -38,60 +38,60 @@
(constr_infos : Domain_Constructors.constr_info list)
(thy : theory) : thm list list * theory =
let
- val {take_consts, take_Suc_thms, deflation_take_thms, ...} = take_info;
- val deflation_thms = Domain_Take_Proofs.get_deflation_thms thy;
+ val {take_consts, take_Suc_thms, deflation_take_thms, ...} = take_info
+ val deflation_thms = Domain_Take_Proofs.get_deflation_thms thy
- val n = Free ("n", @{typ nat});
- val n' = @{const Suc} $ n;
+ val n = Free ("n", @{typ nat})
+ val n' = @{const Suc} $ n
local
- val newTs = map (#absT o #iso_info) constr_infos;
- val subs = newTs ~~ map (fn t => t $ n) take_consts;
+ val newTs = map (#absT o #iso_info) constr_infos
+ val subs = newTs ~~ map (fn t => t $ n) take_consts
fun is_ID (Const (c, _)) = (c = @{const_name ID})
- | is_ID _ = false;
+ | is_ID _ = false
in
fun map_of_arg thy v T =
- let val m = Domain_Take_Proofs.map_of_typ thy subs T;
- in if is_ID m then v else mk_capply (m, v) end;
+ let val m = Domain_Take_Proofs.map_of_typ thy subs T
+ in if is_ID m then v else mk_capply (m, v) end
end
fun prove_take_apps
((dbind, take_const), constr_info) thy =
let
- val {iso_info, con_specs, con_betas, ...} = constr_info;
- val {abs_inverse, ...} = iso_info;
+ val {iso_info, con_specs, con_betas, ...} = constr_info
+ val {abs_inverse, ...} = iso_info
fun prove_take_app (con_const, args) =
let
- val Ts = map snd args;
- val ns = Name.variant_list ["n"] (Datatype_Prop.make_tnames Ts);
- val vs = map Free (ns ~~ Ts);
- val lhs = mk_capply (take_const $ n', list_ccomb (con_const, vs));
- val rhs = list_ccomb (con_const, map2 (map_of_arg thy) vs Ts);
- val goal = mk_trp (mk_eq (lhs, rhs));
+ val Ts = map snd args
+ val ns = Name.variant_list ["n"] (Datatype_Prop.make_tnames Ts)
+ val vs = map Free (ns ~~ Ts)
+ val lhs = mk_capply (take_const $ n', list_ccomb (con_const, vs))
+ val rhs = list_ccomb (con_const, map2 (map_of_arg thy) vs Ts)
+ val goal = mk_trp (mk_eq (lhs, rhs))
val rules =
[abs_inverse] @ con_betas @ @{thms take_con_rules}
- @ take_Suc_thms @ deflation_thms @ deflation_take_thms;
- val tac = simp_tac (HOL_basic_ss addsimps rules) 1;
+ @ take_Suc_thms @ deflation_thms @ deflation_take_thms
+ val tac = simp_tac (HOL_basic_ss addsimps rules) 1
in
Goal.prove_global thy [] [] goal (K tac)
- end;
- val take_apps = map prove_take_app con_specs;
+ end
+ val take_apps = map prove_take_app con_specs
in
yield_singleton Global_Theory.add_thmss
((Binding.qualified true "take_rews" dbind, take_apps),
[Simplifier.simp_add]) thy
- end;
+ end
in
fold_map prove_take_apps
(dbinds ~~ take_consts ~~ constr_infos) thy
-end;
+end
(******************************************************************************)
(****************************** induction rules *******************************)
(******************************************************************************)
val case_UU_allI =
- @{lemma "(!!x. x ~= UU ==> P x) ==> P UU ==> ALL x. P x" by metis};
+ @{lemma "(!!x. x ~= UU ==> P x) ==> P UU ==> ALL x. P x" by metis}
fun prove_induction
(comp_dbind : binding)
@@ -100,135 +100,135 @@
(take_rews : thm list)
(thy : theory) =
let
- val comp_dname = Binding.name_of comp_dbind;
+ val comp_dname = Binding.name_of comp_dbind
- val iso_infos = map #iso_info constr_infos;
- val exhausts = map #exhaust constr_infos;
- val con_rews = maps #con_rews constr_infos;
- val {take_consts, take_induct_thms, ...} = take_info;
+ val iso_infos = map #iso_info constr_infos
+ val exhausts = map #exhaust constr_infos
+ val con_rews = maps #con_rews constr_infos
+ val {take_consts, take_induct_thms, ...} = take_info
- val newTs = map #absT iso_infos;
- val P_names = Datatype_Prop.indexify_names (map (K "P") newTs);
- val x_names = Datatype_Prop.indexify_names (map (K "x") newTs);
- val P_types = map (fn T => T --> HOLogic.boolT) newTs;
- val Ps = map Free (P_names ~~ P_types);
- val xs = map Free (x_names ~~ newTs);
- val n = Free ("n", HOLogic.natT);
+ val newTs = map #absT iso_infos
+ val P_names = Datatype_Prop.indexify_names (map (K "P") newTs)
+ val x_names = Datatype_Prop.indexify_names (map (K "x") newTs)
+ val P_types = map (fn T => T --> HOLogic.boolT) newTs
+ val Ps = map Free (P_names ~~ P_types)
+ val xs = map Free (x_names ~~ newTs)
+ val n = Free ("n", HOLogic.natT)
fun con_assm defined p (con, args) =
let
- val Ts = map snd args;
- val ns = Name.variant_list P_names (Datatype_Prop.make_tnames Ts);
- val vs = map Free (ns ~~ Ts);
- val nonlazy = map snd (filter_out (fst o fst) (args ~~ vs));
+ val Ts = map snd args
+ val ns = Name.variant_list P_names (Datatype_Prop.make_tnames Ts)
+ val vs = map Free (ns ~~ Ts)
+ val nonlazy = map snd (filter_out (fst o fst) (args ~~ vs))
fun ind_hyp (v, T) t =
case AList.lookup (op =) (newTs ~~ Ps) T of NONE => t
- | SOME p' => Logic.mk_implies (mk_trp (p' $ v), t);
- val t1 = mk_trp (p $ list_ccomb (con, vs));
- val t2 = fold_rev ind_hyp (vs ~~ Ts) t1;
- val t3 = Logic.list_implies (map (mk_trp o mk_defined) nonlazy, t2);
- in fold_rev Logic.all vs (if defined then t3 else t2) end;
+ | SOME p' => Logic.mk_implies (mk_trp (p' $ v), t)
+ val t1 = mk_trp (p $ list_ccomb (con, vs))
+ val t2 = fold_rev ind_hyp (vs ~~ Ts) t1
+ val t3 = Logic.list_implies (map (mk_trp o mk_defined) nonlazy, t2)
+ in fold_rev Logic.all vs (if defined then t3 else t2) end
fun eq_assms ((p, T), cons) =
- mk_trp (p $ HOLCF_Library.mk_bottom T) :: map (con_assm true p) cons;
- val assms = maps eq_assms (Ps ~~ newTs ~~ map #con_specs constr_infos);
+ mk_trp (p $ HOLCF_Library.mk_bottom T) :: map (con_assm true p) cons
+ val assms = maps eq_assms (Ps ~~ newTs ~~ map #con_specs constr_infos)
- val take_ss = HOL_ss addsimps (@{thm Rep_cfun_strict1} :: take_rews);
+ val take_ss = HOL_ss addsimps (@{thm Rep_cfun_strict1} :: take_rews)
fun quant_tac ctxt i = EVERY
- (map (fn name => res_inst_tac ctxt [(("x", 0), name)] spec i) x_names);
+ (map (fn name => res_inst_tac ctxt [(("x", 0), name)] spec i) x_names)
(* FIXME: move this message to domain_take_proofs.ML *)
- val is_finite = #is_finite take_info;
+ val is_finite = #is_finite take_info
val _ = if is_finite
then message ("Proving finiteness rule for domain "^comp_dname^" ...")
- else ();
+ else ()
- val _ = trace " Proving finite_ind...";
+ val _ = trace " Proving finite_ind..."
val finite_ind =
let
val concls =
map (fn ((P, t), x) => P $ mk_capply (t $ n, x))
- (Ps ~~ take_consts ~~ xs);
- val goal = mk_trp (foldr1 mk_conj concls);
+ (Ps ~~ take_consts ~~ xs)
+ val goal = mk_trp (foldr1 mk_conj concls)
fun tacf {prems, context} =
let
(* Prove stronger prems, without definedness side conditions *)
fun con_thm p (con, args) =
let
- val subgoal = con_assm false p (con, args);
- val rules = prems @ con_rews @ simp_thms;
- val simplify = asm_simp_tac (HOL_basic_ss addsimps rules);
+ val subgoal = con_assm false p (con, args)
+ val rules = prems @ con_rews @ simp_thms
+ val simplify = asm_simp_tac (HOL_basic_ss addsimps rules)
fun arg_tac (lazy, _) =
- rtac (if lazy then allI else case_UU_allI) 1;
+ rtac (if lazy then allI else case_UU_allI) 1
val tacs =
rewrite_goals_tac @{thms atomize_all atomize_imp} ::
map arg_tac args @
- [REPEAT (rtac impI 1), ALLGOALS simplify];
+ [REPEAT (rtac impI 1), ALLGOALS simplify]
in
Goal.prove context [] [] subgoal (K (EVERY tacs))
- end;
- fun eq_thms (p, cons) = map (con_thm p) cons;
- val conss = map #con_specs constr_infos;
- val prems' = maps eq_thms (Ps ~~ conss);
+ end
+ fun eq_thms (p, cons) = map (con_thm p) cons
+ val conss = map #con_specs constr_infos
+ val prems' = maps eq_thms (Ps ~~ conss)
val tacs1 = [
quant_tac context 1,
simp_tac HOL_ss 1,
InductTacs.induct_tac context [[SOME "n"]] 1,
simp_tac (take_ss addsimps prems) 1,
- TRY (safe_tac HOL_cs)];
+ TRY (safe_tac HOL_cs)]
fun con_tac _ =
asm_simp_tac take_ss 1 THEN
- (resolve_tac prems' THEN_ALL_NEW etac spec) 1;
+ (resolve_tac prems' THEN_ALL_NEW etac spec) 1
fun cases_tacs (cons, exhaust) =
res_inst_tac context [(("y", 0), "x")] exhaust 1 ::
asm_simp_tac (take_ss addsimps prems) 1 ::
- map con_tac cons;
+ map con_tac cons
val tacs = tacs1 @ maps cases_tacs (conss ~~ exhausts)
in
EVERY (map DETERM tacs)
- end;
- in Goal.prove_global thy [] assms goal tacf end;
+ end
+ in Goal.prove_global thy [] assms goal tacf end
- val _ = trace " Proving ind...";
+ val _ = trace " Proving ind..."
val ind =
let
- val concls = map (op $) (Ps ~~ xs);
- val goal = mk_trp (foldr1 mk_conj concls);
- val adms = if is_finite then [] else map (mk_trp o mk_adm) Ps;
+ val concls = map (op $) (Ps ~~ xs)
+ val goal = mk_trp (foldr1 mk_conj concls)
+ val adms = if is_finite then [] else map (mk_trp o mk_adm) Ps
fun tacf {prems, context} =
let
fun finite_tac (take_induct, fin_ind) =
rtac take_induct 1 THEN
(if is_finite then all_tac else resolve_tac prems 1) THEN
- (rtac fin_ind THEN_ALL_NEW solve_tac prems) 1;
- val fin_inds = Project_Rule.projections context finite_ind;
+ (rtac fin_ind THEN_ALL_NEW solve_tac prems) 1
+ val fin_inds = Project_Rule.projections context finite_ind
in
TRY (safe_tac HOL_cs) THEN
EVERY (map finite_tac (take_induct_thms ~~ fin_inds))
- end;
+ end
in Goal.prove_global thy [] (adms @ assms) goal tacf end
(* case names for induction rules *)
- val dnames = map (fst o dest_Type) newTs;
+ val dnames = map (fst o dest_Type) newTs
val case_ns =
let
val adms =
if is_finite then [] else
if length dnames = 1 then ["adm"] else
- map (fn s => "adm_" ^ Long_Name.base_name s) dnames;
+ map (fn s => "adm_" ^ Long_Name.base_name s) dnames
val bottoms =
if length dnames = 1 then ["bottom"] else
- map (fn s => "bottom_" ^ Long_Name.base_name s) dnames;
+ map (fn s => "bottom_" ^ Long_Name.base_name s) dnames
fun one_eq bot constr_info =
- let fun name_of (c, args) = Long_Name.base_name (fst (dest_Const c));
- in bot :: map name_of (#con_specs constr_info) end;
- in adms @ flat (map2 one_eq bottoms constr_infos) end;
+ let fun name_of (c, args) = Long_Name.base_name (fst (dest_Const c))
+ in bot :: map name_of (#con_specs constr_info) end
+ in adms @ flat (map2 one_eq bottoms constr_infos) end
- val inducts = Project_Rule.projections (ProofContext.init_global thy) ind;
+ val inducts = Project_Rule.projections (ProofContext.init_global thy) ind
fun ind_rule (dname, rule) =
((Binding.empty, rule),
- [Rule_Cases.case_names case_ns, Induct.induct_type dname]);
+ [Rule_Cases.case_names case_ns, Induct.induct_type dname])
in
thy
@@ -236,7 +236,7 @@
((Binding.qualified true "finite_induct" comp_dbind, finite_ind), []),
((Binding.qualified true "induct" comp_dbind, ind ), [])]
|> (snd o Global_Theory.add_thms (map ind_rule (dnames ~~ inducts)))
-end; (* prove_induction *)
+end (* prove_induction *)
(******************************************************************************)
(************************ bisimulation and coinduction ************************)
@@ -249,83 +249,83 @@
(take_rews : thm list list)
(thy : theory) : theory =
let
- val iso_infos = map #iso_info constr_infos;
- val newTs = map #absT iso_infos;
+ val iso_infos = map #iso_info constr_infos
+ val newTs = map #absT iso_infos
- val {take_consts, take_0_thms, take_lemma_thms, ...} = take_info;
+ val {take_consts, take_0_thms, take_lemma_thms, ...} = take_info
- val R_names = Datatype_Prop.indexify_names (map (K "R") newTs);
- val R_types = map (fn T => T --> T --> boolT) newTs;
- val Rs = map Free (R_names ~~ R_types);
- val n = Free ("n", natT);
- val reserved = "x" :: "y" :: R_names;
+ val R_names = Datatype_Prop.indexify_names (map (K "R") newTs)
+ val R_types = map (fn T => T --> T --> boolT) newTs
+ val Rs = map Free (R_names ~~ R_types)
+ val n = Free ("n", natT)
+ val reserved = "x" :: "y" :: R_names
(* declare bisimulation predicate *)
- val bisim_bind = Binding.suffix_name "_bisim" comp_dbind;
- val bisim_type = R_types ---> boolT;
+ val bisim_bind = Binding.suffix_name "_bisim" comp_dbind
+ val bisim_type = R_types ---> boolT
val (bisim_const, thy) =
- Sign.declare_const ((bisim_bind, bisim_type), NoSyn) thy;
+ Sign.declare_const ((bisim_bind, bisim_type), NoSyn) thy
(* define bisimulation predicate *)
local
fun one_con T (con, args) =
let
- val Ts = map snd args;
- val ns1 = Name.variant_list reserved (Datatype_Prop.make_tnames Ts);
- val ns2 = map (fn n => n^"'") ns1;
- val vs1 = map Free (ns1 ~~ Ts);
- val vs2 = map Free (ns2 ~~ Ts);
- val eq1 = mk_eq (Free ("x", T), list_ccomb (con, vs1));
- val eq2 = mk_eq (Free ("y", T), list_ccomb (con, vs2));
+ val Ts = map snd args
+ val ns1 = Name.variant_list reserved (Datatype_Prop.make_tnames Ts)
+ val ns2 = map (fn n => n^"'") ns1
+ val vs1 = map Free (ns1 ~~ Ts)
+ val vs2 = map Free (ns2 ~~ Ts)
+ val eq1 = mk_eq (Free ("x", T), list_ccomb (con, vs1))
+ val eq2 = mk_eq (Free ("y", T), list_ccomb (con, vs2))
fun rel ((v1, v2), T) =
case AList.lookup (op =) (newTs ~~ Rs) T of
- NONE => mk_eq (v1, v2) | SOME r => r $ v1 $ v2;
- val eqs = foldr1 mk_conj (map rel (vs1 ~~ vs2 ~~ Ts) @ [eq1, eq2]);
+ NONE => mk_eq (v1, v2) | SOME r => r $ v1 $ v2
+ val eqs = foldr1 mk_conj (map rel (vs1 ~~ vs2 ~~ Ts) @ [eq1, eq2])
in
Library.foldr mk_ex (vs1 @ vs2, eqs)
- end;
+ end
fun one_eq ((T, R), cons) =
let
- val x = Free ("x", T);
- val y = Free ("y", T);
- val disj1 = mk_conj (mk_eq (x, mk_bottom T), mk_eq (y, mk_bottom T));
- val disjs = disj1 :: map (one_con T) cons;
+ val x = Free ("x", T)
+ val y = Free ("y", T)
+ val disj1 = mk_conj (mk_eq (x, mk_bottom T), mk_eq (y, mk_bottom T))
+ val disjs = disj1 :: map (one_con T) cons
in
mk_all (x, mk_all (y, mk_imp (R $ x $ y, foldr1 mk_disj disjs)))
- end;
- val conjs = map one_eq (newTs ~~ Rs ~~ map #con_specs constr_infos);
- val bisim_rhs = lambdas Rs (Library.foldr1 mk_conj conjs);
- val bisim_eqn = Logic.mk_equals (bisim_const, bisim_rhs);
+ end
+ val conjs = map one_eq (newTs ~~ Rs ~~ map #con_specs constr_infos)
+ val bisim_rhs = lambdas Rs (Library.foldr1 mk_conj conjs)
+ val bisim_eqn = Logic.mk_equals (bisim_const, bisim_rhs)
in
val (bisim_def_thm, thy) = thy |>
yield_singleton (Global_Theory.add_defs false)
- ((Binding.qualified true "bisim_def" comp_dbind, bisim_eqn), []);
+ ((Binding.qualified true "bisim_def" comp_dbind, bisim_eqn), [])
end (* local *)
(* prove coinduction lemma *)
val coind_lemma =
let
- val assm = mk_trp (list_comb (bisim_const, Rs));
+ val assm = mk_trp (list_comb (bisim_const, Rs))
fun one ((T, R), take_const) =
let
- val x = Free ("x", T);
- val y = Free ("y", T);
- val lhs = mk_capply (take_const $ n, x);
- val rhs = mk_capply (take_const $ n, y);
+ val x = Free ("x", T)
+ val y = Free ("y", T)
+ val lhs = mk_capply (take_const $ n, x)
+ val rhs = mk_capply (take_const $ n, y)
in
mk_all (x, mk_all (y, mk_imp (R $ x $ y, mk_eq (lhs, rhs))))
- end;
+ end
val goal =
- mk_trp (foldr1 mk_conj (map one (newTs ~~ Rs ~~ take_consts)));
- val rules = @{thm Rep_cfun_strict1} :: take_0_thms;
+ mk_trp (foldr1 mk_conj (map one (newTs ~~ Rs ~~ take_consts)))
+ val rules = @{thm Rep_cfun_strict1} :: take_0_thms
fun tacf {prems, context} =
let
- val prem' = rewrite_rule [bisim_def_thm] (hd prems);
- val prems' = Project_Rule.projections context prem';
- val dests = map (fn th => th RS spec RS spec RS mp) prems';
+ val prem' = rewrite_rule [bisim_def_thm] (hd prems)
+ val prems' = Project_Rule.projections context prem'
+ val dests = map (fn th => th RS spec RS spec RS mp) prems'
fun one_tac (dest, rews) =
dtac dest 1 THEN safe_tac HOL_cs THEN
- ALLGOALS (asm_simp_tac (HOL_basic_ss addsimps rews));
+ ALLGOALS (asm_simp_tac (HOL_basic_ss addsimps rews))
in
rtac @{thm nat.induct} 1 THEN
simp_tac (HOL_ss addsimps rules) 1 THEN
@@ -334,33 +334,33 @@
end
in
Goal.prove_global thy [] [assm] goal tacf
- end;
+ end
(* prove individual coinduction rules *)
fun prove_coind ((T, R), take_lemma) =
let
- val x = Free ("x", T);
- val y = Free ("y", T);
- val assm1 = mk_trp (list_comb (bisim_const, Rs));
- val assm2 = mk_trp (R $ x $ y);
- val goal = mk_trp (mk_eq (x, y));
+ val x = Free ("x", T)
+ val y = Free ("y", T)
+ val assm1 = mk_trp (list_comb (bisim_const, Rs))
+ val assm2 = mk_trp (R $ x $ y)
+ val goal = mk_trp (mk_eq (x, y))
fun tacf {prems, context} =
let
- val rule = hd prems RS coind_lemma;
+ val rule = hd prems RS coind_lemma
in
rtac take_lemma 1 THEN
asm_simp_tac (HOL_basic_ss addsimps (rule :: prems)) 1
- end;
+ end
in
Goal.prove_global thy [] [assm1, assm2] goal tacf
- end;
- val coinds = map prove_coind (newTs ~~ Rs ~~ take_lemma_thms);
- val coind_binds = map (Binding.qualified true "coinduct") dbinds;
+ end
+ val coinds = map prove_coind (newTs ~~ Rs ~~ take_lemma_thms)
+ val coind_binds = map (Binding.qualified true "coinduct") dbinds
in
thy |> snd o Global_Theory.add_thms
(map Thm.no_attributes (coind_binds ~~ coinds))
-end; (* let *)
+end (* let *)
(******************************************************************************)
(******************************* main function ********************************)
@@ -373,67 +373,67 @@
(thy : theory) =
let
-val comp_dname = space_implode "_" (map Binding.name_of dbinds);
-val comp_dbind = Binding.name comp_dname;
+val comp_dname = space_implode "_" (map Binding.name_of dbinds)
+val comp_dbind = Binding.name comp_dname
(* Test for emptiness *)
(* FIXME: reimplement emptiness test
local
- open Domain_Library;
- val dnames = map (fst o fst) eqs;
- val conss = map snd eqs;
+ open Domain_Library
+ val dnames = map (fst o fst) eqs
+ val conss = map snd eqs
fun rec_to ns lazy_rec (n,cons) = forall (exists (fn arg =>
is_rec arg andalso not (member (op =) ns (rec_of arg)) andalso
((rec_of arg = n andalso not (lazy_rec orelse is_lazy arg)) orelse
rec_of arg <> n andalso rec_to (rec_of arg::ns)
(lazy_rec orelse is_lazy arg) (n, (List.nth(conss,rec_of arg))))
- ) o snd) cons;
+ ) o snd) cons
fun warn (n,cons) =
if rec_to [] false (n,cons)
- then (warning ("domain "^List.nth(dnames,n)^" is empty!"); true)
- else false;
+ then (warning ("domain "^List.nth(dnames,n)^" is empty!") true)
+ else false
in
- val n__eqs = mapn (fn n => fn (_,cons) => (n,cons)) 0 eqs;
- val is_emptys = map warn n__eqs;
-end;
+ val n__eqs = mapn (fn n => fn (_,cons) => (n,cons)) 0 eqs
+ val is_emptys = map warn n__eqs
+end
*)
(* Test for indirect recursion *)
local
- val newTs = map (#absT o #iso_info) constr_infos;
+ val newTs = map (#absT o #iso_info) constr_infos
fun indirect_typ (Type (_, Ts)) =
exists (fn T => member (op =) newTs T orelse indirect_typ T) Ts
- | indirect_typ _ = false;
- fun indirect_arg (_, T) = indirect_typ T;
- fun indirect_con (_, args) = exists indirect_arg args;
- fun indirect_eq cons = exists indirect_con cons;
+ | indirect_typ _ = false
+ fun indirect_arg (_, T) = indirect_typ T
+ fun indirect_con (_, args) = exists indirect_arg args
+ fun indirect_eq cons = exists indirect_con cons
in
- val is_indirect = exists indirect_eq (map #con_specs constr_infos);
+ val is_indirect = exists indirect_eq (map #con_specs constr_infos)
val _ =
if is_indirect
then message "Indirect recursion detected, skipping proofs of (co)induction rules"
- else message ("Proving induction properties of domain "^comp_dname^" ...");
-end;
+ else message ("Proving induction properties of domain "^comp_dname^" ...")
+end
(* theorems about take *)
val (take_rewss, thy) =
- take_theorems dbinds take_info constr_infos thy;
+ take_theorems dbinds take_info constr_infos thy
-val {take_lemma_thms, take_0_thms, take_strict_thms, ...} = take_info;
+val {take_lemma_thms, take_0_thms, take_strict_thms, ...} = take_info
-val take_rews = take_0_thms @ take_strict_thms @ flat take_rewss;
+val take_rews = take_0_thms @ take_strict_thms @ flat take_rewss
(* prove induction rules, unless definition is indirect recursive *)
val thy =
if is_indirect then thy else
- prove_induction comp_dbind constr_infos take_info take_rews thy;
+ prove_induction comp_dbind constr_infos take_info take_rews thy
val thy =
if is_indirect then thy else
- prove_coinduction (comp_dbind, dbinds) constr_infos take_info take_rewss thy;
+ prove_coinduction (comp_dbind, dbinds) constr_infos take_info take_rewss thy
in
(take_rews, thy)
-end; (* let *)
-end; (* struct *)
+end (* let *)
+end (* struct *)