(* Title: HOL/Tools/BNF/bnf_fp_util.ML
Author: Dmitriy Traytel, TU Muenchen
Author: Jasmin Blanchette, TU Muenchen
Author: Martin Desharnais, TU Muenchen
Author: Stefan Berghofer, TU Muenchen
Copyright 2012, 2013, 2014
Shared library for the datatype and codatatype constructions.
*)
signature BNF_FP_UTIL =
sig
exception EMPTY_DATATYPE of string
type fp_result =
{Ts: typ list,
bnfs: BNF_Def.bnf list,
pre_bnfs: BNF_Def.bnf list,
absT_infos: BNF_Comp.absT_info list,
ctors: term list,
dtors: term list,
xtor_un_folds: term list,
xtor_co_recs: term list,
xtor_co_induct: thm,
dtor_ctors: thm list,
ctor_dtors: thm list,
ctor_injects: thm list,
dtor_injects: thm list,
xtor_maps: thm list,
xtor_map_unique: thm,
xtor_setss: thm list list,
xtor_rels: thm list,
xtor_un_fold_thms: thm list,
xtor_co_rec_thms: thm list,
xtor_un_fold_unique: thm,
xtor_co_rec_unique: thm,
xtor_un_fold_o_maps: thm list,
xtor_co_rec_o_maps: thm list,
xtor_un_fold_transfers: thm list,
xtor_co_rec_transfers: thm list,
xtor_rel_co_induct: thm,
dtor_set_inducts: thm list}
val morph_fp_result: morphism -> fp_result -> fp_result
val time: Proof.context -> Timer.real_timer -> string -> Timer.real_timer
val fixpoint: ('a * 'a -> bool) -> ('a list -> 'a list) -> 'a list -> 'a list
val IITN: string
val LevN: string
val algN: string
val behN: string
val bisN: string
val carTN: string
val caseN: string
val coN: string
val coinductN: string
val coinduct_strongN: string
val corecN: string
val corec_discN: string
val corec_disc_iffN: string
val ctorN: string
val ctor_dtorN: string
val ctor_exhaustN: string
val ctor_induct2N: string
val ctor_inductN: string
val ctor_injectN: string
val ctor_foldN: string
val ctor_fold_o_mapN: string
val ctor_fold_transferN: string
val ctor_fold_uniqueN: string
val ctor_mapN: string
val ctor_map_uniqueN: string
val ctor_recN: string
val ctor_rec_o_mapN: string
val ctor_rec_transferN: string
val ctor_rec_uniqueN: string
val ctor_relN: string
val ctor_rel_inductN: string
val ctor_set_inclN: string
val ctor_set_set_inclN: string
val dtorN: string
val dtor_coinductN: string
val dtor_corecN: string
val dtor_corec_o_mapN: string
val dtor_corec_transferN: string
val dtor_corec_uniqueN: string
val dtor_ctorN: string
val dtor_exhaustN: string
val dtor_injectN: string
val dtor_mapN: string
val dtor_map_coinductN: string
val dtor_map_coinduct_strongN: string
val dtor_map_uniqueN: string
val dtor_relN: string
val dtor_rel_coinductN: string
val dtor_set_inclN: string
val dtor_set_set_inclN: string
val dtor_coinduct_strongN: string
val dtor_unfoldN: string
val dtor_unfold_o_mapN: string
val dtor_unfold_transferN: string
val dtor_unfold_uniqueN: string
val exhaustN: string
val colN: string
val inductN: string
val injectN: string
val isNodeN: string
val lsbisN: string
val mapN: string
val map_uniqueN: string
val min_algN: string
val morN: string
val nchotomyN: string
val recN: string
val rel_casesN: string
val rel_coinductN: string
val rel_inductN: string
val rel_injectN: string
val rel_introsN: string
val rel_distinctN: string
val rel_selN: string
val rvN: string
val corec_selN: string
val set_inclN: string
val set_set_inclN: string
val setN: string
val simpsN: string
val strTN: string
val str_initN: string
val sum_bdN: string
val sum_bdTN: string
val uniqueN: string
(* TODO: Don't index set facts. Isabelle packages traditionally generate uniform names. *)
val mk_ctor_setN: int -> string
val mk_dtor_setN: int -> string
val mk_dtor_set_inductN: int -> string
val mk_set_inductN: int -> string
val co_prefix: BNF_Util.fp_kind -> string
val split_conj_thm: thm -> thm list
val split_conj_prems: int -> thm -> thm
val mk_sumTN: typ list -> typ
val mk_sumTN_balanced: typ list -> typ
val mk_tupleT_balanced: typ list -> typ
val mk_sumprodT_balanced: typ list list -> typ
val mk_proj: typ -> int -> int -> term
val mk_convol: term * term -> term
val mk_rel_prod: term -> term -> term
val mk_rel_sum: term -> term -> term
val Inl_const: typ -> typ -> term
val Inr_const: typ -> typ -> term
val mk_tuple_balanced: term list -> term
val mk_tuple1_balanced: typ list -> term list -> term
val abs_curried_balanced: typ list -> term -> term
val mk_tupled_fun: term -> term -> term list -> term
val mk_case_sum: term * term -> term
val mk_case_sumN: term list -> term
val mk_case_absumprod: typ -> term -> term list -> term list list -> term list list -> term
val mk_Inl: typ -> term -> term
val mk_Inr: typ -> term -> term
val mk_sumprod_balanced: typ -> int -> int -> term list -> term
val mk_absumprod: typ -> term -> int -> int -> term list -> term
val dest_sumT: typ -> typ * typ
val dest_sumTN_balanced: int -> typ -> typ list
val dest_tupleT_balanced: int -> typ -> typ list
val dest_absumprodT: typ -> typ -> int -> int list -> typ -> typ list list
val If_const: typ -> term
val mk_Field: term -> term
val mk_If: term -> term -> term -> term
val mk_absumprodE: thm -> int list -> thm
val mk_sum_caseN: int -> int -> thm
val mk_sum_caseN_balanced: int -> int -> thm
val mk_sum_Cinfinite: thm list -> thm
val mk_sum_card_order: thm list -> thm
val force_typ: Proof.context -> typ -> term -> term
val mk_xtor_rel_co_induct_thm: BNF_Util.fp_kind -> term list -> term list -> term list ->
term list -> term list -> term list -> term list -> term list ->
({prems: thm list, context: Proof.context} -> tactic) -> Proof.context -> thm
val mk_xtor_co_iter_transfer_thms: BNF_Util.fp_kind -> term list -> term list -> term list ->
term list -> term list -> term list -> term list ->
({prems: thm list, context: Proof.context} -> tactic) -> Proof.context -> thm list
val mk_xtor_co_iter_o_map_thms: BNF_Util.fp_kind -> bool -> int -> thm -> thm list -> thm list ->
thm list -> thm list -> thm list
val derive_xtor_co_recs: BNF_Util.fp_kind -> binding list -> (typ list -> typ list) ->
(typ list list * typ list) -> BNF_Def.bnf list -> term list -> term list ->
thm -> thm list -> thm list -> thm list -> thm list ->
(BNF_Comp.absT_info * BNF_Comp.absT_info) option list ->
local_theory ->
(term list * (thm list * thm * thm list * thm list)) * local_theory
val raw_qualify: (binding -> binding) -> binding -> binding -> binding
val fixpoint_bnf: bool -> (binding -> binding) ->
(binding list -> (string * sort) list -> typ list * typ list list -> BNF_Def.bnf list ->
BNF_Comp.absT_info list -> local_theory -> 'a) ->
binding list -> (string * sort) list -> (string * sort) list -> (string * sort) list ->
typ list -> BNF_Comp.comp_cache -> local_theory ->
((BNF_Def.bnf list * BNF_Comp.absT_info list) * BNF_Comp.comp_cache) * 'a
val fp_antiquote_setup: binding -> theory -> theory
end;
structure BNF_FP_Util : BNF_FP_UTIL =
struct
open Ctr_Sugar
open BNF_Comp
open BNF_Def
open BNF_Util
open BNF_FP_Util_Tactics
exception EMPTY_DATATYPE of string;
type fp_result =
{Ts: typ list,
bnfs: bnf list,
pre_bnfs: BNF_Def.bnf list,
absT_infos: BNF_Comp.absT_info list,
ctors: term list,
dtors: term list,
xtor_un_folds: term list,
xtor_co_recs: term list,
xtor_co_induct: thm,
dtor_ctors: thm list,
ctor_dtors: thm list,
ctor_injects: thm list,
dtor_injects: thm list,
xtor_maps: thm list,
xtor_map_unique: thm,
xtor_setss: thm list list,
xtor_rels: thm list,
xtor_un_fold_thms: thm list,
xtor_co_rec_thms: thm list,
xtor_un_fold_unique: thm,
xtor_co_rec_unique: thm,
xtor_un_fold_o_maps: thm list,
xtor_co_rec_o_maps: thm list,
xtor_un_fold_transfers: thm list,
xtor_co_rec_transfers: thm list,
xtor_rel_co_induct: thm,
dtor_set_inducts: thm list};
fun morph_fp_result phi {Ts, bnfs, pre_bnfs, absT_infos, ctors, dtors, xtor_un_folds,
xtor_co_recs, xtor_co_induct, dtor_ctors, ctor_dtors, ctor_injects, dtor_injects, xtor_maps,
xtor_map_unique, xtor_setss, xtor_rels, xtor_un_fold_thms, xtor_co_rec_thms,
xtor_un_fold_unique, xtor_co_rec_unique, xtor_un_fold_o_maps,
xtor_co_rec_o_maps, xtor_un_fold_transfers, xtor_co_rec_transfers, xtor_rel_co_induct,
dtor_set_inducts} =
{Ts = map (Morphism.typ phi) Ts,
bnfs = map (morph_bnf phi) bnfs,
pre_bnfs = map (morph_bnf phi) pre_bnfs,
absT_infos = map (morph_absT_info phi) absT_infos,
ctors = map (Morphism.term phi) ctors,
dtors = map (Morphism.term phi) dtors,
xtor_un_folds = map (Morphism.term phi) xtor_un_folds,
xtor_co_recs = map (Morphism.term phi) xtor_co_recs,
xtor_co_induct = Morphism.thm phi xtor_co_induct,
dtor_ctors = map (Morphism.thm phi) dtor_ctors,
ctor_dtors = map (Morphism.thm phi) ctor_dtors,
ctor_injects = map (Morphism.thm phi) ctor_injects,
dtor_injects = map (Morphism.thm phi) dtor_injects,
xtor_maps = map (Morphism.thm phi) xtor_maps,
xtor_map_unique = Morphism.thm phi xtor_map_unique,
xtor_setss = map (map (Morphism.thm phi)) xtor_setss,
xtor_rels = map (Morphism.thm phi) xtor_rels,
xtor_un_fold_thms = map (Morphism.thm phi) xtor_un_fold_thms,
xtor_co_rec_thms = map (Morphism.thm phi) xtor_co_rec_thms,
xtor_un_fold_unique = Morphism.thm phi xtor_un_fold_unique,
xtor_co_rec_unique = Morphism.thm phi xtor_co_rec_unique,
xtor_un_fold_o_maps = map (Morphism.thm phi) xtor_un_fold_o_maps,
xtor_co_rec_o_maps = map (Morphism.thm phi) xtor_co_rec_o_maps,
xtor_un_fold_transfers = map (Morphism.thm phi) xtor_un_fold_transfers,
xtor_co_rec_transfers = map (Morphism.thm phi) xtor_co_rec_transfers,
xtor_rel_co_induct = Morphism.thm phi xtor_rel_co_induct,
dtor_set_inducts = map (Morphism.thm phi) dtor_set_inducts};
fun time ctxt timer msg = (if Config.get ctxt bnf_timing
then warning (msg ^ ": " ^ string_of_int (Time.toMilliseconds (Timer.checkRealTimer timer)) ^
" ms")
else (); Timer.startRealTimer ());
val preN = "pre_"
val rawN = "raw_"
val coN = "co"
val unN = "un"
val algN = "alg"
val IITN = "IITN"
val foldN = "fold"
val unfoldN = unN ^ foldN
val uniqueN = "unique"
val transferN = "transfer"
val simpsN = "simps"
val ctorN = "ctor"
val dtorN = "dtor"
val ctor_foldN = ctorN ^ "_" ^ foldN
val dtor_unfoldN = dtorN ^ "_" ^ unfoldN
val ctor_fold_uniqueN = ctor_foldN ^ "_" ^ uniqueN
val ctor_fold_o_mapN = ctor_foldN ^ "_o_" ^ mapN
val dtor_unfold_uniqueN = dtor_unfoldN ^ "_" ^ uniqueN
val dtor_unfold_o_mapN = dtor_unfoldN ^ "_o_" ^ mapN
val ctor_fold_transferN = ctor_foldN ^ "_" ^ transferN
val dtor_unfold_transferN = dtor_unfoldN ^ "_" ^ transferN
val ctor_mapN = ctorN ^ "_" ^ mapN
val dtor_mapN = dtorN ^ "_" ^ mapN
val map_uniqueN = mapN ^ "_" ^ uniqueN
val ctor_map_uniqueN = ctorN ^ "_" ^ map_uniqueN
val dtor_map_uniqueN = dtorN ^ "_" ^ map_uniqueN
val min_algN = "min_alg"
val morN = "mor"
val bisN = "bis"
val lsbisN = "lsbis"
val sum_bdTN = "sbdT"
val sum_bdN = "sbd"
val carTN = "carT"
val strTN = "strT"
val isNodeN = "isNode"
val LevN = "Lev"
val rvN = "recover"
val behN = "beh"
val setN = "set"
val mk_ctor_setN = prefix (ctorN ^ "_") o mk_setN
val mk_dtor_setN = prefix (dtorN ^ "_") o mk_setN
fun mk_set_inductN i = mk_setN i ^ "_induct"
val mk_dtor_set_inductN = prefix (dtorN ^ "_") o mk_set_inductN
val str_initN = "str_init"
val recN = "rec"
val corecN = coN ^ recN
val ctor_recN = ctorN ^ "_" ^ recN
val ctor_rec_o_mapN = ctor_recN ^ "_o_" ^ mapN
val ctor_rec_transferN = ctor_recN ^ "_" ^ transferN
val ctor_rec_uniqueN = ctor_recN ^ "_" ^ uniqueN
val dtor_corecN = dtorN ^ "_" ^ corecN
val dtor_corec_o_mapN = dtor_corecN ^ "_o_" ^ mapN
val dtor_corec_transferN = dtor_corecN ^ "_" ^ transferN
val dtor_corec_uniqueN = dtor_corecN ^ "_" ^ uniqueN
val ctor_dtorN = ctorN ^ "_" ^ dtorN
val dtor_ctorN = dtorN ^ "_" ^ ctorN
val nchotomyN = "nchotomy"
val injectN = "inject"
val exhaustN = "exhaust"
val ctor_injectN = ctorN ^ "_" ^ injectN
val ctor_exhaustN = ctorN ^ "_" ^ exhaustN
val dtor_injectN = dtorN ^ "_" ^ injectN
val dtor_exhaustN = dtorN ^ "_" ^ exhaustN
val ctor_relN = ctorN ^ "_" ^ relN
val dtor_relN = dtorN ^ "_" ^ relN
val inductN = "induct"
val coinductN = coN ^ inductN
val ctor_inductN = ctorN ^ "_" ^ inductN
val ctor_induct2N = ctor_inductN ^ "2"
val dtor_map_coinductN = dtor_mapN ^ "_" ^ coinductN
val dtor_coinductN = dtorN ^ "_" ^ coinductN
val coinduct_strongN = coinductN ^ "_strong"
val dtor_map_coinduct_strongN = dtor_mapN ^ "_" ^ coinduct_strongN
val dtor_coinduct_strongN = dtorN ^ "_" ^ coinduct_strongN
val colN = "col"
val set_inclN = "set_incl"
val ctor_set_inclN = ctorN ^ "_" ^ set_inclN
val dtor_set_inclN = dtorN ^ "_" ^ set_inclN
val set_set_inclN = "set_set_incl"
val ctor_set_set_inclN = ctorN ^ "_" ^ set_set_inclN
val dtor_set_set_inclN = dtorN ^ "_" ^ set_set_inclN
val caseN = "case"
val discN = "disc"
val corec_discN = corecN ^ "_" ^ discN
val iffN = "_iff"
val corec_disc_iffN = corec_discN ^ iffN
val distinctN = "distinct"
val rel_distinctN = relN ^ "_" ^ distinctN
val injectN = "inject"
val rel_casesN = relN ^ "_cases"
val rel_injectN = relN ^ "_" ^ injectN
val rel_introsN = relN ^ "_intros"
val rel_coinductN = relN ^ "_" ^ coinductN
val rel_selN = relN ^ "_sel"
val dtor_rel_coinductN = dtorN ^ "_" ^ rel_coinductN
val rel_inductN = relN ^ "_" ^ inductN
val ctor_rel_inductN = ctorN ^ "_" ^ rel_inductN
val selN = "sel"
val corec_selN = corecN ^ "_" ^ selN
fun co_prefix fp = case_fp fp "" "co";
fun dest_sumT (Type (@{type_name sum}, [T, T'])) = (T, T');
val dest_sumTN_balanced = Balanced_Tree.dest dest_sumT;
fun dest_tupleT_balanced 0 @{typ unit} = []
| dest_tupleT_balanced n T = Balanced_Tree.dest HOLogic.dest_prodT n T;
fun dest_absumprodT absT repT n ms =
map2 dest_tupleT_balanced ms o dest_sumTN_balanced n o mk_repT absT repT;
val mk_sumTN = Library.foldr1 mk_sumT;
val mk_sumTN_balanced = Balanced_Tree.make mk_sumT;
fun mk_tupleT_balanced [] = HOLogic.unitT
| mk_tupleT_balanced Ts = Balanced_Tree.make HOLogic.mk_prodT Ts;
val mk_sumprodT_balanced = mk_sumTN_balanced o map mk_tupleT_balanced;
fun mk_proj T n k =
let val (binders, _) = strip_typeN n T in
fold_rev (fn T => fn t => Abs (Name.uu, T, t)) binders (Bound (n - k - 1))
end;
fun mk_convol (f, g) =
let
val (fU, fTU) = `range_type (fastype_of f);
val ((gT, gU), gTU) = `dest_funT (fastype_of g);
val convolT = fTU --> gTU --> gT --> HOLogic.mk_prodT (fU, gU);
in Const (@{const_name convol}, convolT) $ f $ g end;
fun mk_rel_prod R S =
let
val ((A1, A2), RT) = `dest_pred2T (fastype_of R);
val ((B1, B2), ST) = `dest_pred2T (fastype_of S);
val rel_prodT = RT --> ST --> mk_pred2T (HOLogic.mk_prodT (A1, B1)) (HOLogic.mk_prodT (A2, B2));
in Const (@{const_name rel_prod}, rel_prodT) $ R $ S end;
fun mk_rel_sum R S =
let
val ((A1, A2), RT) = `dest_pred2T (fastype_of R);
val ((B1, B2), ST) = `dest_pred2T (fastype_of S);
val rel_sumT = RT --> ST --> mk_pred2T (mk_sumT (A1, B1)) (mk_sumT (A2, B2));
in Const (@{const_name rel_sum}, rel_sumT) $ R $ S end;
fun Inl_const LT RT = Const (@{const_name Inl}, LT --> mk_sumT (LT, RT));
fun mk_Inl RT t = Inl_const (fastype_of t) RT $ t;
fun Inr_const LT RT = Const (@{const_name Inr}, RT --> mk_sumT (LT, RT));
fun mk_Inr LT t = Inr_const LT (fastype_of t) $ t;
fun mk_prod1 bound_Ts (t, u) =
HOLogic.pair_const (fastype_of1 (bound_Ts, t)) (fastype_of1 (bound_Ts, u)) $ t $ u;
fun mk_tuple1_balanced _ [] = HOLogic.unit
| mk_tuple1_balanced bound_Ts ts = Balanced_Tree.make (mk_prod1 bound_Ts) ts;
val mk_tuple_balanced = mk_tuple1_balanced [];
fun abs_curried_balanced Ts t =
t $ mk_tuple1_balanced (List.rev Ts) (map Bound (length Ts - 1 downto 0))
|> fold_rev (Term.abs o pair Name.uu) Ts;
fun mk_sumprod_balanced T n k ts = Sum_Tree.mk_inj T n k (mk_tuple_balanced ts);
fun mk_absumprod absT abs0 n k ts =
let val abs = mk_abs absT abs0;
in abs $ mk_sumprod_balanced (domain_type (fastype_of abs)) n k ts end;
fun mk_case_sum (f, g) =
let
val (fT, T') = dest_funT (fastype_of f);
val (gT, _) = dest_funT (fastype_of g);
in
Sum_Tree.mk_sumcase fT gT T' f g
end;
val mk_case_sumN = Library.foldr1 mk_case_sum;
val mk_case_sumN_balanced = Balanced_Tree.make mk_case_sum;
fun mk_tupled_fun f x xs =
if xs = [x] then f else HOLogic.tupled_lambda x (Term.list_comb (f, xs));
fun mk_case_absumprod absT rep fs xss xss' =
HOLogic.mk_comp (mk_case_sumN_balanced
(@{map 3} mk_tupled_fun fs (map mk_tuple_balanced xss) xss'), mk_rep absT rep);
fun If_const T = Const (@{const_name If}, HOLogic.boolT --> T --> T --> T);
fun mk_If p t f = let val T = fastype_of t in If_const T $ p $ t $ f end;
fun mk_Field r =
let val T = fst (dest_relT (fastype_of r));
in Const (@{const_name Field}, mk_relT (T, T) --> HOLogic.mk_setT T) $ r end;
(*dangerous; use with monotonic, converging functions only!*)
fun fixpoint eq f X = if subset eq (f X, X) then X else fixpoint eq f (f X);
(* stolen from "~~/src/HOL/Tools/Datatype/datatype_aux.ML" *)
fun split_conj_thm th =
((th RS conjunct1) :: split_conj_thm (th RS conjunct2)) handle THM _ => [th];
fun split_conj_prems limit th =
let
fun split n i th =
if i = n then th else split n (i + 1) (conjI RSN (i, th)) handle THM _ => th;
in split limit 1 th end;
fun mk_obj_sumEN_balanced n =
Balanced_Tree.make (fn (thm1, thm2) => thm1 RSN (1, thm2 RSN (2, @{thm obj_sumE_f})))
(replicate n asm_rl);
fun mk_tupled_allIN_balanced 0 = @{thm unit_all_impI}
| mk_tupled_allIN_balanced n =
let
val (tfrees, _) = BNF_Util.mk_TFrees n @{context};
val T = mk_tupleT_balanced tfrees;
in
@{thm asm_rl[of "\<forall>x. P x \<longrightarrow> Q x" for P Q]}
|> Thm.instantiate' [SOME (Thm.ctyp_of @{context} T)] []
|> Raw_Simplifier.rewrite_goals_rule @{context} @{thms split_paired_All[THEN eq_reflection]}
|> (fn thm => impI RS funpow n (fn th => allI RS th) thm)
|> Thm.varifyT_global
end;
fun mk_absumprodE type_definition ms =
let val n = length ms in
mk_obj_sumEN_balanced n OF map mk_tupled_allIN_balanced ms RS
(type_definition RS @{thm type_copy_obj_one_point_absE})
end;
fun mk_sum_caseN 1 1 = refl
| mk_sum_caseN _ 1 = @{thm sum.case(1)}
| mk_sum_caseN 2 2 = @{thm sum.case(2)}
| mk_sum_caseN n k = trans OF [@{thm case_sum_step(2)}, mk_sum_caseN (n - 1) (k - 1)];
fun mk_sum_step base step thm =
if Thm.eq_thm_prop (thm, refl) then base else trans OF [step, thm];
fun mk_sum_caseN_balanced 1 1 = refl
| mk_sum_caseN_balanced n k =
Balanced_Tree.access {left = mk_sum_step @{thm sum.case(1)} @{thm case_sum_step(1)},
right = mk_sum_step @{thm sum.case(2)} @{thm case_sum_step(2)}, init = refl} n k;
fun mk_sum_Cinfinite [thm] = thm
| mk_sum_Cinfinite (thm :: thms) = @{thm Cinfinite_csum_weak} OF [thm, mk_sum_Cinfinite thms];
fun mk_sum_card_order [thm] = thm
| mk_sum_card_order (thm :: thms) = @{thm card_order_csum} OF [thm, mk_sum_card_order thms];
fun mk_xtor_rel_co_induct_thm fp pre_rels pre_phis rels phis xs ys xtors xtor's tac lthy =
let
val pre_relphis = map (fn rel => Term.list_comb (rel, phis @ pre_phis)) pre_rels;
val relphis = map (fn rel => Term.list_comb (rel, phis)) rels;
fun mk_xtor fp' xtor x = if fp = fp' then xtor $ x else x;
val dtor = mk_xtor Greatest_FP;
val ctor = mk_xtor Least_FP;
fun flip f x y = if fp = Greatest_FP then f y x else f x y;
fun mk_prem pre_relphi phi x y xtor xtor' =
HOLogic.mk_Trueprop (list_all_free [x, y] (flip (curry HOLogic.mk_imp)
(pre_relphi $ (dtor xtor x) $ (dtor xtor' y)) (phi $ (ctor xtor x) $ (ctor xtor' y))));
val prems = @{map 6} mk_prem pre_relphis pre_phis xs ys xtors xtor's;
val concl = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
(map2 (flip mk_leq) relphis pre_phis));
in
Goal.prove_sorry lthy (map (fst o dest_Free) (phis @ pre_phis)) prems concl tac
|> Thm.close_derivation
|> (fn thm => thm OF (replicate (length pre_rels) @{thm allI[OF allI[OF impI]]}))
end;
fun mk_xtor_co_iter_transfer_thms fp pre_rels pre_iphis pre_ophis rels phis un_folds un_folds' tac lthy =
let
val pre_relphis = map (fn rel => Term.list_comb (rel, phis @ pre_iphis)) pre_rels;
val relphis = map (fn rel => Term.list_comb (rel, phis)) rels;
fun flip f x y = if fp = Greatest_FP then f y x else f x y;
val arg_rels = map2 (flip mk_rel_fun) pre_relphis pre_ophis;
fun mk_transfer relphi pre_phi un_fold un_fold' =
fold_rev mk_rel_fun arg_rels (flip mk_rel_fun relphi pre_phi) $ un_fold $ un_fold';
val transfers = @{map 4} mk_transfer relphis pre_ophis un_folds un_folds';
val goal = fold_rev Logic.all (phis @ pre_ophis)
(HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj transfers));
in
Goal.prove_sorry lthy [] [] goal tac
|> Thm.close_derivation
|> split_conj_thm
end;
fun mk_xtor_co_iter_o_map_thms fp is_rec m un_fold_unique xtor_maps xtor_un_folds sym_map_comps
map_cong0s =
let
val n = length sym_map_comps;
val rewrite_comp_comp2 = case_fp fp @{thm rewriteR_comp_comp2} @{thm rewriteL_comp_comp2};
val rewrite_comp_comp = case_fp fp @{thm rewriteR_comp_comp} @{thm rewriteL_comp_comp};
val map_cong_passive_args1 = replicate m (case_fp fp @{thm id_comp} @{thm comp_id} RS fun_cong);
val map_cong_active_args1 = replicate n (if is_rec
then case_fp fp @{thm convol_o} @{thm o_case_sum} RS fun_cong
else refl);
val map_cong_passive_args2 = replicate m (case_fp fp @{thm comp_id} @{thm id_comp} RS fun_cong);
val map_cong_active_args2 = replicate n (if is_rec
then case_fp fp @{thm map_prod_o_convol_id} @{thm case_sum_o_map_sum_id}
else case_fp fp @{thm id_comp} @{thm comp_id} RS fun_cong);
fun mk_map_congs passive active =
map (fn thm => thm OF (passive @ active) RS @{thm ext}) map_cong0s;
val map_cong1s = mk_map_congs map_cong_passive_args1 map_cong_active_args1;
val map_cong2s = mk_map_congs map_cong_passive_args2 map_cong_active_args2;
fun mk_rewrites map_congs = map2 (fn sym_map_comp => fn map_cong =>
mk_trans sym_map_comp map_cong RS rewrite_comp_comp) sym_map_comps map_congs;
val rewrite1s = mk_rewrites map_cong1s;
val rewrite2s = mk_rewrites map_cong2s;
val unique_prems =
@{map 4} (fn xtor_map => fn un_fold => fn rewrite1 => fn rewrite2 =>
mk_trans (rewrite_comp_comp2 OF [xtor_map, un_fold])
(mk_trans rewrite1 (mk_sym rewrite2)))
xtor_maps xtor_un_folds rewrite1s rewrite2s;
in
split_conj_thm (un_fold_unique OF map (case_fp fp I mk_sym) unique_prems)
end;
fun force_typ ctxt T =
Term.map_types Type_Infer.paramify_vars
#> Type.constraint T
#> Syntax.check_term ctxt
#> singleton (Variable.polymorphic ctxt);
fun absT_info_encodeT thy (SOME (src : absT_info, dst : absT_info)) src_absT =
let
val src_repT = mk_repT (#absT src) (#repT src) src_absT;
val dst_absT = mk_absT thy (#repT dst) (#absT dst) src_repT;
in
dst_absT
end
| absT_info_encodeT _ NONE T = T;
fun absT_info_decodeT thy = absT_info_encodeT thy o Option.map swap;
fun absT_info_encode thy fp (opt as SOME (src : absT_info, dst : absT_info)) t =
let
val co_alg_funT = case_fp fp domain_type range_type;
fun co_swap pair = case_fp fp I swap pair;
val mk_co_comp = curry (HOLogic.mk_comp o co_swap);
val mk_co_abs = case_fp fp mk_abs mk_rep;
val mk_co_rep = case_fp fp mk_rep mk_abs;
val co_abs = case_fp fp #abs #rep;
val co_rep = case_fp fp #rep #abs;
val src_absT = co_alg_funT (fastype_of t);
val dst_absT = absT_info_encodeT thy opt src_absT;
val co_src_abs = mk_co_abs src_absT (co_abs src);
val co_dst_rep = mk_co_rep dst_absT (co_rep dst);
in
mk_co_comp (mk_co_comp t co_src_abs) co_dst_rep
end
| absT_info_encode _ _ NONE t = t;
fun absT_info_decode thy fp = absT_info_encode thy fp o Option.map swap;
fun mk_xtor_un_fold_xtor_thms ctxt fp un_folds xtors xtor_un_fold_unique map_id0s
absT_info_opts =
let
val thy = Proof_Context.theory_of ctxt;
fun mk_goal un_fold =
let
val rhs = list_comb (un_fold, @{map 2} (absT_info_encode thy fp) absT_info_opts xtors);
val T = range_type (fastype_of rhs);
in
HOLogic.mk_eq (HOLogic.id_const T, rhs)
end;
val goal = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map mk_goal un_folds));
fun mk_inverses NONE = []
| mk_inverses (SOME (src, dst)) =
[#type_definition dst RS @{thm type_definition.Abs_inverse[OF _ UNIV_I]},
#type_definition src RS @{thm type_definition.Rep_inverse}];
val inverses = maps mk_inverses absT_info_opts;
in
Goal.prove_sorry ctxt [] [] goal (fn {context = ctxt, prems = _} =>
mk_xtor_un_fold_xtor_tac ctxt xtor_un_fold_unique map_id0s inverses)
|> split_conj_thm |> map mk_sym
end;
fun derive_xtor_co_recs fp bs mk_Ts (Dss, resDs) pre_bnfs xtors0 un_folds0
xtor_un_fold_unique xtor_un_folds xtor_un_fold_transfers xtor_maps xtor_rels
absT_info_opts lthy =
let
val thy = Proof_Context.theory_of lthy;
fun co_swap pair = case_fp fp I swap pair;
val mk_co_comp = curry (HOLogic.mk_comp o co_swap);
fun mk_co_algT T U = case_fp fp (T --> U) (U --> T);
val co_alg_funT = case_fp fp domain_type range_type;
val mk_co_product = curry (case_fp fp mk_convol mk_case_sum);
val co_proj1_const = case_fp fp fst_const (uncurry Inl_const o dest_sumT) o co_alg_funT;
val co_proj2_const = case_fp fp snd_const (uncurry Inr_const o dest_sumT) o co_alg_funT;
val mk_co_productT = curry (case_fp fp HOLogic.mk_prodT mk_sumT);
val rewrite_comp_comp = case_fp fp @{thm rewriteL_comp_comp} @{thm rewriteR_comp_comp};
val n = length pre_bnfs;
val live = live_of_bnf (hd pre_bnfs);
val m = live - n;
val ks = 1 upto n;
val map_id0s = map map_id0_of_bnf pre_bnfs;
val map_comps = map map_comp_of_bnf pre_bnfs;
val map_cong0s = map map_cong0_of_bnf pre_bnfs;
val map_transfers = map map_transfer_of_bnf pre_bnfs;
val sym_map_comp0s = map (mk_sym o map_comp0_of_bnf) pre_bnfs;
val deads = fold (union (op =)) Dss resDs;
val ((((As, Bs), Xs), Ys), names_lthy) = lthy
|> fold Variable.declare_typ deads
|> mk_TFrees m
||>> mk_TFrees m
||>> mk_TFrees n
||>> mk_TFrees n;
val XFTs = @{map 2} (fn Ds => mk_T_of_bnf Ds (As @ Xs)) Dss pre_bnfs;
val co_algXFTs = @{map 2} mk_co_algT XFTs Xs;
val Ts = mk_Ts As;
val un_foldTs = @{map 2} (fn T => fn X => co_algXFTs ---> mk_co_algT T X) Ts Xs;
val un_folds = @{map 2} (force_typ names_lthy) un_foldTs un_folds0;
val ABs = As ~~ Bs;
val XYs = Xs ~~ Ys;
val Us = map (typ_subst_atomic ABs) Ts;
val TFTs = @{map 2} (fn Ds => mk_T_of_bnf Ds (As @ Ts)) Dss pre_bnfs;
val TFTs' = @{map 2} (absT_info_decodeT thy) absT_info_opts TFTs;
val xtors = @{map 3} (force_typ names_lthy oo mk_co_algT) TFTs' Ts xtors0;
val ids = map HOLogic.id_const As;
val co_rec_Xs = @{map 2} mk_co_productT Ts Xs;
val co_rec_Ys = @{map 2} mk_co_productT Us Ys;
val co_rec_algXs = @{map 2} mk_co_algT co_rec_Xs Xs;
val co_proj1s = map co_proj1_const co_rec_algXs;
val co_rec_maps = @{map 2} (fn Ds =>
mk_map_of_bnf Ds (As @ case_fp fp co_rec_Xs Ts) (As @ case_fp fp Ts co_rec_Xs)) Dss pre_bnfs;
val co_rec_Ts = @{map 2} (fn Ds => mk_T_of_bnf Ds (As @ co_rec_Xs)) Dss pre_bnfs
val co_rec_argTs = @{map 2} mk_co_algT co_rec_Ts Xs;
val co_rec_resTs = @{map 2} mk_co_algT Ts Xs;
val (((co_rec_ss, fs), xs), names_lthy) = names_lthy
|> mk_Frees "s" co_rec_argTs
||>> mk_Frees "f" co_rec_resTs
||>> mk_Frees "x" (case_fp fp TFTs' Xs);
val co_rec_strs =
@{map 4} (fn xtor => fn s => fn mapx => fn absT_info_opt =>
mk_co_product (mk_co_comp (absT_info_encode thy fp absT_info_opt xtor)
(list_comb (mapx, ids @ co_proj1s))) s)
xtors co_rec_ss co_rec_maps absT_info_opts;
val theta = Xs ~~ co_rec_Xs;
val co_rec_un_folds = map (subst_atomic_types theta) un_folds;
val co_rec_spec0s = map (fn un_fold => list_comb (un_fold, co_rec_strs)) co_rec_un_folds;
val co_rec_ids = @{map 2} (mk_co_comp o co_proj1_const) co_rec_algXs co_rec_spec0s;
val co_rec_specs = @{map 2} (mk_co_comp o co_proj2_const) co_rec_algXs co_rec_spec0s;
val co_recN = case_fp fp ctor_recN dtor_corecN;
fun co_rec_bind i = nth bs (i - 1) |> Binding.prefix_name (co_recN ^ "_");
val co_rec_def_bind = rpair [] o Binding.concealed o Thm.def_binding o co_rec_bind;
fun co_rec_spec i =
fold_rev (Term.absfree o Term.dest_Free) co_rec_ss (nth co_rec_specs (i - 1));
val ((co_rec_frees, (_, co_rec_def_frees)), (lthy, lthy_old)) =
lthy
|> Local_Theory.open_target |> snd
|> fold_map (fn i =>
Local_Theory.define ((co_rec_bind i, NoSyn), (co_rec_def_bind i, co_rec_spec i))) ks
|>> apsnd split_list o split_list
||> `Local_Theory.close_target;
val phi = Proof_Context.export_morphism lthy_old lthy;
val co_rec_names = map (fst o dest_Const o Morphism.term phi) co_rec_frees;
val co_recs = @{map 2} (fn name => fn resT =>
Const (name, co_rec_argTs ---> resT)) co_rec_names co_rec_resTs;
val co_rec_defs = map (fn def =>
mk_unabs_def n (HOLogic.mk_obj_eq (Morphism.thm phi def))) co_rec_def_frees;
val xtor_un_fold_xtor_thms =
mk_xtor_un_fold_xtor_thms lthy fp (map (Term.subst_atomic_types (Xs ~~ Ts)) un_folds)
xtors xtor_un_fold_unique map_id0s absT_info_opts;
val co_rec_id_thms =
let
val goal = @{map 2} (fn T => fn t => HOLogic.mk_eq (t, HOLogic.id_const T)) Ts co_rec_ids
|> Library.foldr1 HOLogic.mk_conj |> HOLogic.mk_Trueprop;
val vars = Variable.add_free_names lthy goal [];
in
Goal.prove_sorry lthy vars [] goal
(fn {context = ctxt, prems = _} => mk_xtor_co_rec_id_tac ctxt xtor_un_fold_xtor_thms
xtor_un_fold_unique xtor_un_folds map_comps)
|> Thm.close_derivation
|> split_conj_thm
end;
val co_rec_app_ss = map (fn co_rec => list_comb (co_rec, co_rec_ss)) co_recs;
val co_products = @{map 2} (fn T => mk_co_product (HOLogic.id_const T)) Ts co_rec_app_ss;
val co_rec_maps_rev = @{map 2} (fn Ds =>
mk_map_of_bnf Ds (As @ case_fp fp Ts co_rec_Xs) (As @ case_fp fp co_rec_Xs Ts)) Dss pre_bnfs;
fun mk_co_app f g x = case_fp fp (f $ (g $ x)) (g $ (f $ x));
val co_rec_expand_thms = map (fn thm => thm RS
case_fp fp @{thm convol_expand_snd} @{thm case_sum_expand_Inr_pointfree}) co_rec_id_thms;
val xtor_co_rec_thms =
let
fun mk_goal co_rec s mapx xtor x absT_info_opt =
let
val lhs = mk_co_app co_rec xtor x;
val rhs = mk_co_app s
(list_comb (mapx, ids @ co_products) |> absT_info_decode thy fp absT_info_opt) x;
in
mk_Trueprop_eq (lhs, rhs)
end;
val goals =
@{map 6} mk_goal co_rec_app_ss co_rec_ss co_rec_maps_rev xtors xs absT_info_opts;
in
map2 (fn goal => fn un_fold =>
Variable.add_free_names lthy goal []
|> (fn vars => Goal.prove_sorry lthy vars [] goal
(fn {context = ctxt, prems = _} =>
mk_xtor_co_rec_tac ctxt un_fold co_rec_defs co_rec_expand_thms))
|> Thm.close_derivation)
goals xtor_un_folds
end;
val co_product_fs = @{map 2} (fn T => mk_co_product (HOLogic.id_const T)) Ts fs;
val co_rec_expand'_thms = map (fn thm =>
thm RS case_fp fp @{thm convol_expand_snd'} @{thm case_sum_expand_Inr'}) co_rec_id_thms;
val xtor_co_rec_unique_thm =
let
fun mk_prem f s mapx xtor absT_info_opt =
let
val lhs = mk_co_comp f xtor;
val rhs = mk_co_comp s (list_comb (mapx, ids @ co_product_fs))
|> absT_info_decode thy fp absT_info_opt;
in
mk_Trueprop_eq (co_swap (lhs, rhs))
end;
val prems = @{map 5} mk_prem fs co_rec_ss co_rec_maps_rev xtors absT_info_opts;
val concl = @{map 2} (curry HOLogic.mk_eq) fs co_rec_app_ss
|> Library.foldr1 HOLogic.mk_conj |> HOLogic.mk_Trueprop;
val goal = Logic.list_implies (prems, concl);
val vars = Variable.add_free_names lthy goal [];
fun mk_inverses NONE = []
| mk_inverses (SOME (src, dst)) =
[#type_definition dst RS @{thm type_copy_Rep_o_Abs} RS rewrite_comp_comp,
#type_definition src RS @{thm type_copy_Abs_o_Rep}];
val inverses = maps mk_inverses absT_info_opts;
in
Goal.prove_sorry lthy vars [] goal
(fn {context = ctxt, prems = _} => mk_xtor_co_rec_unique_tac ctxt fp co_rec_defs
co_rec_expand'_thms xtor_un_fold_unique map_id0s sym_map_comp0s inverses)
|> Thm.close_derivation
end;
val xtor_co_rec_o_map_thms = if forall is_none absT_info_opts
then
mk_xtor_co_iter_o_map_thms fp true m xtor_co_rec_unique_thm
(map (mk_pointfree2 lthy) xtor_maps) (map (mk_pointfree2 lthy) xtor_co_rec_thms)
sym_map_comp0s map_cong0s
else
replicate n refl (* FIXME *);
val ABphiTs = @{map 2} mk_pred2T As Bs;
val XYphiTs = @{map 2} mk_pred2T Xs Ys;
val ((ABphis, XYphis), names_lthy) = names_lthy
|> mk_Frees "R" ABphiTs
||>> mk_Frees "S" XYphiTs;
val xtor_co_rec_transfer_thms = if forall is_none absT_info_opts
then
let
val pre_rels =
@{map 2} (fn Ds => mk_rel_of_bnf Ds (As @ co_rec_Xs) (Bs @ co_rec_Ys)) Dss pre_bnfs;
val rels = @{map 3} (fn T => fn T' => Thm.prop_of #> HOLogic.dest_Trueprop
#> fst o dest_comb #> fst o dest_comb #> funpow n (snd o dest_comb)
#> case_fp fp (fst o dest_comb #> snd o dest_comb) (snd o dest_comb) #> head_of
#> force_typ names_lthy (ABphiTs ---> mk_pred2T T T'))
Ts Us xtor_un_fold_transfers;
fun tac {context = ctxt, prems = _} = mk_xtor_co_rec_transfer_tac ctxt fp n m co_rec_defs
xtor_un_fold_transfers map_transfers xtor_rels;
val mk_rel_co_product = case_fp fp mk_rel_prod mk_rel_sum;
val rec_phis =
map2 (fn rel => mk_rel_co_product (Term.list_comb (rel, ABphis))) rels XYphis;
in
mk_xtor_co_iter_transfer_thms fp pre_rels rec_phis XYphis rels ABphis
co_recs (map (subst_atomic_types (ABs @ XYs)) co_recs) tac lthy
end
else
replicate n TrueI (* FIXME *);
val notes =
[(case_fp fp ctor_recN dtor_corecN, xtor_co_rec_thms),
(case_fp fp ctor_rec_uniqueN dtor_corec_uniqueN, split_conj_thm xtor_co_rec_unique_thm),
(case_fp fp ctor_rec_o_mapN dtor_corec_o_mapN, xtor_co_rec_o_map_thms),
(case_fp fp ctor_rec_transferN dtor_corec_transferN, xtor_co_rec_transfer_thms)]
|> map (apsnd (map single))
|> maps (fn (thmN, thmss) =>
map2 (fn b => fn thms =>
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
bs thmss);
val lthy = lthy |> Config.get lthy bnf_internals ? snd o Local_Theory.notes notes;
in
((co_recs,
(xtor_co_rec_thms, xtor_co_rec_unique_thm, xtor_co_rec_o_map_thms, xtor_co_rec_transfer_thms)),
lthy)
end;
fun raw_qualify extra_qualify base_b =
let
val qs = Binding.path_of base_b;
val n = Binding.name_of base_b;
in
Binding.prefix_name rawN
#> fold_rev (fn (s, mand) => Binding.qualify mand s) (qs @ [(n, true)])
#> extra_qualify #> Binding.concealed
end;
fun fixpoint_bnf force_out_of_line extra_qualify construct_fp bs resBs Ds0 Xs rhsXs comp_cache0
lthy =
let
val time = time lthy;
val timer = time (Timer.startRealTimer ());
fun flatten_tyargs Ass =
subtract (op =) Xs (filter (fn T => exists (fn Ts => member (op =) Ts T) Ass) resBs) @ Xs;
val ((bnfs, (deadss, livess)), (comp_cache_unfold_set, lthy')) =
apfst (apsnd split_list o split_list)
(@{fold_map 2}
(fn b => bnf_of_typ true Smart_Inline (raw_qualify extra_qualify b) flatten_tyargs Xs Ds0)
bs rhsXs ((comp_cache0, empty_unfolds), lthy));
fun norm_qualify i =
Binding.qualify true (Binding.name_of (nth bs (Int.max (0, i - 1))))
#> extra_qualify #> Binding.concealed;
val Ass = map (map dest_TFree) livess;
val Ds' = fold (fold Term.add_tfreesT) deadss [];
val Ds = union (op =) Ds' Ds0;
val missing = resBs |> fold (subtract (op =)) (Ds' :: Ass);
val (dead_phantoms, live_phantoms) = List.partition (member (op =) Ds0) missing;
val resBs' = resBs |> fold (subtract (op =)) [dead_phantoms, Ds];
val timer = time (timer "Construction of BNFs");
val ((kill_posss, _), (bnfs', ((comp_cache', unfold_set'), lthy''))) =
normalize_bnfs norm_qualify Ass Ds (K (resBs' @ Xs)) bnfs (comp_cache_unfold_set, lthy');
val Dss = @{map 3} (fn lives => fn kill_posss => fn deads => deads @ map (nth lives) kill_posss)
livess kill_posss deadss;
val all_Dss = Dss |> force_out_of_line ? map (fn Ds' => union (op =) Ds' (map TFree Ds0));
fun pre_qualify b =
Binding.qualify false (Binding.name_of b)
#> extra_qualify
#> not (Config.get lthy'' bnf_internals) ? Binding.concealed;
val ((pre_bnfs, (deadss, absT_infos)), lthy''') = lthy''
|> @{fold_map 5} (fn b => seal_bnf (pre_qualify b) unfold_set' (Binding.prefix_name preN b))
bs (replicate (length rhsXs) (force_out_of_line orelse not (null live_phantoms))) Dss
all_Dss bnfs'
|>> split_list
|>> apsnd split_list;
val timer = time (timer "Normalization & sealing of BNFs");
val res = construct_fp bs resBs (map TFree dead_phantoms, deadss) pre_bnfs absT_infos lthy''';
val timer = time (timer "FP construction in total");
in
(((pre_bnfs, absT_infos), comp_cache'), res)
end;
fun fp_antiquote_setup binding =
Thy_Output.antiquotation_pretty_source_embedded binding
(Args.type_name {proper = true, strict = true})
(fn ctxt => fn fcT_name =>
(case Ctr_Sugar.ctr_sugar_of ctxt fcT_name of
NONE => error ("Not a known freely generated type name: " ^ quote fcT_name)
| SOME {T = T0, ctrs = ctrs0, ...} =>
let
val freezeT = Term.map_atyps (fn TVar ((s, _), S) => TFree (s, S) | T => T);
val T = freezeT T0;
val ctrs = map (Term.map_types freezeT) ctrs0;
val pretty_typ_bracket = Syntax.pretty_typ (Config.put pretty_priority 1001 ctxt);
fun pretty_ctr ctr =
Pretty.block (Pretty.breaks (Syntax.pretty_term ctxt ctr ::
map pretty_typ_bracket (binder_types (fastype_of ctr))));
in
Pretty.block (Pretty.keyword1 (Binding.name_of binding) :: Pretty.brk 1 ::
Syntax.pretty_typ ctxt T :: Pretty.str " =" :: Pretty.brk 1 ::
flat (separate [Pretty.brk 1, Pretty.str "| "] (map (single o pretty_ctr) ctrs)))
end));
end;