(* Title: HOL/Tools/Lifting/lifting_def_code_dt.ML
Author: Ondrej Kuncar
Workaround that allows us to execute lifted constants that have
as a return type a datatype containing a subtype; lift_definition command
*)
signature LIFTING_DEF_CODE_DT =
sig
type rep_isom_data
val isom_of_rep_isom_data: rep_isom_data -> term
val transfer_of_rep_isom_data: rep_isom_data -> thm
val bundle_name_of_rep_isom_data: rep_isom_data -> string
val pointer_of_rep_isom_data: rep_isom_data -> string
type code_dt
val rty_of_code_dt: code_dt -> typ
val qty_of_code_dt: code_dt -> typ
val wit_of_code_dt: code_dt -> term
val wit_thm_of_code_dt: code_dt -> thm
val rep_isom_data_of_code_dt: code_dt -> rep_isom_data option
val morph_code_dt: morphism -> code_dt -> code_dt
val mk_witness_of_code_dt: typ -> code_dt -> term
val mk_rep_isom_of_code_dt: typ -> code_dt -> term option
val code_dt_of: Proof.context -> typ * typ -> code_dt option
val code_dt_of_global: theory -> typ * typ -> code_dt option
val all_code_dt_of: Proof.context -> code_dt list
val all_code_dt_of_global: theory -> code_dt list
type config_code_dt = { code_dt: bool, lift_config: Lifting_Def.config }
val default_config_code_dt: config_code_dt
val add_lift_def_code_dt:
config_code_dt -> binding * mixfix -> typ -> term -> thm -> thm list -> local_theory ->
Lifting_Def.lift_def * local_theory
val lift_def_code_dt:
config_code_dt -> binding * mixfix -> typ -> term -> (Proof.context -> tactic) -> thm list ->
local_theory -> Lifting_Def.lift_def * local_theory
val lift_def_cmd:
string list * (binding * string option * mixfix) * string * (Facts.ref * Token.src list) list ->
local_theory -> Proof.state
end
structure Lifting_Def_Code_Dt: LIFTING_DEF_CODE_DT =
struct
open Ctr_Sugar_Util BNF_Util BNF_FP_Util BNF_FP_Def_Sugar Lifting_Def Lifting_Util
infix 0 MRSL
(** data structures **)
(* all type variables in qty are in rty *)
datatype rep_isom_data = REP_ISOM of { isom: term, transfer: thm, bundle_name: string, pointer: string }
fun isom_of_rep_isom_data (REP_ISOM rep_isom) = #isom rep_isom;
fun transfer_of_rep_isom_data (REP_ISOM rep_isom) = #transfer rep_isom;
fun bundle_name_of_rep_isom_data (REP_ISOM rep_isom) = #bundle_name rep_isom;
fun pointer_of_rep_isom_data (REP_ISOM rep_isom) = #pointer rep_isom;
datatype code_dt = CODE_DT of { rty: typ, qty: typ, wit: term, wit_thm: thm,
rep_isom_data: rep_isom_data option };
fun rty_of_code_dt (CODE_DT code_dt) = #rty code_dt;
fun qty_of_code_dt (CODE_DT code_dt) = #qty code_dt;
fun wit_of_code_dt (CODE_DT code_dt) = #wit code_dt;
fun wit_thm_of_code_dt (CODE_DT code_dt) = #wit_thm code_dt;
fun rep_isom_data_of_code_dt (CODE_DT code_dt) = #rep_isom_data code_dt;
fun ty_alpha_equiv (T, U) = Type.raw_instance (T, U) andalso Type.raw_instance (U, T);
fun code_dt_eq c = (ty_alpha_equiv o apply2 rty_of_code_dt) c
andalso (ty_alpha_equiv o apply2 qty_of_code_dt) c;
fun term_of_code_dt code_dt = code_dt |> `rty_of_code_dt ||> qty_of_code_dt |> HOLogic.mk_prodT
|> Net.encode_type |> single;
(* modulo renaming, typ must contain TVars *)
fun is_code_dt_of_type (rty, qty) code_dt = code_dt |> `rty_of_code_dt ||> qty_of_code_dt
|> HOLogic.mk_prodT |> curry ty_alpha_equiv (HOLogic.mk_prodT (rty, qty));
fun mk_rep_isom_data isom transfer bundle_name pointer =
REP_ISOM { isom = isom, transfer = transfer, bundle_name = bundle_name, pointer = pointer}
fun mk_code_dt rty qty wit wit_thm rep_isom_data =
CODE_DT { rty = rty, qty = qty, wit = wit, wit_thm = wit_thm, rep_isom_data = rep_isom_data };
fun map_rep_isom_data f1 f2 f3 f4
(REP_ISOM { isom = isom, transfer = transfer, bundle_name = bundle_name, pointer = pointer }) =
REP_ISOM { isom = f1 isom, transfer = f2 transfer, bundle_name = f3 bundle_name, pointer = f4 pointer };
fun map_code_dt f1 f2 f3 f4 f5 f6 f7 f8
(CODE_DT {rty = rty, qty = qty, wit = wit, wit_thm = wit_thm, rep_isom_data = rep_isom_data}) =
CODE_DT {rty = f1 rty, qty = f2 qty, wit = f3 wit, wit_thm = f4 wit_thm,
rep_isom_data = Option.map (map_rep_isom_data f5 f6 f7 f8) rep_isom_data};
fun update_rep_isom isom transfer binding pointer i = mk_code_dt (rty_of_code_dt i) (qty_of_code_dt i)
(wit_of_code_dt i) (wit_thm_of_code_dt i) (SOME (mk_rep_isom_data isom transfer binding pointer))
fun morph_code_dt phi =
let
val mty = Morphism.typ phi
val mterm = Morphism.term phi
val mthm = Morphism.thm phi
in
map_code_dt mty mty mterm mthm mterm mthm I I
end
val transfer_code_dt = morph_code_dt o Morphism.transfer_morphism;
structure Data = Generic_Data
(
type T = code_dt Item_Net.T
val empty = Item_Net.init code_dt_eq term_of_code_dt
val extend = I
val merge = Item_Net.merge
);
fun code_dt_of_generic context (rty, qty) =
let
val typ = HOLogic.mk_prodT (rty, qty)
val prefiltred = Item_Net.retrieve_matching (Data.get context) (Net.encode_type typ)
in
prefiltred |> filter (is_code_dt_of_type (rty, qty))
|> map (transfer_code_dt (Context.theory_of context)) |> find_first (fn _ => true)
end;
fun code_dt_of ctxt (rty, qty) =
let
val sch_rty = Logic.type_map (singleton (Variable.polymorphic ctxt)) rty
val sch_qty = Logic.type_map (singleton (Variable.polymorphic ctxt)) qty
in
code_dt_of_generic (Context.Proof ctxt) (sch_rty, sch_qty)
end;
fun code_dt_of_global thy (rty, qty) =
let
val sch_rty = Logic.varifyT_global rty
val sch_qty = Logic.varifyT_global qty
in
code_dt_of_generic (Context.Theory thy) (sch_rty, sch_qty)
end;
fun all_code_dt_of_generic context =
Item_Net.content (Data.get context) |> map (transfer_code_dt (Context.theory_of context));
val all_code_dt_of = all_code_dt_of_generic o Context.Proof;
val all_code_dt_of_global = all_code_dt_of_generic o Context.Theory;
fun update_code_dt code_dt =
(snd o Local_Theory.begin_nested)
#> Local_Theory.declaration {syntax = false, pervasive = true}
(fn phi => Data.map (Item_Net.update (morph_code_dt phi code_dt)))
#> Local_Theory.end_nested
fun mk_match_of_code_dt qty code_dt = Vartab.empty |> Type.raw_match (qty_of_code_dt code_dt, qty)
|> Vartab.dest |> map (fn (x, (S, T)) => (TVar (x, S), T));
fun mk_witness_of_code_dt qty code_dt =
Term.subst_atomic_types (mk_match_of_code_dt qty code_dt) (wit_of_code_dt code_dt)
fun mk_rep_isom_of_code_dt qty code_dt = Option.map
(isom_of_rep_isom_data #> Term.subst_atomic_types (mk_match_of_code_dt qty code_dt))
(rep_isom_data_of_code_dt code_dt)
(** unique name for a type **)
fun var_name name sort = if sort = \<^sort>\<open>{type}\<close> orelse sort = [] then ["x" ^ name]
else "x" ^ name :: "x_" :: sort @ ["x_"];
fun concat_Tnames (Type (name, ts)) = name :: maps concat_Tnames ts
| concat_Tnames (TFree (name, sort)) = var_name name sort
| concat_Tnames (TVar ((name, _), sort)) = var_name name sort;
fun unique_Tname (rty, qty) =
let
val Tnames = map Long_Name.base_name (concat_Tnames rty @ ["x_x"] @ concat_Tnames qty);
in
fold (Binding.qualify false) (tl Tnames) (Binding.name (hd Tnames))
end;
(** witnesses **)
fun mk_undefined T = Const (\<^const_name>\<open>undefined\<close>, T);
fun mk_witness quot_thm =
let
val wit_thm = quot_thm RS @{thm type_definition_Quotient_not_empty_witness}
val wit = quot_thm_rep quot_thm $ mk_undefined (quot_thm_rty_qty quot_thm |> snd)
in
(wit, wit_thm)
end
(** config **)
type config_code_dt = { code_dt: bool, lift_config: config }
val default_config_code_dt = { code_dt = false, lift_config = default_config }
(** Main code **)
val ld_no_notes = { notes = false }
fun comp_lift_error _ _ = error "Composition of abstract types has not been implemented yet."
fun lift qty (quot_thm, (lthy, rel_eq_onps)) =
let
val quot_thm = Lifting_Term.force_qty_type lthy qty quot_thm
val (rty, qty) = quot_thm_rty_qty quot_thm;
in
if is_none (code_dt_of lthy (rty, qty)) then
let
val (wit, wit_thm) = (mk_witness quot_thm
handle THM _ => error ("code_dt: " ^ quote (Tname qty) ^ " was not defined as a subtype."))
val code_dt = mk_code_dt rty qty wit wit_thm NONE
in
(quot_thm, (update_code_dt code_dt lthy, rel_eq_onps))
end
else
(quot_thm, (lthy, rel_eq_onps))
end;
fun case_tac rule =
Subgoal.FOCUS_PARAMS (fn {context = ctxt, params, ...} =>
HEADGOAL (rtac ctxt (infer_instantiate' ctxt [SOME (snd (hd params))] rule)));
fun bundle_name_of_bundle_binding binding phi context =
Name_Space.full_name (Name_Space.naming_of context) (Morphism.binding phi binding);
fun prove_schematic_quot_thm actions ctxt =
Lifting_Term.prove_schematic_quot_thm actions (Lifting_Info.get_quotients ctxt) ctxt
fun prove_code_dt (rty, qty) lthy =
let
val (fold_quot_thm: (local_theory * thm list) Lifting_Term.fold_quot_thm) =
{ constr = constr, lift = lift, comp_lift = comp_lift_error };
in prove_schematic_quot_thm fold_quot_thm lthy (rty, qty) (lthy, []) |> snd end
and add_lift_def_code_dt config var qty rhs rsp_thm par_thms lthy =
let
fun binop_conv2 cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
fun ret_rel_conv conv ctm =
case (Thm.term_of ctm) of
Const (\<^const_name>\<open>rel_fun\<close>, _) $ _ $ _ =>
binop_conv2 Conv.all_conv conv ctm
| _ => conv ctm
fun R_conv rel_eq_onps = Transfer.top_sweep_rewr_conv @{thms eq_onp_top_eq_eq[symmetric, THEN eq_reflection]}
then_conv Transfer.bottom_rewr_conv rel_eq_onps
val (ret_lift_def, lthy1) = add_lift_def (#lift_config config) var qty rhs rsp_thm par_thms lthy
in
if (not (#code_dt config) orelse (code_eq_of_lift_def ret_lift_def <> NONE_EQ)
andalso (code_eq_of_lift_def ret_lift_def <> UNKNOWN_EQ))
(* Let us try even in case of UNKNOWN_EQ. If this leads to problems, the user can always
say that they do not want this workaround. *)
then (ret_lift_def, lthy1)
else
let
val lift_def = inst_of_lift_def lthy1 qty ret_lift_def
val rty = rty_of_lift_def lift_def
val rty_ret = body_type rty
val qty_ret = body_type qty
val (lthy2, rel_eq_onps) = prove_code_dt (rty_ret, qty_ret) lthy1
val code_dt = code_dt_of lthy2 (rty_ret, qty_ret)
in
if is_none code_dt orelse is_none (rep_isom_data_of_code_dt (the code_dt))
then (ret_lift_def, lthy2)
else
let
val code_dt = the code_dt
val rhs = dest_comb (rhs_of_lift_def lift_def) |> snd
val rep_isom_data = code_dt |> rep_isom_data_of_code_dt |> the
val pointer = pointer_of_rep_isom_data rep_isom_data
val quot_active =
Lifting_Info.lookup_restore_data lthy2 pointer |> the |> #quotient |> #quot_thm
|> Lifting_Info.lookup_quot_thm_quotients lthy2 |> is_some
val qty_code_dt_bundle_name = bundle_name_of_rep_isom_data rep_isom_data
val rep_isom = mk_rep_isom_of_code_dt qty_ret code_dt |> the
val lthy3 = if quot_active then lthy2 else Bundle.includes [qty_code_dt_bundle_name] lthy2
fun qty_isom_of_rep_isom rep = rep |> dest_Const |> snd |> domain_type
val qty_isom = qty_isom_of_rep_isom rep_isom
val f'_var = (Binding.suffix_name "_aux" (fst var), NoSyn);
val f'_qty = strip_type qty |> fst |> rpair qty_isom |> op --->
val f'_rsp_rel = Lifting_Term.equiv_relation lthy3 (rty, f'_qty);
val rsp = rsp_thm_of_lift_def lift_def
val rel_eq_onps_conv = HOLogic.Trueprop_conv (Conv.fun2_conv (ret_rel_conv (R_conv rel_eq_onps)))
val rsp_norm = Conv.fconv_rule rel_eq_onps_conv rsp
val f'_rsp_goal = HOLogic.mk_Trueprop (f'_rsp_rel $ rhs $ rhs);
val f'_rsp = Goal.prove_sorry lthy3 [] [] f'_rsp_goal
(fn {context = ctxt, prems = _} =>
HEADGOAL (CONVERSION (rel_eq_onps_conv) THEN' rtac ctxt rsp_norm))
|> Thm.close_derivation \<^here>
val (f'_lift_def, lthy4) = add_lift_def ld_no_notes f'_var f'_qty rhs f'_rsp [] lthy3
val f'_lift_def = inst_of_lift_def lthy4 f'_qty f'_lift_def
val f'_lift_const = mk_lift_const_of_lift_def f'_qty f'_lift_def
val (args, args_ctxt) = mk_Frees "x" (binder_types qty) lthy4
val f_alt_def_goal_lhs = list_comb (lift_const_of_lift_def lift_def, args);
val f_alt_def_goal_rhs = rep_isom $ list_comb (f'_lift_const, args);
val f_alt_def_goal = HOLogic.mk_Trueprop (HOLogic.mk_eq (f_alt_def_goal_lhs, f_alt_def_goal_rhs));
fun f_alt_def_tac ctxt i =
EVERY' [Transfer.gen_frees_tac [] ctxt, DETERM o Transfer.transfer_tac true ctxt,
SELECT_GOAL (Local_Defs.unfold0_tac ctxt [id_apply]), rtac ctxt refl] i;
val rep_isom_transfer = transfer_of_rep_isom_data rep_isom_data
val (_, transfer_ctxt) = args_ctxt
|> Proof_Context.note_thms ""
(Binding.empty_atts, [([rep_isom_transfer], [Transfer.transfer_add])])
val f_alt_def =
Goal.prove_sorry transfer_ctxt [] [] f_alt_def_goal
(fn {context = goal_ctxt, ...} => HEADGOAL (f_alt_def_tac goal_ctxt))
|> Thm.close_derivation \<^here>
|> singleton (Variable.export transfer_ctxt lthy4)
val lthy5 = lthy4
|> Local_Theory.note ((Binding.empty, @{attributes [code]}), [f_alt_def])
|> snd
(* if processing a mutual datatype (there is a cycle!) the corresponding quotient
will be needed later and will be forgotten later *)
|> (if quot_active then I else Lifting_Setup.lifting_forget pointer)
in
(ret_lift_def, lthy5)
end
end
end
and mk_rep_isom qty_isom_bundle (rty, qty, qty_isom) lthy0 =
let
(* logical definition of qty qty_isom isomorphism *)
val uTname = unique_Tname (rty, qty)
fun eq_onp_to_top_tac ctxt = SELECT_GOAL (Local_Defs.unfold0_tac ctxt
(@{thm eq_onp_top_eq_eq[symmetric]} :: Lifting_Info.get_relator_eq_onp_rules ctxt))
fun lift_isom_tac ctxt = HEADGOAL (eq_onp_to_top_tac ctxt
THEN' (rtac ctxt @{thm id_transfer}));
val (rep_isom_lift_def, lthy1) = lthy0
|> (snd o Local_Theory.begin_nested)
|> lift_def ld_no_notes (Binding.qualify_name true uTname "Rep_isom", NoSyn)
(qty_isom --> qty) (HOLogic.id_const rty) lift_isom_tac []
|>> inst_of_lift_def lthy0 (qty_isom --> qty);
val (abs_isom, lthy2) = lthy1
|> lift_def ld_no_notes (Binding.qualify_name true uTname "Abs_isom", NoSyn)
(qty --> qty_isom) (HOLogic.id_const rty) lift_isom_tac []
|>> mk_lift_const_of_lift_def (qty --> qty_isom);
val rep_isom = lift_const_of_lift_def rep_isom_lift_def
val pointer = Lifting_Setup.pointer_of_bundle_binding lthy2 qty_isom_bundle
fun code_dt phi context =
code_dt_of lthy2 (rty, qty) |> the
|> update_rep_isom rep_isom (transfer_rules_of_lift_def rep_isom_lift_def |> hd)
(bundle_name_of_bundle_binding qty_isom_bundle phi context) pointer;
val lthy3 = lthy2
|> Local_Theory.declaration {syntax = false, pervasive = true}
(fn phi => fn context => Data.map (Item_Net.update (morph_code_dt phi (code_dt phi context))) context)
|> Local_Theory.end_nested
(* in order to make the qty qty_isom isomorphism executable we have to define discriminators
and selectors for qty_isom *)
val (rty_name, typs) = dest_Type rty
val (_, qty_typs) = dest_Type qty
val fp = BNF_FP_Def_Sugar.fp_sugar_of lthy3 rty_name
val fp = if is_some fp then the fp
else error ("code_dt: " ^ quote rty_name ^ " is not a datatype.")
val ctr_sugar = fp |> #fp_ctr_sugar |> #ctr_sugar
val ctrs = map (Ctr_Sugar.mk_ctr typs) (#ctrs ctr_sugar);
val qty_ctrs = map (Ctr_Sugar.mk_ctr qty_typs) (#ctrs ctr_sugar);
val ctr_Tss = map (dest_Const #> snd #> binder_types) ctrs;
val qty_ctr_Tss = map (dest_Const #> snd #> binder_types) qty_ctrs;
val n = length ctrs;
val ks = 1 upto n;
val (xss, _) = mk_Freess "x" ctr_Tss lthy3;
fun sel_retT (rty' as Type (s, rtys'), qty' as Type (s', qtys')) =
if (rty', qty') = (rty, qty) then qty_isom else (if s = s'
then Type (s, map sel_retT (rtys' ~~ qtys')) else qty')
| sel_retT (_, qty') = qty';
val sel_retTs = map2 (map2 (sel_retT oo pair)) ctr_Tss qty_ctr_Tss
fun lazy_prove_code_dt (rty, qty) lthy =
if is_none (code_dt_of lthy (rty, qty)) then prove_code_dt (rty, qty) lthy |> fst else lthy;
val lthy4 = fold2 (fold2 (lazy_prove_code_dt oo pair)) ctr_Tss sel_retTs lthy3
val sel_argss = @{map 4} (fn k => fn xs => @{map 2} (fn x => fn qty_ret =>
(k, qty_ret, (xs, x)))) ks xss xss sel_retTs;
fun mk_sel_casex (_, _, (_, x)) = Ctr_Sugar.mk_case typs (x |> dest_Free |> snd) (#casex ctr_sugar);
val dis_casex = Ctr_Sugar.mk_case typs HOLogic.boolT (#casex ctr_sugar);
fun mk_sel_case_args lthy ctr_Tss ks (k, qty_ret, (xs, x)) =
let
val T = x |> dest_Free |> snd;
fun gen_undef_wit Ts wits =
case code_dt_of lthy (T, qty_ret) of
SOME code_dt =>
(fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_witness_of_code_dt qty_ret code_dt),
wit_thm_of_code_dt code_dt :: wits)
| NONE => (fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T), wits)
in
@{fold_map 2} (fn Ts => fn k' => fn wits =>
(if k = k' then (fold_rev Term.lambda xs x, wits) else gen_undef_wit Ts wits)) ctr_Tss ks []
end;
fun mk_sel_rhs arg =
let val (sel_rhs, wits) = mk_sel_case_args lthy4 ctr_Tss ks arg
in (arg |> #2, wits, list_comb (mk_sel_casex arg, sel_rhs)) end;
fun mk_dis_case_args args k = map (fn (k', arg) => (if k = k'
then fold_rev Term.lambda arg \<^const>\<open>True\<close> else fold_rev Term.lambda arg \<^const>\<open>False\<close>)) args;
val sel_rhs = map (map mk_sel_rhs) sel_argss
val dis_rhs = map (fn k => list_comb (dis_casex, mk_dis_case_args (ks ~~ xss) k)) ks
val dis_qty = qty_isom --> HOLogic.boolT;
val dis_names = map (fn k => Binding.qualify_name true uTname ("dis" ^ string_of_int k)) ks;
val (diss, lthy5) = @{fold_map 2} (fn b => fn rhs => fn lthy =>
lift_def ld_no_notes (b, NoSyn) dis_qty rhs (K all_tac) [] lthy
|>> mk_lift_const_of_lift_def dis_qty) dis_names dis_rhs lthy4
val unfold_lift_sel_rsp = @{lemma "(\x. P1 x \ P2 (f x)) \ (rel_fun (eq_onp P1) (eq_onp P2)) f f"
by (simp add: eq_onp_same_args rel_fun_eq_onp_rel)}
fun lift_sel_tac exhaust_rule dt_rules wits ctxt i =
(Method.insert_tac ctxt wits THEN'
eq_onp_to_top_tac ctxt THEN' (* normalize *)
rtac ctxt unfold_lift_sel_rsp THEN'
case_tac exhaust_rule ctxt THEN_ALL_NEW (
EVERY' [hyp_subst_tac ctxt, (* does not kill wits because = was rewritten to eq_onp top *)
Raw_Simplifier.rewrite_goal_tac ctxt (map safe_mk_meta_eq dt_rules),
REPEAT_DETERM o etac ctxt conjE, assume_tac ctxt])) i
val pred_simps = Transfer.lookup_pred_data lthy5 (Tname rty) |> the |> Transfer.pred_simps
val sel_tac = lift_sel_tac (#exhaust ctr_sugar) (#case_thms ctr_sugar @ pred_simps)
val sel_names =
map (fn (k, xs) =>
map (fn k' => Binding.qualify_name true uTname ("sel" ^ string_of_int k ^ string_of_int k'))
(1 upto length xs)) (ks ~~ ctr_Tss);
val (selss, lthy6) = @{fold_map 2} (@{fold_map 2} (fn b => fn (qty_ret, wits, rhs) => fn lthy =>
lift_def_code_dt { code_dt = true, lift_config = ld_no_notes }
(b, NoSyn) (qty_isom --> qty_ret) rhs (HEADGOAL o sel_tac wits) [] lthy
|>> mk_lift_const_of_lift_def (qty_isom --> qty_ret))) sel_names sel_rhs lthy5
(* now we can execute the qty qty_isom isomorphism *)
fun mk_type_definition newT oldT RepC AbsC A =
let
val typedefC =
Const (\<^const_name>\<open>type_definition\<close>,
(newT --> oldT) --> (oldT --> newT) --> HOLogic.mk_setT oldT --> HOLogic.boolT);
in typedefC $ RepC $ AbsC $ A end;
val typedef_goal = mk_type_definition qty_isom qty rep_isom abs_isom (HOLogic.mk_UNIV qty) |>
HOLogic.mk_Trueprop;
fun typ_isom_tac ctxt i =
EVERY' [ SELECT_GOAL (Local_Defs.unfold0_tac ctxt @{thms type_definition_def}),
DETERM o Transfer.transfer_tac true ctxt,
SELECT_GOAL (Local_Defs.unfold0_tac ctxt @{thms eq_onp_top_eq_eq}) (* normalize *),
Raw_Simplifier.rewrite_goal_tac ctxt
(map safe_mk_meta_eq @{thms id_apply simp_thms Ball_def}),
rtac ctxt TrueI] i;
val (_, transfer_ctxt) =
Proof_Context.note_thms ""
(Binding.empty_atts,
[(@{thms right_total_UNIV_transfer}, [Transfer.transfer_add]),
(@{thms Domain_eq_top}, [Transfer.transfer_domain_add])]) lthy6;
val quot_thm_isom =
Goal.prove_sorry transfer_ctxt [] [] typedef_goal
(fn {context = goal_ctxt, ...} => typ_isom_tac goal_ctxt 1)
|> Thm.close_derivation \<^here>
|> singleton (Variable.export transfer_ctxt lthy6)
|> (fn thm => @{thm UNIV_typedef_to_Quotient} OF [thm, @{thm reflexive}])
val qty_isom_name = Tname qty_isom;
val quot_isom_rep =
let
val (quotients : Lifting_Term.quotients) =
Symtab.insert (Lifting_Info.quotient_eq)
(qty_isom_name, {quot_thm = quot_thm_isom, pcr_info = NONE}) Symtab.empty
val id_actions = { constr = K I, lift = K I, comp_lift = K I }
in
fn ctxt => fn (rty, qty) => Lifting_Term.prove_schematic_quot_thm id_actions quotients
ctxt (rty, qty) () |> fst |> Lifting_Term.force_qty_type ctxt qty
|> quot_thm_rep
end;
val (x, x_ctxt) = yield_singleton (mk_Frees "x") qty_isom lthy6;
fun mk_ctr ctr ctr_Ts sels =
let
val sel_ret_Ts = map (dest_Const #> snd #> body_type) sels;
fun rep_isom lthy t (rty, qty) =
let
val rep = quot_isom_rep lthy (rty, qty)
in
if is_Const rep andalso (rep |> dest_Const |> fst) = \<^const_name>\<open>id\<close> then
t else rep $ t
end;
in
@{fold 3} (fn sel => fn ctr_T => fn sel_ret_T => fn ctr =>
ctr $ rep_isom x_ctxt (sel $ x) (ctr_T, sel_ret_T)) sels ctr_Ts sel_ret_Ts ctr
end;
(* stolen from Metis *)
exception BREAK_LIST
fun break_list (x :: xs) = (x, xs)
| break_list _ = raise BREAK_LIST
val (ctr, ctrs) = qty_ctrs |> rev |> break_list;
val (ctr_Ts, ctr_Tss) = qty_ctr_Tss |> rev |> break_list;
val (sel, rselss) = selss |> rev |> break_list;
val rdiss = rev diss |> tl;
val first_ctr = mk_ctr ctr ctr_Ts sel;
fun mk_If_ctr dis ctr ctr_Ts sel elsex = mk_If (dis$x) (mk_ctr ctr ctr_Ts sel) elsex;
val rhs = @{fold 4} mk_If_ctr rdiss ctrs ctr_Tss rselss first_ctr;
val rep_isom_code_goal = HOLogic.mk_Trueprop (HOLogic.mk_eq (rep_isom$x, rhs));
local
val rep_isom_code_tac_rules = map safe_mk_meta_eq @{thms refl id_apply if_splits simp_thms}
in
fun rep_isom_code_tac (ctr_sugar:Ctr_Sugar.ctr_sugar) ctxt i =
let
val exhaust = ctr_sugar |> #exhaust
val cases = ctr_sugar |> #case_thms
val map_ids = fp |> #fp_nesting_bnfs |> map BNF_Def.map_id0_of_bnf
val simp_rules = map safe_mk_meta_eq (cases @ map_ids) @ rep_isom_code_tac_rules
in
EVERY' [Transfer.gen_frees_tac [] ctxt, DETERM o (Transfer.transfer_tac true ctxt),
case_tac exhaust ctxt THEN_ALL_NEW EVERY' [hyp_subst_tac ctxt,
Raw_Simplifier.rewrite_goal_tac ctxt simp_rules, rtac ctxt TrueI ]] i
end
end
(* stolen from bnf_fp_n2m.ML *)
fun force_typ ctxt T =
Term.map_types Type_Infer.paramify_vars
#> Type.constraint T
#> singleton (Type_Infer_Context.infer_types ctxt);
(* The following tests that types in rty have corresponding arities imposed by constraints of
the datatype fp. Otherwise rep_isom_code_tac could fail (especially transfer in it) is such
a way that it is not easy to infer the problem with sorts.
*)
val _ = yield_singleton (mk_Frees "x") (#T fp) x_ctxt |> fst |> force_typ x_ctxt qty
val rep_isom_code =
Goal.prove_sorry x_ctxt [] [] rep_isom_code_goal
(fn {context = goal_ctxt, ...} => rep_isom_code_tac ctr_sugar goal_ctxt 1)
|> Thm.close_derivation \<^here>
|> singleton(Variable.export x_ctxt lthy6)
in
lthy6
|> snd o Local_Theory.note ((Binding.empty, @{attributes [code]}), [rep_isom_code])
|> Lifting_Setup.lifting_forget pointer
|> pair (selss, diss, rep_isom_code)
end
and constr qty (quot_thm, (lthy0, rel_eq_onps)) =
let
val quot_thm = Lifting_Term.force_qty_type lthy0 qty quot_thm
val (rty, qty) = quot_thm_rty_qty quot_thm
val rty_name = Tname rty;
val pred_data = Transfer.lookup_pred_data lthy0 rty_name
val pred_data = if is_some pred_data then the pred_data
else error ("code_dt: " ^ quote rty_name ^ " is not a datatype.")
val rel_eq_onp = safe_mk_meta_eq (Transfer.rel_eq_onp pred_data);
val rel_eq_onps = insert Thm.eq_thm rel_eq_onp rel_eq_onps
val R_conv = Transfer.top_sweep_rewr_conv @{thms eq_onp_top_eq_eq[symmetric, THEN eq_reflection]}
then_conv Conv.rewr_conv rel_eq_onp
val quot_thm = Conv.fconv_rule(HOLogic.Trueprop_conv (Quotient_R_conv R_conv)) quot_thm;
in
if is_none (code_dt_of lthy0 (rty, qty)) then
let
val non_empty_pred = quot_thm RS @{thm type_definition_Quotient_not_empty}
val pred = quot_thm_rel quot_thm |> dest_comb |> snd;
val (pred, lthy1) = lthy0
|> (snd o Local_Theory.begin_nested)
|> yield_singleton (Variable.import_terms true) pred;
val TFrees = Term.add_tfreesT qty []
fun non_empty_typedef_tac non_empty_pred ctxt i =
(Method.insert_tac ctxt [non_empty_pred] THEN'
SELECT_GOAL (Local_Defs.unfold0_tac ctxt [mem_Collect_eq]) THEN' assume_tac ctxt) i
val uTname = unique_Tname (rty, qty)
val Tdef_set = HOLogic.mk_Collect ("x", rty, pred $ Free("x", rty));
val ((_, tcode_dt), lthy2) = lthy1
|> conceal_naming_result
(typedef (Binding.concealed uTname, TFrees, NoSyn)
Tdef_set NONE (fn lthy => HEADGOAL (non_empty_typedef_tac non_empty_pred lthy)));
val type_definition_thm = tcode_dt |> snd |> #type_definition;
val qty_isom = tcode_dt |> fst |> #abs_type;
val (binding, lthy3) = lthy2
|> conceal_naming_result
(Lifting_Setup.setup_by_typedef_thm {notes = false} type_definition_thm)
||> Local_Theory.end_nested
val (wit, wit_thm) = mk_witness quot_thm;
val code_dt = mk_code_dt rty qty wit wit_thm NONE;
val lthy4 = lthy3
|> update_code_dt code_dt
|> mk_rep_isom binding (rty, qty, qty_isom) |> snd
in
(quot_thm, (lthy4, rel_eq_onps))
end
else
(quot_thm, (lthy0, rel_eq_onps))
end
and lift_def_code_dt config = gen_lift_def (add_lift_def_code_dt config)
(** from parsed parameters to the config record **)
fun map_config_code_dt f1 f2 ({code_dt = code_dt, lift_config = lift_config}: config_code_dt) =
{code_dt = f1 code_dt, lift_config = f2 lift_config}
fun update_config_code_dt nval = map_config_code_dt (K nval) I
val config_flags = [("code_dt", update_config_code_dt true)]
fun evaluate_params params =
let
fun eval_param param config =
case AList.lookup (op =) config_flags param of
SOME update => update config
| NONE => error ("Unknown parameter: " ^ (quote param))
in
fold eval_param params default_config_code_dt
end
(**
lift_definition command. It opens a proof of a corresponding respectfulness
theorem in a user-friendly, readable form. Then add_lift_def_code_dt is called internally.
**)
local
val eq_onp_assms_tac_fixed_rules = map (Transfer.prep_transfer_domain_thm \<^context>)
[@{thm pcr_Domainp_total}, @{thm pcr_Domainp_par_left_total}, @{thm pcr_Domainp_par},
@{thm pcr_Domainp}]
in
fun mk_readable_rsp_thm_eq tm ctxt =
let
val ctm = Thm.cterm_of ctxt tm
fun assms_rewr_conv tactic rule ct =
let
fun prove_extra_assms thm =
let
val assms = cprems_of thm
fun finish thm = if Thm.no_prems thm then SOME (Goal.conclude thm) else NONE
fun prove ctm = Option.mapPartial finish (SINGLE tactic (Goal.init ctm))
in
map_interrupt prove assms
end
fun cconl_of thm = Drule.strip_imp_concl (Thm.cprop_of thm)
fun lhs_of thm = fst (Thm.dest_equals (cconl_of thm))
fun rhs_of thm = snd (Thm.dest_equals (cconl_of thm))
val rule1 = Thm.incr_indexes (Thm.maxidx_of_cterm ct + 1) rule;
val lhs = lhs_of rule1;
val rule2 = Thm.rename_boundvars (Thm.term_of lhs) (Thm.term_of ct) rule1;
val rule3 =
Thm.instantiate (Thm.match (lhs, ct)) rule2
handle Pattern.MATCH => raise CTERM ("assms_rewr_conv", [lhs, ct]);
val proved_assms = prove_extra_assms rule3
in
case proved_assms of
SOME proved_assms =>
let
val rule3 = proved_assms MRSL rule3
val rule4 =
if lhs_of rule3 aconvc ct then rule3
else
let val ceq = Thm.dest_fun2 (Thm.cprop_of rule3)
in rule3 COMP Thm.trivial (Thm.mk_binop ceq ct (rhs_of rule3)) end
in Thm.transitive rule4 (Thm.beta_conversion true (rhs_of rule4)) end
| NONE => Conv.no_conv ct
end
fun assms_rewrs_conv tactic rules = Conv.first_conv (map (assms_rewr_conv tactic) rules)
fun simp_arrows_conv ctm =
let
val unfold_conv = Conv.rewrs_conv
[@{thm rel_fun_eq_eq_onp[THEN eq_reflection]},
@{thm rel_fun_eq_onp_rel[THEN eq_reflection]},
@{thm rel_fun_eq[THEN eq_reflection]},
@{thm rel_fun_eq_rel[THEN eq_reflection]},
@{thm rel_fun_def[THEN eq_reflection]}]
fun binop_conv2 cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
val eq_onp_assms_tac_rules = @{thm left_unique_OO} ::
eq_onp_assms_tac_fixed_rules @ (Transfer.get_transfer_raw ctxt)
val intro_top_rule = @{thm eq_onp_top_eq_eq[symmetric, THEN eq_reflection]}
val kill_tops = Transfer.top_sweep_rewr_conv [@{thm eq_onp_top_eq_eq[THEN eq_reflection]}]
val eq_onp_assms_tac = (CONVERSION kill_tops THEN'
TRY o REPEAT_ALL_NEW (resolve_tac ctxt eq_onp_assms_tac_rules)
THEN_ALL_NEW (DETERM o Transfer.eq_tac ctxt)) 1
val relator_eq_onp_conv = Conv.bottom_conv
(K (Conv.try_conv (assms_rewrs_conv eq_onp_assms_tac
(intro_top_rule :: Lifting_Info.get_relator_eq_onp_rules ctxt)))) ctxt
then_conv kill_tops
val relator_eq_conv = Conv.bottom_conv
(K (Conv.try_conv (Conv.rewrs_conv (Transfer.get_relator_eq ctxt)))) ctxt
in
case (Thm.term_of ctm) of
Const (\<^const_name>\<open>rel_fun\<close>, _) $ _ $ _ =>
(binop_conv2 simp_arrows_conv simp_arrows_conv then_conv unfold_conv) ctm
| _ => (relator_eq_onp_conv then_conv relator_eq_conv) ctm
end
val unfold_ret_val_invs = Conv.bottom_conv
(K (Conv.try_conv (Conv.rewr_conv @{thm eq_onp_same_args[THEN eq_reflection]}))) ctxt
val unfold_inv_conv =
Conv.top_sweep_conv (K (Conv.rewr_conv @{thm eq_onp_def[THEN eq_reflection]})) ctxt
val simp_conv = HOLogic.Trueprop_conv (Conv.fun2_conv simp_arrows_conv)
val univq_conv = Conv.rewr_conv @{thm HOL.all_simps(6)[symmetric, THEN eq_reflection]}
val univq_prenex_conv = Conv.top_conv (K (Conv.try_conv univq_conv)) ctxt
val beta_conv = Thm.beta_conversion true
val eq_thm =
(simp_conv then_conv univq_prenex_conv then_conv beta_conv then_conv unfold_ret_val_invs
then_conv unfold_inv_conv) ctm
in
Object_Logic.rulify ctxt (eq_thm RS Drule.equal_elim_rule2)
end
end
fun rename_to_tnames ctxt term =
let
fun all_typs (Const (\<^const_name>\<open>Pure.all\<close>, _) $ Abs (_, T, t)) = T :: all_typs t
| all_typs _ = []
fun rename (Const (\<^const_name>\<open>Pure.all\<close>, T1) $ Abs (_, T2, t)) (new_name :: names) =
(Const (\<^const_name>\<open>Pure.all\<close>, T1) $ Abs (new_name, T2, rename t names))
| rename t _ = t
val (fixed_def_t, _) = yield_singleton (Variable.importT_terms) term ctxt
val new_names = Old_Datatype_Prop.make_tnames (all_typs fixed_def_t)
in
rename term new_names
end
fun quot_thm_err ctxt (rty, qty) pretty_msg =
let
val error_msg = cat_lines
["Lifting failed for the following types:",
Pretty.string_of (Pretty.block
[Pretty.str "Raw type:", Pretty.brk 2, Syntax.pretty_typ ctxt rty]),
Pretty.string_of (Pretty.block
[Pretty.str "Abstract type:", Pretty.brk 2, Syntax.pretty_typ ctxt qty]),
"",
(Pretty.string_of (Pretty.block
[Pretty.str "Reason:", Pretty.brk 2, pretty_msg]))]
in
error error_msg
end
fun check_rty_err ctxt (rty_schematic, rty_forced) (raw_var, rhs_raw) =
let
val (_, ctxt') = Proof_Context.read_var raw_var ctxt
val rhs = Syntax.read_term ctxt' rhs_raw
val error_msg = cat_lines
["Lifting failed for the following term:",
Pretty.string_of (Pretty.block
[Pretty.str "Term:", Pretty.brk 2, Syntax.pretty_term ctxt rhs]),
Pretty.string_of (Pretty.block
[Pretty.str "Type:", Pretty.brk 2, Syntax.pretty_typ ctxt rty_schematic]),
"",
(Pretty.string_of (Pretty.block
[Pretty.str "Reason:",
Pretty.brk 2,
Pretty.str "The type of the term cannot be instantiated to",
Pretty.brk 1,
Pretty.quote (Syntax.pretty_typ ctxt rty_forced),
Pretty.str "."]))]
in
error error_msg
end
fun lift_def_cmd (params, raw_var, rhs_raw, par_xthms) lthy0 =
let
val config = evaluate_params params
val ((binding, SOME qty, mx), lthy1) = Proof_Context.read_var raw_var lthy0
val var = (binding, mx)
val rhs = Syntax.read_term lthy1 rhs_raw
val par_thms = Attrib.eval_thms lthy1 par_xthms
val (goal, after_qed) = lthy1
|> prepare_lift_def (add_lift_def_code_dt config) var qty rhs par_thms
val (goal, after_qed) =
case goal of
NONE => (goal, K (after_qed Drule.dummy_thm))
| SOME prsp_tm =>
let
val readable_rsp_thm_eq = mk_readable_rsp_thm_eq prsp_tm lthy1
val (readable_rsp_tm, _) = Logic.dest_implies (Thm.prop_of readable_rsp_thm_eq)
val readable_rsp_tm_tnames = rename_to_tnames lthy1 readable_rsp_tm
fun after_qed' [[thm]] lthy =
let
val internal_rsp_thm =
Goal.prove lthy [] [] prsp_tm (fn {context = goal_ctxt, ...} =>
rtac goal_ctxt readable_rsp_thm_eq 1 THEN
Proof_Context.fact_tac goal_ctxt [thm] 1)
in after_qed internal_rsp_thm lthy end
in (SOME readable_rsp_tm_tnames, after_qed') end
fun after_qed_with_err_handling thmss ctxt = (after_qed thmss ctxt
handle Lifting_Term.QUOT_THM (rty, qty, msg) => quot_thm_err lthy1 (rty, qty) msg)
handle Lifting_Term.CHECK_RTY (rty_schematic, rty_forced) =>
check_rty_err lthy1 (rty_schematic, rty_forced) (raw_var, rhs_raw);
in
lthy1
|> Proof.theorem NONE (snd oo after_qed_with_err_handling) [map (rpair []) (the_list goal)]
end
fun lift_def_cmd_with_err_handling (params, (raw_var, rhs_raw, par_xthms)) lthy =
(lift_def_cmd (params, raw_var, rhs_raw, par_xthms) lthy
handle Lifting_Term.QUOT_THM (rty, qty, msg) => quot_thm_err lthy (rty, qty) msg)
handle Lifting_Term.CHECK_RTY (rty_schematic, rty_forced) =>
check_rty_err lthy (rty_schematic, rty_forced) (raw_var, rhs_raw);
val parse_param = Parse.name
val parse_params = Scan.optional (Args.parens (Parse.list parse_param)) [];
(* command syntax *)
val _ =
Outer_Syntax.local_theory_to_proof \<^command_keyword>\<open>lift_definition\<close>
"definition for constants over the quotient type"
(parse_params --
(((Parse.binding -- (\<^keyword>\<open>::\<close> |-- (Parse.typ >> SOME) -- Parse.opt_mixfix')
>> Scan.triple2) --
(\<^keyword>\<open>is\<close> |-- Parse.term) --
Scan.optional (\<^keyword>\<open>parametric\<close> |-- Parse.!!! Parse.thms1) []) >> Scan.triple1)
>> lift_def_cmd_with_err_handling);
end
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