(* Title: HOL/Tools/BNF/bnf_gfp_grec_sugar.ML
Author: Aymeric Bouzy, Ecole polytechnique
Author: Jasmin Blanchette, Inria, LORIA, MPII
Author: Dmitriy Traytel, ETH Zürich
Copyright 2015, 2016
Generalized corecursor sugar ("corec" and friends).
*)
signature BNF_GFP_GREC_SUGAR =
sig
datatype corec_option =
Plugins_Option of Proof.context -> Plugin_Name.filter |
Friend_Option |
Transfer_Option
val parse_corec_equation: Proof.context -> term list -> term -> term list * term
val explore_corec_equation: Proof.context -> bool -> bool -> string -> term ->
BNF_GFP_Grec_Sugar_Util.s_parse_info -> typ -> term list * term -> term list * term
val build_corecUU_arg_and_goals: bool -> term -> term list * term -> local_theory ->
(((thm list * thm list * thm list) * term list) * term) * local_theory
val derive_eq_corecUU: Proof.context -> BNF_GFP_Grec.corec_info -> term -> term -> thm -> thm
val derive_unique: Proof.context -> morphism -> term -> BNF_GFP_Grec.corec_info -> string ->
thm -> thm
val corec_cmd: corec_option list -> (binding * string option * mixfix) list * string ->
local_theory -> local_theory
val corecursive_cmd: corec_option list -> (binding * string option * mixfix) list * string ->
local_theory -> Proof.state
val friend_of_corec_cmd: (string * string option) * string -> local_theory -> Proof.state
val coinduction_upto_cmd: string * string -> local_theory -> local_theory
end;
structure BNF_GFP_Grec_Sugar : BNF_GFP_GREC_SUGAR =
struct
open Ctr_Sugar
open BNF_Util
open BNF_Tactics
open BNF_Def
open BNF_Comp
open BNF_FP_Util
open BNF_FP_Def_Sugar
open BNF_FP_N2M_Sugar
open BNF_GFP_Util
open BNF_GFP_Rec_Sugar
open BNF_FP_Rec_Sugar_Transfer
open BNF_GFP_Grec
open BNF_GFP_Grec_Sugar_Util
open BNF_GFP_Grec_Sugar_Tactics
val cong_N = "cong_";
val baseN = "base";
val reflN = "refl";
val symN = "sym";
val transN = "trans";
val cong_introsN = prefix cong_N "intros";
val codeN = "code";
val coinductN = "coinduct";
val coinduct_uptoN = "coinduct_upto";
val corecN = "corec";
val ctrN = "ctr";
val discN = "disc";
val disc_iffN = "disc_iff";
val eq_algrhoN = "eq_algrho";
val eq_corecUUN = "eq_corecUU";
val friendN = "friend";
val inner_elimN = "inner_elim";
val inner_inductN = "inner_induct";
val inner_simpN = "inner_simp";
val rhoN = "rho";
val selN = "sel";
val uniqueN = "unique";
val inner_fp_suffix = "_inner_fp";
val nitpicksimp_attrs = @{attributes [nitpick_simp]};
val simp_attrs = @{attributes [simp]};
val unfold_id_thms1 =
map (fn thm => thm RS eq_reflection) @{thms id_bnf_o o_id_bnf id_apply o_apply} @
@{thms fst_def[abs_def, symmetric] snd_def[abs_def, symmetric]};
fun unfold_id_bnf_etc lthy =
let val thy = Proof_Context.theory_of lthy in
Raw_Simplifier.rewrite_term thy unfold_id_thms1 []
#> Raw_Simplifier.rewrite_term thy @{thms BNF_Composition.id_bnf_def} []
end;
fun unexpected_corec_call ctxt eqns t =
error_at ctxt eqns ("Unexpected corecursive call in " ^ quote (Syntax.string_of_term ctxt t));
fun unsupported_case_around_corec_call ctxt eqns t =
error_at ctxt eqns ("Unsupported corecursive call under case expression " ^
quote (Syntax.string_of_term ctxt t) ^ "\n(Define " ^
quote (Syntax.string_of_typ ctxt (domain_type (fastype_of t))) ^
" with discriminators and selectors to circumvent this limitation.)");
datatype corec_option =
Plugins_Option of Proof.context -> Plugin_Name.filter |
Friend_Option |
Transfer_Option;
val corec_option_parser = Parse.group (K "option")
(Plugin_Name.parse_filter >> Plugins_Option
|| Parse.reserved "friend" >> K Friend_Option
|| Parse.reserved "transfer" >> K Transfer_Option);
type codatatype_extra =
{case_dtor: thm,
case_trivial: thm,
abs_rep_transfers: thm list};
fun morph_codatatype_extra phi ({case_dtor, case_trivial, abs_rep_transfers} : codatatype_extra) =
{case_dtor = Morphism.thm phi case_dtor, case_trivial = Morphism.thm phi case_trivial,
abs_rep_transfers = map (Morphism.thm phi) abs_rep_transfers};
val transfer_codatatype_extra = morph_codatatype_extra o Morphism.transfer_morphism;
type coinduct_extra =
{coinduct: thm,
coinduct_attrs: Token.src list,
cong_intro_pairs: (string * thm) list};
fun morph_coinduct_extra phi ({coinduct, coinduct_attrs, cong_intro_pairs} : coinduct_extra) =
{coinduct = Morphism.thm phi coinduct, coinduct_attrs = coinduct_attrs,
cong_intro_pairs = map (apsnd (Morphism.thm phi)) cong_intro_pairs};
val transfer_coinduct_extra = morph_coinduct_extra o Morphism.transfer_morphism;
type friend_extra =
{eq_algrhos: thm list,
algrho_eqs: thm list};
val empty_friend_extra = {eq_algrhos = [], algrho_eqs = []};
fun merge_friend_extras ({eq_algrhos = eq_algrhos1, algrho_eqs = algrho_eqs1},
{eq_algrhos = eq_algrhos2, algrho_eqs = algrho_eqs2}) =
{eq_algrhos = union Thm.eq_thm_prop eq_algrhos1 eq_algrhos2,
algrho_eqs = union Thm.eq_thm_prop algrho_eqs1 algrho_eqs2};
type corec_sugar_data =
codatatype_extra Symtab.table * coinduct_extra Symtab.table * friend_extra Symtab.table;
structure Data = Generic_Data
(
type T = corec_sugar_data;
val empty = (Symtab.empty, Symtab.empty, Symtab.empty);
val extend = I;
fun merge data : T =
(Symtab.merge (K true) (apply2 #1 data), Symtab.merge (K true) (apply2 #2 data),
Symtab.join (K merge_friend_extras) (apply2 #3 data));
);
fun register_codatatype_extra fpT_name extra =
Local_Theory.declaration {syntax = false, pervasive = true} (fn phi =>
Data.map (@{apply 3(1)} (Symtab.update (fpT_name, morph_codatatype_extra phi extra))));
fun codatatype_extra_of ctxt =
Symtab.lookup (#1 (Data.get (Context.Proof ctxt)))
#> Option.map (transfer_codatatype_extra (Proof_Context.theory_of ctxt));
fun all_codatatype_extras_of ctxt =
Symtab.dest (#1 (Data.get (Context.Proof ctxt)));
fun register_coinduct_extra fpT_name extra =
Local_Theory.declaration {syntax = false, pervasive = true} (fn phi =>
Data.map (@{apply 3(2)} (Symtab.update (fpT_name, morph_coinduct_extra phi extra))));
fun coinduct_extra_of ctxt =
Symtab.lookup (#2 (Data.get (Context.Proof ctxt)))
#> Option.map (transfer_coinduct_extra (Proof_Context.theory_of ctxt));
fun register_friend_extra fun_name eq_algrho algrho_eq =
Local_Theory.declaration {syntax = false, pervasive = true} (fn phi =>
Data.map (@{apply 3(3)} (Symtab.map_default (fun_name, empty_friend_extra)
(fn {eq_algrhos, algrho_eqs} =>
{eq_algrhos = Morphism.thm phi eq_algrho :: eq_algrhos,
algrho_eqs = Morphism.thm phi algrho_eq :: algrho_eqs}))));
fun all_friend_extras_of ctxt =
Symtab.dest (#3 (Data.get (Context.Proof ctxt)));
fun coinduct_extras_of_generic context =
corec_infos_of_generic context
#> map (#corecUU #> dest_Const #> fst #> Symtab.lookup (#2 (Data.get context)) #> the
#> transfer_coinduct_extra (Context.theory_of context));
fun get_coinduct_uptos fpT_name context =
coinduct_extras_of_generic context fpT_name |> map #coinduct;
fun get_cong_all_intros fpT_name context =
coinduct_extras_of_generic context fpT_name |> maps (#cong_intro_pairs #> map snd);
fun get_cong_intros fpT_name name context =
coinduct_extras_of_generic context fpT_name
|> map_filter (#cong_intro_pairs #> (fn ps => AList.lookup (op =) ps name));
fun ctr_names_of_fp_name lthy fpT_name =
fpT_name |> fp_sugar_of lthy |> the |> #fp_ctr_sugar |> #ctr_sugar |> #ctrs
|> map (Long_Name.base_name o name_of_ctr);
fun register_coinduct_dynamic_base fpT_name lthy =
let val fp_b = Binding.name (Long_Name.base_name fpT_name) in
lthy
|> fold Local_Theory.add_thms_dynamic
((mk_fp_binding fp_b coinduct_uptoN, get_coinduct_uptos fpT_name) ::
map (fn N =>
let val N = cong_N ^ N in
(mk_fp_binding fp_b N, get_cong_intros fpT_name N)
end)
([baseN, reflN, symN, transN] @ ctr_names_of_fp_name lthy fpT_name))
|> Local_Theory.add_thms_dynamic
(mk_fp_binding fp_b cong_introsN, get_cong_all_intros fpT_name)
end;
fun register_coinduct_dynamic_friend fpT_name friend_name =
let
val fp_b = Binding.name (Long_Name.base_name fpT_name);
val friend_base_name = cong_N ^ Long_Name.base_name friend_name;
in
Local_Theory.add_thms_dynamic
(mk_fp_binding fp_b friend_base_name, get_cong_intros fpT_name friend_base_name)
end;
fun derive_case_dtor ctxt fpT_name =
let
val thy = Proof_Context.theory_of ctxt;
val SOME ({fp_res_index, fp_res = {dtors = dtors0, dtor_ctors, ...},
absT_info = {rep = rep0, abs_inverse, ...},
fp_ctr_sugar = {ctr_defs, ctr_sugar = {casex, exhaust, case_thms, ...}, ...}, ...}) =
fp_sugar_of ctxt fpT_name;
val (f_Ts, Type (_, [fpT as Type (_, As), _])) = strip_fun_type (fastype_of casex);
val x_Tss = map binder_types f_Ts;
val (((u, fs), xss), _) = ctxt
|> yield_singleton (mk_Frees "y") fpT
||>> mk_Frees "f" f_Ts
||>> mk_Freess "x" x_Tss;
val dtor0 = nth dtors0 fp_res_index;
val dtor = mk_dtor As dtor0;
val u' = dtor $ u;
val absT = fastype_of u';
val rep = mk_rep absT rep0;
val goal = mk_Trueprop_eq (list_comb (casex, fs) $ u,
mk_case_absumprod absT rep fs xss xss $ u')
|> Raw_Simplifier.rewrite_term thy @{thms comp_def[THEN eq_reflection]} [];
val vars = map (fst o dest_Free) (u :: fs);
val dtor_ctor = nth dtor_ctors fp_res_index;
in
Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} =>
mk_case_dtor_tac ctxt u abs_inverse dtor_ctor ctr_defs exhaust case_thms)
|> Thm.close_derivation
end;
fun derive_case_trivial ctxt fpT_name =
let
val SOME {casex, exhaust, case_thms, ...} = ctr_sugar_of ctxt fpT_name;
val Type (_, As0) = domain_type (body_fun_type (fastype_of casex));
val (As, _) = ctxt
|> mk_TFrees' (map Type.sort_of_atyp As0);
val fpT = Type (fpT_name, As);
val (var_name, ()) = singleton (Variable.variant_frees ctxt []) ("x", ());
val var = Free (var_name, fpT);
val goal = mk_Trueprop_eq (expand_to_ctr_term ctxt fpT var, var);
val exhaust' = infer_instantiate' ctxt [SOME (Thm.cterm_of ctxt var)] exhaust;
in
Goal.prove_sorry ctxt [var_name] [] goal (fn {context = ctxt, prems = _} =>
HEADGOAL (rtac ctxt exhaust') THEN ALLGOALS (hyp_subst_tac ctxt) THEN
unfold_thms_tac ctxt case_thms THEN ALLGOALS (rtac ctxt refl))
|> Thm.close_derivation
end;
fun mk_abs_rep_transfers ctxt fpT_name =
[mk_abs_transfer ctxt fpT_name, mk_rep_transfer ctxt fpT_name]
handle Fail _ => [];
fun ensure_codatatype_extra fpT_name ctxt =
(case codatatype_extra_of ctxt fpT_name of
NONE =>
let val abs_rep_transfers = mk_abs_rep_transfers ctxt fpT_name in
ctxt
|> register_codatatype_extra fpT_name
{case_dtor = derive_case_dtor ctxt fpT_name,
case_trivial = derive_case_trivial ctxt fpT_name,
abs_rep_transfers = abs_rep_transfers}
|> set_transfer_rule_attrs abs_rep_transfers
end
| SOME {abs_rep_transfers, ...} => ctxt |> set_transfer_rule_attrs abs_rep_transfers);
fun setup_base fpT_name =
register_coinduct_dynamic_base fpT_name
#> ensure_codatatype_extra fpT_name;
fun is_set ctxt (const_name, T) =
(case T of
Type (@{type_name fun}, [Type (fpT_name, _), Type (@{type_name set}, [_])]) =>
(case bnf_of ctxt fpT_name of
SOME bnf => exists (fn Const (s, _) => s = const_name | _ => false) (sets_of_bnf bnf)
| NONE => false)
| _ => false);
fun case_eq_if_thms_of_term ctxt t =
let val ctr_sugars = map_filter (ctr_sugar_of_case ctxt o fst) (Term.add_consts t []) in
maps #case_eq_ifs ctr_sugars
end;
fun all_algrho_eqs_of ctxt =
maps (#algrho_eqs o snd) (all_friend_extras_of ctxt);
fun derive_code ctxt inner_fp_simps goal
{sig_fp_sugars, ssig_fp_sugar, eval, eval_simps, all_algLam_algs, corecUU_thm, ...} fun_t
fun_def =
let
val fun_T = fastype_of fun_t;
val (arg_Ts, Type (fpT_name, _)) = strip_type fun_T;
val num_args = length arg_Ts;
val SOME {pre_bnf, fp_bnf, absT_info, fp_nesting_bnfs, live_nesting_bnfs, fp_ctr_sugar, ...} =
fp_sugar_of ctxt fpT_name;
val SOME {case_trivial, ...} = codatatype_extra_of ctxt fpT_name;
val ctr_sugar = #ctr_sugar fp_ctr_sugar;
val pre_map_def = map_def_of_bnf pre_bnf;
val abs_inverse = #abs_inverse absT_info;
val ctr_defs = #ctr_defs fp_ctr_sugar;
val case_eq_ifs = #case_eq_ifs ctr_sugar @ case_eq_if_thms_of_term ctxt goal;
val all_sig_map_thms = maps (#map_thms o #fp_bnf_sugar) sig_fp_sugars;
val fp_map_ident = map_ident_of_bnf fp_bnf;
val fpsig_nesting_bnfs = fp_nesting_bnfs @ maps #live_nesting_bnfs sig_fp_sugars;
val fpsig_nesting_T_names = map (fst o dest_Type o T_of_bnf) fpsig_nesting_bnfs;
val fpsig_nesting_fp_sugars = map_filter (fp_sugar_of ctxt) fpsig_nesting_T_names;
val fpsig_nesting_fp_bnf_sugars = map #fp_bnf_sugar fpsig_nesting_fp_sugars;
val ssig_fp_bnf_sugar = #fp_bnf_sugar ssig_fp_sugar;
val ssig_bnf = #fp_bnf ssig_fp_sugar;
val ssig_map = map_of_bnf ssig_bnf;
val fpsig_nesting_maps = map map_of_bnf fpsig_nesting_bnfs;
val fpsig_nesting_map_ident0s = map map_ident0_of_bnf fpsig_nesting_bnfs;
val fpsig_nesting_map_comps = map map_comp_of_bnf fpsig_nesting_bnfs;
val fpsig_nesting_map_thms = maps #map_thms fpsig_nesting_fp_bnf_sugars;
val live_nesting_map_ident0s = map map_ident0_of_bnf live_nesting_bnfs;
val ssig_map_thms = #map_thms ssig_fp_bnf_sugar;
val all_algLam_alg_pointfuls = map (mk_pointful ctxt) all_algLam_algs;
in
Variable.add_free_names ctxt goal []
|> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} =>
mk_code_tac ctxt num_args fpsig_nesting_maps ssig_map eval pre_map_def abs_inverse
fpsig_nesting_map_ident0s fpsig_nesting_map_comps fpsig_nesting_map_thms
live_nesting_map_ident0s fp_map_ident case_trivial ctr_defs case_eq_ifs corecUU_thm
all_sig_map_thms ssig_map_thms all_algLam_alg_pointfuls (all_algrho_eqs_of ctxt) eval_simps
inner_fp_simps fun_def))
|> Thm.close_derivation
end;
fun derive_unique ctxt phi code_goal
{sig_fp_sugars, ssig_fp_sugar, eval, eval_simps, all_algLam_algs, corecUU_unique, ...} fpT_name
eq_corecUU =
let
val SOME {pre_bnf, fp_bnf, absT_info, fp_nesting_bnfs, live_nesting_bnfs, fp_ctr_sugar, ...} =
fp_sugar_of ctxt fpT_name;
val SOME {case_trivial, ...} = codatatype_extra_of ctxt fpT_name;
val ctr_sugar = #ctr_sugar fp_ctr_sugar;
val pre_map_def = map_def_of_bnf pre_bnf;
val abs_inverse = #abs_inverse absT_info;
val ctr_defs = #ctr_defs fp_ctr_sugar;
val case_eq_ifs = #case_eq_ifs ctr_sugar @ case_eq_if_thms_of_term ctxt code_goal;
val all_sig_map_thms = maps (#map_thms o #fp_bnf_sugar) sig_fp_sugars;
val fp_map_ident = map_ident_of_bnf fp_bnf;
val fpsig_nesting_bnfs = fp_nesting_bnfs @ maps #live_nesting_bnfs sig_fp_sugars;
val fpsig_nesting_T_names = map (fst o dest_Type o T_of_bnf) fpsig_nesting_bnfs;
val fpsig_nesting_fp_sugars = map_filter (fp_sugar_of ctxt) fpsig_nesting_T_names;
val fpsig_nesting_fp_bnf_sugars = map #fp_bnf_sugar fpsig_nesting_fp_sugars;
val ssig_fp_bnf_sugar = #fp_bnf_sugar ssig_fp_sugar;
val ssig_bnf = #fp_bnf ssig_fp_sugar;
val ssig_map = map_of_bnf ssig_bnf;
val fpsig_nesting_maps = map map_of_bnf fpsig_nesting_bnfs;
val fpsig_nesting_map_ident0s = map map_ident0_of_bnf fpsig_nesting_bnfs;
val fpsig_nesting_map_comps = map map_comp_of_bnf fpsig_nesting_bnfs;
val fpsig_nesting_map_thms = maps #map_thms fpsig_nesting_fp_bnf_sugars;
val live_nesting_map_ident0s = map map_ident0_of_bnf live_nesting_bnfs;
val ssig_map_thms = #map_thms ssig_fp_bnf_sugar;
val all_algLam_alg_pointfuls = map (mk_pointful ctxt) all_algLam_algs;
val @{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ lhs $ rhs) = code_goal;
val (fun_t, args) = strip_comb lhs;
val closed_rhs = fold_rev lambda args rhs;
val fun_T = fastype_of fun_t;
val num_args = num_binder_types fun_T;
val f = Free (singleton (Variable.variant_frees ctxt []) ("f", fun_T));
val is_self_call = curry (op aconv) fun_t;
val has_self_call = exists_subterm is_self_call;
fun fify args (t $ u) = fify (u :: args) t $ fify [] u
| fify _ (Abs (s, T, t)) = Abs (s, T, fify [] t)
| fify args t = if t = fun_t andalso not (exists has_self_call args) then f else t;
val goal = Logic.mk_implies (mk_Trueprop_eq (f, fify [] closed_rhs), mk_Trueprop_eq (f, fun_t))
|> Morphism.term phi;
in
Goal.prove_sorry ctxt [fst (dest_Free f)] [] goal (fn {context = ctxt, prems = _} =>
mk_unique_tac ctxt num_args fpsig_nesting_maps ssig_map eval pre_map_def abs_inverse
fpsig_nesting_map_ident0s fpsig_nesting_map_comps fpsig_nesting_map_thms
live_nesting_map_ident0s fp_map_ident case_trivial ctr_defs case_eq_ifs all_sig_map_thms
ssig_map_thms all_algLam_alg_pointfuls (all_algrho_eqs_of ctxt) eval_simps corecUU_unique
eq_corecUU)
|> Thm.close_derivation
end;
fun derive_last_disc ctxt fcT_name =
let
val SOME {T = fcT, discs, exhaust, disc_thmss, ...} = ctr_sugar_of ctxt fcT_name;
val (u, _) = ctxt
|> yield_singleton (mk_Frees "x") fcT;
val udiscs = map (rapp u) discs;
val (not_udiscs, last_udisc) = split_last udiscs
|>> map HOLogic.mk_not;
val goal = mk_Trueprop_eq (last_udisc, foldr1 HOLogic.mk_conj not_udiscs);
in
Goal.prove_sorry ctxt [fst (dest_Free u)] [] goal (fn {context = ctxt, prems = _} =>
mk_last_disc_tac ctxt u exhaust (flat disc_thmss))
|> Thm.close_derivation
end;
fun derive_eq_algrho ctxt {sig_fp_sugars, ssig_fp_sugar, eval, eval_simps, all_algLam_algs,
corecUU_unique, ...}
({algrho = algrho0, dtor_algrho, ...} : friend_info) fun_t k_T code_goal const_transfers rho_def
eq_corecUU =
let
val fun_T = fastype_of fun_t;
val (arg_Ts, Type (fpT_name, Ts)) = strip_type fun_T;
val num_args = length arg_Ts;
val SOME {fp_res_index, fp_res, pre_bnf, fp_bnf, absT_info, fp_nesting_bnfs, live_nesting_bnfs,
fp_ctr_sugar, ...} =
fp_sugar_of ctxt fpT_name;
val SOME {case_dtor, ...} = codatatype_extra_of ctxt fpT_name;
val fp_nesting_Ts = map T_of_bnf fp_nesting_bnfs;
fun is_nullary_disc_def (@{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ _
$ (Const (@{const_name HOL.eq}, _) $ _ $ _))) = true
| is_nullary_disc_def (Const (@{const_name Pure.eq}, _) $ _
$ (Const (@{const_name HOL.eq}, _) $ _ $ _)) = true
| is_nullary_disc_def _ = false;
val dtor_ctor = nth (#dtor_ctors fp_res) fp_res_index;
val ctor_iff_dtor = #ctor_iff_dtor fp_ctr_sugar;
val ctr_sugar = #ctr_sugar fp_ctr_sugar;
val pre_map_def = map_def_of_bnf pre_bnf;
val abs_inverse = #abs_inverse absT_info;
val ctr_defs = #ctr_defs fp_ctr_sugar;
val nullary_disc_defs = filter (is_nullary_disc_def o Thm.prop_of) (#disc_defs ctr_sugar);
val disc_sel_eq_cases = #disc_eq_cases ctr_sugar @ #sel_defs ctr_sugar;
val case_eq_ifs = #case_eq_ifs ctr_sugar @ case_eq_if_thms_of_term ctxt code_goal;
val all_sig_map_thms = maps (#map_thms o #fp_bnf_sugar) sig_fp_sugars;
fun add_tnameT (Type (s, Ts)) = insert (op =) s #> fold add_tnameT Ts
| add_tnameT _ = I;
fun map_disc_sels'_of s =
(case fp_sugar_of ctxt s of
SOME {fp_bnf_sugar = {map_disc_iffs, map_selss, ...}, ...} =>
let
val map_selss' =
if length map_selss <= 1 then map_selss
else map (map (unfold_thms ctxt (no_refl [derive_last_disc ctxt s]))) map_selss;
in
map_disc_iffs @ flat map_selss'
end
| NONE => []);
fun mk_const_pointful_natural const_transfer =
SOME (mk_pointful_natural_from_transfer ctxt const_transfer)
handle UNNATURAL () => NONE;
val const_pointful_natural_opts = map mk_const_pointful_natural const_transfers;
val const_pointful_naturals = map_filter I const_pointful_natural_opts;
val fp_nesting_k_T_names = fold add_tnameT (k_T :: fp_nesting_Ts) [];
val fp_nesting_k_map_disc_sels' = maps map_disc_sels'_of fp_nesting_k_T_names;
val fp_map_ident = map_ident_of_bnf fp_bnf;
val fpsig_nesting_bnfs = fp_nesting_bnfs @ maps #live_nesting_bnfs sig_fp_sugars;
val fpsig_nesting_T_names = map (fst o dest_Type o T_of_bnf) fpsig_nesting_bnfs;
val fpsig_nesting_fp_sugars = map_filter (fp_sugar_of ctxt) fpsig_nesting_T_names;
val fpsig_nesting_fp_bnf_sugars = map #fp_bnf_sugar fpsig_nesting_fp_sugars;
val ssig_fp_bnf_sugar = #fp_bnf_sugar ssig_fp_sugar;
val ssig_bnf = #fp_bnf ssig_fp_sugar;
val ssig_map = map_of_bnf ssig_bnf;
val fpsig_nesting_maps = map map_of_bnf fpsig_nesting_bnfs;
val fpsig_nesting_map_ident0s = map map_ident0_of_bnf fpsig_nesting_bnfs;
val fpsig_nesting_map_comps = map map_comp_of_bnf fpsig_nesting_bnfs;
val fpsig_nesting_map_thms = maps #map_thms fpsig_nesting_fp_bnf_sugars;
val live_nesting_map_ident0s = map map_ident0_of_bnf live_nesting_bnfs;
val ssig_map_thms = #map_thms ssig_fp_bnf_sugar;
val all_algLam_alg_pointfuls = map (mk_pointful ctxt) all_algLam_algs;
val ctor = nth (#ctors fp_res) fp_res_index;
val abs = #abs absT_info;
val rep = #rep absT_info;
val algrho = mk_ctr Ts algrho0;
val goal = mk_Trueprop_eq (fun_t, abs_curried_balanced arg_Ts algrho);
fun const_of_transfer thm =
(case Thm.prop_of thm of @{const Trueprop} $ (_ $ cst $ _) => cst);
val eq_algrho =
Goal.prove (*no sorry*) ctxt [] [] goal (fn {context = ctxt, prems = _} =>
mk_eq_algrho_tac ctxt fpsig_nesting_maps abs rep ctor ssig_map eval pre_map_def abs_inverse
fpsig_nesting_map_ident0s fpsig_nesting_map_comps fpsig_nesting_map_thms
live_nesting_map_ident0s fp_map_ident dtor_ctor ctor_iff_dtor ctr_defs nullary_disc_defs
disc_sel_eq_cases case_dtor case_eq_ifs const_pointful_naturals
fp_nesting_k_map_disc_sels' rho_def dtor_algrho corecUU_unique eq_corecUU all_sig_map_thms
ssig_map_thms all_algLam_alg_pointfuls (all_algrho_eqs_of ctxt) eval_simps)
|> Thm.close_derivation
handle e as ERROR _ =>
(case filter (is_none o snd) (const_transfers ~~ const_pointful_natural_opts) of
[] => Exn.reraise e
| thm_nones =>
error ("Failed to state naturality property for " ^
commas (map (Syntax.string_of_term ctxt o const_of_transfer o fst) thm_nones)));
val algrho_eq = eq_algrho RS (mk_curry_uncurryN_balanced ctxt num_args RS iffD2) RS sym;
in
(eq_algrho, algrho_eq)
end;
fun prime_rho_transfer_goal ctxt fpT_name rho_def goal =
let
val thy = Proof_Context.theory_of ctxt;
val SOME {pre_bnf, ...} = fp_sugar_of ctxt fpT_name;
val SOME {abs_rep_transfers, ...} = codatatype_extra_of ctxt fpT_name;
val simps = rel_def_of_bnf pre_bnf :: rho_transfer_simps;
val fold_rho = unfold_thms ctxt [rho_def RS @{thm symmetric}];
fun derive_unprimed rho_transfer' =
Variable.add_free_names ctxt goal []
|> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} =>
unfold_thms_tac ctxt simps THEN HEADGOAL (rtac ctxt rho_transfer')))
|> Thm.close_derivation;
val goal' = Raw_Simplifier.rewrite_term thy simps [] goal;
in
if null abs_rep_transfers then (goal', derive_unprimed #> fold_rho)
else (goal, fold_rho)
end;
fun derive_rho_transfer_folded ctxt fpT_name const_transfers rho_def goal =
let
val SOME {pre_bnf, ...} = fp_sugar_of ctxt fpT_name;
val SOME {abs_rep_transfers, ...} = codatatype_extra_of ctxt fpT_name;
in
Variable.add_free_names ctxt goal []
|> (fn vars => Goal.prove (*no sorry*) ctxt vars [] goal (fn {context = ctxt, prems = _} =>
mk_rho_transfer_tac ctxt (null abs_rep_transfers) (rel_def_of_bnf pre_bnf)
const_transfers))
|> unfold_thms ctxt [rho_def RS @{thm symmetric}]
|> Thm.close_derivation
end;
fun mk_cong_intro_ctr_or_friend_goal ctxt fpT Rcong alg =
let
val xy_Ts = binder_types (fastype_of alg);
val ((xs, ys), _) = ctxt
|> mk_Frees "x" xy_Ts
||>> mk_Frees "y" xy_Ts;
fun mk_prem xy_T x y =
build_rel [] ctxt [fpT] (fn (T, _) => if T = fpT then Rcong else HOLogic.eq_const T)
(xy_T, xy_T) $ x $ y;
val prems = @{map 3} mk_prem xy_Ts xs ys;
val concl = Rcong $ list_comb (alg, xs) $ list_comb (alg, ys);
in
Logic.list_implies (map HOLogic.mk_Trueprop prems, HOLogic.mk_Trueprop concl)
end;
fun derive_cong_ctr_intros ctxt cong_ctor_intro =
let
val @{const Pure.imp} $ _ $ (@{const Trueprop} $ ((Rcong as _ $ _) $ _ $ (ctor $ _))) =
Thm.prop_of cong_ctor_intro;
val fpT as Type (fpT_name, fp_argTs) = range_type (fastype_of ctor);
val SOME {pre_bnf, absT_info = {abs_inverse, ...},
fp_ctr_sugar = {ctr_defs, ctr_sugar = {ctrs = ctrs0, ...}, ...}, ...} =
fp_sugar_of ctxt fpT_name;
val ctrs = map (mk_ctr fp_argTs) ctrs0;
val pre_rel_def = rel_def_of_bnf pre_bnf;
fun prove ctr_def goal =
Variable.add_free_names ctxt goal []
|> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} =>
mk_cong_intro_ctr_or_friend_tac ctxt ctr_def [pre_rel_def, abs_inverse] cong_ctor_intro))
|> Thm.close_derivation;
val goals = map (mk_cong_intro_ctr_or_friend_goal ctxt fpT Rcong) ctrs;
in
map2 prove ctr_defs goals
end;
fun derive_cong_friend_intro ctxt cong_algrho_intro =
let
val @{const Pure.imp} $ _ $ (@{const Trueprop} $ ((Rcong as _ $ _) $ _
$ ((algrho as Const (algrho_name, _)) $ _))) =
Thm.prop_of cong_algrho_intro;
val fpT as Type (_, fp_argTs) = range_type (fastype_of algrho);
fun has_algrho (@{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ _ $ rhs)) =
fst (dest_Const (head_of (strip_abs_body rhs))) = algrho_name;
val eq_algrho :: _ =
maps (filter (has_algrho o Thm.prop_of) o #eq_algrhos o snd) (all_friend_extras_of ctxt);
val @{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ friend0 $ _) = Thm.prop_of eq_algrho;
val friend = mk_ctr fp_argTs friend0;
val goal = mk_cong_intro_ctr_or_friend_goal ctxt fpT Rcong friend;
in
Variable.add_free_names ctxt goal []
|> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} =>
mk_cong_intro_ctr_or_friend_tac ctxt eq_algrho [] cong_algrho_intro))
|> Thm.close_derivation
end;
fun derive_cong_intros lthy ctr_names friend_names
({cong_base, cong_refl, cong_sym, cong_trans, cong_alg_intros, ...} : dtor_coinduct_info) =
let
val cong_ctor_intro :: cong_algrho_intros = rev cong_alg_intros;
val names = map (prefix cong_N) ([baseN, reflN, symN, transN] @ ctr_names @ friend_names);
val thms = [cong_base, cong_refl, cong_sym, cong_trans] @
derive_cong_ctr_intros lthy cong_ctor_intro @
map (derive_cong_friend_intro lthy) cong_algrho_intros;
in
names ~~ thms
end;
fun derive_coinduct ctxt (fpT as Type (fpT_name, fpT_args)) dtor_coinduct =
let
val thy = Proof_Context.theory_of ctxt;
val @{const Pure.imp} $ (@{const Trueprop} $ (_ $ Abs (_, _, _ $
Abs (_, _, @{const implies} $ _ $ (_ $ (cong0 $ _) $ _ $ _))))) $ _ =
Thm.prop_of dtor_coinduct;
val SOME {X as TVar ((X_s, _), _), fp_res = {dtor_ctors, ...}, pre_bnf,
absT_info = {abs_inverse, ...}, live_nesting_bnfs,
fp_ctr_sugar = {ctrXs_Tss, ctr_defs,
ctr_sugar = ctr_sugar0 as {T = Type (_, T0_args), ctrs = ctrs0, discs = discs0, ...},
...}, ...} =
fp_sugar_of ctxt fpT_name;
val n = length ctrXs_Tss;
val ms = map length ctrXs_Tss;
val X' = TVar ((X_s, maxidx_of_typ fpT + 1), @{sort type});
val As_rho = tvar_subst thy T0_args fpT_args;
val substXAT = Term.typ_subst_TVars As_rho o Tsubst X X';
val substXA = Term.subst_TVars As_rho o substT X X';
val phi = Morphism.typ_morphism "BNF" substXAT $> Morphism.term_morphism "BNF" substXA;
fun mk_applied_cong arg =
enforce_type ctxt domain_type (fastype_of arg) cong0 $ arg;
val thm = derive_coinduct_thms_for_types false mk_applied_cong [pre_bnf] dtor_coinduct
dtor_ctors live_nesting_bnfs [fpT] [substXAT X] [map (map substXAT) ctrXs_Tss] [n]
[abs_inverse] [abs_inverse] I [ctr_defs] [morph_ctr_sugar phi ctr_sugar0] ctxt
|> map snd |> the_single;
val (attrs, _) = mk_coinduct_attrs [fpT] [ctrs0] [discs0] [ms];
in
(thm, attrs)
end;
type explore_parameters =
{bound_Us: typ list,
bound_Ts: typ list,
U: typ,
T: typ};
fun update_UT {bound_Us, bound_Ts, ...} U T =
{bound_Us = bound_Us, bound_Ts = bound_Ts, U = U, T = T};
fun explore_nested lthy explore {bound_Us, bound_Ts, U, T} t =
let
fun build_simple (T, U) =
if T = U then
@{term "%y. y"}
else
Bound 0
|> explore {bound_Us = T :: bound_Us, bound_Ts = T :: bound_Ts, U = U, T = T}
|> (fn t => Abs (Name.uu, T, t));
in
betapply (build_map lthy [] build_simple (T, U), t)
end;
fun add_boundvar t = betapply (incr_boundvars 1 t, Bound 0);
fun explore_fun (arg_U :: arg_Us) explore {bound_Us, bound_Ts, U, T} t =
let val arg_name = the_default Name.uu (try (fn (Abs (s, _, _)) => s) t) in
add_boundvar t
|> explore_fun arg_Us explore
{bound_Us = arg_U :: bound_Us, bound_Ts = domain_type T :: bound_Ts, U = range_type U,
T = range_type T}
|> (fn t => Abs (arg_name, arg_U, t))
end
| explore_fun [] explore params t = explore params t;
fun massage_fun explore (params as {T, U, ...}) =
if can dest_funT T then explore_fun [domain_type U] explore params else explore params;
fun massage_star massages explore =
let
fun after_massage massages' t params t' =
if t aconv t' then massage_any massages' params t else massage_any massages params t'
and massage_any [] params t = explore params t
| massage_any (massage :: massages') params t =
massage (after_massage massages' t) params t;
in
massage_any massages
end;
fun massage_let explore params t =
(case strip_comb t of
(Const (@{const_name Let}, _), [_, _]) => unfold_lets_splits t
| _ => t)
|> explore params;
fun check_corec_equation ctxt fun_frees (lhs, rhs) =
let
val (fun_t, arg_ts) = strip_comb lhs;
fun check_fun_name () =
null fun_frees orelse member (op aconv) fun_frees fun_t orelse
error (quote (Syntax.string_of_term ctxt fun_t) ^
" is not the function currently being defined");
fun check_args_are_vars () =
let
fun is_ok_Free_or_Var (Free (s, _)) = not (String.isSuffix inner_fp_suffix s)
| is_ok_Free_or_Var (Var _) = true
| is_ok_Free_or_Var _ = false;
fun is_valid arg =
(is_ok_Free_or_Var arg andalso not (member (op aconv) fun_frees arg)) orelse
error ("Argument " ^ quote (Syntax.string_of_term ctxt arg) ^ " is not free");
in
forall is_valid arg_ts
end;
fun check_no_duplicate_arg () =
(case duplicates (op =) arg_ts of
[] => ()
| arg :: _ => error ("Repeated argument: " ^ quote (Syntax.string_of_term ctxt arg)));
fun check_no_other_frees () =
(case Term.add_frees rhs [] |> map Free |> subtract (op =) (fun_frees @ arg_ts)
|> filter_out (Variable.is_fixed ctxt o fst o dest_Free) of
[] => ()
| Free (s, _) :: _ => error ("Extra variable on right-hand side: " ^ quote s));
in
check_no_duplicate_arg ();
check_fun_name ();
check_args_are_vars ();
check_no_other_frees ()
end;
fun parse_corec_equation ctxt fun_frees eq =
let
val (lhs, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop (drop_all eq))
handle TERM _ => error "Expected HOL equation";
val _ = check_corec_equation ctxt fun_frees (lhs, rhs);
val (fun_t, arg_ts) = strip_comb lhs;
val (arg_Ts, _) = strip_type (fastype_of fun_t);
val added_Ts = drop (length arg_ts) arg_Ts;
val free_names = mk_names (length added_Ts) "x" ~~ added_Ts;
val free_args = Variable.variant_frees ctxt [rhs, lhs] free_names |> map Free;
in
(arg_ts @ free_args, list_comb (rhs, free_args))
end;
fun morph_views phi (code, ctrs, discs, disc_iffs, sels) =
(Morphism.term phi code, map (Morphism.term phi) ctrs, map (Morphism.term phi) discs,
map (Morphism.term phi) disc_iffs, map (Morphism.term phi) sels);
fun generate_views ctxt eq fun_t (lhs_free_args, rhs) =
let
val lhs = list_comb (fun_t, lhs_free_args);
val T as Type (T_name, Ts) = fastype_of rhs;
val SOME {fp_ctr_sugar = {ctr_sugar = {ctrs = ctrs0, discs = discs0, selss = selss0, ...}, ...},
...} =
fp_sugar_of ctxt T_name;
val ctrs = map (mk_ctr Ts) ctrs0;
val discs = map (mk_disc_or_sel Ts) discs0;
val selss = map (map (mk_disc_or_sel Ts)) selss0;
val code_view = drop_all eq;
fun can_case_expand t = not (can (dest_ctr ctxt T_name) t);
fun generate_raw_views conds t raw_views =
let
fun analyse (ctr :: ctrs) (disc :: discs) ctr' =
if ctr = ctr' then
(conds, disc, ctr)
else
analyse ctrs discs ctr';
in
(analyse ctrs discs (fst (strip_comb t))) :: raw_views
end;
fun generate_disc_views raw_views =
if length discs = 1 then
([], [])
else
let
fun collect_condss_disc condss [] _ = condss
| collect_condss_disc condss ((conds, disc', _) :: raw_views) disc =
collect_condss_disc (condss |> disc = disc' ? cons conds) raw_views disc;
val grouped_disc_views = discs
|> map (collect_condss_disc [] raw_views)
|> curry (op ~~) (map (fn disc => disc $ lhs) discs);
fun mk_disc_iff_props props [] = props
| mk_disc_iff_props _ ((lhs, @{const HOL.True}) :: _) = [lhs]
| mk_disc_iff_props props ((lhs, rhs) :: views) =
mk_disc_iff_props ((HOLogic.mk_eq (lhs, rhs)) :: props) views;
in
(grouped_disc_views
|> map swap,
grouped_disc_views
|> map (apsnd (s_dnf #> mk_conjs))
|> mk_disc_iff_props []
|> map (fn eq => ([[]], eq)))
end;
fun generate_ctr_views raw_views =
let
fun collect_condss_ctr condss [] _ = condss
| collect_condss_ctr condss ((conds, _, ctr') :: raw_views) ctr =
collect_condss_ctr (condss |> ctr = ctr' ? cons conds) raw_views ctr;
fun mk_ctr_eq ctr_sels ctr =
let
fun extract_arg n sel _(*bound_Ts*) fun_t arg_ts =
if ctr = fun_t then
nth arg_ts n
else
let val t = list_comb (fun_t, arg_ts) in
if can_case_expand t then
sel $ t
else
Term.dummy_pattern (range_type (fastype_of sel))
end;
in
ctr_sels
|> map_index (uncurry extract_arg)
|> map (fn extract => massage_corec_code_rhs ctxt extract [] rhs)
|> curry list_comb ctr
|> curry HOLogic.mk_eq lhs
end;
fun remove_condss_if_alone [(_, concl)] = [([[]], concl)]
| remove_condss_if_alone views = views;
in
ctrs
|> `(map (collect_condss_ctr [] raw_views))
||> map2 mk_ctr_eq selss
|> op ~~
|> filter_out (null o fst)
|> remove_condss_if_alone
end;
fun generate_sel_views raw_views only_one_ctr =
let
fun mk_sel_positions sel =
let
fun get_sel_position _ [] = NONE
| get_sel_position i (sel' :: sels) =
if sel = sel' then SOME i else get_sel_position (i + 1) sels;
in
ctrs ~~ map (get_sel_position 0) selss
|> map_filter (fn (ctr, pos_opt) =>
if is_some pos_opt then SOME (ctr, the pos_opt) else NONE)
end;
fun collect_sel_condss0 condss [] _ = condss
| collect_sel_condss0 condss ((conds, _, ctr) :: raw_views) sel_positions =
let val condss' = condss |> is_some (AList.lookup (op =) sel_positions ctr) ? cons conds
in
collect_sel_condss0 condss' raw_views sel_positions
end;
val collect_sel_condss =
if only_one_ctr then K [[]] else collect_sel_condss0 [] raw_views;
fun mk_sel_rhs sel_positions sel =
let
val sel_T = range_type (fastype_of sel);
fun extract_sel_value _(*bound_Ts*) fun_t arg_ts =
(case AList.lookup (op =) sel_positions fun_t of
SOME n => nth arg_ts n
| NONE =>
let val t = list_comb (fun_t, arg_ts) in
if can_case_expand t then
sel $ t
else
Term.dummy_pattern sel_T
end);
in
massage_corec_code_rhs ctxt extract_sel_value [] rhs
end;
val ordered_sels = distinct (op =) (flat selss);
val sel_positionss = map mk_sel_positions ordered_sels;
val sel_rhss = map2 mk_sel_rhs sel_positionss ordered_sels;
val sel_lhss = map (rapp lhs o mk_disc_or_sel Ts) ordered_sels;
val sel_condss = map collect_sel_condss sel_positionss;
fun is_undefined (Const (@{const_name undefined}, _)) = true
| is_undefined _ = false;
in
sel_condss ~~ (sel_lhss ~~ sel_rhss)
|> filter_out (is_undefined o snd o snd)
|> map (apsnd HOLogic.mk_eq)
end;
fun mk_atomic_prop fun_args (condss, concl) =
(Logic.list_all (map dest_Free fun_args, abstract_over_list fun_args
(Logic.list_implies (map HOLogic.mk_Trueprop (s_dnf condss), HOLogic.mk_Trueprop concl))));
val raw_views = rhs
|> massage_let_if_case ctxt (K false) (fn _(*bound_Ts*) => fn t => t
|> can_case_expand t ? expand_to_ctr_term ctxt T) (K (K ())) (K I) []
|> (fn expanded_rhs => fold_rev_let_if_case ctxt generate_raw_views [] expanded_rhs [])
|> rev;
val (disc_views, disc_iff_views) = generate_disc_views raw_views;
val ctr_views = generate_ctr_views raw_views;
val sel_views = generate_sel_views raw_views (length ctr_views = 1);
val mk_props = filter_out (null o fst) #> map (mk_atomic_prop lhs_free_args);
in
(code_view, mk_props ctr_views, mk_props disc_views, mk_props disc_iff_views,
mk_props sel_views)
end;
fun find_all_associated_types [] _ = []
| find_all_associated_types ((Type (_, Ts1), Type (_, Ts2)) :: TTs) T =
find_all_associated_types ((Ts1 ~~ Ts2) @ TTs) T
| find_all_associated_types ((T1, T2) :: TTs) T =
find_all_associated_types TTs T |> T1 = T ? cons T2;
fun as_member_of tab = try dest_Const #> Option.mapPartial (fst #> Symtab.lookup tab);
fun extract_rho_from_equation
({ctr_guards, inner_buffer = {Oper, VLeaf, CLeaf, ctr_wrapper, friends}, ...},
{pattern_ctrs, discs, sels, it, mk_case})
b version Y preT ssig_T friend_tm (lhs_args, rhs) lthy =
let
val thy = Proof_Context.theory_of lthy;
val res_T = fastype_of rhs;
val YpreT = HOLogic.mk_prodT (Y, preT);
fun fpT_to new_T T =
if T = res_T then
new_T
else
(case T of
Type (s, Ts) => Type (s, map (fpT_to new_T) Ts)
| _ => T);
fun build_params bound_Us bound_Ts T =
{bound_Us = bound_Us, bound_Ts = bound_Ts, U = T, T = T};
fun typ_before explore {bound_Us, bound_Ts, ...} t =
explore (build_params bound_Us bound_Ts (fastype_of1 (bound_Ts, t))) t;
val is_self_call = curry (op aconv) friend_tm;
val has_self_call = Term.exists_subterm is_self_call;
fun has_res_T bound_Ts t = fastype_of1 (bound_Ts, t) = res_T;
fun contains_res_T (Type (s, Ts)) = s = fst (dest_Type res_T) orelse exists contains_res_T Ts
| contains_res_T _ = false;
val is_lhs_arg = member (op =) lhs_args;
fun is_constant t =
not (Term.exists_subterm is_lhs_arg t orelse has_self_call t orelse loose_bvar (t, 0));
fun is_nested_type T = T <> res_T andalso T <> YpreT andalso T <> ssig_T;
val is_valid_case_argumentT = not o member (op =) [Y, ssig_T];
fun is_same_type_constr (Type (s, _)) (Type (s', _)) = (s = s')
| is_same_type_constr _ _ = false;
exception NO_ENCAPSULATION of unit;
val parametric_consts = Unsynchronized.ref [];
(* We are assuming that set functions are marked with "[transfer_rule]" (cf. the "transfer"
plugin). Otherwise, the "eq_algrho" tactic might fail. *)
fun is_special_parametric_const (x as (s, _)) =
s = @{const_name id} orelse is_set lthy x;
fun add_parametric_const s general_T T U =
let
fun tupleT_of_funT T =
let val (Ts, T) = strip_type T in
mk_tupleT_balanced (Ts @ [T])
end;
fun funT_of_tupleT n =
dest_tupleT_balanced (n + 1)
#> split_last
#> op --->;
val m = num_binder_types general_T;
val param1_T = Type_Infer.paramify_vars general_T;
val param2_T = Type_Infer.paramify_vars param1_T;
val deadfixed_T =
build_map lthy [] (mk_undefined o op -->) (apply2 tupleT_of_funT (param1_T, param2_T))
|> singleton (Type_Infer_Context.infer_types lthy)
|> singleton (Type_Infer.fixate lthy false)
|> type_of
|> dest_funT
|-> generalize_types 1
|> funT_of_tupleT m;
val j = maxidx_of_typ deadfixed_T + 1;
fun varifyT (Type (s, Ts)) = Type (s, map varifyT Ts)
| varifyT (TFree (s, T)) = TVar ((s, j), T)
| varifyT T = T;
val dedvarified_T = varifyT deadfixed_T;
val new_vars = Sign.typ_match thy (dedvarified_T, T) Vartab.empty
|> Vartab.dest
|> filter (curry (op =) j o snd o fst)
|> Vartab.make;
val deadinstantiated_T = map_atyps (Type.devar new_vars) dedvarified_T;
val final_T =
if Sign.typ_instance thy (U, deadinstantiated_T) then deadfixed_T else general_T;
in
parametric_consts := insert (op =) (s, final_T) (!parametric_consts)
end;
fun encapsulate (params as {U, T, ...}) t =
if U = T then
t
else if T = Y then
VLeaf $ t
else if T = res_T then
CLeaf $ t
else if T = YpreT then
it $ t
else if is_nested_type T andalso is_same_type_constr T U then
explore_nested lthy encapsulate params t
else
raise NO_ENCAPSULATION ();
fun build_function_after_encapsulation fun_t fun_t' (params as {bound_Us, ...}) arg_ts arg_ts' =
let
val arg_Us' = fst (strip_typeN (length arg_ts) (fastype_of1 (bound_Us, fun_t')));
fun the_or_error arg NONE =
error ("Illegal argument " ^ quote (Syntax.string_of_term lthy arg) ^
" to " ^ quote (Syntax.string_of_term lthy fun_t))
| the_or_error _ (SOME arg') = arg';
in
arg_ts'
|> `(map (curry fastype_of1 bound_Us))
|>> map2 (update_UT params) arg_Us'
|> op ~~
|> map (try (uncurry encapsulate))
|> map2 the_or_error arg_ts
|> curry list_comb fun_t'
end;
fun rebuild_function_after_exploration old_fn new_fn explore params arg_ts =
arg_ts
|> map (typ_before explore params)
|> build_function_after_encapsulation old_fn new_fn params arg_ts;
fun update_case Us U casex =
let
val Type (T_name, _) = domain_type (snd (strip_fun_type (fastype_of casex)));
val SOME {fp_ctr_sugar = {ctr_sugar = {T = Type (_, Ts), casex, ...}, ...}, ...} =
fp_sugar_of lthy T_name;
val T = body_type (fastype_of casex);
in
Term.subst_atomic_types ((T :: Ts) ~~ (U :: Us)) casex
end;
fun deduce_according_type default_T [] = default_T
| deduce_according_type default_T Ts = (case distinct (op =) Ts of
U :: [] => U
| _ => fpT_to ssig_T default_T);
fun massage_if explore_cond explore (params as {bound_Us, bound_Ts, ...}) t =
(case strip_comb t of
(const as Const (@{const_name If}, _), obj :: (branches as [_, _])) =>
(case List.partition Term.is_dummy_pattern (map (explore params) branches) of
(dummy_branch' :: _, []) => dummy_branch'
| (_, [branch']) => branch'
| (_, branches') =>
let
val brancheUs = map (curry fastype_of1 bound_Us) branches';
val U = deduce_according_type (fastype_of1 (bound_Ts, hd branches)) brancheUs;
val const_obj' = (If_const U, obj)
||> explore_cond (update_UT params @{typ bool} @{typ bool})
|> op $;
in
build_function_after_encapsulation (const $ obj) const_obj' params branches branches'
end)
| _ => explore params t);
fun massage_map explore (params as {bound_Us, bound_Ts, T = Type (T_name, Ts), ...})
(t as func $ mapped_arg) =
if is_self_call (head_of func) then
explore params t
else
(case try (dest_map lthy T_name) func of
SOME (map_tm, fs) =>
let
val n = length fs;
val mapped_arg' = mapped_arg
|> `(curry fastype_of1 bound_Ts)
|>> build_params bound_Us bound_Ts
|-> explore;
in
(case fastype_of1 (bound_Us, mapped_arg') of
Type (U_name, Us0) =>
if U_name = T_name then
let
val Us = map (fpT_to ssig_T) Us0;
val temporary_map = map_tm
|> mk_map n Us Ts;
val map_fn_Ts = fastype_of #> strip_fun_type #> fst;
val binder_Uss = map_fn_Ts temporary_map
|> map (map (fpT_to ssig_T) o binder_types);
val fun_paramss = map_fn_Ts (head_of func)
|> map (build_params bound_Us bound_Ts);
val fs' = fs
|> @{map 4} explore_fun binder_Uss (replicate n explore) fun_paramss;
val SOME bnf = bnf_of lthy T_name;
val Type (_, bnf_Ts) = T_of_bnf bnf;
val typ_alist =
lives_of_bnf bnf ~~ map (curry fastype_of1 bound_Us #> range_type) fs';
val Us' = map2 the_default Us (map (AList.lookup (op =) typ_alist) bnf_Ts);
val map_tm' = map_tm |> mk_map n Us Us';
in
build_function_after_encapsulation func (list_comb (map_tm', fs')) params
[mapped_arg] [mapped_arg']
end
else
explore params t
| _ => explore params t)
end
| NONE => explore params t)
| massage_map explore params t = explore params t;
fun massage_comp explore (params as {bound_Us, ...}) t =
(case strip_comb t of
(Const (@{const_name comp}, _), f1 :: f2 :: args) =>
let
val args' = map (typ_before explore params) args;
val f2' = typ_before (explore_fun (map (curry fastype_of1 bound_Us) args') explore) params
f2;
val f1' = typ_before (explore_fun [range_type (fastype_of1 (bound_Us, f2'))] explore)
params f1;
in
betapply (f1', list_comb (f2', args'))
end
| _ => explore params t);
fun massage_ctr explore (params as {T = T as Type (s, Ts), bound_Us, ...}) t =
if T <> res_T then
(case try (dest_ctr lthy s) t of
SOME (ctr, args) =>
let
val args' = map (typ_before explore params) args;
val SOME {T = Type (_, ctr_Ts), ...} = ctr_sugar_of lthy s;
val temp_ctr = mk_ctr ctr_Ts ctr;
val argUs = map (curry fastype_of1 bound_Us) args';
val typ_alist = binder_types (fastype_of temp_ctr) ~~ argUs;
val Us = ctr_Ts
|> map (find_all_associated_types typ_alist)
|> map2 deduce_according_type Ts;
val ctr' = mk_ctr Us ctr;
in
build_function_after_encapsulation ctr ctr' params args args'
end
| NONE => explore params t)
else
explore params t
| massage_ctr explore params t = explore params t;
fun const_of [] _ = NONE
| const_of ((sel as Const (s1, _)) :: r) (const as Const (s2, _)) =
if s1 = s2 then SOME sel else const_of r const
| const_of _ _ = NONE;
fun massage_disc explore (params as {T, bound_Us, bound_Ts, ...}) t =
(case (strip_comb t, T = @{typ bool}) of
((fun_t, arg :: []), true) =>
let val arg_T = fastype_of1 (bound_Ts, arg) in
if arg_T <> res_T then
(case arg_T |> try (fst o dest_Type) |> Option.mapPartial (ctr_sugar_of lthy) of
SOME {discs, T = Type (_, Ts), ...} =>
(case const_of discs fun_t of
SOME disc =>
let
val arg' = arg |> typ_before explore params;
val Type (_, Us) = fastype_of1 (bound_Us, arg');
val disc' = disc |> Term.subst_TVars (map (fst o dest_TVar) Ts ~~ Us);
in
disc' $ arg'
end
| NONE => explore params t)
| NONE => explore params t)
else
explore params t
end
| _ => explore params t);
fun massage_sel explore (params as {bound_Us, bound_Ts, ...}) t =
let val (fun_t, args) = strip_comb t in
if args = [] then
explore params t
else
let val T = fastype_of1 (bound_Ts, hd args) in
(case (Option.mapPartial (ctr_sugar_of lthy) (try (fst o dest_Type) T), T <> res_T) of
(SOME {selss, T = Type (_, Ts), ...}, true) =>
(case const_of (flat selss) fun_t of
SOME sel =>
let
val args' = args |> map (typ_before explore params);
val Type (_, Us) = fastype_of1 (bound_Us, hd args');
val sel' = sel |> Term.subst_TVars (map (fst o dest_TVar) Ts ~~ Us);
in
build_function_after_encapsulation sel sel' params args args'
end
| NONE => explore params t)
| _ => explore params t)
end
end;
fun massage_equality explore (params as {bound_Us, bound_Ts, ...})
(t as Const (@{const_name HOL.eq}, _) $ t1 $ t2) =
let
val check_is_VLeaf =
not o (Term.exists_subterm (fn t => t aconv CLeaf orelse t aconv Oper));
fun try_pattern_matching (fun_t, arg_ts) t =
(case as_member_of pattern_ctrs fun_t of
SOME (disc, sels) =>
let val t' = typ_before explore params t in
if fastype_of1 (bound_Us, t') = YpreT then
let
val arg_ts' = map (typ_before explore params) arg_ts;
val sels_t' = map (fn sel => betapply (sel, t')) sels;
val Ts = map (curry fastype_of1 bound_Us) arg_ts';
val Us = map (curry fastype_of1 bound_Us) sels_t';
val arg_ts' = map2 encapsulate (map2 (update_UT params) Us Ts) arg_ts';
in
if forall check_is_VLeaf arg_ts' then
SOME (Library.foldl1 HOLogic.mk_conj
(betapply (disc, t') :: (map HOLogic.mk_eq (arg_ts' ~~ sels_t'))))
else
NONE
end
else
NONE
end
| NONE => NONE);
in
(case try_pattern_matching (strip_comb t1) t2 of
SOME cond => cond
| NONE => (case try_pattern_matching (strip_comb t2) t1 of
SOME cond => cond
| NONE =>
let
val T = fastype_of1 (bound_Ts, t1);
val params' = build_params bound_Us bound_Ts T;
val t1' = explore params' t1;
val t2' = explore params' t2;
in
if fastype_of1 (bound_Us, t1') = T andalso fastype_of1 (bound_Us, t2') = T then
HOLogic.mk_eq (t1', t2')
else
error ("Unsupported condition: " ^ quote (Syntax.string_of_term lthy t))
end))
end
| massage_equality explore params t = explore params t;
fun infer_types (TVar _) (TVar _) = []
| infer_types (U as TVar _) T = [(U, T)]
| infer_types (Type (s', Us)) (Type (s, Ts)) =
if s' = s then flat (map2 infer_types Us Ts) else []
| infer_types _ _ = [];
fun group_by_fst associations [] = associations
| group_by_fst associations ((a, b) :: r) = group_by_fst (add_association a b associations) r
and add_association a b [] = [(a, [b])]
| add_association a b ((c, d) :: r) =
if a = c then (c, b :: d) :: r
else (c, d) :: (add_association a b r);
fun new_TVar known_TVars =
Name.invent_list (map (fst o fst o dest_TVar) known_TVars) "x" 1
|> (fn [s] => TVar ((s, 0), []));
fun instantiate_type inferred_types =
Term.typ_subst_TVars (map (apfst (fst o dest_TVar)) inferred_types);
fun chose_unknown_TVar (T as TVar _) = SOME T
| chose_unknown_TVar (Type (_, Ts)) =
fold (curry merge_options) (map chose_unknown_TVar Ts) NONE
| chose_unknown_TVar _ = NONE;
(* The function under definition might not be defined yet when this is queried. *)
fun maybe_const_type ctxt (s, T) =
Sign.const_type (Proof_Context.theory_of ctxt) s |> the_default T;
fun massage_const polymorphic explore (params as {bound_Us, ...}) t =
let val (fun_t, arg_ts) = strip_comb t in
(case fun_t of
Const (fun_x as (s, fun_T)) =>
let val general_T = if polymorphic then maybe_const_type lthy fun_x else fun_T in
if fun_t aconv friend_tm orelse contains_res_T (body_type general_T) orelse
is_constant t then
explore params t
else
let
val inferred_types = infer_types general_T fun_T;
fun prepare_skeleton [] _ = []
| prepare_skeleton ((T, U) :: inferred_types) As =
let
fun schematize_res_T U As =
if U = res_T then
let val A = new_TVar As in
(A, A :: As)
end
else
(case U of
Type (s, Us) => fold_map schematize_res_T Us As |>> curry Type s
| _ => (U, As));
val (U', As') = schematize_res_T U As;
in
(T, U') :: (prepare_skeleton inferred_types As')
end;
val inferred_types' = prepare_skeleton inferred_types (map fst inferred_types);
val skeleton_T = instantiate_type inferred_types' general_T;
fun explore_if_possible (exp_arg as (_, true)) _ = exp_arg
| explore_if_possible (exp_arg as (arg, false)) arg_T =
if exists (exists_subtype is_TVar) (binder_types arg_T) then exp_arg
else (typ_before (explore_fun (binder_types arg_T) explore) params arg, true);
fun collect_inferred_types [] _ = []
| collect_inferred_types ((arg, explored) :: exp_arg_ts) (arg_T :: arg_Ts) =
(if explored then infer_types arg_T (fastype_of1 (bound_Us, arg)) else []) @
collect_inferred_types exp_arg_ts arg_Ts;
fun propagate exp_arg_ts skeleton_T =
let
val arg_gen_Ts = binder_types skeleton_T;
val exp_arg_ts = map2 explore_if_possible exp_arg_ts arg_gen_Ts;
val inferred_types = collect_inferred_types exp_arg_ts arg_gen_Ts
|> group_by_fst []
|> map (apsnd (deduce_according_type ssig_T));
in
(exp_arg_ts, instantiate_type inferred_types skeleton_T)
end;
val remaining_to_be_explored = filter_out snd #> length;
fun try_exploring_args exp_arg_ts skeleton_T =
let
val n = remaining_to_be_explored exp_arg_ts;
val (exp_arg_ts', skeleton_T') = propagate exp_arg_ts skeleton_T;
val n' = remaining_to_be_explored exp_arg_ts';
fun try_instantiating A T =
try (try_exploring_args exp_arg_ts') (instantiate_type [(A, T)] skeleton_T');
in
if n' = 0 then
SOME (exp_arg_ts', skeleton_T')
else if n = n' then
if exists_subtype is_TVar skeleton_T' then
let val SOME A = chose_unknown_TVar skeleton_T' in
(case try_instantiating A ssig_T of
SOME result => result
| NONE => (case try_instantiating A YpreT of
SOME result => result
| NONE => (case try_instantiating A res_T of
SOME result => result
| NONE => NONE)))
end
else
NONE
else
try_exploring_args exp_arg_ts' skeleton_T'
end;
in
(case try_exploring_args (map (fn arg => (arg, false)) arg_ts) skeleton_T of
SOME (exp_arg_ts, fun_U) =>
let
val arg_ts' = map fst exp_arg_ts;
val fun_t' = Const (s, fun_U);
fun finish_off () =
let
val t' =
build_function_after_encapsulation fun_t fun_t' params arg_ts arg_ts';
in
if can type_of1 (bound_Us, t') then
(if fun_T = fun_U orelse is_special_parametric_const (s, fun_T) then ()
else add_parametric_const s general_T fun_T fun_U;
t')
else
explore params t
end;
in
if polymorphic then
finish_off ()
else
(case try finish_off () of
SOME t' => t'
| NONE => explore params t)
end
| NONE => explore params t)
end
end
| _ => explore params t)
end;
fun massage_rho explore =
massage_star [massage_let, massage_if explore_cond, massage_case, massage_fun, massage_comp,
massage_map, massage_ctr, massage_sel, massage_disc, massage_equality,
massage_const false, massage_const true]
explore
and massage_case explore (params as {bound_Ts, bound_Us, ...}) t =
(case strip_comb t of
(casex as Const (case_x as (c, _)), args as _ :: _ :: _) =>
(case try strip_fun_type (maybe_const_type lthy case_x) 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;
val (branches, obj_leftovers) = chop n args;
in
if n < length args then
(case gen_body_fun_T of
Type (_, [Type (T_name, _), _]) =>
if case_of lthy T_name = SOME (c, true) then
let
val brancheTs = binder_fun_types (fastype_of1 (bound_Ts, casex));
val obj_leftover_Ts = map (curry fastype_of1 bound_Ts) obj_leftovers;
val obj_leftovers' =
if is_constant (hd obj_leftovers) then
obj_leftovers
else
(obj_leftover_Ts, obj_leftovers)
|>> map (build_params bound_Us bound_Ts)
|> op ~~
|> map (uncurry explore_inner);
val obj_leftoverUs = obj_leftovers' |> map (curry fastype_of1 bound_Us);
val _ = is_valid_case_argumentT (hd obj_leftoverUs) orelse
error (quote (Syntax.string_of_term lthy (hd obj_leftovers)) ^
" is not a valid case argument");
val Us = obj_leftoverUs |> hd |> dest_Type |> snd;
val branche_binderUss =
(if hd obj_leftoverUs = YpreT then mk_case HOLogic.boolT
else update_case Us HOLogic.boolT casex)
|> fastype_of
|> binder_fun_types
|> map binder_types;
val b_params = map (build_params bound_Us bound_Ts) brancheTs;
val branches' = branches
|> @{map 4} explore_fun branche_binderUss (replicate n explore) b_params;
val brancheUs = map (curry fastype_of1 bound_Us) branches';
val U = deduce_according_type (body_type (hd brancheTs))
(map body_type brancheUs);
val casex' =
if hd obj_leftoverUs = YpreT then mk_case U else update_case Us U casex;
in
build_function_after_encapsulation casex casex' params
(branches @ obj_leftovers) (branches' @ obj_leftovers')
end
else
explore params t
| _ => explore params t)
else
explore params t
end
| NONE => explore params t)
| _ => explore params t)
and explore_cond params t =
if has_self_call t then
error ("Unallowed corecursive call in condition " ^ quote (Syntax.string_of_term lthy t))
else
explore_inner params t
and explore_inner params t =
massage_rho explore_inner_general params t
and explore_inner_general (params as {bound_Us, bound_Ts, T, ...}) t =
let val (fun_t, arg_ts) = strip_comb t in
if is_constant t then
t
else
(case (as_member_of discs fun_t,
length arg_ts = 1 andalso has_res_T bound_Ts (the_single arg_ts)) of
(SOME disc', true) =>
let
val arg' = explore_inner params (the_single arg_ts);
val arg_U = fastype_of1 (bound_Us, arg');
in
if arg_U = res_T then
fun_t $ arg'
else if arg_U = YpreT then
disc' $ arg'
else
error ("Discriminator " ^ quote (Syntax.string_of_term lthy fun_t) ^
" cannot be applied to non-lhs argument " ^
quote (Syntax.string_of_term lthy (hd arg_ts)))
end
| _ =>
(case as_member_of sels fun_t of
SOME sel' =>
let
val arg_ts' = map (explore_inner params) arg_ts;
val arg_U = fastype_of1 (bound_Us, hd arg_ts');
in
if arg_U = res_T then
build_function_after_encapsulation fun_t fun_t params arg_ts arg_ts'
else if arg_U = YpreT then
build_function_after_encapsulation fun_t sel' params arg_ts arg_ts'
else
error ("Selector " ^ quote (Syntax.string_of_term lthy fun_t) ^
" cannot be applied to non-lhs argument " ^
quote (Syntax.string_of_term lthy (hd arg_ts)))
end
| NONE =>
(case as_member_of friends fun_t of
SOME (_, friend') =>
rebuild_function_after_exploration fun_t friend' explore_inner params arg_ts
|> curry (op $) Oper
| NONE =>
(case as_member_of ctr_guards fun_t of
SOME ctr_guard' =>
rebuild_function_after_exploration fun_t ctr_guard' explore_inner params arg_ts
|> curry (op $) ctr_wrapper
|> curry (op $) Oper
| NONE =>
if is_Bound fun_t then
rebuild_function_after_exploration fun_t fun_t explore_inner params arg_ts
else if is_Free fun_t then
let val fun_t' = map_types (fpT_to YpreT) fun_t in
rebuild_function_after_exploration fun_t fun_t' explore_inner params arg_ts
end
else if T = res_T then
error (quote (Syntax.string_of_term lthy fun_t) ^
" not polymorphic enough to be applied like this and no friend")
else
error (quote (Syntax.string_of_term lthy fun_t) ^
" not polymorphic enough to be applied like this")))))
end;
fun explore_ctr params t =
massage_rho explore_ctr_general params t
and explore_ctr_general params t =
let
val (fun_t, arg_ts) = strip_comb t;
val ctr_opt = as_member_of ctr_guards fun_t;
in
if is_some ctr_opt then
rebuild_function_after_exploration fun_t (the ctr_opt) explore_inner params arg_ts
else
error ("Constructor expected on right-hand side, " ^
quote (Syntax.string_of_term lthy fun_t) ^ " found instead")
end;
val rho_rhs = rhs
|> explore_ctr (build_params [] [] (fastype_of rhs))
|> abs_tuple_balanced (map (map_types (fpT_to YpreT)) lhs_args)
|> unfold_id_bnf_etc lthy;
in
lthy
|> define_const false b version rhoN rho_rhs
|>> pair (!parametric_consts, rho_rhs)
end;
fun mk_rho_parametricity_goal ctxt Y Z preT ssig_T dead_pre_rel dead_k_rel dead_ssig_rel rho_rhs =
let
val YpreT = HOLogic.mk_prodT (Y, preT);
val ZpreT = Tsubst Y Z YpreT;
val ssigZ_T = Tsubst Y Z ssig_T;
val dead_pre_rel' = Term.subst_atomic_types [(Y, ssig_T), (Z, ssigZ_T)] dead_pre_rel;
val dead_k_rel' = Term.subst_atomic_types [(Y, YpreT), (Z, ZpreT)] dead_k_rel;
val (R, _) = ctxt
|> yield_singleton (mk_Frees "R") (mk_pred2T Y Z);
val rho_rel = mk_rel_fun (dead_k_rel' $ mk_rel_prod R (dead_pre_rel $ R))
(dead_pre_rel' $ (dead_ssig_rel $ R));
val rho_rhsZ = substT Y Z rho_rhs;
in
HOLogic.mk_Trueprop (rho_rel $ rho_rhs $ rho_rhsZ)
end;
fun extract_rho_return_transfer_goals fun_b version dead_pre_bnf dead_k_bnf Y Z preT fun_T k_T
ssig_T ssig_fp_sugar friend_parse_info fun_t parsed_eq lthy =
let
val Type (fpT_name, _) = body_type fun_T;
fun mk_rel T bnf =
let
val ZT = Tsubst Y Z T;
val rel_T = mk_predT [mk_pred2T Y Z, T, ZT];
in
enforce_type lthy I rel_T (rel_of_bnf bnf)
end;
val ssig_bnf = #fp_bnf ssig_fp_sugar;
val (dead_ssig_bnf, lthy) = bnf_kill_all_but 1 ssig_bnf lthy;
val dead_pre_rel = mk_rel preT dead_pre_bnf;
val dead_k_rel = mk_rel k_T dead_k_bnf;
val dead_ssig_rel = mk_rel ssig_T dead_ssig_bnf;
val (((parametric_consts, rho_rhs), rho_data), lthy) =
extract_rho_from_equation friend_parse_info fun_b version Y preT ssig_T fun_t parsed_eq lthy;
val const_transfer_goals = map (mk_const_transfer_goal lthy) parametric_consts;
val rho_transfer_goal =
mk_rho_parametricity_goal lthy Y Z preT ssig_T dead_pre_rel dead_k_rel dead_ssig_rel rho_rhs;
in
((rho_data, (const_transfer_goals, rho_transfer_goal)), lthy)
end;
fun explore_corec_equation ctxt could_be_friend friend fun_name fun_free
{outer_buffer, ctr_guards, inner_buffer} res_T (args, rhs) =
let
val is_self_call = curry (op aconv) fun_free;
val has_self_call = Term.exists_subterm is_self_call;
val outer_ssig_T = body_type (fastype_of (#Oper outer_buffer));
fun inner_fp_of (Free (s, _)) =
Free (s ^ inner_fp_suffix, mk_tupleT_balanced (map fastype_of args) --> outer_ssig_T);
fun build_params bound_Ts U T =
{bound_Us = bound_Ts, bound_Ts = bound_Ts, U = U, T = T};
fun rebuild_function_after_exploration new_fn explore {bound_Ts, ...} arg_ts =
let
val binder_types_old_fn = map (curry fastype_of1 bound_Ts) arg_ts;
val binder_types_new_fn = new_fn
|> binder_types o (curry fastype_of1 bound_Ts)
|> take (length binder_types_old_fn);
val paramss =
map2 (build_params bound_Ts) binder_types_new_fn binder_types_old_fn;
in
map2 explore paramss arg_ts
|> curry list_comb new_fn
end;
fun massage_map_corec explore {bound_Ts, U, T, ...} t =
let val explore' = explore ooo build_params in
massage_nested_corec_call ctxt has_self_call explore' explore' bound_Ts U T t
end;
fun massage_comp explore params t =
(case strip_comb t of
(Const (@{const_name comp}, _), f1 :: f2 :: args) =>
explore params (betapply (f1, (betapplys (f2, args))))
| _ => explore params t);
fun massage_fun explore (params as {bound_Us, bound_Ts, U, T}) t =
if can dest_funT T then
let
val arg_T = domain_type T;
val arg_name = the_default Name.uu (try (fn (Abs (s, _, _)) => s) t);
in
add_boundvar t
|> explore {bound_Us = arg_T :: bound_Us, bound_Ts = arg_T :: bound_Ts,
U = range_type U, T = range_type T}
|> (fn t => Abs (arg_name, arg_T, t))
end
else
explore params t
fun massage_let_if_case_corec explore {bound_Ts, U, T, ...} t =
massage_let_if_case ctxt has_self_call (fn bound_Ts => explore (build_params bound_Ts U T))
(K (unexpected_corec_call ctxt [t])) (K (unsupported_case_around_corec_call ctxt [t]))
bound_Ts t;
val massage_map_let_if_case =
massage_star [massage_map_corec, massage_fun, massage_comp, massage_let_if_case_corec];
fun explore_arg _ t =
if has_self_call t then
error (quote (Syntax.string_of_term ctxt t) ^ " contains a nested corecursive call" ^
(if could_be_friend then " (try specifying \"(friend)\")" else ""))
else
t;
fun explore_inner params t =
massage_map_let_if_case explore_inner_general params t
and explore_inner_general (params as {bound_Ts, T, ...}) t =
if T = res_T then
let val (f_t, arg_ts) = strip_comb t in
if has_self_call t then
(case as_member_of (#friends inner_buffer) f_t of
SOME (_, friend') =>
rebuild_function_after_exploration friend' explore_inner params arg_ts
|> curry (op $) (#Oper inner_buffer)
| NONE =>
(case as_member_of ctr_guards f_t of
SOME ctr_guard' =>
rebuild_function_after_exploration ctr_guard' explore_inner params arg_ts
|> curry (op $) (#ctr_wrapper inner_buffer)
|> curry (op $) (#Oper inner_buffer)
| NONE =>
if is_self_call f_t then
if friend andalso exists has_self_call arg_ts then
(case Symtab.lookup (#friends inner_buffer) fun_name of
SOME (_, friend') =>
rebuild_function_after_exploration friend' explore_inner params arg_ts
|> curry (op $) (#Oper inner_buffer))
else
let val arg_Ts = binder_types (fastype_of1 (bound_Ts, f_t)) in
map2 explore_arg (map2 (update_UT params) arg_Ts arg_Ts) arg_ts
|> mk_tuple1_balanced bound_Ts
|> curry (op $) (#VLeaf inner_buffer)
end
else
error (quote (Syntax.string_of_term ctxt f_t) ^ " not registered as friend")))
else
#CLeaf inner_buffer $ t
end
else if has_self_call t then
error (quote (Syntax.string_of_term ctxt t) ^ " contains a corecursive call but has type " ^
quote (Syntax.string_of_typ ctxt T))
else
explore_nested ctxt explore_inner_general params t;
fun explore_outer params t =
massage_map_let_if_case explore_outer_general params t
and explore_outer_general (params as {bound_Ts, T, ...}) t =
if T = res_T then
let val (f_t, arg_ts) = strip_comb t in
(case as_member_of ctr_guards f_t of
SOME ctr_guard' =>
rebuild_function_after_exploration ctr_guard' explore_inner params arg_ts
|> curry (op $) (#VLeaf outer_buffer)
| NONE =>
if not (has_self_call t) then
t
|> expand_to_ctr_term ctxt T
|> massage_let_if_case_corec explore_outer_general params
else
(case as_member_of (#friends outer_buffer) f_t of
SOME (_, friend') =>
rebuild_function_after_exploration friend' explore_outer params arg_ts
|> curry (op $) (#Oper outer_buffer)
| NONE =>
if is_self_call f_t then
let val arg_Ts = binder_types (fastype_of1 (bound_Ts, f_t)) in
map2 explore_arg (map2 (update_UT params) arg_Ts arg_Ts) arg_ts
|> mk_tuple1_balanced bound_Ts
|> curry (op $) (inner_fp_of f_t)
end
else
error (quote (Syntax.string_of_term ctxt f_t) ^ " not registered as friend")))
end
else if has_self_call t then
error (quote (Syntax.string_of_term ctxt t) ^ " contains a corecursive call but has type " ^
quote (Syntax.string_of_typ ctxt T))
else
explore_nested ctxt explore_outer_general params t;
in
(args, rhs
|> explore_outer (build_params [] outer_ssig_T res_T)
|> abs_tuple_balanced args)
end;
fun mk_corec_fun_def_rhs ctxt arg_Ts corecUU0 corecUU_arg =
let val corecUU = enforce_type ctxt domain_type (fastype_of corecUU_arg) corecUU0 in
abs_curried_balanced arg_Ts (corecUU $ unfold_id_bnf_etc ctxt corecUU_arg)
end;
fun get_options ctxt opts =
let
val plugins = get_first (fn Plugins_Option f => SOME (f ctxt) | _ => NONE) (rev opts)
|> the_default Plugin_Name.default_filter;
val friend = exists (can (fn Friend_Option => ())) opts;
val transfer = exists (can (fn Transfer_Option => ())) opts;
in
(plugins, friend, transfer)
end;
fun add_function binding parsed_eq lthy =
let
fun pat_completeness_auto ctxt =
Pat_Completeness.pat_completeness_tac ctxt 1 THEN auto_tac ctxt;
val ({defname, pelims = [[pelim]], pinducts = [pinduct], psimps = [psimp], ...}, lthy) =
Function.add_function [(Binding.concealed binding, NONE, NoSyn)]
[(((Binding.concealed Binding.empty, []), parsed_eq), [], [])]
Function_Common.default_config pat_completeness_auto lthy;
in
((defname, (pelim, pinduct, psimp)), lthy)
end;
fun build_corecUU_arg_and_goals prove_termin (Free (fun_base_name, _)) (arg_ts, explored_rhs) lthy =
let
val inner_fp_name0 = fun_base_name ^ inner_fp_suffix;
val inner_fp_free = Free (inner_fp_name0, fastype_of explored_rhs);
in
if Term.exists_subterm (curry (op aconv) inner_fp_free) explored_rhs then
let
val arg = mk_tuple_balanced arg_ts;
val inner_fp_eq =
mk_Trueprop_eq (betapply (inner_fp_free, arg), betapply (explored_rhs, arg));
val ((inner_fp_name, (pelim, pinduct, psimp)), lthy') =
add_function (Binding.name inner_fp_name0) inner_fp_eq lthy;
fun mk_triple elim induct simp = ([elim], [induct], [simp]);
fun prepare_termin () =
let
val {goal, ...} = Proof.goal (Function.termination NONE lthy');
val termin_goal = goal |> Thm.concl_of |> Logic.unprotect |> Envir.beta_eta_contract;
in
(lthy', (mk_triple pelim pinduct psimp, [termin_goal]))
end;
val (lthy'', (inner_fp_triple, termin_goals)) =
if prove_termin then
(case try (Function.prove_termination NONE
(Function_Common.termination_prover_tac true lthy')) lthy' of
NONE => prepare_termin ()
| SOME ({elims = SOME [[elim]], inducts = SOME [induct], simps = SOME [simp], ...},
lthy'') =>
(lthy'', (mk_triple elim induct simp, [])))
else
prepare_termin ();
val inner_fp_const = (Binding.name_of inner_fp_name, fastype_of explored_rhs)
|>> Proof_Context.read_const {proper = true, strict = false} lthy'
|> (fn (Const (s, _), T) => Const (s, T));
in
(((inner_fp_triple, termin_goals), inner_fp_const), lthy'')
end
else
(((([], [], []), []), explored_rhs), lthy)
end;
fun derive_eq_corecUU ctxt {sig_fp_sugars, ssig_fp_sugar, eval, corecUU, eval_simps,
all_algLam_algs, corecUU_unique, ...}
fun_t corecUU_arg fun_code =
let
val fun_T = fastype_of fun_t;
val (arg_Ts, Type (fpT_name, _)) = strip_type fun_T;
val num_args = length arg_Ts;
val SOME {pre_bnf, fp_bnf, absT_info, fp_nesting_bnfs, live_nesting_bnfs, fp_ctr_sugar, ...} =
fp_sugar_of ctxt fpT_name;
val SOME {case_trivial, ...} = codatatype_extra_of ctxt fpT_name;
val ctr_sugar = #ctr_sugar fp_ctr_sugar;
val pre_map_def = map_def_of_bnf pre_bnf;
val abs_inverse = #abs_inverse absT_info;
val ctr_defs = #ctr_defs fp_ctr_sugar;
val case_eq_ifs = #case_eq_ifs ctr_sugar @ case_eq_if_thms_of_term ctxt (Thm.prop_of fun_code);
val all_sig_map_thms = maps (#map_thms o #fp_bnf_sugar) sig_fp_sugars;
val fp_map_ident = map_ident_of_bnf fp_bnf;
val fpsig_nesting_bnfs = fp_nesting_bnfs @ maps #live_nesting_bnfs sig_fp_sugars;
val fpsig_nesting_T_names = map (fst o dest_Type o T_of_bnf) fpsig_nesting_bnfs;
val fpsig_nesting_fp_sugars = map_filter (fp_sugar_of ctxt) fpsig_nesting_T_names;
val fpsig_nesting_fp_bnf_sugars = map #fp_bnf_sugar fpsig_nesting_fp_sugars;
val ssig_fp_bnf_sugar = #fp_bnf_sugar ssig_fp_sugar;
val ssig_bnf = #fp_bnf ssig_fp_sugar;
val ssig_map = map_of_bnf ssig_bnf;
val fpsig_nesting_maps = map map_of_bnf fpsig_nesting_bnfs;
val fpsig_nesting_map_ident0s = map map_ident0_of_bnf fpsig_nesting_bnfs;
val fpsig_nesting_map_comps = map map_comp_of_bnf fpsig_nesting_bnfs;
val fpsig_nesting_map_thms = maps #map_thms fpsig_nesting_fp_bnf_sugars;
val live_nesting_map_ident0s = map map_ident0_of_bnf live_nesting_bnfs;
val ssig_map_thms = #map_thms ssig_fp_bnf_sugar;
val all_algLam_alg_pointfuls = map (mk_pointful ctxt) all_algLam_algs;
val def_rhs = mk_corec_fun_def_rhs ctxt arg_Ts corecUU corecUU_arg;
val goal = mk_Trueprop_eq (fun_t, def_rhs);
in
Goal.prove_sorry ctxt [] [] goal (fn {context = ctxt, prems = _} =>
mk_eq_corecUU_tac ctxt num_args fpsig_nesting_maps ssig_map eval pre_map_def abs_inverse
fpsig_nesting_map_ident0s fpsig_nesting_map_comps fpsig_nesting_map_thms
live_nesting_map_ident0s fp_map_ident case_trivial ctr_defs case_eq_ifs all_sig_map_thms
ssig_map_thms all_algLam_alg_pointfuls (all_algrho_eqs_of ctxt) eval_simps corecUU_unique
fun_code)
|> Thm.close_derivation
end;
fun derive_coinduct_cong_intros
({fpT = fpT0 as Type (fpT_name, _), friend_names = friend_names0,
corecUU = Const (corecUU_name, _), dtor_coinduct_info as {dtor_coinduct, ...}, ...})
lthy =
let
val thy = Proof_Context.theory_of lthy;
val phi = Proof_Context.export_morphism lthy (Local_Theory.target_of lthy);
val fpT = Morphism.typ phi fpT0;
val general_fpT = body_type (Sign.the_const_type thy corecUU_name);
val most_general = Sign.typ_instance thy (general_fpT, fpT);
in
(case (most_general, coinduct_extra_of lthy corecUU_name) of
(true, SOME extra) => ((false, extra), lthy)
| _ =>
let
val ctr_names = ctr_names_of_fp_name lthy fpT_name;
val friend_names = friend_names0 |> map Long_Name.base_name |> rev;
val cong_intro_pairs = derive_cong_intros lthy ctr_names friend_names dtor_coinduct_info;
val (coinduct, coinduct_attrs) = derive_coinduct lthy fpT0 dtor_coinduct;
val ((_, [coinduct]), lthy) = (* TODO check: only if most_general?*)
Local_Theory.note ((Binding.empty, coinduct_attrs), [coinduct]) lthy;
val extra = {coinduct = coinduct, coinduct_attrs = coinduct_attrs,
cong_intro_pairs = cong_intro_pairs};
in
((most_general, extra), lthy |> most_general ? register_coinduct_extra corecUU_name extra)
end)
end;
fun update_coinduct_cong_intross_dynamic fpT_name lthy =
let val all_corec_infos = corec_infos_of lthy fpT_name in
lthy
|> fold_map (apfst snd oo derive_coinduct_cong_intros) all_corec_infos
|> snd
end;
fun derive_and_update_coinduct_cong_intross [] = pair (false, [])
| derive_and_update_coinduct_cong_intross (corec_infos as {fpT = Type (fpT_name, _), ...} :: _) =
fold_map derive_coinduct_cong_intros corec_infos
#>> split_list
#> (fn ((changeds, extras), lthy) =>
if exists I changeds then
((true, extras), lthy |> update_coinduct_cong_intross_dynamic fpT_name)
else
((false, extras), lthy));
fun prepare_corec_ursive_cmd long_cmd opts (raw_fixes, raw_eq) lthy =
let
val _ = can the_single raw_fixes orelse
error "Mutually corecursive functions not supported";
val (plugins, friend, transfer) = get_options lthy opts;
val ([((b, fun_T), mx)], [(_, eq)]) =
fst (Specification.read_multi_specs raw_fixes [((Binding.empty_atts, raw_eq), [], [])] lthy);
val _ = Sign.of_sort (Proof_Context.theory_of lthy) (fun_T, @{sort type}) orelse
error ("Type of " ^ Binding.print b ^ " contains top sort");
val (arg_Ts, res_T) = strip_type fun_T;
val fpT_name = (case res_T of Type (s, _) => s | _ => not_codatatype lthy res_T);
val fun_free = Free (Binding.name_of b, fun_T);
val parsed_eq = parse_corec_equation lthy [fun_free] eq;
val fun_name = Local_Theory.full_name lthy b;
val fun_t = Const (fun_name, fun_T);
(* FIXME: does this work with locales that fix variables? *)
val no_base = has_no_corec_info lthy fpT_name;
val lthy = lthy |> no_base ? setup_base fpT_name;
fun extract_rho lthy =
let
val lthy = lthy |> Variable.declare_typ fun_T;
val (prepared as (_, _, version, Y, Z, preT, k_T, ssig_T, dead_pre_bnf, dead_k_bnf, _,
ssig_fp_sugar, buffer), lthy) =
prepare_friend_corec fun_name fun_T lthy;
val friend_parse_info = friend_parse_info_of lthy arg_Ts res_T buffer;
val parsed_eq' = parsed_eq ||> subst_atomic [(fun_free, fun_t)];
in
lthy
|> extract_rho_return_transfer_goals b version dead_pre_bnf dead_k_bnf Y Z preT fun_T k_T
ssig_T ssig_fp_sugar friend_parse_info fun_t parsed_eq'
|>> pair prepared
end;
val ((prepareds, (rho_datas, transfer_goal_datas)), lthy) =
if friend then extract_rho lthy |>> (apfst single ##> (apfst single #> apsnd single))
else (([], ([], [])), lthy);
val ((buffer, corec_infos), lthy) =
if friend then
((#13 (the_single prepareds), []), lthy)
else
corec_info_of res_T lthy
||> no_base ? update_coinduct_cong_intross_dynamic fpT_name
|>> (fn info as {buffer, ...} => (buffer, [info]));
val corec_parse_info = corec_parse_info_of lthy arg_Ts res_T buffer;
val explored_eq =
explore_corec_equation lthy true friend fun_name fun_free corec_parse_info res_T parsed_eq;
val (((inner_fp_triple, termin_goals), corecUU_arg), lthy) =
build_corecUU_arg_and_goals (not long_cmd) fun_free explored_eq lthy;
fun def_fun (inner_fp_elims0, inner_fp_inducts0, inner_fp_simps0) const_transfers
rho_transfers_foldeds lthy =
let
fun register_friend lthy =
let
val [(old_corec_info, fp_b, version, Y, Z, _, k_T, _, _, dead_k_bnf, sig_fp_sugar,
ssig_fp_sugar, _)] = prepareds;
val [(rho, rho_def)] = rho_datas;
val [(_, rho_transfer_goal)] = transfer_goal_datas;
val Type (fpT_name, _) = res_T;
val rho_transfer_folded =
(case rho_transfers_foldeds of
[] =>
derive_rho_transfer_folded lthy fpT_name const_transfers rho_def rho_transfer_goal
| [thm] => thm);
in
lthy
|> register_coinduct_dynamic_friend fpT_name fun_name
|> register_friend_corec fun_name fp_b version Y Z k_T dead_k_bnf sig_fp_sugar
ssig_fp_sugar fun_t rho rho_transfer_folded old_corec_info
end;
val (friend_infos, lthy) = lthy |> (if friend then register_friend #>> single else pair []);
val (corec_info as {corecUU = corecUU0, ...}, lthy) =
(case corec_infos of
[] => corec_info_of res_T lthy
| [info] => (info, lthy));
val def_rhs = mk_corec_fun_def_rhs lthy arg_Ts corecUU0 corecUU_arg;
val def = ((b, mx), ((Binding.concealed (Thm.def_binding b), []), def_rhs));
val ((fun_t0, (_, fun_def0)), (lthy, lthy_old)) = lthy
|> Local_Theory.open_target |> snd
|> Local_Theory.define def
||> `Local_Theory.close_target;
val parsed_eq = parse_corec_equation lthy [fun_free] eq;
val views0 = generate_views lthy eq fun_free parsed_eq;
val lthy' = lthy |> fold Variable.declare_typ (res_T :: arg_Ts);
val phi = Proof_Context.export_morphism lthy_old lthy';
val fun_t = Morphism.term phi fun_t0; (* FIXME: shadows "fun_t" -- identical? *)
val fun_def = Morphism.thm phi fun_def0;
val inner_fp_elims = map (Morphism.thm phi) inner_fp_elims0;
val inner_fp_inducts = map (Morphism.thm phi) inner_fp_inducts0;
val inner_fp_simps = map (Morphism.thm phi) inner_fp_simps0;
val (code_goal, _, _, _, _) = morph_views phi views0;
fun derive_and_note_friend_extra_theorems lthy =
let
val k_T = #7 (the_single prepareds);
val rho_def = snd (the_single rho_datas);
val (eq_algrho, algrho_eq) = derive_eq_algrho lthy corec_info (the_single friend_infos)
fun_t k_T code_goal const_transfers rho_def fun_def;
val notes =
(if Config.get lthy bnf_internals then
[(eq_algrhoN, [eq_algrho])]
else
[])
|> map (fn (thmN, thms) =>
((Binding.qualify true (Binding.name_of b)
(Binding.qualify false friendN (Binding.name thmN)), []),
[(thms, [])]));
in
lthy
|> register_friend_extra fun_name eq_algrho algrho_eq
|> Local_Theory.notes notes |> snd
end;
val lthy = lthy |> friend ? derive_and_note_friend_extra_theorems;
val code_thm = derive_code lthy inner_fp_simps code_goal corec_info fun_t fun_def;
(* TODO:
val ctr_thmss = map mk_thm (#2 views);
val disc_thmss = map mk_thm (#3 views);
val disc_iff_thmss = map mk_thm (#4 views);
val sel_thmss = map mk_thm (#5 views);
*)
val uniques =
if null inner_fp_simps then
[derive_unique lthy phi (#1 views0) corec_info fpT_name fun_def]
else
[];
(* TODO:
val disc_iff_or_disc_thmss =
map2 (fn [] => I | disc_iffs => K disc_iffs) disc_iff_thmss disc_thmss;
val simp_thmss = map2 append disc_iff_or_disc_thmss sel_thmss;
*)
val ((_, [{cong_intro_pairs, coinduct, coinduct_attrs}]), lthy) = lthy
|> derive_and_update_coinduct_cong_intross [corec_info];
val cong_intros_pairs = AList.group (op =) cong_intro_pairs;
val code_attrs = if plugins code_plugin then [Code.add_default_eqn_attrib Code.Equation] else [];
val anonymous_notes = [];
(* TODO:
[(flat disc_iff_or_disc_thmss, simp_attrs)]
|> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
*)
val notes =
[(cong_introsN, maps snd cong_intros_pairs, []),
(codeN, [code_thm], code_attrs @ nitpicksimp_attrs),
(coinductN, [coinduct], coinduct_attrs),
(inner_inductN, inner_fp_inducts, []),
(uniqueN, uniques, [])] @
map (fn (thmN, thms) => (thmN, thms, [])) cong_intros_pairs @
(if Config.get lthy bnf_internals then
[(inner_elimN, inner_fp_elims, []),
(inner_simpN, inner_fp_simps, [])]
else
[])
(* TODO:
(ctrN, ctr_thms, []),
(discN, disc_thms, []),
(disc_iffN, disc_iff_thms, []),
(selN, sel_thms, simp_attrs),
(simpsN, simp_thms, []),
*)
|> map (fn (thmN, thms, attrs) =>
((Binding.qualify true (Binding.name_of b)
(Binding.qualify false corecN (Binding.name thmN)), attrs),
[(thms, [])]))
|> filter_out (null o fst o hd o snd);
in
lthy
(* TODO:
|> Spec_Rules.add Spec_Rules.Equational ([fun_t0], flat sel_thmss)
|> Spec_Rules.add Spec_Rules.Equational ([fun_t0], flat ctr_thmss)
*)
|> Spec_Rules.add Spec_Rules.Equational ([fun_t0], [code_thm])
|> Local_Theory.notes (anonymous_notes @ notes)
|> snd
end;
fun prove_transfer_goal ctxt goal =
Variable.add_free_names ctxt goal []
|> (fn vars => Goal.prove (*no sorry*) ctxt vars [] goal (fn {context = ctxt, prems = _} =>
HEADGOAL (Transfer.transfer_prover_tac ctxt)))
|> Thm.close_derivation;
fun maybe_prove_transfer_goal ctxt goal =
(case try (prove_transfer_goal ctxt) goal of
SOME thm => apfst (cons thm)
| NONE => apsnd (cons goal));
val const_transfer_goals = fold (union (op aconv) o fst) transfer_goal_datas [];
val (const_transfers, const_transfer_goals') =
if long_cmd then ([], const_transfer_goals)
else fold (maybe_prove_transfer_goal lthy) const_transfer_goals ([], []);
in
((def_fun, (([res_T], prepareds, rho_datas, map snd transfer_goal_datas),
(inner_fp_triple, termin_goals), (const_transfers, const_transfer_goals'))), lthy)
end;
fun corec_cmd opts (raw_fixes, raw_eq) lthy =
let
val ((def_fun, (_, (inner_fp_triple, termin_goals), (const_transfers, const_transfer_goals))),
lthy) =
prepare_corec_ursive_cmd false opts (raw_fixes, raw_eq) lthy;
in
if not (null termin_goals) then
error ("Termination prover failed (try " ^ quote (#1 @{command_keyword corecursive}) ^
" instead of " ^ quote (#1 @{command_keyword corec}) ^ ")")
else if not (null const_transfer_goals) then
error ("Transfer prover failed (try " ^ quote (#1 @{command_keyword corecursive}) ^
" instead of " ^ quote (#1 @{command_keyword corec}) ^ ")")
else
def_fun inner_fp_triple const_transfers [] lthy
end;
fun corecursive_cmd opts (raw_fixes, raw_eq) lthy =
let
val ((def_fun, (([Type (fpT_name, _)], prepareds, rho_datas, rho_transfer_goals),
(inner_fp_triple, termin_goals), (const_transfers, const_transfer_goals))), lthy) =
prepare_corec_ursive_cmd true opts (raw_fixes, raw_eq) lthy;
val (rho_transfer_goals', unprime_rho_transfer_and_folds) =
@{map 3} (fn (_, _, _, _, _, _, _, _, _, _, _, _, _) => fn (_, rho_def) =>
prime_rho_transfer_goal lthy fpT_name rho_def)
prepareds rho_datas rho_transfer_goals
|> split_list;
in
Proof.theorem NONE (fn [termin_thms, const_transfers', rho_transfers'] =>
let
val remove_domain_condition =
full_simplify (put_simpset HOL_basic_ss lthy
addsimps (@{thm True_implies_equals} :: termin_thms));
in
def_fun (@{apply 3} (map remove_domain_condition) inner_fp_triple)
(const_transfers @ const_transfers')
(map2 (fn f => f) unprime_rho_transfer_and_folds rho_transfers')
end)
(map (map (rpair [])) [termin_goals, const_transfer_goals, rho_transfer_goals']) lthy
end;
fun friend_of_corec_cmd ((raw_fun_name, raw_fun_T_opt), raw_eq) lthy =
let
val Const (fun_name, _) =
Proof_Context.read_const {proper = true, strict = false} lthy raw_fun_name;
val fake_lthy = lthy
|> (case raw_fun_T_opt of
SOME raw_T =>
Proof_Context.add_const_constraint (fun_name, SOME (Syntax.read_typ lthy raw_T))
| NONE => I)
handle TYPE (s, _, _) => error s;
val fun_b = Binding.name (Long_Name.base_name fun_name);
val code_goal = Syntax.read_prop fake_lthy raw_eq;
val fun_T =
(case code_goal of
@{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ t $ _) => fastype_of (head_of t)
| _ => error "Expected HOL equation");
val fun_t = Const (fun_name, fun_T);
val (arg_Ts, res_T as Type (fpT_name, _)) = strip_type fun_T;
val no_base = has_no_corec_info lthy fpT_name;
val lthy = lthy |> no_base ? setup_base fpT_name;
val lthy = lthy |> Variable.declare_typ fun_T;
val ((old_corec_info, fp_b, version, Y, Z, preT, k_T, ssig_T, dead_pre_bnf, dead_k_bnf,
sig_fp_sugar, ssig_fp_sugar, buffer), lthy) =
prepare_friend_corec fun_name fun_T lthy;
val friend_parse_info = friend_parse_info_of lthy arg_Ts res_T buffer;
val parsed_eq = parse_corec_equation lthy [] code_goal;
val (((rho, rho_def), (const_transfer_goals, rho_transfer_goal)), lthy) =
extract_rho_return_transfer_goals fun_b version dead_pre_bnf dead_k_bnf Y Z preT fun_T k_T
ssig_T ssig_fp_sugar friend_parse_info fun_t parsed_eq lthy;
fun register_friend_extra_and_note_thms code_goal code_thm const_transfers k_T friend_info
lthy =
let
val (corec_info, lthy) = corec_info_of res_T lthy;
val fun_free = Free (Binding.name_of fun_b, fun_T);
fun freeze_fun (t as Const (s, T)) = if s = fun_name andalso T = fun_T then fun_free else t
| freeze_fun t = t;
val eq = Term.map_aterms freeze_fun code_goal;
val parsed_eq = parse_corec_equation lthy [fun_free] eq;
val corec_parse_info = corec_parse_info_of lthy arg_Ts res_T buffer;
val explored_eq = explore_corec_equation lthy false false fun_name fun_free corec_parse_info
res_T parsed_eq;
val ((_, corecUU_arg), _) = build_corecUU_arg_and_goals false fun_free explored_eq lthy;
val eq_corecUU = derive_eq_corecUU lthy corec_info fun_t corecUU_arg code_thm;
val (eq_algrho, algrho_eq) = derive_eq_algrho lthy corec_info friend_info fun_t k_T
code_goal const_transfers rho_def eq_corecUU;
val ((_, [{cong_intro_pairs, coinduct, coinduct_attrs}]), lthy) = lthy
|> register_friend_extra fun_name eq_algrho algrho_eq
|> register_coinduct_dynamic_friend fpT_name fun_name
|> derive_and_update_coinduct_cong_intross [corec_info];
val cong_intros_pairs = AList.group (op =) cong_intro_pairs;
val unique = derive_unique lthy Morphism.identity code_goal corec_info fpT_name eq_corecUU;
val notes =
[(codeN, [code_thm], []),
(coinductN, [coinduct], coinduct_attrs),
(cong_introsN, maps snd cong_intros_pairs, []),
(uniqueN, [unique], [])] @
map (fn (thmN, thms) => (thmN, thms, [])) cong_intros_pairs @
(if Config.get lthy bnf_internals then
[(eq_algrhoN, [eq_algrho], []),
(eq_corecUUN, [eq_corecUU], [])]
else
[])
|> map (fn (thmN, thms, attrs) =>
((Binding.qualify true (Binding.name_of fun_b)
(Binding.qualify false friendN (Binding.name thmN)), attrs),
[(thms, [])]));
in
lthy
|> Local_Theory.notes notes |> snd
end;
val (rho_transfer_goal', unprime_rho_transfer_and_fold) =
prime_rho_transfer_goal lthy fpT_name rho_def rho_transfer_goal;
in
lthy
|> Proof.theorem NONE (fn [[code_thm], const_transfers, [rho_transfer']] =>
register_friend_corec fun_name fp_b version Y Z k_T dead_k_bnf sig_fp_sugar ssig_fp_sugar
fun_t rho (unprime_rho_transfer_and_fold rho_transfer') old_corec_info
#-> register_friend_extra_and_note_thms code_goal code_thm const_transfers k_T)
(map (map (rpair [])) [[code_goal], const_transfer_goals, [rho_transfer_goal']])
|> Proof.refine_singleton (Method.primitive_text (K I))
end;
fun coinduction_upto_cmd (base_name, raw_fpT) lthy =
let
val fpT as Type (fpT_name, _) = Syntax.read_typ lthy raw_fpT;
val no_base = has_no_corec_info lthy fpT_name;
val (corec_info as {version, ...}, lthy) = lthy
|> corec_info_of fpT;
val lthy = lthy |> no_base ? setup_base fpT_name;
val ((changed, [{cong_intro_pairs, coinduct, coinduct_attrs}]), lthy) = lthy
|> derive_and_update_coinduct_cong_intross [corec_info];
val lthy = lthy |> (changed orelse no_base) ? update_coinduct_cong_intross_dynamic fpT_name;
val cong_intros_pairs = AList.group (op =) cong_intro_pairs;
val notes =
[(cong_introsN, maps snd cong_intros_pairs, []),
(coinduct_uptoN, [coinduct], coinduct_attrs)] @
map (fn (thmN, thms) => (thmN, thms, [])) cong_intros_pairs
|> map (fn (thmN, thms, attrs) =>
(((Binding.qualify true base_name
(Binding.qualify false ("v" ^ string_of_int version) (Binding.name thmN))), attrs),
[(thms, [])]));
in
lthy |> Local_Theory.notes notes |> snd
end;
fun consolidate lthy =
let
val corec_infoss = map (corec_infos_of lthy o fst) (all_codatatype_extras_of lthy);
val (changeds, lthy) = lthy
|> fold_map (apfst fst oo derive_and_update_coinduct_cong_intross) corec_infoss;
in
if exists I changeds then lthy else raise Same.SAME
end;
fun consolidate_global thy =
SOME (Named_Target.theory_map consolidate thy)
handle Same.SAME => NONE;
val _ = Outer_Syntax.local_theory @{command_keyword corec}
"define nonprimitive corecursive functions"
((Scan.optional (@{keyword "("} |-- Parse.!!! (Parse.list1 corec_option_parser)
--| @{keyword ")"}) []) -- (Parse.vars --| Parse.where_ -- Parse.prop)
>> uncurry corec_cmd);
val _ = Outer_Syntax.local_theory_to_proof @{command_keyword corecursive}
"define nonprimitive corecursive functions"
((Scan.optional (@{keyword "("} |-- Parse.!!! (Parse.list1 corec_option_parser)
--| @{keyword ")"}) []) -- (Parse.vars --| Parse.where_ -- Parse.prop)
>> uncurry corecursive_cmd);
val _ = Outer_Syntax.local_theory_to_proof @{command_keyword friend_of_corec}
"register a function as a legal context for nonprimitive corecursion"
(Parse.const -- Scan.option (Parse.$$$ "::" |-- Parse.typ) --| Parse.where_ -- Parse.prop
>> friend_of_corec_cmd);
val _ = Outer_Syntax.local_theory @{command_keyword coinduction_upto}
"derive a coinduction up-to principle and a corresponding congruence closure"
(Parse.name --| Parse.$$$ ":" -- Parse.typ >> coinduction_upto_cmd);
val _ = Theory.setup (Theory.at_begin consolidate_global);
end;