take out possibility of moving corecursive calls past constructors -- this doesn't work in the general case
(* Title: HOL/BNF/Tools/bnf_gfp_rec_sugar.ML
Author: Lorenz Panny, TU Muenchen
Author: Jasmin Blanchette, TU Muenchen
Copyright 2013
Corecursor sugar.
*)
signature BNF_GFP_REC_SUGAR =
sig
val add_primcorecursive_cmd: bool ->
(binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list ->
Proof.context -> Proof.state
val add_primcorec_cmd: bool ->
(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
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_GFP_Rec_Sugar_Tactics
val codeN = "code"
val ctrN = "ctr"
val discN = "disc"
val selN = "sel"
val nitpicksimp_attrs = @{attributes [nitpick_simp]};
val simp_attrs = @{attributes [simp]};
val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
exception Primcorec_Error of string * term list;
fun primcorec_error str = raise Primcorec_Error (str, []);
fun primcorec_error_eqn str eqn = raise Primcorec_Error (str, [eqn]);
fun primcorec_error_eqns str eqns = raise Primcorec_Error (str, eqns);
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,
collapse: thm,
corec_thm: thm,
disc_corec: thm,
sel_corecs: thm list};
type corec_spec =
{corec: term,
nested_maps: thm list,
nested_map_idents: thm list,
nested_map_comps: thm list,
ctr_specs: corec_ctr_spec list};
exception AINT_NO_MAP of term;
fun not_codatatype ctxt T =
error ("Not a codatatype: " ^ Syntax.string_of_typ ctxt T);
fun ill_formed_corec_call ctxt t =
error ("Ill-formed corecursive call: " ^ quote (Syntax.string_of_term ctxt t));
fun invalid_map ctxt t =
error ("Invalid map function in " ^ quote (Syntax.string_of_term ctxt t));
fun unexpected_corec_call ctxt t =
error ("Unexpected corecursive call: " ^ quote (Syntax.string_of_term ctxt t));
val mk_conjs = try (foldr1 HOLogic.mk_conj) #> the_default @{const True};
val mk_disjs = try (foldr1 HOLogic.mk_disj) #> the_default @{const False};
val conjuncts_s = filter_out (curry (op =) @{const True}) o HOLogic.conjuncts;
fun s_not @{const True} = @{const False}
| s_not @{const False} = @{const True}
| s_not (@{const Not} $ t) = t
| s_not (@{const conj} $ t $ u) = @{const disj} $ s_not t $ s_not u
| s_not (@{const disj} $ t $ u) = @{const conj} $ s_not t $ s_not u
| s_not t = @{const Not} $ 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 False}] 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 False} then @{const False}
else mk_conjs (remove (op aconv) @{const True} cs);
fun s_disjs ds =
if member (op aconv) ds @{const True} then @{const True}
else mk_disjs (remove (op aconv) @{const False} ds);
fun s_dnf css0 =
let val css = propagate_units css0 in
if null css then
[@{const False}]
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 t =
let
val thy = Proof_Context.theory_of ctxt;
fun fld conds t =
(case Term.strip_comb t of
(Const (@{const_name Let}, _), [_, _]) => fld conds (unfold_let t)
| (Const (@{const_name If}, _), [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
NONE => apsnd (f conds t)
| SOME (conds', branches) =>
apfst (cons s) o fold_rev (uncurry fld)
(map (append conds o conjuncts_s) conds' ~~ branches))
| _ => apsnd (f conds t))
else
apsnd (f conds t)
end
| _ => apsnd (f conds t))
in
fld [] t o pair []
end;
fun case_of ctxt = ctr_sugar_of ctxt #> Option.map (fst o dest_Const o #casex);
fun massage_let_if_case ctxt has_call massage_leaf =
let
val thy = Proof_Context.theory_of ctxt;
fun check_no_call t = if has_call t then unexpected_corec_call ctxt 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 Let}, _), [_, _]) => massage_rec bound_Ts (unfold_let t)
| (Const (@{const_name If}, _), obj :: (branches as [_, _])) =>
let val branches' = map (massage_rec bound_Ts) branches in
Term.list_comb (If_const (typof (hd branches')) $ tap check_no_call obj, branches')
end
| (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, _), _]) =>
if case_of ctxt T_name = SOME c 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) obj_leftovers)
end
else
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
end;
val massage_mutual_corec_call = massage_let_if_case;
fun curried_type (Type (@{type_name fun}, [Type (@{type_name prod}, Ts), T])) = Ts ---> T;
fun massage_nested_corec_call ctxt has_call raw_massage_call bound_Ts U t =
let
fun check_no_call t = if has_call t then unexpected_corec_call ctxt t else ();
val build_map_Inl = build_map ctxt (uncurry Inl_const o dest_sumT o snd);
fun massage_mutual_call bound_Ts U T t =
if has_call t then
(case try dest_sumT U of
SOME (U1, U2) => if U1 = T then raw_massage_call bound_Ts T U2 t else invalid_map ctxt t
| NONE => invalid_map ctxt t)
else
build_map_Inl (T, U) $ t;
fun massage_mutual_fun bound_Ts U T t =
(case t of
Const (@{const_name comp}, _) $ t1 $ t2 =>
mk_comp bound_Ts (massage_mutual_fun bound_Ts U T t1, tap check_no_call t2)
| _ =>
let
val var = Var ((Name.uu, Term.maxidx_of_term t + 1),
domain_type (fastype_of1 (bound_Ts, t)));
in
Term.lambda var (massage_mutual_call bound_Ts U T (t $ var))
end);
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 (map3 (massage_map_or_map_arg bound_Ts) Us Ts) fs;
in
Term.list_comb (map', fs')
end
| NONE => raise AINT_NO_MAP t)
| massage_map _ _ _ t = raise AINT_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 AINT_NO_MAP _ => massage_mutual_fun bound_Ts U T t;
fun massage_call bound_Ts U T =
massage_let_if_case ctxt has_call (fn bound_Ts => fn t =>
if has_call t then
(case t of
Const (@{const_name prod_case}, _) $ t' =>
let
val U' = curried_type U;
val T' = curried_type T;
in
Const (@{const_name prod_case}, U' --> U) $ massage_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 AINT_NO_MAP _ => massage_mutual_call bound_Ts U T t)
| Abs (s, T', t') =>
Abs (s, T', massage_call (T' :: bound_Ts) (range_type U) (range_type T) t')
| _ => massage_mutual_call bound_Ts U T t)
else
build_map_Inl (T, U) $ t) bound_Ts;
val T = fastype_of1 (bound_Ts, t);
in
if has_call t then massage_call bound_Ts U T t else build_map_Inl (T, U) $ t
end;
val fold_rev_corec_call = fold_rev_let_if_case;
fun expand_to_ctr_term ctxt s Ts t =
(case ctr_sugar_of ctxt s of
SOME {ctrs, casex, ...} =>
Term.list_comb (mk_case Ts (Type (s, Ts)) 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
Type (s, Ts) =>
massage_let_if_case ctxt has_call (fn _ => fn t =>
if can (dest_ctr ctxt s) t then t else expand_to_ctr_term ctxt s Ts t) bound_Ts t
| _ => raise Fail "expand_corec_code_rhs");
fun massage_corec_code_rhs ctxt massage_ctr =
massage_let_if_case ctxt (K false)
(fn bound_Ts => uncurry (massage_ctr bound_Ts) o Term.strip_comb);
fun fold_rev_corec_code_rhs ctxt f =
snd ooo fold_rev_let_if_case ctxt (fn conds => uncurry (f conds) o Term.strip_comb);
fun case_thms_of_term ctxt bound_Ts t =
let
val (caseT_names, _) = fold_rev_let_if_case ctxt (K (K I)) bound_Ts t ();
val ctr_sugars = map (the o ctr_sugar_of ctxt) caseT_names;
in
(maps #distincts ctr_sugars, maps #discIs ctr_sugars, maps #sel_splits ctr_sugars,
maps #sel_split_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 {ctrs, discs, selss, ...} =>
let
val thy = Proof_Context.theory_of ctxt;
val gfpT = body_type (fastype_of (hd ctrs));
val As_rho = tvar_subst thy [gfpT] [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
map3 mk_spec ctrs discs selss
end)
| _ => not_codatatype ctxt res_T);
(*FIXME: remove special cases for product and sum once they are registered as datatypes*)
fun map_thms_of_typ ctxt (Type (s, _)) =
if s = @{type_name prod} then
@{thms map_pair_simp}
else if s = @{type_name sum} then
@{thms sum_map.simps}
else
(case fp_sugar_of ctxt s of
SOME {index, mapss, ...} => nth mapss index
| NONE => [])
| map_thms_of_typ _ _ = [];
fun corec_specs_of bs arg_Ts res_Ts get_indices callssss0 lthy =
let
val thy = Proof_Context.theory_of lthy;
val ((missing_res_Ts, perm0_kks,
fp_sugars as {nested_bnfs, fp_res = {xtor_co_iterss = dtor_coiters1 :: _, ...},
co_inducts = coinduct_thms, ...} :: _, (_, gfp_sugar_thms)), lthy') =
nested_to_mutual_fps Greatest_FP bs res_Ts get_indices callssss0 lthy;
val perm_fp_sugars = sort (int_ord o pairself #index) fp_sugars;
val indices = map #index fp_sugars;
val perm_indices = map #index perm_fp_sugars;
val perm_ctrss = map (#ctrs o of_fp_sugar #ctr_sugars) perm_fp_sugars;
val perm_ctr_Tsss = map (map (binder_types o fastype_of)) perm_ctrss;
val perm_gfpTs = map (body_type o fastype_of o hd) perm_ctrss;
val nn0 = length res_Ts;
val nn = length perm_gfpTs;
val kks = 0 upto nn - 1;
val perm_ns = map length perm_ctr_Tsss;
val perm_Cs = map (domain_type o body_fun_type o fastype_of o co_rec_of o
of_fp_sugar (#xtor_co_iterss o #fp_res)) perm_fp_sugars;
val (perm_p_Tss, (perm_q_Tssss, _, perm_f_Tssss, _)) =
mk_coiter_fun_arg_types perm_ctr_Tsss perm_Cs perm_ns (co_rec_of dtor_coiters1);
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 (map3 flat_corec_preds_predsss_gettersss perm_p_hss perm_q_hssss perm_f_hssss);
fun unpermute0 perm0_xs = permute_like (op =) perm0_kks kks perm0_xs;
fun unpermute perm_xs = permute_like (op =) perm_indices indices perm_xs;
val coinduct_thmss = map (unpermute0 o conj_dests nn) 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 gfpTs = unpermute perm_gfpTs;
val Cs = unpermute perm_Cs;
val As_rho = tvar_subst thy (take nn0 gfpTs) 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 fun}, [_, 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_ho q_iss f_iss f_Tss discI sel_thms collapse corec_thm
disc_corec sel_corecs =
let val nullary = not (can dest_funT (fastype_of ctr)) in
{ctr = substA ctr, disc = substA disc, sels = map substA sels, pred = p_ho,
calls = map3 (call_of nullary) q_iss f_iss f_Tss, discI = discI, sel_thms = sel_thms,
collapse = collapse, corec_thm = corec_thm, disc_corec = disc_corec,
sel_corecs = sel_corecs}
end;
fun mk_ctr_specs index (ctr_sugars : ctr_sugar list) p_is q_isss f_isss f_Tsss coiter_thmsss
disc_coitersss sel_coiterssss =
let
val ctrs = #ctrs (nth ctr_sugars index);
val discs = #discs (nth ctr_sugars index);
val selss = #selss (nth ctr_sugars index);
val p_ios = map SOME p_is @ [NONE];
val discIs = #discIs (nth ctr_sugars index);
val sel_thmss = #sel_thmss (nth ctr_sugars index);
val collapses = #collapses (nth ctr_sugars index);
val corec_thms = co_rec_of (nth coiter_thmsss index);
val disc_corecs = co_rec_of (nth disc_coitersss index);
val sel_corecss = co_rec_of (nth sel_coiterssss index);
in
map13 mk_ctr_spec ctrs discs selss p_ios q_isss f_isss f_Tsss discIs sel_thmss collapses
corec_thms disc_corecs sel_corecss
end;
fun mk_spec ({T, index, ctr_sugars, co_iterss = coiterss, co_iter_thmsss = coiter_thmsss,
disc_co_itersss = disc_coitersss, sel_co_iterssss = sel_coiterssss, ...} : fp_sugar)
p_is q_isss f_isss f_Tsss =
{corec = mk_co_iter thy Greatest_FP (substAT T) perm_Cs' (co_rec_of (nth coiterss index)),
nested_maps = maps (map_thms_of_typ lthy o T_of_bnf) nested_bnfs,
nested_map_idents = map (unfold_thms lthy @{thms id_def} o map_id0_of_bnf) nested_bnfs,
nested_map_comps = map map_comp_of_bnf nested_bnfs,
ctr_specs = mk_ctr_specs index ctr_sugars p_is q_isss f_isss f_Tsss coiter_thmsss
disc_coitersss sel_coiterssss};
in
((is_some gfp_sugar_thms, map5 mk_spec fp_sugars p_iss q_issss f_issss f_Tssss, missing_res_Ts,
co_induct_of coinduct_thms, strong_co_induct_of coinduct_thms, co_induct_of coinduct_thmss,
strong_co_induct_of coinduct_thmss), lthy')
end;
val undef_const = Const (@{const_name undefined}, dummyT);
val abs_tuple = HOLogic.tupled_lambda o HOLogic.mk_tuple;
fun abstract vs =
let fun a n (t $ u) = a n t $ a n u
| a n (Abs (v, T, b)) = Abs (v, T, a (n + 1) b)
| a n t = let val idx = find_index (equal t) vs in
if idx < 0 then t else Bound (n + idx) end
in a 0 end;
fun mk_prod1 bound_Ts (t, u) =
HOLogic.pair_const (fastype_of1 (bound_Ts, t)) (fastype_of1 (bound_Ts, u)) $ t $ u;
fun mk_tuple1 bound_Ts = the_default HOLogic.unit o try (foldr1 (mk_prod1 bound_Ts));
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,
maybe_ctr_rhs: term option,
maybe_code_rhs: term option,
user_eqn: term
};
type coeqn_data_sel = {
fun_name: string,
fun_T: typ,
fun_args: term list,
ctr: term,
sel: term,
rhs_term: term,
user_eqn: term
};
datatype coeqn_data =
Disc of coeqn_data_disc |
Sel of coeqn_data_sel;
fun dissect_coeqn_disc seq fun_names (basic_ctr_specss : basic_corec_ctr_spec list list)
maybe_ctr_rhs maybe_code_rhs prems' 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 => primcorec_error_eqn "malformed discriminator formula" concl;
val ((fun_name, fun_T), fun_args) = strip_comb applied_fun |>> dest_Free;
val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ 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 Not};
val _ = not_disc andalso length ctrs <> 2 andalso
primcorec_error_eqn "negated discriminator for a type with \<noteq> 2 constructors" concl;
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 (equal t) ctrs in
if n >= 0 then SOME n else NONE end | _ => NONE);
val _ = is_some disc' orelse is_some eq_ctr0 orelse
primcorec_error_eqn "no discriminator in equation" concl;
val ctr_no' =
if is_none disc' then the eq_ctr0 else find_index (equal (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 = try (fst o dest_Free o the_single) prems' = SOME Name.uu_;
val matchedss = AList.lookup (op =) matchedsss fun_name |> the_default [];
val prems = map (abstract (List.rev fun_args)) prems';
val real_prems =
(if catch_all orelse seq 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 seq then matchedss @ [prems] else matchedss @ [real_prems]);
val user_eqn =
(real_prems, concl)
|>> map HOLogic.mk_Trueprop ||> HOLogic.mk_Trueprop o abstract (List.rev fun_args)
|> curry Logic.list_all (map dest_Free fun_args) o Logic.list_implies;
in
(Disc {
fun_name = fun_name,
fun_T = fun_T,
fun_args = fun_args,
ctr = ctr,
ctr_no = ctr_no,
disc = disc,
prems = real_prems,
auto_gen = catch_all,
maybe_ctr_rhs = maybe_ctr_rhs,
maybe_code_rhs = maybe_code_rhs,
user_eqn = user_eqn
}, matchedsss')
end;
fun dissect_coeqn_sel fun_names (basic_ctr_specss : basic_corec_ctr_spec list list) eqn'
maybe_of_spec eqn =
let
val (lhs, rhs) = HOLogic.dest_eq eqn
handle TERM _ =>
primcorec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn;
val sel = head_of lhs;
val ((fun_name, fun_T), fun_args) = dest_comb lhs |> snd |> strip_comb |> apfst dest_Free
handle TERM _ =>
primcorec_error_eqn "malformed selector argument in left-hand side" eqn;
val basic_ctr_specs = the (AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name)
handle Option.Option =>
primcorec_error_eqn "malformed selector argument in left-hand side" eqn;
val {ctr, ...} =
(case maybe_of_spec of
SOME of_spec => the (find_first (equal of_spec o #ctr) basic_ctr_specs)
| NONE => filter (exists (equal sel) o #sels) basic_ctr_specs |> the_single
handle List.Empty => primcorec_error_eqn "ambiguous selector - use \"of\"" eqn);
val user_eqn = drop_All eqn';
in
Sel {
fun_name = fun_name,
fun_T = fun_T,
fun_args = fun_args,
ctr = ctr,
sel = sel,
rhs_term = rhs,
user_eqn = user_eqn
}
end;
fun dissect_coeqn_ctr seq fun_names (basic_ctr_specss : basic_corec_ctr_spec list list) eqn'
maybe_code_rhs prems concl matchedsss =
let
val (lhs, rhs) = HOLogic.dest_eq concl;
val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name;
val (ctr, ctr_args) = strip_comb (unfold_let rhs);
val {disc, sels, ...} = the (find_first (equal ctr o #ctr) basic_ctr_specs)
handle Option.Option => primcorec_error_eqn "not a constructor" ctr;
val disc_concl = betapply (disc, lhs);
val (maybe_eqn_data_disc, matchedsss') = if length basic_ctr_specs = 1
then (NONE, matchedsss)
else apfst SOME (dissect_coeqn_disc seq fun_names basic_ctr_specss
(SOME (abstract (List.rev fun_args) rhs)) maybe_code_rhs prems disc_concl matchedsss);
val sel_concls = sels ~~ ctr_args
|> map (fn (sel, ctr_arg) => HOLogic.mk_eq (betapply (sel, lhs), ctr_arg));
(*
val _ = tracing ("reduced\n " ^ Syntax.string_of_term @{context} concl ^ "\nto\n \<cdot> " ^
(is_some maybe_eqn_data_disc ? K (Syntax.string_of_term @{context} disc_concl ^ "\n \<cdot> ")) "" ^
space_implode "\n \<cdot> " (map (Syntax.string_of_term @{context}) sel_concls) ^
"\nfor premise(s)\n \<cdot> " ^
space_implode "\n \<cdot> " (map (Syntax.string_of_term @{context}) prems));
*)
val eqns_data_sel =
map (dissect_coeqn_sel fun_names basic_ctr_specss eqn' (SOME ctr)) sel_concls;
in
(the_list maybe_eqn_data_disc @ eqns_data_sel, matchedsss')
end;
fun dissect_coeqn_code lthy has_call fun_names basic_ctr_specss eqn' concl matchedsss =
let
val (lhs, (rhs', rhs)) = HOLogic.dest_eq concl ||> `(expand_corec_code_rhs lthy has_call []);
val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name;
val cond_ctrs = fold_rev_corec_code_rhs lthy (fn cs => fn ctr => fn _ =>
if member ((op =) o apsnd #ctr) basic_ctr_specs ctr
then cons (ctr, cs)
else primcorec_error_eqn "not a constructor" 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 lthy (fn _ => fn ctr' => fn args =>
if ctr' = ctr then nth args n else Const (@{const_name undefined}, T)) [] rhs')
|> curry list_comb ctr
|> curry HOLogic.mk_eq lhs);
in
fold_map2 (dissect_coeqn_ctr false fun_names basic_ctr_specss eqn'
(SOME (abstract (List.rev fun_args) rhs)))
ctr_premss ctr_concls matchedsss
end;
fun dissect_coeqn lthy seq has_call fun_names (basic_ctr_specss : basic_corec_ctr_spec list list)
eqn' maybe_of_spec matchedsss =
let
val eqn = drop_All eqn'
handle TERM _ => primcorec_error_eqn "malformed function equation" eqn';
val (prems, concl) = Logic.strip_horn eqn
|> apfst (map HOLogic.dest_Trueprop) o apsnd HOLogic.dest_Trueprop;
val head = concl
|> perhaps (try HOLogic.dest_not) |> perhaps (try (fst o HOLogic.dest_eq))
|> head_of;
val maybe_rhs = concl |> perhaps (try HOLogic.dest_not) |> try (snd o HOLogic.dest_eq);
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 maybe_rhs andalso
member (op =) (filter (null o binder_types o fastype_of) ctrs) (the maybe_rhs) then
dissect_coeqn_disc seq fun_names basic_ctr_specss NONE NONE prems concl matchedsss
|>> single
else if member (op =) sels head then
([dissect_coeqn_sel fun_names basic_ctr_specss eqn' maybe_of_spec concl], matchedsss)
else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso
member (op =) ctrs (head_of (unfold_let (the maybe_rhs))) then
dissect_coeqn_ctr seq fun_names basic_ctr_specss eqn' NONE prems concl matchedsss
else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso
null prems then
dissect_coeqn_code lthy has_call fun_names basic_ctr_specss eqn' concl matchedsss
|>> flat
else
primcorec_error_eqn "malformed function equation" eqn
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)
|> HOLogic.tupled_lambda (HOLogic.mk_tuple 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 (equal sel o #sel) sel_eqns
|> try (fn SOME {fun_args, rhs_term, ...} => abs_tuple fun_args rhs_term)
|> the_default undef_const
|> K;
fun build_corec_args_mutual_call lthy has_call (sel_eqns : coeqn_data_sel list) sel =
(case find_first (equal 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 False} else @{term True};
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 bound_Ts (snd (strip_comb t)) else undef_const;
fun massage f _ = massage_mutual_corec_call lthy has_call f bound_Ts rhs_term
|> abs_tuple fun_args;
in
(massage rewrite_stop, massage rewrite_end, massage rewrite_cont)
end);
fun build_corec_arg_nested_call lthy has_call (sel_eqns : coeqn_data_sel list) sel =
(case find_first (equal sel o #sel) sel_eqns of
NONE => I
| SOME {fun_args, rhs_term, ...} =>
let
val bound_Ts = List.rev (map fastype_of fun_args);
fun rewrite bound_Ts U T (Abs (v, V, b)) = Abs (v, V, rewrite (V :: bound_Ts) U T b)
| rewrite bound_Ts U T (t as _ $ _) =
let val (u, vs) = strip_comb t in
if is_Free u andalso has_call u then
Inr_const U T $ mk_tuple1 bound_Ts vs
else if try (fst o dest_Const) u = SOME @{const_name prod_case} then
map (rewrite bound_Ts U T) vs |> chop 1 |>> HOLogic.mk_split o the_single |> list_comb
else
list_comb (rewrite bound_Ts U T u, map (rewrite bound_Ts U T) vs)
end
| rewrite _ U T t =
if is_Free t andalso has_call t then Inr_const U T $ HOLogic.unit else t;
fun massage t =
rhs_term
|> massage_nested_corec_call lthy has_call rewrite bound_Ts (range_type (fastype_of t))
|> abs_tuple fun_args;
in
massage
end);
fun build_corec_args_sel lthy has_call (all_sel_eqns : coeqn_data_sel list)
(ctr_spec : corec_ctr_spec) =
(case filter (equal (#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 lthy 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 lthy has_call sel_eqns sel)) nested_calls'
end);
fun build_codefs lthy 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 (Const o pair @{const_name undefined})
|> fold2 (fold o build_corec_arg_disc) ctr_specss disc_eqnss
|> fold2 (fold o build_corec_args_sel lthy has_call) sel_eqnss ctr_specss;
fun currys [] t = t
| currys Ts t = t $ mk_tuple1 (List.rev Ts) (map Bound (length Ts - 1 downto 0))
|> fold_rev (Term.abs o pair Name.uu) Ts;
(*
val _ = tracing ("corecursor arguments:\n \<cdot> " ^
space_implode "\n \<cdot> " (map (Syntax.string_of_term lthy) corec_args));
*)
val exclss' =
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)))
||> apfst (map HOLogic.mk_Trueprop) o apsnd HOLogic.mk_Trueprop
||> Logic.list_implies
||> curry Logic.list_all (map dest_Free fun_args))))
in
map (list_comb o rpair corec_args) corecs
|> map2 (fn Ts => fn t => if length Ts = 0 then t $ HOLogic.unit else t) arg_Tss
|> map2 currys arg_Tss
|> Syntax.check_terms lthy
|> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.conceal (Thm.def_binding b), []), t)))
bs mxs
|> rpair exclss'
end;
fun mk_real_disc_eqns fun_binding arg_Ts ({ctr_specs, ...} : corec_spec)
(sel_eqns : coeqn_data_sel list) (disc_eqns : coeqn_data_disc list) =
if length disc_eqns <> length ctr_specs - 1 then disc_eqns else
let
val n = 0 upto length ctr_specs
|> the o find_first (fn idx => not (exists (equal idx o #ctr_no) disc_eqns));
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 extra_disc_eqn = {
fun_name = Binding.name_of fun_binding,
fun_T = arg_Ts ---> body_type (fastype_of (#ctr (hd ctr_specs))),
fun_args = fun_args,
ctr = #ctr (nth ctr_specs n),
ctr_no = n,
disc = #disc (nth ctr_specs n),
prems = maps (s_not_conj o #prems) disc_eqns,
auto_gen = true,
maybe_ctr_rhs = NONE,
maybe_code_rhs = NONE,
user_eqn = undef_const};
in
chop n disc_eqns ||> cons extra_disc_eqn |> (op @)
end;
fun find_corec_calls ctxt has_call basic_ctr_specs ({ctr, sel, rhs_term, ...} : coeqn_data_sel) =
let
val sel_no = find_first (equal ctr o #ctr) basic_ctr_specs
|> find_index (equal sel) o #sels o the;
fun find t = if has_call t then snd (fold_rev_corec_call ctxt (K cons) [] t []) else [];
in
find rhs_term
|> K |> nth_map sel_no |> AList.map_entry (op =) ctr
end;
fun add_primcorec_ursive maybe_tac seq fixes specs maybe_of_specs lthy =
let
val thy = Proof_Context.theory_of lthy;
val (bs, mxs) = map_split (apfst fst) fixes;
val (arg_Ts, res_Ts) = map (strip_type o snd o fst #>> HOLogic.mk_tupleT) fixes |> split_list;
val _ = (case filter_out (fn (_, T) => Sign.of_sort thy (T, HOLogic.typeS)) (bs ~~ arg_Ts) of
[] => ()
| (b, _) :: _ => primcorec_error ("type of " ^ Binding.print b ^ " contains top sort"));
val fun_names = map Binding.name_of bs;
val basic_ctr_specss = map (basic_corec_specs_of lthy) res_Ts;
val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
val eqns_data =
fold_map2 (dissect_coeqn lthy seq has_call fun_names basic_ctr_specss) (map snd specs)
maybe_of_specs []
|> flat o fst;
val callssss =
map_filter (try (fn Sel x => x)) eqns_data
|> partition_eq ((op =) o pairself #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 _ = tracing ("callssss = " ^ @{make_string} callssss);
*)
val ((n2m, corec_specs', _, coinduct_thm, strong_coinduct_thm, coinduct_thms,
strong_coinduct_thms), lthy') =
corec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy;
val actual_nn = length bs;
val corec_specs = take actual_nn corec_specs'; (*###*)
val ctr_specss = map #ctr_specs corec_specs;
val disc_eqnss' = map_filter (try (fn Disc x => x)) eqns_data
|> partition_eq ((op =) o pairself #fun_name)
|> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
|> map (sort ((op <) o pairself #ctr_no |> make_ord) o flat o snd);
val _ = disc_eqnss' |> map (fn x =>
let val d = duplicates ((op =) o pairself #ctr_no) x in null d orelse
primcorec_error_eqns "excess discriminator formula in definition"
(maps (fn t => filter (equal (#ctr_no t) o #ctr_no) x) d |> map #user_eqn) end);
val sel_eqnss = map_filter (try (fn Sel x => x)) eqns_data
|> partition_eq ((op =) o pairself #fun_name)
|> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
|> map (flat o snd);
val arg_Tss = map (binder_types o snd o fst) fixes;
val disc_eqnss = map5 mk_real_disc_eqns bs arg_Tss corec_specs sel_eqnss disc_eqnss';
val (defs, exclss') =
build_codefs lthy' bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss;
fun excl_tac (c, c', a) =
if a orelse c = c' orelse seq then SOME (K (HEADGOAL (mk_primcorec_assumption_tac lthy [])))
else maybe_tac;
(*
val _ = tracing ("exclusiveness properties:\n \<cdot> " ^
space_implode "\n \<cdot> " (maps (map (Syntax.string_of_term lthy o snd)) exclss'));
*)
val exclss'' = exclss' |> map (map (fn (idx, t) =>
(idx, (Option.map (Goal.prove lthy [] [] t #> Thm.close_derivation) (excl_tac idx), t))));
val taut_thmss = map (map (apsnd (the o fst)) o filter (is_some o fst o snd)) exclss'';
val (goal_idxss, goalss) = exclss''
|> map (map (apsnd (rpair [] o snd)) o filter (is_none o fst o snd))
|> split_list o map split_list;
fun prove thmss' def_thms' lthy =
let
val def_thms = map (snd o snd) def_thms';
val exclss' = map (op ~~) (goal_idxss ~~ thmss');
fun mk_exclsss excls n =
(excls, map (fn k => replicate k [TrueI] @ replicate (n - k) []) (0 upto n - 1))
|-> fold (fn ((c, c', _), thm) => nth_map c (nth_map c' (K [thm])));
val exclssss = (exclss' ~~ taut_thmss |> map (op @), fun_names ~~ corec_specs)
|-> map2 (fn excls => fn (_, {ctr_specs, ...}) => mk_exclsss excls (length ctr_specs));
fun prove_disc ({ctr_specs, ...} : corec_spec) exclsss
({fun_name, fun_T, fun_args, ctr_no, prems, ...} : coeqn_data_disc) =
if Term.aconv_untyped (#disc (nth ctr_specs ctr_no), @{term "\<lambda>x. x = x"}) then
[]
else
let
val {disc_corec, ...} = nth ctr_specs ctr_no;
val k = 1 + ctr_no;
val m = length prems;
val t =
list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
|> curry betapply (#disc (nth ctr_specs ctr_no)) (*###*)
|> 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 False}] then [] else
mk_primcorec_disc_tac lthy def_thms disc_corec k m exclsss
|> K |> Goal.prove lthy [] [] t
|> Thm.close_derivation
|> pair (#disc (nth ctr_specs ctr_no))
|> single
end;
fun prove_sel ({nested_maps, nested_map_idents, nested_map_comps, ctr_specs, ...}
: corec_spec) (disc_eqns : coeqn_data_disc list) exclsss
({fun_name, fun_T, fun_args, ctr, sel, rhs_term, ...} : coeqn_data_sel) =
let
val SOME ctr_spec = find_first (equal ctr o #ctr) ctr_specs;
val ctr_no = find_index (equal ctr o #ctr) ctr_specs;
val prems = the_default (maps (s_not_conj o #prems) disc_eqns)
(find_first (equal ctr_no o #ctr_no) disc_eqns |> Option.map #prems);
val sel_corec = find_index (equal sel) (#sels ctr_spec)
|> nth (#sel_corecs ctr_spec);
val k = 1 + ctr_no;
val m = length prems;
val t =
list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
|> curry betapply sel
|> rpair (abstract (List.rev 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, _, sel_splits, sel_split_asms) = case_thms_of_term lthy [] rhs_term;
in
mk_primcorec_sel_tac lthy def_thms distincts sel_splits sel_split_asms nested_maps
nested_map_idents nested_map_comps sel_corec k m exclsss
|> K |> Goal.prove lthy [] [] t
|> Thm.close_derivation
|> pair sel
end;
fun prove_ctr disc_alist sel_alist (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 (equal ctr o #ctr) disc_eqns)
andalso not (exists (equal ctr o #ctr) sel_eqns)
orelse
filter (equal 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, maybe_rhs) =
(find_first (equal ctr o #ctr) disc_eqns, find_first (equal ctr o #ctr) sel_eqns)
|>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #prems x,
#maybe_ctr_rhs x))
||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, [], NONE))
|> the o merge_options;
val m = length prems;
val t = (if is_some maybe_rhs then the maybe_rhs else
filter (equal ctr o #ctr) sel_eqns
|> fst o finds ((op =) o apsnd #sel) sels
|> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x)) #-> abstract)
|> curry list_comb ctr)
|> curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
map Bound (length fun_args - 1 downto 0)))
|> HOLogic.mk_Trueprop
|> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
|> curry Logic.list_all (map dest_Free fun_args);
val maybe_disc_thm = AList.lookup (op =) disc_alist disc;
val sel_thms = map snd (filter (member (op =) sels o fst) sel_alist);
in
if prems = [@{term False}] then [] else
mk_primcorec_ctr_of_dtr_tac lthy m collapse maybe_disc_thm sel_thms
|> K |> Goal.prove lthy [] [] t
|> Thm.close_derivation
|> pair ctr
|> single
end;
fun prove_code disc_eqns sel_eqns ctr_alist ctr_specs =
let
val (fun_name, fun_T, fun_args, maybe_rhs) =
(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, #maybe_code_rhs x))
||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, NONE))
|> the o merge_options;
val bound_Ts = List.rev (map fastype_of fun_args);
val lhs = list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0));
val maybe_rhs_info =
(case maybe_rhs 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 o AList.lookup (op =) ctr_alist o snd) cond_ctrs;
in SOME (rhs, raw_rhs, ctr_thms) end
| NONE =>
let
fun prove_code_ctr {ctr, sels, ...} =
if not (exists (equal ctr o fst) ctr_alist) then NONE else
let
val prems = find_first (equal ctr o #ctr) disc_eqns
|> Option.map #prems |> the_default [];
val t =
filter (equal ctr o #ctr) sel_eqns
|> fst o finds ((op =) o apsnd #sel) sels
|> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x))
#-> abstract)
|> curry list_comb ctr;
in
SOME (prems, t)
end;
val maybe_ctr_conds_argss = map prove_code_ctr ctr_specs;
in
if exists is_none maybe_ctr_conds_argss then NONE else
let
val rhs = fold_rev (fn SOME (prems, u) => fn t => mk_If (s_conjs prems) u t)
maybe_ctr_conds_argss
(Const (@{const_name Code.abort}, @{typ String.literal} -->
(@{typ unit} --> body_type fun_T) --> body_type fun_T) $
HOLogic.mk_literal fun_name $
absdummy @{typ unit} (incr_boundvars 1 lhs));
in SOME (rhs, rhs, map snd ctr_alist) end
end);
in
(case maybe_rhs_info of
NONE => []
| SOME (rhs, raw_rhs, ctr_thms) =>
let
val ms = map (Logic.count_prems o prop_of) ctr_thms;
val (raw_t, t) = (raw_rhs, rhs)
|> pairself
(curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
map Bound (length fun_args - 1 downto 0)))
#> HOLogic.mk_Trueprop
#> curry Logic.list_all (map dest_Free fun_args));
val (distincts, discIs, sel_splits, sel_split_asms) =
case_thms_of_term lthy bound_Ts raw_rhs;
val raw_code_thm = mk_primcorec_raw_code_of_ctr_tac lthy distincts discIs sel_splits
sel_split_asms ms ctr_thms
|> K |> Goal.prove lthy [] [] raw_t
|> Thm.close_derivation;
in
mk_primcorec_code_of_raw_code_tac lthy distincts sel_splits raw_code_thm
|> K |> Goal.prove lthy [] [] t
|> Thm.close_derivation
|> single
end)
end;
val disc_alists = map3 (maps oo prove_disc) corec_specs exclssss disc_eqnss;
val sel_alists = map4 (map ooo prove_sel) corec_specs disc_eqnss exclssss sel_eqnss;
val disc_thmss = map (map snd) disc_alists;
val sel_thmss = map (map snd) sel_alists;
val ctr_alists = map5 (maps oooo prove_ctr) disc_alists sel_alists disc_eqnss sel_eqnss
ctr_specss;
val ctr_thmss = map (map snd) ctr_alists;
val code_thmss = map4 prove_code disc_eqnss sel_eqnss ctr_alists ctr_specss;
val simp_thmss = map2 append disc_thmss sel_thmss
val common_name = mk_common_name fun_names;
val notes =
[(coinductN, map (if n2m then single else K []) coinduct_thms, []),
(codeN, code_thmss, code_nitpicksimp_attrs),
(ctrN, ctr_thmss, []),
(discN, disc_thmss, simp_attrs),
(selN, sel_thmss, simp_attrs),
(simpsN, simp_thmss, []),
(strong_coinductN, map (if n2m then single else K []) strong_coinduct_thms, [])]
|> maps (fn (thmN, thmss, attrs) =>
map2 (fn fun_name => fn thms =>
((Binding.qualify true fun_name (Binding.name thmN), attrs), [(thms, [])]))
fun_names (take actual_nn thmss))
|> filter_out (null o fst o hd o snd);
val common_notes =
[(coinductN, if n2m then [coinduct_thm] else [], []),
(strong_coinductN, if n2m then [strong_coinduct_thm] else [], [])]
|> filter_out (null o #2)
|> map (fn (thmN, thms, attrs) =>
((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
in
lthy |> Local_Theory.notes (notes @ common_notes) |> snd
end;
fun after_qed thmss' = fold_map Local_Theory.define defs #-> prove thmss';
in
(goalss, after_qed, lthy')
end;
fun add_primcorec_ursive_cmd maybe_tac seq (raw_fixes, raw_specs') lthy =
let
val (raw_specs, maybe_of_specs) =
split_list raw_specs' ||> map (Option.map (Syntax.read_term lthy));
val ((fixes, specs), _) = Specification.read_spec raw_fixes raw_specs lthy;
in
add_primcorec_ursive maybe_tac seq fixes specs maybe_of_specs lthy
handle ERROR str => primcorec_error str
end
handle Primcorec_Error (str, eqns) =>
if null eqns
then error ("primcorec error:\n " ^ str)
else error ("primcorec error:\n " ^ str ^ "\nin\n " ^
space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns));
val add_primcorecursive_cmd = (fn (goalss, after_qed, lthy) =>
lthy
|> Proof.theorem NONE after_qed goalss
|> Proof.refine (Method.primitive_text I)
|> Seq.hd) ooo add_primcorec_ursive_cmd NONE;
val add_primcorec_cmd = (fn (goalss, after_qed, lthy) =>
lthy
|> after_qed (map (fn [] => []
| _ => primcorec_error "need exclusiveness proofs - use primcorecursive instead of primcorec")
goalss)) ooo add_primcorec_ursive_cmd (SOME (fn {context = ctxt, ...} => auto_tac ctxt));
end;