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(* Title: HOL/Tools/BNF/bnf_gfp_rec_sugar.ML
Author: Lorenz Panny, TU Muenchen
Author: Jasmin Blanchette, TU Muenchen
Copyright 2013
Corecursor sugar ("primcorec" and "primcorecursive").
*)
signature BNF_GFP_REC_SUGAR =
sig
datatype corec_option =
Plugins_Option of Proof.context -> Plugin_Name.filter |
Sequential_Option |
Exhaustive_Option |
Transfer_Option
datatype corec_call =
Dummy_No_Corec of int |
No_Corec of int |
Mutual_Corec of int * int * int |
Nested_Corec of int
type corec_ctr_spec =
{ctr: term,
disc: term,
sels: term list,
pred: int option,
calls: corec_call list,
discI: thm,
sel_thms: thm list,
distinct_discss: thm list list,
collapse: thm,
corec_thm: thm,
corec_disc: thm,
corec_sels: thm list}
type corec_spec =
{T: typ,
corec: term,
exhaust_discs: thm list,
sel_defs: thm list,
fp_nesting_maps: thm list,
fp_nesting_map_ident0s: thm list,
fp_nesting_map_comps: thm list,
ctr_specs: corec_ctr_spec list}
val abstract_over_list: term list -> term -> term
val abs_tuple_balanced: term list -> term -> term
val mk_conjs: term list -> term
val mk_disjs: term list -> term
val mk_dnf: term list list -> term
val conjuncts_s: term -> term list
val s_not: term -> term
val s_not_conj: term list -> term list
val s_conjs: term list -> term
val s_disjs: term list -> term
val s_dnf: term list list -> term list
val case_of: Proof.context -> string -> (string * bool) option
val fold_rev_let_if_case: Proof.context -> (term list -> term -> 'a -> 'a) -> typ list ->
term -> 'a -> 'a
val massage_let_if_case: Proof.context -> (term -> bool) -> (typ list -> term -> term) ->
(typ list -> term -> unit) -> (typ list -> term -> term) -> typ list -> term -> term
val massage_nested_corec_call: Proof.context -> (term -> bool) ->
(typ list -> typ -> typ -> term -> term) -> (typ list -> typ -> typ -> term -> term) ->
typ list -> typ -> typ -> term -> term
val expand_to_ctr_term: Proof.context -> typ -> term -> term
val massage_corec_code_rhs: Proof.context -> (typ list -> term -> term list -> term) ->
typ list -> term -> term
val fold_rev_corec_code_rhs: Proof.context -> (term list -> term -> term list -> 'a -> 'a) ->
typ list -> term -> 'a -> 'a
val case_thms_of_term: Proof.context -> term ->
thm list * thm list * thm list * thm list * thm list
val map_thms_of_type: Proof.context -> typ -> thm list
val corec_specs_of: binding list -> typ list -> typ list -> term list ->
(term * term list list) list list -> local_theory ->
corec_spec list * typ list * thm * thm * thm list * thm list * (Token.src list * Token.src list)
* bool * local_theory
val gfp_rec_sugar_interpretation: string ->
(BNF_FP_Rec_Sugar_Util.fp_rec_sugar -> local_theory -> local_theory) -> theory -> theory
val primcorec_ursive: bool -> bool -> corec_option list -> ((binding * typ) * mixfix) list ->
((binding * Token.T list list) * term) list -> term option list -> Proof.context ->
(term * 'a list) list list * (thm list list -> local_theory -> local_theory) * local_theory
val primcorec_ursive_cmd: bool -> bool -> corec_option list ->
(binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list ->
Proof.context ->
(term * 'a list) list list * (thm list list -> local_theory -> local_theory) * local_theory
val primcorecursive_cmd: bool -> corec_option list ->
(binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list ->
Proof.context -> Proof.state
val primcorec_cmd: bool -> corec_option list ->
(binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list ->
local_theory -> local_theory
end;
structure BNF_GFP_Rec_Sugar : BNF_GFP_REC_SUGAR =
struct
open Ctr_Sugar_General_Tactics
open Ctr_Sugar
open BNF_Util
open BNF_Def
open BNF_FP_Util
open BNF_FP_Def_Sugar
open BNF_FP_N2M_Sugar
open BNF_FP_Rec_Sugar_Util
open BNF_FP_Rec_Sugar_Transfer
open BNF_GFP_Rec_Sugar_Tactics
val codeN = "code";
val ctrN = "ctr";
val discN = "disc";
val disc_iffN = "disc_iff";
val excludeN = "exclude";
val selN = "sel";
val nitpicksimp_attrs = @{attributes [nitpick_simp]};
val simp_attrs = @{attributes [simp]};
fun use_primcorecursive () =
error ("\"auto\" failed (try " ^ quote (#1 \<^command_keyword>\<open>primcorecursive\<close>) ^ " instead of " ^
quote (#1 \<^command_keyword>\<open>primcorec\<close>) ^ ")");
datatype corec_option =
Plugins_Option of Proof.context -> Plugin_Name.filter |
Sequential_Option |
Exhaustive_Option |
Transfer_Option;
datatype corec_call =
Dummy_No_Corec of int |
No_Corec of int |
Mutual_Corec of int * int * int |
Nested_Corec of int;
type basic_corec_ctr_spec =
{ctr: term,
disc: term,
sels: term list};
type corec_ctr_spec =
{ctr: term,
disc: term,
sels: term list,
pred: int option,
calls: corec_call list,
discI: thm,
sel_thms: thm list,
distinct_discss: thm list list,
collapse: thm,
corec_thm: thm,
corec_disc: thm,
corec_sels: thm list};
type corec_spec =
{T: typ,
corec: term,
exhaust_discs: thm list,
sel_defs: thm list,
fp_nesting_maps: thm list,
fp_nesting_map_ident0s: thm list,
fp_nesting_map_comps: thm list,
ctr_specs: corec_ctr_spec list};
exception NO_MAP of term;
fun abstract_over_list rev_vs =
let
val vs = rev rev_vs;
fun abs n (t $ u) = abs n t $ abs n u
| abs n (Abs (s, T, t)) = Abs (s, T, abs (n + 1) t)
| abs n t =
let val j = find_index (curry (op =) t) vs in
if j < 0 then t else Bound (n + j)
end;
in
abs 0
end;
val abs_tuple_balanced = HOLogic.tupled_lambda o mk_tuple_balanced;
fun curried_type (Type (\<^type_name>\<open>fun\<close>, [Type (\<^type_name>\<open>prod\<close>, Ts), T])) =
Ts ---> T;
fun sort_list_duplicates xs = map snd (sort (int_ord o apply2 fst) xs);
val mk_conjs = try (foldr1 HOLogic.mk_conj) #> the_default \<^const>\<open>True\<close>;
val mk_disjs = try (foldr1 HOLogic.mk_disj) #> the_default \<^const>\<open>False\<close>;
val mk_dnf = mk_disjs o map mk_conjs;
val conjuncts_s = filter_out (curry (op aconv) \<^const>\<open>True\<close>) o HOLogic.conjuncts;
fun s_not \<^const>\<open>True\<close> = \<^const>\<open>False\<close>
| s_not \<^const>\<open>False\<close> = \<^const>\<open>True\<close>
| s_not (\<^const>\<open>Not\<close> $ t) = t
| s_not (\<^const>\<open>conj\<close> $ t $ u) = \<^const>\<open>disj\<close> $ s_not t $ s_not u
| s_not (\<^const>\<open>disj\<close> $ t $ u) = \<^const>\<open>conj\<close> $ s_not t $ s_not u
| s_not t = \<^const>\<open>Not\<close> $ t;
val s_not_conj = conjuncts_s o s_not o mk_conjs;
fun propagate_unit_pos u cs = if member (op aconv) cs u then [\<^const>\<open>False\<close>] else cs;
fun propagate_unit_neg not_u cs = remove (op aconv) not_u cs;
fun propagate_units css =
(case List.partition (can the_single) css of
([], _) => css
| ([u] :: uss, css') =>
[u] :: propagate_units (map (propagate_unit_neg (s_not u))
(map (propagate_unit_pos u) (uss @ css'))));
fun s_conjs cs =
if member (op aconv) cs \<^const>\<open>False\<close> then \<^const>\<open>False\<close>
else mk_conjs (remove (op aconv) \<^const>\<open>True\<close> cs);
fun s_disjs ds =
if member (op aconv) ds \<^const>\<open>True\<close> then \<^const>\<open>True\<close>
else mk_disjs (remove (op aconv) \<^const>\<open>False\<close> ds);
fun s_dnf css0 =
let val css = propagate_units css0 in
if null css then
[\<^const>\<open>False\<close>]
else if exists null css then
[]
else
map (fn c :: cs => (c, cs)) css
|> AList.coalesce (op =)
|> map (fn (c, css) => c :: s_dnf css)
|> (fn [cs] => cs | css => [s_disjs (map s_conjs css)])
end;
fun fold_rev_let_if_case ctxt f bound_Ts =
let
val thy = Proof_Context.theory_of ctxt;
fun fld conds t =
(case Term.strip_comb t of
(Const (\<^const_name>\<open>Let\<close>, _), [_, _]) => fld conds (unfold_lets_splits t)
| (Const (\<^const_name>\<open>If\<close>, _), [cond, then_branch, else_branch]) =>
fld (conds @ conjuncts_s cond) then_branch o fld (conds @ s_not_conj [cond]) else_branch
| (Const (c, _), args as _ :: _ :: _) =>
let val n = num_binder_types (Sign.the_const_type thy c) - 1 in
if n >= 0 andalso n < length args then
(case fastype_of1 (bound_Ts, nth args n) of
Type (s, Ts) =>
(case dest_case ctxt s Ts t of
SOME ({split_sels = _ :: _, ...}, conds', branches) =>
fold_rev (uncurry fld) (map (append conds o conjuncts_s) conds' ~~ branches)
| _ => f conds t)
| _ => f conds t)
else
f conds t
end
| _ => f conds t);
in
fld []
end;
fun case_of ctxt s =
(case ctr_sugar_of ctxt s of
SOME {casex = Const (s', _), split_sels, ...} => SOME (s', not (null split_sels))
| _ => NONE);
fun massage_let_if_case ctxt has_call massage_leaf unexpected_call unsupported_case bound_Ts t0 =
let
val thy = Proof_Context.theory_of ctxt;
fun check_no_call bound_Ts t = if has_call t then unexpected_call bound_Ts t else ();
fun massage_abs bound_Ts 0 t = massage_rec bound_Ts t
| massage_abs bound_Ts m (Abs (s, T, t)) = Abs (s, T, massage_abs (T :: bound_Ts) (m - 1) t)
| massage_abs bound_Ts m t =
let val T = domain_type (fastype_of1 (bound_Ts, t)) in
Abs (Name.uu, T, massage_abs (T :: bound_Ts) (m - 1) (incr_boundvars 1 t $ Bound 0))
end
and massage_rec bound_Ts t =
let val typof = curry fastype_of1 bound_Ts in
(case Term.strip_comb t of
(Const (\<^const_name>\<open>Let\<close>, _), [_, _]) => massage_rec bound_Ts (unfold_lets_splits t)
| (Const (\<^const_name>\<open>If\<close>, _), obj :: (branches as [_, _])) =>
(case List.partition Term.is_dummy_pattern (map (massage_rec bound_Ts) branches) of
(dummy_branch' :: _, []) => dummy_branch'
| (_, [branch']) => branch'
| (_, branches') =>
Term.list_comb (If_const (typof (hd branches')) $ tap (check_no_call bound_Ts) obj,
branches'))
| (c as Const (\<^const_name>\<open>case_prod\<close>, _), arg :: args) =>
massage_rec bound_Ts
(unfold_splits_lets (Term.list_comb (c $ Envir.eta_long bound_Ts arg, args)))
| (Const (c, _), args as _ :: _ :: _) =>
(case try strip_fun_type (Sign.the_const_type thy c) of
SOME (gen_branch_Ts, gen_body_fun_T) =>
let
val gen_branch_ms = map num_binder_types gen_branch_Ts;
val n = length gen_branch_ms;
in
if n < length args then
(case gen_body_fun_T of
Type (_, [Type (T_name, _), _]) =>
(case case_of ctxt T_name of
SOME (c', has_split_sels) =>
if c' = c then
if has_split_sels then
let
val (branches, obj_leftovers) = chop n args;
val branches' = map2 (massage_abs bound_Ts) gen_branch_ms branches;
val branch_Ts' = map typof branches';
val body_T' = snd (strip_typeN (hd gen_branch_ms) (hd branch_Ts'));
val casex' =
Const (c, branch_Ts' ---> map typof obj_leftovers ---> body_T');
in
Term.list_comb (casex',
branches' @ tap (List.app (check_no_call bound_Ts)) obj_leftovers)
end
else
unsupported_case bound_Ts t
else
massage_leaf bound_Ts t
| NONE => massage_leaf bound_Ts t)
| _ => massage_leaf bound_Ts t)
else
massage_leaf bound_Ts t
end
| NONE => massage_leaf bound_Ts t)
| _ => massage_leaf bound_Ts t)
end;
in
massage_rec bound_Ts t0
|> Term.map_aterms (fn t =>
if Term.is_dummy_pattern t then Const (\<^const_name>\<open>undefined\<close>, fastype_of t) else t)
end;
fun massage_let_if_case_corec ctxt has_call massage_leaf bound_Ts t0 =
massage_let_if_case ctxt has_call massage_leaf (K (unexpected_corec_call_in ctxt [t0]))
(K (unsupported_case_around_corec_call ctxt [t0])) bound_Ts t0;
fun massage_nested_corec_call ctxt has_call massage_call massage_noncall bound_Ts U T t0 =
let
fun check_no_call t = if has_call t then unexpected_corec_call_in ctxt [t0] t else ();
fun massage_mutual_call bound_Ts (Type (\<^type_name>\<open>fun\<close>, [_, U2]))
(Type (\<^type_name>\<open>fun\<close>, [T1, T2])) t =
Abs (Name.uu, T1, massage_mutual_call (T1 :: bound_Ts) U2 T2 (incr_boundvars 1 t $ Bound 0))
| massage_mutual_call bound_Ts U T t =
(if has_call t then massage_call else massage_noncall) bound_Ts U T t;
fun massage_map bound_Ts (Type (_, Us)) (Type (s, Ts)) t =
(case try (dest_map ctxt s) t of
SOME (map0, fs) =>
let
val Type (_, dom_Ts) = domain_type (fastype_of1 (bound_Ts, t));
val map' = mk_map (length fs) dom_Ts Us map0;
val fs' =
map_flattened_map_args ctxt s (@{map 3} (massage_map_or_map_arg bound_Ts) Us Ts) fs;
in
Term.list_comb (map', fs')
end
| NONE => raise NO_MAP t)
| massage_map _ _ _ t = raise NO_MAP t
and massage_map_or_map_arg bound_Ts U T t =
if T = U then
tap check_no_call t
else
massage_map bound_Ts U T t
handle NO_MAP _ => massage_mutual_fun bound_Ts U T t
and massage_mutual_fun bound_Ts U T t =
let
val j = Term.maxidx_of_term t + 1;
val var = Var ((Name.uu, j), domain_type (fastype_of1 (bound_Ts, t)));
fun massage_body () =
Term.lambda var (Term.incr_boundvars 1 (massage_any_call bound_Ts U T
(betapply (t, var))));
in
(case t of
Const (\<^const_name>\<open>comp\<close>, _) $ t1 $ t2 =>
if has_call t2 then massage_body ()
else mk_comp bound_Ts (massage_mutual_fun bound_Ts U T t1, t2)
| _ => massage_body ())
end
and massage_any_call bound_Ts U T =
massage_let_if_case_corec ctxt has_call (fn bound_Ts => fn t =>
if has_call t then
(case U of
Type (s, Us) =>
(case try (dest_ctr ctxt s) t of
SOME (f, args) =>
let
val typof = curry fastype_of1 bound_Ts;
val f' = mk_ctr Us f
val f'_T = typof f';
val arg_Ts = map typof args;
in
Term.list_comb (f',
@{map 3} (massage_any_call bound_Ts) (binder_types f'_T) arg_Ts args)
end
| NONE =>
(case t of
Const (\<^const_name>\<open>case_prod\<close>, _) $ t' =>
let
val U' = curried_type U;
val T' = curried_type T;
in
Const (\<^const_name>\<open>case_prod\<close>, U' --> U) $ massage_any_call bound_Ts U' T' t'
end
| t1 $ t2 =>
(if has_call t2 then
massage_mutual_call bound_Ts U T t
else
massage_map bound_Ts U T t1 $ t2
handle NO_MAP _ => massage_mutual_call bound_Ts U T t)
| Abs (s, T', t') =>
Abs (s, T', massage_any_call (T' :: bound_Ts) (range_type U) (range_type T) t')
| _ => massage_mutual_call bound_Ts U T t))
| _ => ill_formed_corec_call ctxt t)
else
massage_noncall bound_Ts U T t) bound_Ts;
in
(if has_call t0 then massage_any_call else massage_noncall) bound_Ts U T t0
end;
fun expand_to_ctr_term ctxt (T as Type (s, Ts)) t =
(case ctr_sugar_of ctxt s of
SOME {ctrs, casex, ...} => Term.list_comb (mk_case Ts T casex, map (mk_ctr Ts) ctrs) $ t
| NONE => raise Fail "expand_to_ctr_term");
fun expand_corec_code_rhs ctxt has_call bound_Ts t =
(case fastype_of1 (bound_Ts, t) of
T as Type (s, _) =>
massage_let_if_case_corec ctxt has_call (fn _ => fn t =>
if can (dest_ctr ctxt s) t then t else expand_to_ctr_term ctxt T t) bound_Ts t
| _ => raise Fail "expand_corec_code_rhs");
fun massage_corec_code_rhs ctxt massage_ctr =
massage_let_if_case_corec ctxt (K false)
(fn bound_Ts => uncurry (massage_ctr bound_Ts) o Term.strip_comb);
fun fold_rev_corec_code_rhs ctxt f =
fold_rev_let_if_case ctxt (fn conds => uncurry (f conds) o Term.strip_comb);
fun case_thms_of_term ctxt t =
let val ctr_sugars = map_filter (Ctr_Sugar.ctr_sugar_of_case ctxt o fst) (Term.add_consts t []) in
(maps #distincts ctr_sugars, maps #discIs ctr_sugars, maps #exhaust_discs ctr_sugars,
maps #split_sels ctr_sugars, maps #split_sel_asms ctr_sugars)
end;
fun basic_corec_specs_of ctxt res_T =
(case res_T of
Type (T_name, _) =>
(case Ctr_Sugar.ctr_sugar_of ctxt T_name of
NONE => not_codatatype ctxt res_T
| SOME {T = fpT, ctrs, discs, selss, ...} =>
let
val thy = Proof_Context.theory_of ctxt;
val As_rho = tvar_subst thy [fpT] [res_T];
val substA = Term.subst_TVars As_rho;
fun mk_spec ctr disc sels = {ctr = substA ctr, disc = substA disc, sels = map substA sels};
in
@{map 3} mk_spec ctrs discs selss
handle ListPair.UnequalLengths => not_codatatype ctxt res_T
end)
| _ => not_codatatype ctxt res_T);
fun map_thms_of_type ctxt (Type (s, _)) =
(case fp_sugar_of ctxt s of SOME {fp_bnf_sugar = {map_thms, ...}, ...} => map_thms | NONE => [])
| map_thms_of_type _ _ = [];
structure GFP_Rec_Sugar_Plugin = Plugin(type T = fp_rec_sugar);
fun gfp_rec_sugar_interpretation name f =
GFP_Rec_Sugar_Plugin.interpretation name (fn fp_rec_sugar => fn lthy =>
f (transfer_fp_rec_sugar (Proof_Context.theory_of lthy) fp_rec_sugar) lthy);
val interpret_gfp_rec_sugar = GFP_Rec_Sugar_Plugin.data;
fun corec_specs_of bs arg_Ts res_Ts callers callssss0 lthy0 =
let
val thy = Proof_Context.theory_of lthy0;
val ((missing_res_Ts, perm0_kks, fp_sugars as {fp_nesting_bnfs,
fp_co_induct_sugar = SOME {common_co_inducts = common_coinduct_thms, ...}, ...} :: _,
(_, gfp_sugar_thms)), lthy) =
nested_to_mutual_fps (K true) Greatest_FP bs res_Ts callers callssss0 lthy0;
val coinduct_attrs_pair =
(case gfp_sugar_thms of SOME ((_, attrs_pair), _, _, _, _) => attrs_pair | NONE => ([], []));
val perm_fp_sugars = sort (int_ord o apply2 #fp_res_index) fp_sugars;
val indices = map #fp_res_index fp_sugars;
val perm_indices = map #fp_res_index perm_fp_sugars;
val perm_fpTs = map #T perm_fp_sugars;
val perm_ctrXs_Tsss' =
map (repair_nullary_single_ctr o #ctrXs_Tss o #fp_ctr_sugar) perm_fp_sugars;
val nn0 = length res_Ts;
val nn = length perm_fpTs;
val kks = 0 upto nn - 1;
val perm_ns' = map length perm_ctrXs_Tsss';
val perm_Ts = map #T perm_fp_sugars;
val perm_Xs = map #X perm_fp_sugars;
val perm_Cs =
map (domain_type o body_fun_type o fastype_of o #co_rec o the o #fp_co_induct_sugar)
perm_fp_sugars;
val Xs_TCs = perm_Xs ~~ (perm_Ts ~~ perm_Cs);
fun zip_corecT (Type (s, Us)) = [Type (s, map (mk_sumTN o zip_corecT) Us)]
| zip_corecT U =
(case AList.lookup (op =) Xs_TCs U of
SOME (T, C) => [T, C]
| NONE => [U]);
val perm_p_Tss = mk_corec_p_pred_types perm_Cs perm_ns';
val perm_f_Tssss =
map2 (fn C => map (map (map (curry (op -->) C) o zip_corecT))) perm_Cs perm_ctrXs_Tsss';
val perm_q_Tssss =
map (map (map (fn [_] => [] | [_, T] => [mk_pred1T (domain_type T)]))) perm_f_Tssss;
val (perm_p_hss, h) = indexedd perm_p_Tss 0;
val (perm_q_hssss, h') = indexedddd perm_q_Tssss h;
val (perm_f_hssss, _) = indexedddd perm_f_Tssss h';
val fun_arg_hs =
flat (@{map 3} flat_corec_preds_predsss_gettersss perm_p_hss perm_q_hssss perm_f_hssss);
fun unpermute0 perm0_xs = permute_like_unique (op =) perm0_kks kks perm0_xs;
fun unpermute perm_xs = permute_like_unique (op =) perm_indices indices perm_xs;
val coinduct_thmss = map (unpermute0 o conj_dests nn) common_coinduct_thms;
val p_iss = map (map (find_index_eq fun_arg_hs)) (unpermute perm_p_hss);
val q_issss = map (map (map (map (find_index_eq fun_arg_hs)))) (unpermute perm_q_hssss);
val f_issss = map (map (map (map (find_index_eq fun_arg_hs)))) (unpermute perm_f_hssss);
val f_Tssss = unpermute perm_f_Tssss;
val fpTs = unpermute perm_fpTs;
val Cs = unpermute perm_Cs;
val As_rho = tvar_subst thy (take nn0 fpTs) res_Ts;
val Cs_rho = map (fst o dest_TVar) Cs ~~ pad_list HOLogic.unitT nn arg_Ts;
val substA = Term.subst_TVars As_rho;
val substAT = Term.typ_subst_TVars As_rho;
val substCT = Term.typ_subst_TVars Cs_rho;
val perm_Cs' = map substCT perm_Cs;
fun call_of nullary [] [g_i] [Type (\<^type_name>\<open>fun\<close>, [_, T])] =
(if exists_subtype_in Cs T then Nested_Corec
else if nullary then Dummy_No_Corec
else No_Corec) g_i
| call_of _ [q_i] [g_i, g_i'] _ = Mutual_Corec (q_i, g_i, g_i');
fun mk_ctr_spec ctr disc sels p_io q_iss f_iss f_Tss discI sel_thms distinct_discss collapse
corec_thm corec_disc corec_sels =
let val nullary = not (can dest_funT (fastype_of ctr)) in
{ctr = substA ctr, disc = substA disc, sels = map substA sels, pred = p_io,
calls = @{map 3} (call_of nullary) q_iss f_iss f_Tss, discI = discI, sel_thms = sel_thms,
distinct_discss = distinct_discss, collapse = collapse, corec_thm = corec_thm,
corec_disc = corec_disc, corec_sels = corec_sels}
end;
fun mk_ctr_specs ({ctrs, discs, selss, discIs, sel_thmss, distinct_discsss, collapses, ...}
: ctr_sugar) p_is q_isss f_isss f_Tsss corec_thms corec_discs corec_selss =
let val p_ios = map SOME p_is @ [NONE] in
@{map 14} mk_ctr_spec ctrs discs selss p_ios q_isss f_isss f_Tsss discIs sel_thmss
distinct_discsss collapses corec_thms corec_discs corec_selss
end;
fun mk_spec ({T, fp_ctr_sugar = {ctr_sugar as {exhaust_discs, sel_defs, ...}, ...},
fp_co_induct_sugar = SOME {co_rec = corec, co_rec_thms = corec_thms,
co_rec_discs = corec_discs, co_rec_selss = corec_selss, ...}, ...} : fp_sugar) p_is q_isss
f_isss f_Tsss =
{T = T, corec = mk_co_rec thy Greatest_FP perm_Cs' (substAT T) corec,
exhaust_discs = exhaust_discs, sel_defs = sel_defs,
fp_nesting_maps = maps (map_thms_of_type lthy o T_of_bnf) fp_nesting_bnfs,
fp_nesting_map_ident0s = map map_ident0_of_bnf fp_nesting_bnfs,
fp_nesting_map_comps = map map_comp_of_bnf fp_nesting_bnfs,
ctr_specs = mk_ctr_specs ctr_sugar p_is q_isss f_isss f_Tsss corec_thms corec_discs
corec_selss};
in
(@{map 5} mk_spec fp_sugars p_iss q_issss f_issss f_Tssss, missing_res_Ts,
co_induct_of common_coinduct_thms, strong_co_induct_of common_coinduct_thms,
co_induct_of coinduct_thmss, strong_co_induct_of coinduct_thmss, coinduct_attrs_pair,
is_some gfp_sugar_thms, lthy)
end;
val undef_const = Const (\<^const_name>\<open>undefined\<close>, dummyT);
type coeqn_data_disc =
{fun_name: string,
fun_T: typ,
fun_args: term list,
ctr: term,
ctr_no: int,
disc: term,
prems: term list,
auto_gen: bool,
ctr_rhs_opt: term option,
code_rhs_opt: term option,
eqn_pos: int,
user_eqn: term};
type coeqn_data_sel =
{fun_name: string,
fun_T: typ,
fun_args: term list,
ctr: term,
sel: term,
rhs_term: term,
ctr_rhs_opt: term option,
code_rhs_opt: term option,
eqn_pos: int,
user_eqn: term};
fun ctr_sel_of ({ctr, sel, ...} : coeqn_data_sel) = (ctr, sel);
datatype coeqn_data =
Disc of coeqn_data_disc |
Sel of coeqn_data_sel;
fun is_free_in frees (Free (s, _)) = member (op =) frees s
| is_free_in _ _ = false;
fun is_catch_all_prem (Free (s, _)) = s = Name.uu_
| is_catch_all_prem _ = false;
fun add_extra_frees ctxt frees names =
fold_aterms (fn x as Free (s, _) =>
(not (member (op =) frees x) andalso not (member (op =) names s) andalso
not (Variable.is_fixed ctxt s) andalso not (is_catch_all_prem x))
? cons x | _ => I);
fun check_extra_frees ctxt frees names t =
let val bads = add_extra_frees ctxt frees names t [] in
null bads orelse extra_variable_in_rhs ctxt [t] (hd bads)
end;
fun check_fun_args ctxt eqn fun_args =
(check_duplicate_variables_in_lhs ctxt [eqn] fun_args;
check_all_fun_arg_frees ctxt [eqn] fun_args);
fun dissect_coeqn_disc ctxt fun_names sequentials
(basic_ctr_specss : basic_corec_ctr_spec list list) eqn_pos ctr_rhs_opt code_rhs_opt prems0
concl matchedsss =
let
fun find_subterm p =
let (* FIXME \<exists>? *)
fun find (t as u $ v) = if p t then SOME t else merge_options (find u, find v)
| find t = if p t then SOME t else NONE;
in find end;
val applied_fun = concl
|> find_subterm (member (op = o apsnd SOME) fun_names o try (fst o dest_Free o head_of))
|> the
handle Option.Option => error_at ctxt [concl] "Ill-formed discriminator formula";
val ((fun_name, fun_T), fun_args) = strip_comb applied_fun |>> dest_Free;
val _ = check_fun_args ctxt concl fun_args;
val bads = filter (Term.exists_subterm (is_free_in fun_names)) prems0;
val _ = null bads orelse unexpected_rec_call_in ctxt [] (hd bads);
val (sequential, basic_ctr_specs) =
the (AList.lookup (op =) (fun_names ~~ (sequentials ~~ basic_ctr_specss)) fun_name);
val discs = map #disc basic_ctr_specs;
val ctrs = map #ctr basic_ctr_specs;
val not_disc = head_of concl = \<^term>\<open>Not\<close>;
val _ = not_disc andalso length ctrs <> 2 andalso
error_at ctxt [concl] "Negated discriminator for a type with \ 2 constructors";
val disc' = find_subterm (member (op =) discs o head_of) concl;
val eq_ctr0 = concl |> perhaps (try HOLogic.dest_not) |> try (HOLogic.dest_eq #> snd)
|> (fn SOME t => let val n = find_index (curry (op =) t) ctrs in
if n >= 0 then SOME n else NONE end | _ => NONE);
val _ = is_none disc' orelse perhaps (try HOLogic.dest_not) concl = the disc' orelse
error_at ctxt [concl] "Ill-formed discriminator formula";
val _ = is_some disc' orelse is_some eq_ctr0 orelse
error_at ctxt [concl] "No discriminator in equation";
val ctr_no' =
if is_none disc' then the eq_ctr0 else find_index (curry (op =) (head_of (the disc'))) discs;
val ctr_no = if not_disc then 1 - ctr_no' else ctr_no';
val {ctr, disc, ...} = nth basic_ctr_specs ctr_no;
val catch_all =
(case prems0 of
[prem] => is_catch_all_prem prem
| _ =>
if exists is_catch_all_prem prems0 then error_at ctxt [concl] "Superfluous premises"
else false);
val matchedss = AList.lookup (op =) matchedsss fun_name |> the_default [];
val prems = map (abstract_over_list fun_args) prems0;
val actual_prems =
(if catch_all orelse sequential then maps s_not_conj matchedss else []) @
(if catch_all then [] else prems);
val matchedsss' = AList.delete (op =) fun_name matchedsss
|> cons (fun_name, if sequential then matchedss @ [prems] else matchedss @ [actual_prems]);
val user_eqn =
(actual_prems, concl)
|>> map HOLogic.mk_Trueprop ||> HOLogic.mk_Trueprop o abstract_over_list fun_args
|> curry Logic.list_all (map dest_Free fun_args) o Logic.list_implies;
val _ = check_extra_frees ctxt fun_args fun_names user_eqn;
in
(Disc {fun_name = fun_name, fun_T = fun_T, fun_args = fun_args, ctr = ctr, ctr_no = ctr_no,
disc = disc, prems = actual_prems, auto_gen = catch_all, ctr_rhs_opt = ctr_rhs_opt,
code_rhs_opt = code_rhs_opt, eqn_pos = eqn_pos, user_eqn = user_eqn},
matchedsss')
end;
fun dissect_coeqn_sel ctxt fun_names (basic_ctr_specss : basic_corec_ctr_spec list list) eqn_pos
ctr_rhs_opt code_rhs_opt eqn0 of_spec_opt eqn =
let
val (lhs, rhs) = HOLogic.dest_eq eqn
handle TERM _ => ill_formed_equation_lhs_rhs ctxt [eqn];
val sel = head_of lhs;
val ((fun_name, fun_T), fun_args) = dest_comb lhs |> snd |> strip_comb |> apfst dest_Free
handle TERM _ => error_at ctxt [eqn] "Ill-formed selector argument in left-hand side";
val _ = check_fun_args ctxt eqn fun_args;
val basic_ctr_specs = the (AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name)
handle Option.Option => error_at ctxt [eqn] "Ill-formed selector argument in left-hand side";
val {ctr, ...} =
(case of_spec_opt of
SOME of_spec => the (find_first (curry (op =) of_spec o #ctr) basic_ctr_specs)
| NONE => filter (exists (curry (op =) sel) o #sels) basic_ctr_specs |> the_single
handle List.Empty => error_at ctxt [eqn] "Ambiguous selector (without \"of\")");
val user_eqn = drop_all eqn0;
val _ = check_extra_frees ctxt fun_args fun_names user_eqn;
in
Sel {fun_name = fun_name, fun_T = fun_T, fun_args = fun_args, ctr = ctr, sel = sel,
rhs_term = rhs, ctr_rhs_opt = ctr_rhs_opt, code_rhs_opt = code_rhs_opt, eqn_pos = eqn_pos,
user_eqn = user_eqn}
end;
fun dissect_coeqn_ctr ctxt fun_names sequentials (basic_ctr_specss : basic_corec_ctr_spec list list)
eqn_pos eqn0 code_rhs_opt prems concl matchedsss =
let
val (lhs, rhs) = HOLogic.dest_eq concl;
val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
val _ = check_fun_args ctxt concl fun_args;
val _ = check_extra_frees ctxt fun_args fun_names (drop_all eqn0);
val basic_ctr_specs = the (AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name);
val (ctr, ctr_args) = strip_comb (unfold_lets_splits rhs);
val {disc, sels, ...} = the (find_first (curry (op =) ctr o #ctr) basic_ctr_specs)
handle Option.Option => not_constructor_in_rhs ctxt [] ctr;
val disc_concl = betapply (disc, lhs);
val (eqn_data_disc_opt, matchedsss') =
if null (tl basic_ctr_specs) andalso not (null sels) then
(NONE, matchedsss)
else
apfst SOME (dissect_coeqn_disc ctxt fun_names sequentials basic_ctr_specss eqn_pos
(SOME (abstract_over_list fun_args rhs)) code_rhs_opt prems disc_concl matchedsss);
val sel_concls = sels ~~ ctr_args
|> map (fn (sel, ctr_arg) => HOLogic.mk_eq (betapply (sel, lhs), ctr_arg))
handle ListPair.UnequalLengths => partially_applied_ctr_in_rhs ctxt [rhs];
val eqns_data_sel =
map (dissect_coeqn_sel ctxt fun_names basic_ctr_specss eqn_pos
(SOME (abstract_over_list fun_args rhs)) code_rhs_opt eqn0 (SOME ctr))
sel_concls;
in
(the_list eqn_data_disc_opt @ eqns_data_sel, matchedsss')
end;
fun dissect_coeqn_code ctxt has_call fun_names basic_ctr_specss eqn_pos eqn0 concl matchedsss =
let
val (lhs, (rhs', rhs)) = HOLogic.dest_eq concl ||> `(expand_corec_code_rhs ctxt has_call []);
val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
val _ = check_fun_args ctxt concl fun_args;
val _ = check_extra_frees ctxt fun_args fun_names concl;
val basic_ctr_specs = the (AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name);
val cond_ctrs = fold_rev_corec_code_rhs ctxt (fn cs => fn ctr => fn _ =>
if member (op = o apsnd #ctr) basic_ctr_specs ctr then cons (ctr, cs)
else not_constructor_in_rhs ctxt [] ctr) [] rhs' []
|> AList.group (op =);
val ctr_premss = (case cond_ctrs of [_] => [[]] | _ => map (s_dnf o snd) cond_ctrs);
val ctr_concls = cond_ctrs |> map (fn (ctr, _) =>
binder_types (fastype_of ctr)
|> map_index (fn (n, T) => massage_corec_code_rhs ctxt (fn _ => fn ctr' => fn args =>
if ctr' = ctr then nth args n else Term.dummy_pattern T) [] rhs')
|> curry Term.list_comb ctr
|> curry HOLogic.mk_eq lhs);
val bads = maps (filter (Term.exists_subterm (is_free_in fun_names))) ctr_premss;
val _ = null bads orelse unexpected_corec_call_in ctxt [eqn0] rhs;
val sequentials = replicate (length fun_names) false;
in
@{fold_map 2} (dissect_coeqn_ctr ctxt fun_names sequentials basic_ctr_specss eqn_pos eqn0
(SOME (abstract_over_list fun_args rhs)))
ctr_premss ctr_concls matchedsss
end;
fun dissect_coeqn ctxt has_call fun_names sequentials
(basic_ctr_specss : basic_corec_ctr_spec list list) (eqn_pos, eqn0) of_spec_opt matchedsss =
let
val eqn = drop_all eqn0
handle TERM _ => ill_formed_formula ctxt eqn0;
val (prems, concl) = Logic.strip_horn eqn
|> map_prod (map HOLogic.dest_Trueprop) HOLogic.dest_Trueprop
handle TERM _ => ill_formed_equation ctxt eqn;
val head = concl
|> perhaps (try HOLogic.dest_not) |> perhaps (try (fst o HOLogic.dest_eq))
|> head_of;
val rhs_opt = concl |> perhaps (try HOLogic.dest_not) |> try (HOLogic.dest_eq #> snd);
fun check_num_args () =
is_none rhs_opt orelse not (can dest_funT (fastype_of (the rhs_opt))) orelse
missing_args_to_fun_on_lhs ctxt [eqn];
val discs = maps (map #disc) basic_ctr_specss;
val sels = maps (maps #sels) basic_ctr_specss;
val ctrs = maps (map #ctr) basic_ctr_specss;
in
if member (op =) discs head orelse
(is_some rhs_opt andalso
member (op =) (map SOME fun_names) (try (fst o dest_Free) head) andalso
member (op =) (filter (null o binder_types o fastype_of) ctrs) (the rhs_opt)) then
(dissect_coeqn_disc ctxt fun_names sequentials basic_ctr_specss eqn_pos NONE NONE prems concl
matchedsss
|>> single)
else if member (op =) sels head then
(null prems orelse error_at ctxt [eqn] "Unexpected condition in selector formula";
([dissect_coeqn_sel ctxt fun_names basic_ctr_specss eqn_pos NONE NONE eqn0 of_spec_opt
concl], matchedsss))
else if is_some rhs_opt andalso is_Free head andalso is_free_in fun_names head then
if member (op =) ctrs (head_of (unfold_lets_splits (the rhs_opt))) then
(check_num_args ();
dissect_coeqn_ctr ctxt fun_names sequentials basic_ctr_specss eqn_pos eqn0
(if null prems then
SOME (snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (Logic.strip_assums_concl eqn0))))
else
NONE)
prems concl matchedsss)
else if null prems then
(check_num_args ();
dissect_coeqn_code ctxt has_call fun_names basic_ctr_specss eqn_pos eqn0 concl matchedsss
|>> flat)
else
error_at ctxt [eqn] "Cannot mix constructor and code views"
else if is_some rhs_opt then
error_at ctxt [eqn] ("Ill-formed equation head: " ^ quote (Syntax.string_of_term ctxt head))
else
error_at ctxt [eqn] "Expected equation or discriminator formula"
end;
fun build_corec_arg_disc (ctr_specs : corec_ctr_spec list)
({fun_args, ctr_no, prems, ...} : coeqn_data_disc) =
if is_none (#pred (nth ctr_specs ctr_no)) then
I
else
s_conjs prems
|> curry subst_bounds (List.rev fun_args)
|> abs_tuple_balanced fun_args
|> K |> nth_map (the (#pred (nth ctr_specs ctr_no)));
fun build_corec_arg_no_call (sel_eqns : coeqn_data_sel list) sel =
find_first (curry (op =) sel o #sel) sel_eqns
|> try (fn SOME {fun_args, rhs_term, ...} => abs_tuple_balanced fun_args rhs_term)
|> the_default undef_const
|> K;
fun build_corec_args_mutual_call ctxt has_call (sel_eqns : coeqn_data_sel list) sel =
(case find_first (curry (op =) sel o #sel) sel_eqns of
NONE => (I, I, I)
| SOME {fun_args, rhs_term, ... } =>
let
val bound_Ts = List.rev (map fastype_of fun_args);
fun rewrite_stop _ t = if has_call t then \<^term>\<open>False\<close> else \<^term>\<open>True\<close>;
fun rewrite_end _ t = if has_call t then undef_const else t;
fun rewrite_cont bound_Ts t =
if has_call t then mk_tuple1_balanced bound_Ts (snd (strip_comb t)) else undef_const;
fun massage f _ = massage_let_if_case_corec ctxt has_call f bound_Ts rhs_term
|> abs_tuple_balanced fun_args;
in
(massage rewrite_stop, massage rewrite_end, massage rewrite_cont)
end);
fun build_corec_arg_nested_call ctxt has_call (sel_eqns : coeqn_data_sel list) sel =
(case find_first (curry (op =) sel o #sel) sel_eqns of
NONE => I
| SOME {fun_args, rhs_term, ...} =>
let
fun massage_call bound_Ts U T t0 =
let
val U2 =
(case try dest_sumT U of
SOME (U1, U2) => if U1 = T then U2 else invalid_map ctxt [] t0
| NONE => invalid_map ctxt [] t0);
fun rewrite bound_Ts (Abs (s, T', t')) = Abs (s, T', rewrite (T' :: bound_Ts) t')
| rewrite bound_Ts (t as _ $ _) =
let val (u, vs) = strip_comb t in
if is_Free u andalso has_call u then
Inr_const T U2 $ mk_tuple1_balanced bound_Ts vs
else if try (fst o dest_Const) u = SOME \<^const_name>\<open>case_prod\<close> then
map (rewrite bound_Ts) vs |> chop 1
|>> HOLogic.mk_case_prod o the_single
|> Term.list_comb
else
Term.list_comb (rewrite bound_Ts u, map (rewrite bound_Ts) vs)
end
| rewrite _ t =
if is_Free t andalso has_call t then Inr_const T U2 $ HOLogic.unit else t;
in
rewrite bound_Ts t0
end;
fun massage_noncall U T t =
build_map ctxt [] [] (uncurry Inl_const o dest_sumT o snd) (T, U) $ t;
val bound_Ts = List.rev (map fastype_of fun_args);
in
fn t =>
rhs_term
|> massage_nested_corec_call ctxt has_call massage_call (K massage_noncall) bound_Ts
(range_type (fastype_of t)) (fastype_of1 (bound_Ts, rhs_term))
|> abs_tuple_balanced fun_args
end);
fun build_corec_args_sel ctxt has_call (all_sel_eqns : coeqn_data_sel list)
(ctr_spec : corec_ctr_spec) =
(case filter (curry (op =) (#ctr ctr_spec) o #ctr) all_sel_eqns of
[] => I
| sel_eqns =>
let
val sel_call_list = #sels ctr_spec ~~ #calls ctr_spec;
val no_calls' = map_filter (try (apsnd (fn No_Corec n => n))) sel_call_list;
val mutual_calls' = map_filter (try (apsnd (fn Mutual_Corec n => n))) sel_call_list;
val nested_calls' = map_filter (try (apsnd (fn Nested_Corec n => n))) sel_call_list;
in
I
#> fold (fn (sel, n) => nth_map n (build_corec_arg_no_call sel_eqns sel)) no_calls'
#> fold (fn (sel, (q, g, h)) =>
let val (fq, fg, fh) = build_corec_args_mutual_call ctxt has_call sel_eqns sel in
nth_map q fq o nth_map g fg o nth_map h fh end) mutual_calls'
#> fold (fn (sel, n) => nth_map n
(build_corec_arg_nested_call ctxt has_call sel_eqns sel)) nested_calls'
end);
fun build_defs ctxt bs mxs has_call arg_Tss (corec_specs : corec_spec list)
(disc_eqnss : coeqn_data_disc list list) (sel_eqnss : coeqn_data_sel list list) =
let
val corecs = map #corec corec_specs;
val ctr_specss = map #ctr_specs corec_specs;
val corec_args = hd corecs
|> fst o split_last o binder_types o fastype_of
|> map (fn T =>
if range_type T = HOLogic.boolT then Abs (Name.uu_, domain_type T, \<^term>\<open>False\<close>)
else Const (\<^const_name>\<open>undefined\<close>, T))
|> fold2 (fold o build_corec_arg_disc) ctr_specss disc_eqnss
|> fold2 (fold o build_corec_args_sel ctxt has_call) sel_eqnss ctr_specss;
val bad = fold (add_extra_frees ctxt [] []) corec_args [];
val _ = null bad orelse
(if exists has_call corec_args then nonprimitive_corec ctxt []
else extra_variable_in_rhs ctxt [] (hd bad));
val excludess' =
disc_eqnss
|> map (map (fn x => (#fun_args x, #ctr_no x, #prems x, #auto_gen x))
#> fst o (fn xs => fold_map (fn x => fn ys => ((x, ys), ys @ [x])) xs [])
#> maps (uncurry (map o pair)
#> map (fn ((fun_args, c, x, a), (_, c', y, a')) =>
((c, c', a orelse a'), (x, s_not (s_conjs y)))
||> map_prod (map HOLogic.mk_Trueprop) HOLogic.mk_Trueprop
||> Logic.list_implies
||> curry Logic.list_all (map dest_Free fun_args))));
in
map (Term.list_comb o rpair corec_args) corecs
|> map2 abs_curried_balanced arg_Tss
|> (fn ts => Syntax.check_terms ctxt ts
handle ERROR _ => nonprimitive_corec ctxt [])
|> @{map 3} (fn b => fn mx => fn t =>
((b, mx), ((Binding.concealed (Thm.def_binding b), []), t))) bs mxs
|> rpair excludess'
end;
fun mk_actual_disc_eqns fun_binding arg_Ts exhaustive ({ctr_specs, ...} : corec_spec)
(sel_eqns : coeqn_data_sel list) (disc_eqns : coeqn_data_disc list) =
let
val fun_name = Binding.name_of fun_binding;
val num_disc_eqns = length disc_eqns;
val num_ctrs = length ctr_specs;
in
if (exhaustive andalso num_disc_eqns <> 0) orelse num_disc_eqns <> num_ctrs - 1 then
(num_disc_eqns > 0 orelse error ("Missing discriminator formula for " ^ quote fun_name);
disc_eqns)
else
let
val ctr_no = 0 upto length ctr_specs
|> the o find_first (fn j => not (exists (curry (op =) j o #ctr_no) disc_eqns));
val {ctr, disc, ...} = nth ctr_specs ctr_no;
val sel_eqn_opt = find_first (equal ctr o #ctr) sel_eqns;
val fun_T = arg_Ts ---> body_type (fastype_of (#ctr (hd ctr_specs)));
val fun_args = (try (#fun_args o hd) disc_eqns, try (#fun_args o hd) sel_eqns)
|> the_default (map (curry Free Name.uu) arg_Ts) o merge_options;
val prems = maps (s_not_conj o #prems) disc_eqns;
val ctr_rhs_opt = Option.map #ctr_rhs_opt sel_eqn_opt |> the_default NONE;
val code_rhs_opt = Option.map #code_rhs_opt sel_eqn_opt |> the_default NONE;
val eqn_pos = Option.map (curry (op +) 1 o #eqn_pos) sel_eqn_opt
|> the_default 100000; (* FIXME *)
val extra_disc_eqn =
{fun_name = fun_name, fun_T = fun_T, fun_args = fun_args, ctr = ctr, ctr_no = ctr_no,
disc = disc, prems = prems, auto_gen = true, ctr_rhs_opt = ctr_rhs_opt,
code_rhs_opt = code_rhs_opt, eqn_pos = eqn_pos, user_eqn = undef_const};
in
chop ctr_no disc_eqns ||> cons extra_disc_eqn |> op @
end
end;
fun find_corec_calls ctxt has_call (basic_ctr_specs : basic_corec_ctr_spec list)
({ctr, sel, rhs_term, ...} : coeqn_data_sel) =
let
val sel_no = find_first (curry (op =) ctr o #ctr) basic_ctr_specs
|> find_index (curry (op =) sel) o #sels o the;
in
K (if has_call rhs_term then fold_rev_let_if_case ctxt (K cons) [] rhs_term [] else [])
|> nth_map sel_no |> AList.map_entry (op =) ctr
end;
fun applied_fun_of fun_name fun_T fun_args =
Term.list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0));
fun is_trivial_implies thm =
uncurry (member (op aconv)) (Logic.strip_horn (Thm.prop_of thm));
fun primcorec_ursive int auto opts fixes specs of_specs_opt lthy =
let
val (bs, mxs) = map_split (apfst fst) fixes;
val (arg_Ts, res_Ts) = map (strip_type o snd o fst #>> mk_tupleT_balanced) fixes |> split_list;
val primcorec_types = map (#1 o dest_Type) res_Ts;
val _ = check_duplicate_const_names bs;
val _ = List.app (uncurry (check_top_sort lthy)) (bs ~~ arg_Ts);
val actual_nn = length bs;
val plugins = get_first (fn Plugins_Option f => SOME (f lthy) | _ => NONE) (rev opts)
|> the_default Plugin_Name.default_filter;
val sequentials = replicate actual_nn (exists (can (fn Sequential_Option => ())) opts);
val exhaustives = replicate actual_nn (exists (can (fn Exhaustive_Option => ())) opts);
val transfers = replicate actual_nn (exists (can (fn Transfer_Option => ())) opts);
val fun_names = map Binding.name_of bs;
val qualifys = map (fold_rev (uncurry Binding.qualify o swap) o Binding.path_of) bs;
val basic_ctr_specss = map (basic_corec_specs_of lthy) res_Ts;
val frees = map (fst #>> Binding.name_of #> Free) fixes;
val has_call = Term.exists_subterm (member (op =) frees);
val eqns_data =
@{fold_map 2} (dissect_coeqn lthy has_call fun_names sequentials basic_ctr_specss)
(tag_list 0 (map snd specs)) of_specs_opt []
|> flat o fst;
val missing = fun_names
|> filter (map (fn Disc x => #fun_name x | Sel x => #fun_name x) eqns_data
|> not oo member (op =));
val _ = null missing orelse missing_equations_for_const (hd missing);
val callssss =
map_filter (try (fn Sel x => x)) eqns_data
|> partition_eq (op = o apply2 #fun_name)
|> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
|> map (flat o snd)
|> map2 (fold o find_corec_calls lthy has_call) basic_ctr_specss
|> map2 (curry (op |>)) (map (map (fn {ctr, sels, ...} =>
(ctr, map (K []) sels))) basic_ctr_specss);
val (corec_specs0, _, coinduct_thm, coinduct_strong_thm, coinduct_thms, coinduct_strong_thms,
(coinduct_attrs, common_coinduct_attrs), n2m, lthy) =
corec_specs_of bs arg_Ts res_Ts frees callssss lthy;
val corec_specs = take actual_nn corec_specs0;
val ctr_specss = map #ctr_specs corec_specs;
val disc_eqnss0 = map_filter (try (fn Disc x => x)) eqns_data
|> partition_eq (op = o apply2 #fun_name)
|> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
|> map (sort (op < o apply2 #ctr_no |> make_ord) o flat o snd);
val _ = disc_eqnss0 |> map (fn x =>
let val dups = duplicates (op = o apply2 #ctr_no) x in
null dups orelse
error_at lthy
(maps (fn t => filter (curry (op =) (#ctr_no t) o #ctr_no) x) dups
|> map (fn {ctr_rhs_opt = SOME t, ...} => t | {user_eqn, ...} => user_eqn))
"Overspecified case(s)"
end);
val sel_eqnss = map_filter (try (fn Sel x => x)) eqns_data
|> partition_eq (op = o apply2 #fun_name)
|> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
|> map (flat o snd);
val _ = sel_eqnss |> map (fn x =>
let val dups = duplicates (op = o apply2 ctr_sel_of) x in
null dups orelse
error_at lthy
(maps (fn t => filter (curry (op =) (ctr_sel_of t) o ctr_sel_of) x) dups
|> map (fn {ctr_rhs_opt = SOME t, ...} => t | {user_eqn, ...} => user_eqn))
"Overspecified case(s)"
end);
val arg_Tss = map (binder_types o snd o fst) fixes;
val disc_eqnss = @{map 6} mk_actual_disc_eqns bs arg_Tss exhaustives corec_specs sel_eqnss
disc_eqnss0;
val (defs, excludess') =
build_defs lthy bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss;
val tac_opts =
map (fn {code_rhs_opt, ...} :: _ =>
if auto orelse is_some code_rhs_opt then SOME (auto_tac o #context) else NONE) disc_eqnss;
fun exclude_tac tac_opt sequential (c, c', a) =
if a orelse c = c' orelse sequential then
SOME (fn {context = ctxt, prems = _} => HEADGOAL (mk_primcorec_assumption_tac ctxt []))
else
tac_opt;
val excludess'' = @{map 3} (fn tac_opt => fn sequential => map (fn (j, goal) =>
(j, (Option.map (Goal.prove (*no sorry*) lthy [] [] goal #> Thm.close_derivation \<^here>)
(exclude_tac tac_opt sequential j), goal))))
tac_opts sequentials excludess'
handle ERROR _ => use_primcorecursive ();
val taut_thmss = map (map (apsnd (the o fst)) o filter (is_some o fst o snd)) excludess'';
val (goal_idxss, exclude_goalss) = excludess''
|> map (map (apsnd (rpair [] o snd)) o filter (is_none o fst o snd))
|> split_list o map split_list;
fun list_all_fun_args extras =
map2 (fn [] => I
| {fun_args, ...} :: _ => map (curry Logic.list_all (extras @ map dest_Free fun_args)))
disc_eqnss;
val syntactic_exhaustives =
map (fn disc_eqns => forall (null o #prems orf is_some o #code_rhs_opt) disc_eqns
orelse exists #auto_gen disc_eqns)
disc_eqnss;
val de_facto_exhaustives =
map2 (fn b => fn b' => b orelse b') exhaustives syntactic_exhaustives;
val nchotomy_goalss =
map2 (fn false => K [] | true => single o HOLogic.mk_Trueprop o mk_dnf o map #prems)
de_facto_exhaustives disc_eqnss
|> list_all_fun_args []
val nchotomy_taut_thmss =
@{map 5} (fn tac_opt => fn {exhaust_discs = res_exhaust_discs, ...} =>
fn {code_rhs_opt, ...} :: _ => fn [] => K []
| [goal] => fn true =>
let
val (_, _, arg_exhaust_discs, _, _) =
case_thms_of_term lthy (the_default Term.dummy code_rhs_opt);
in
[Goal.prove (*no sorry*) lthy [] [] goal (fn {context = ctxt, ...} =>
mk_primcorec_nchotomy_tac ctxt (res_exhaust_discs @ arg_exhaust_discs))
|> Thm.close_derivation \<^here>]
handle ERROR _ => use_primcorecursive ()
end
| false =>
(case tac_opt of
SOME tac => [Goal.prove_sorry lthy [] [] goal tac |> Thm.close_derivation \<^here>]
| NONE => []))
tac_opts corec_specs disc_eqnss nchotomy_goalss syntactic_exhaustives;
val syntactic_exhaustives =
map (fn disc_eqns => forall (null o #prems orf is_some o #code_rhs_opt) disc_eqns
orelse exists #auto_gen disc_eqns)
disc_eqnss;
val nchotomy_goalss =
map2 (fn (NONE, false) => map (rpair []) | _ => K []) (tac_opts ~~ syntactic_exhaustives)
nchotomy_goalss;
val goalss = nchotomy_goalss @ exclude_goalss;
fun prove thmss'' def_infos lthy =
let
val def_thms = map (snd o snd) def_infos;
val ts = map fst def_infos;
val (nchotomy_thmss, exclude_thmss) =
(map2 append (take actual_nn thmss'') nchotomy_taut_thmss, drop actual_nn thmss'');
val ps =
Variable.variant_frees lthy (maps (maps #fun_args) disc_eqnss) [("P", HOLogic.boolT)];
val exhaust_thmss =
map2 (fn false => K []
| true => fn disc_eqns as {fun_args, ...} :: _ =>
let
val p = Bound (length fun_args);
fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
in
[mk_imp_p (map (mk_imp_p o map HOLogic.mk_Trueprop o #prems) disc_eqns)]
end)
de_facto_exhaustives disc_eqnss
|> list_all_fun_args ps
|> @{map 3} (fn disc_eqns as {fun_args, ...} :: _ => fn [] => K []
| [nchotomy_thm] => fn [goal] =>
[Goal.prove_sorry lthy [] [] goal
(fn {context = ctxt, prems = _} =>
mk_primcorec_exhaust_tac ctxt
("" (* for "P" *) :: map (fst o dest_Free) fun_args)
(length disc_eqns) nchotomy_thm)
|> Thm.close_derivation \<^here>])
disc_eqnss nchotomy_thmss;
val nontriv_exhaust_thmss = map (filter_out is_trivial_implies) exhaust_thmss;
val excludess' = map (op ~~) (goal_idxss ~~ exclude_thmss);
fun mk_excludesss excludes n =
fold (fn ((c, c', _), thm) => nth_map c (nth_map c' (K [thm])))
excludes (map (fn k => replicate k [asm_rl] @ replicate (n - k) []) (0 upto n - 1));
val excludessss =
map2 (fn excludes => mk_excludesss excludes o length o #ctr_specs)
(map2 append excludess' taut_thmss) corec_specs;
fun prove_disc ({ctr_specs, ...} : corec_spec) excludesss
({fun_name, fun_T, fun_args, ctr_no, prems, eqn_pos, ...} : coeqn_data_disc) =
if Term.aconv_untyped (#disc (nth ctr_specs ctr_no), \<^term>\<open>\<lambda>x. x = x\<close>) then
[]
else
let
val {disc, corec_disc, ...} = nth ctr_specs ctr_no;
val k = 1 + ctr_no;
val m = length prems;
val goal =
applied_fun_of fun_name fun_T fun_args
|> curry betapply disc
|> HOLogic.mk_Trueprop
|> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
|> curry Logic.list_all (map dest_Free fun_args);
in
if prems = [\<^term>\<open>False\<close>] then
[]
else
Goal.prove_sorry lthy [] [] goal
(fn {context = ctxt, prems = _} =>
mk_primcorec_disc_tac ctxt def_thms corec_disc k m excludesss)
|> Thm.close_derivation \<^here>
|> pair (#disc (nth ctr_specs ctr_no))
|> pair eqn_pos
|> single
end;
fun prove_sel ({sel_defs, fp_nesting_maps, fp_nesting_map_ident0s, fp_nesting_map_comps,
ctr_specs, ...} : corec_spec) (disc_eqns : coeqn_data_disc list) excludesss
({fun_name, fun_T, fun_args, ctr, sel, rhs_term, code_rhs_opt, eqn_pos, ...}
: coeqn_data_sel) =
let
val ctr_spec = the (find_first (curry (op =) ctr o #ctr) ctr_specs);
val ctr_no = find_index (curry (op =) ctr o #ctr) ctr_specs;
val prems = the_default (maps (s_not_conj o #prems) disc_eqns)
(find_first (curry (op =) ctr_no o #ctr_no) disc_eqns |> Option.map #prems);
val corec_sel = find_index (curry (op =) sel) (#sels ctr_spec)
|> nth (#corec_sels ctr_spec);
val k = 1 + ctr_no;
val m = length prems;
val goal =
applied_fun_of fun_name fun_T fun_args
|> curry betapply sel
|> rpair (abstract_over_list fun_args rhs_term)
|> HOLogic.mk_Trueprop o HOLogic.mk_eq
|> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
|> curry Logic.list_all (map dest_Free fun_args);
val (distincts, _, _, split_sels, split_sel_asms) = case_thms_of_term lthy rhs_term;
in
Goal.prove_sorry lthy [] [] goal
(fn {context = ctxt, prems = _} =>
mk_primcorec_sel_tac ctxt def_thms distincts split_sels split_sel_asms
fp_nesting_maps fp_nesting_map_ident0s fp_nesting_map_comps corec_sel k m
excludesss)
|> Thm.close_derivation \<^here>
|> `(is_some code_rhs_opt ? Local_Defs.fold lthy sel_defs) (*mildly too aggressive*)
|> pair sel
|> pair eqn_pos
end;
fun prove_ctr disc_alist sel_alist ({sel_defs, ...} : corec_spec)
(disc_eqns : coeqn_data_disc list) (sel_eqns : coeqn_data_sel list)
({ctr, disc, sels, collapse, ...} : corec_ctr_spec) =
(* don't try to prove theorems when some sel_eqns are missing *)
if not (exists (curry (op =) ctr o #ctr) disc_eqns)
andalso not (exists (curry (op =) ctr o #ctr) sel_eqns)
orelse
filter (curry (op =) ctr o #ctr) sel_eqns
|> fst o finds (op = o apsnd #sel) sels
|> exists (null o snd) then
[]
else
let
val (fun_name, fun_T, fun_args, prems, ctr_rhs_opt, code_rhs_opt, eqn_pos) =
(find_first (curry (op =) ctr o #ctr) disc_eqns,
find_first (curry (op =) ctr o #ctr) sel_eqns)
|>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #prems x,
#ctr_rhs_opt x, #code_rhs_opt x, #eqn_pos x))
||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, [],
#ctr_rhs_opt x, #code_rhs_opt x, #eqn_pos x))
|> the o merge_options;
val m = length prems;
val goal =
(case ctr_rhs_opt of
SOME rhs => rhs
| NONE =>
filter (curry (op =) ctr o #ctr) sel_eqns
|> fst o finds (op = o apsnd #sel) sels
|> map (snd #> (fn [x] => (#fun_args x, #rhs_term x))
#-> abstract_over_list)
|> curry Term.list_comb ctr)
|> curry mk_Trueprop_eq (applied_fun_of fun_name fun_T fun_args)
|> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
|> curry Logic.list_all (map dest_Free fun_args);
val disc_thm_opt = AList.lookup (op =) disc_alist disc;
val sel_thms = map (snd o snd) (filter (member (op =) sels o fst) sel_alist);
in
if prems = [\<^term>\<open>False\<close>] then
[]
else
Goal.prove_sorry lthy [] [] goal
(fn {context = ctxt, prems = _} =>
mk_primcorec_ctr_tac ctxt m collapse disc_thm_opt sel_thms)
|> is_some code_rhs_opt ? Local_Defs.fold lthy sel_defs (*mildly too aggressive*)
|> Thm.close_derivation \<^here>
|> pair ctr
|> pair eqn_pos
|> single
end;
fun prove_code exhaustive (disc_eqns : coeqn_data_disc list)
(sel_eqns : coeqn_data_sel list) nchotomys ctr_alist ctr_specs =
let
val fun_data_opt =
(find_first (member (op =) (map #ctr ctr_specs) o #ctr) disc_eqns,
find_first (member (op =) (map #ctr ctr_specs) o #ctr) sel_eqns)
|>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #code_rhs_opt x))
||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #code_rhs_opt x))
|> merge_options;
in
(case fun_data_opt of
NONE => []
| SOME (fun_name, fun_T, fun_args, rhs_opt) =>
let
val bound_Ts = List.rev (map fastype_of fun_args);
val lhs = applied_fun_of fun_name fun_T fun_args;
val rhs_info_opt =
(case rhs_opt of
SOME rhs =>
let
val raw_rhs = expand_corec_code_rhs lthy has_call bound_Ts rhs;
val cond_ctrs =
fold_rev_corec_code_rhs lthy (K oo (cons oo pair)) bound_Ts raw_rhs [];
val ctr_thms =
map (the_default FalseE o AList.lookup (op =) ctr_alist o snd) cond_ctrs;
in SOME (false, rhs, raw_rhs, ctr_thms) end
| NONE =>
let
fun prove_code_ctr ({ctr, sels, ...} : corec_ctr_spec) =
if not (exists (curry (op =) ctr o fst) ctr_alist) then
NONE
else
let
val prems = find_first (curry (op =) ctr o #ctr) disc_eqns
|> Option.map #prems |> the_default [];
val t =
filter (curry (op =) ctr o #ctr) sel_eqns
|> fst o finds (op = o apsnd #sel) sels
|> map (snd #> (fn [x] => (#fun_args x, #rhs_term x))
#-> abstract_over_list)
|> curry Term.list_comb ctr;
in
SOME (prems, t)
end;
val ctr_conds_argss_opt = map prove_code_ctr ctr_specs;
val exhaustive_code =
exhaustive
orelse exists (is_some andf (null o fst o the)) ctr_conds_argss_opt
orelse forall is_some ctr_conds_argss_opt
andalso exists #auto_gen disc_eqns;
val rhs =
(if exhaustive_code then
split_last (map_filter I ctr_conds_argss_opt) ||> snd
else
Const (\<^const_name>\<open>Code.abort\<close>, \<^typ>\<open>String.literal\<close> -->
(HOLogic.unitT --> body_type fun_T) --> body_type fun_T) $
HOLogic.mk_literal fun_name $
absdummy HOLogic.unitT (incr_boundvars 1 lhs)
|> pair (map_filter I ctr_conds_argss_opt))
|-> fold_rev (fn (prems, u) => mk_If (s_conjs prems) u)
in
SOME (exhaustive_code, rhs, rhs, map snd ctr_alist)
end);
in
(case rhs_info_opt of
NONE => []
| SOME (exhaustive_code, rhs, raw_rhs, ctr_thms) =>
let
val ms = map (Logic.count_prems o Thm.prop_of) ctr_thms;
val (raw_goal, goal) = (raw_rhs, rhs)
|> apply2 (curry mk_Trueprop_eq (applied_fun_of fun_name fun_T fun_args)
#> abstract_over_list fun_args
#> curry Logic.list_all (map dest_Free fun_args));
val (distincts, discIs, _, split_sels, split_sel_asms) =
case_thms_of_term lthy raw_rhs;
val raw_code_thm =
Goal.prove_sorry lthy [] [] raw_goal
(fn {context = ctxt, prems = _} =>
mk_primcorec_raw_code_tac ctxt distincts discIs split_sels split_sel_asms
ms ctr_thms
(if exhaustive_code then try the_single nchotomys else NONE))
|> Thm.close_derivation \<^here>;
in
Goal.prove_sorry lthy [] [] goal
(fn {context = ctxt, prems = _} =>
mk_primcorec_code_tac ctxt distincts split_sels raw_code_thm)
|> Thm.close_derivation \<^here>
|> single
end)
end)
end;
val disc_alistss = @{map 3} (map oo prove_disc) corec_specs excludessss disc_eqnss;
val disc_alists = map (map snd o flat) disc_alistss;
val sel_alists = @{map 4} (map ooo prove_sel) corec_specs disc_eqnss excludessss sel_eqnss;
val disc_thmss = map (map snd o sort_list_duplicates o flat) disc_alistss;
val disc_thmsss' = map (map (map (snd o snd))) disc_alistss;
val sel_thmss = map (map (fst o snd) o sort_list_duplicates) sel_alists;
fun prove_disc_iff ({ctr_specs, ...} : corec_spec) exhaust_thms disc_thmss'
(({fun_args = exhaust_fun_args, ...} : coeqn_data_disc) :: _) disc_thms
({fun_name, fun_T, fun_args, ctr_no, prems, eqn_pos, ...} : coeqn_data_disc) =
if null exhaust_thms orelse null disc_thms then
[]
else
let
val {disc, distinct_discss, ...} = nth ctr_specs ctr_no;
val goal =
mk_Trueprop_eq (applied_fun_of fun_name fun_T fun_args |> curry betapply disc,
mk_conjs prems)
|> curry Logic.list_all (map dest_Free fun_args);
in
Goal.prove_sorry lthy [] [] goal
(fn {context = ctxt, prems = _} =>
mk_primcorec_disc_iff_tac ctxt (map (fst o dest_Free) exhaust_fun_args)
(the_single exhaust_thms) disc_thms disc_thmss' (flat distinct_discss))
|> Thm.close_derivation \<^here>
|> fold (fn rule => perhaps (try (fn thm => Meson.first_order_resolve lthy thm rule)))
@{thms eqTrueE eq_False[THEN iffD1] notnotD}
|> pair eqn_pos
|> single
end;
val disc_iff_thmss = @{map 6} (flat ooo map2 oooo prove_disc_iff) corec_specs exhaust_thmss
disc_thmsss' disc_eqnss disc_thmsss' disc_eqnss
|> map sort_list_duplicates;
val ctr_alists = @{map 6} (fn disc_alist => maps oooo prove_ctr disc_alist) disc_alists
(map (map snd) sel_alists) corec_specs disc_eqnss sel_eqnss ctr_specss;
val ctr_thmss0 = map (map snd) ctr_alists;
val ctr_thmss = map (map (snd o snd) o sort (int_ord o apply2 fst)) ctr_alists;
val code_thmss =
@{map 6} prove_code exhaustives disc_eqnss sel_eqnss nchotomy_thmss ctr_thmss0 ctr_specss;
val disc_iff_or_disc_thmss =
--> --------------------
--> maximum size reached
--> --------------------
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