(* Title: HOL/BNF/Tools/bnf_fp_util.ML
Author: Dmitriy Traytel, TU Muenchen
Author: Jasmin Blanchette, TU Muenchen
Copyright 2012, 2013
Shared library for the datatype and codatatype constructions.
*)
signature BNF_FP_UTIL =
sig
type fp_result =
{Ts: typ list,
bnfs: BNF_Def.bnf list,
ctors: term list,
dtors: term list,
un_folds: term list,
co_recs: term list,
co_induct: thm,
strong_co_induct: thm,
dtor_ctors: thm list,
ctor_dtors: thm list,
ctor_injects: thm list,
map_thms: thm list,
set_thmss: thm list list,
rel_thms: thm list,
un_fold_thms: thm list,
co_rec_thms: thm list}
val morph_fp_result: morphism -> fp_result -> fp_result
val eq_fp_result: fp_result * fp_result -> bool
val time: Timer.real_timer -> string -> Timer.real_timer
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 corecN: string
val ctorN: string
val ctor_dtorN: string
val ctor_dtor_corecN: string
val ctor_dtor_unfoldN: string
val ctor_exhaustN: string
val ctor_induct2N: string
val ctor_inductN: string
val ctor_injectN: string
val ctor_foldN: string
val ctor_fold_uniqueN: string
val ctor_mapN: string
val ctor_map_uniqueN: string
val ctor_recN: string
val ctor_rec_uniqueN: string
val ctor_relN: string
val ctor_set_inclN: string
val ctor_set_set_inclN: string
val disc_unfoldN: string
val disc_unfold_iffN: string
val disc_corecN: string
val disc_corec_iffN: string
val dtorN: string
val dtor_coinductN: string
val dtor_corecN: 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_strong_coinductN: string
val dtor_map_uniqueN: string
val dtor_relN: string
val dtor_set_inclN: string
val dtor_set_set_inclN: string
val dtor_strong_coinductN: string
val dtor_unfoldN: string
val dtor_unfold_uniqueN: string
val exhaustN: string
val foldN: string
val hsetN: string
val hset_recN: 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_coinductN: string
val rel_inductN: string
val rel_injectN: string
val rel_distinctN: string
val rvN: string
val sel_corecN: string
val set_inclN: string
val set_set_inclN: string
val sel_unfoldN: string
val setsN: string
val simpsN: string
val strTN: string
val str_initN: string
val strong_coinductN: string
val sum_bdN: string
val sum_bdTN: string
val unfoldN: 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 datatype_word: bool -> string
val base_name_of_typ: typ -> string
val mk_common_name: string list -> string
val variant_types: string list -> sort list -> Proof.context ->
(string * sort) list * Proof.context
val variant_tfrees: string list -> Proof.context -> typ list * Proof.context
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 id_const: typ -> term
val Inl_const: typ -> typ -> term
val Inr_const: typ -> typ -> term
val mk_Inl: typ -> term -> term
val mk_Inr: typ -> term -> term
val mk_InN: typ list -> term -> int -> term
val mk_InN_balanced: typ -> int -> term -> int -> term
val mk_sum_case: term * term -> term
val mk_sum_caseN: term list -> term
val mk_sum_caseN_balanced: term list -> term
val dest_sumT: typ -> typ * typ
val dest_sumTN: int -> typ -> typ list
val dest_sumTN_balanced: int -> typ -> typ list
val dest_tupleT: int -> typ -> typ list
val mk_Field: term -> term
val mk_If: term -> term -> term -> term
val mk_union: term * term -> term
val mk_sumEN: int -> thm
val mk_sumEN_balanced: int -> thm
val mk_sumEN_tupled_balanced: int list -> thm
val mk_sum_casesN: int -> int -> thm
val mk_sum_casesN_balanced: int -> int -> thm
val fixpoint: ('a * 'a -> bool) -> ('a list -> 'a list) -> 'a list -> 'a list
val fp_bnf: (binding list -> (string * sort) list -> typ list * typ list list ->
BNF_Def.bnf list -> local_theory -> 'a) ->
binding list -> (string * sort) list -> ((string * sort) * typ) list -> local_theory ->
BNF_Def.bnf list * 'a
end;
structure BNF_FP_Util : BNF_FP_UTIL =
struct
open BNF_Comp
open BNF_Def
open BNF_Util
type fp_result =
{Ts: typ list,
bnfs: BNF_Def.bnf list,
ctors: term list,
dtors: term list,
un_folds: term list,
co_recs: term list,
co_induct: thm,
strong_co_induct: thm,
dtor_ctors: thm list,
ctor_dtors: thm list,
ctor_injects: thm list,
map_thms: thm list,
set_thmss: thm list list,
rel_thms: thm list,
un_fold_thms: thm list,
co_rec_thms: thm list};
fun morph_fp_result phi {Ts, bnfs, ctors, dtors, un_folds, co_recs, co_induct, strong_co_induct,
dtor_ctors, ctor_dtors, ctor_injects, map_thms, set_thmss, rel_thms, un_fold_thms,
co_rec_thms} =
{Ts = map (Morphism.typ phi) Ts,
bnfs = map (morph_bnf phi) bnfs,
ctors = map (Morphism.term phi) ctors,
dtors = map (Morphism.term phi) dtors,
un_folds = map (Morphism.term phi) un_folds,
co_recs = map (Morphism.term phi) co_recs,
co_induct = Morphism.thm phi co_induct,
strong_co_induct = Morphism.thm phi strong_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,
map_thms = map (Morphism.thm phi) map_thms,
set_thmss = map (map (Morphism.thm phi)) set_thmss,
rel_thms = map (Morphism.thm phi) rel_thms,
un_fold_thms = map (Morphism.thm phi) un_fold_thms,
co_rec_thms = map (Morphism.thm phi) co_rec_thms};
fun eq_fp_result ({bnfs = bnfs1, ...} : fp_result, {bnfs = bnfs2, ...} : fp_result) =
eq_list eq_bnf (bnfs1, bnfs2);
val timing = true;
fun time timer msg = (if timing
then warning (msg ^ ": " ^ ATP_Util.string_of_time (Timer.checkRealTimer timer))
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 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 dtor_unfold_uniqueN = dtor_unfoldN ^ uniqueN
val ctor_dtor_unfoldN = ctorN ^ "_" ^ dtor_unfoldN
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 setsN = "sets"
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_uniqueN = ctor_recN ^ uniqueN
val dtor_corecN = dtorN ^ "_" ^ corecN
val dtor_corec_uniqueN = dtor_corecN ^ uniqueN
val ctor_dtor_corecN = ctorN ^ "_" ^ dtor_corecN
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 strong_coinductN = "strong_" ^ coinductN
val dtor_map_strong_coinductN = dtor_mapN ^ "_" ^ strong_coinductN
val dtor_strong_coinductN = dtorN ^ "_" ^ strong_coinductN
val hsetN = "Hset"
val hset_recN = hsetN ^ "_rec"
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 disc_unfoldN = discN ^ "_" ^ unfoldN
val disc_corecN = discN ^ "_" ^ corecN
val iffN = "_iff"
val disc_unfold_iffN = discN ^ "_" ^ unfoldN ^ iffN
val disc_corec_iffN = discN ^ "_" ^ corecN ^ iffN
val distinctN = "distinct"
val rel_distinctN = relN ^ "_" ^ distinctN
val injectN = "inject"
val rel_injectN = relN ^ "_" ^ injectN
val rel_coinductN = relN ^ "_" ^ coinductN
val rel_inductN = relN ^ "_" ^ inductN
val selN = "sel"
val sel_unfoldN = selN ^ "_" ^ unfoldN
val sel_corecN = selN ^ "_" ^ corecN
fun datatype_word lfp = (if lfp then "" else "co") ^ "datatype";
fun add_components_of_typ (Type (s, Ts)) =
fold add_components_of_typ Ts #> cons (Long_Name.base_name s)
| add_components_of_typ _ = I;
fun base_name_of_typ T = space_implode "_" (add_components_of_typ T []);
val mk_common_name = space_implode "_";
fun dest_sumT (Type (@{type_name sum}, [T, T'])) = (T, T');
fun dest_sumTN 1 T = [T]
| dest_sumTN n (Type (@{type_name sum}, [T, T'])) = T :: dest_sumTN (n - 1) T';
val dest_sumTN_balanced = Balanced_Tree.dest dest_sumT;
(* TODO: move something like this to "HOLogic"? *)
fun dest_tupleT 0 @{typ unit} = []
| dest_tupleT 1 T = [T]
| dest_tupleT n (Type (@{type_name prod}, [T, T'])) = T :: dest_tupleT (n - 1) T';
val mk_sumTN = Library.foldr1 mk_sumT;
val mk_sumTN_balanced = Balanced_Tree.make mk_sumT;
fun id_const T = Const (@{const_name id}, T --> T);
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_InN [_] t 1 = t
| mk_InN (_ :: Ts) t 1 = mk_Inl (mk_sumTN Ts) t
| mk_InN (LT :: Ts) t m = mk_Inr LT (mk_InN Ts t (m - 1))
| mk_InN Ts t _ = raise (TYPE ("mk_InN", Ts, [t]));
fun mk_InN_balanced sum_T n t k =
let
fun repair_types T (Const (s as @{const_name Inl}, _) $ t) = repair_inj_types T s fst t
| repair_types T (Const (s as @{const_name Inr}, _) $ t) = repair_inj_types T s snd t
| repair_types _ t = t
and repair_inj_types T s get t =
let val T' = get (dest_sumT T) in
Const (s, T' --> T) $ repair_types T' t
end;
in
Balanced_Tree.access {left = mk_Inl dummyT, right = mk_Inr dummyT, init = t} n k
|> repair_types sum_T
end;
fun mk_sum_case (f, g) =
let
val fT = fastype_of f;
val gT = fastype_of g;
in
Const (@{const_name sum_case},
fT --> gT --> mk_sumT (domain_type fT, domain_type gT) --> range_type fT) $ f $ g
end;
val mk_sum_caseN = Library.foldr1 mk_sum_case;
val mk_sum_caseN_balanced = Balanced_Tree.make mk_sum_case;
fun mk_If p t f =
let val T = fastype_of t;
in Const (@{const_name If}, HOLogic.boolT --> T --> T --> 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;
val mk_union = HOLogic.mk_binop @{const_name sup};
(*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);
fun variant_types ss Ss ctxt =
let
val (tfrees, _) =
fold_map2 (fn s => fn S => Name.variant s #> apfst (rpair S)) ss Ss (Variable.names_of ctxt);
val ctxt' = fold (Variable.declare_constraints o Logic.mk_type o TFree) tfrees ctxt;
in (tfrees, ctxt') end;
fun variant_tfrees ss =
apfst (map TFree) o variant_types (map (prefix "'") ss) (replicate (length ss) HOLogic.typeS);
(* 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_sumEN 1 = @{thm one_pointE}
| mk_sumEN 2 = @{thm sumE}
| mk_sumEN n =
(fold (fn i => fn thm => @{thm obj_sum_step} RSN (i, thm)) (2 upto n - 1) @{thm obj_sumE}) OF
replicate n (impI RS allI);
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_sumEN_balanced' n all_impIs = mk_obj_sumEN_balanced n OF all_impIs RS @{thm obj_one_pointE};
fun mk_sumEN_balanced 1 = @{thm one_pointE} (*optimization*)
| mk_sumEN_balanced 2 = @{thm sumE} (*optimization*)
| mk_sumEN_balanced n = mk_sumEN_balanced' n (replicate n (impI RS allI));
fun mk_tupled_allIN 0 = @{thm unit_all_impI}
| mk_tupled_allIN 1 = @{thm impI[THEN allI]}
| mk_tupled_allIN 2 = @{thm prod_all_impI} (*optimization*)
| mk_tupled_allIN n = mk_tupled_allIN (n - 1) RS @{thm prod_all_impI_step};
fun mk_sumEN_tupled_balanced ms =
let val n = length ms in
if forall (curry (op =) 1) ms then mk_sumEN_balanced n
else mk_sumEN_balanced' n (map mk_tupled_allIN ms)
end;
fun mk_sum_casesN 1 1 = refl
| mk_sum_casesN _ 1 = @{thm sum.cases(1)}
| mk_sum_casesN 2 2 = @{thm sum.cases(2)}
| mk_sum_casesN n k = trans OF [@{thm sum_case_step(2)}, mk_sum_casesN (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_casesN_balanced 1 1 = refl
| mk_sum_casesN_balanced n k =
Balanced_Tree.access {left = mk_sum_step @{thm sum.cases(1)} @{thm sum_case_step(1)},
right = mk_sum_step @{thm sum.cases(2)} @{thm sum_case_step(2)}, init = refl} n k;
fun fp_bnf construct_fp bs resBs eqs lthy =
let
val timer = time (Timer.startRealTimer ());
val (lhss, rhss) = split_list eqs;
(* FIXME: because of "@ lhss", the output could contain type variables that are not in the
input; also, "fp_sort" should put the "resBs" first and in the order in which they appear *)
fun fp_sort Ass =
subtract (op =) lhss (filter (fn T => exists (fn Ts => member (op =) Ts T) Ass) resBs) @ lhss;
fun raw_qualify b = Binding.qualify true (Binding.name_of (Binding.prefix_name rawN b));
val ((bnfs, (deadss, livess)), (unfold_set, lthy)) = apfst (apsnd split_list o split_list)
(fold_map2 (fn b => bnf_of_typ Smart_Inline (raw_qualify b) fp_sort) bs rhss
(empty_unfolds, lthy));
val name = mk_common_name (map Binding.name_of bs);
fun qualify i =
let val namei = name ^ nonzero_string_of_int i;
in Binding.qualify true namei end;
val Ass = map (map dest_TFree) livess;
val resDs = fold (subtract (op =)) Ass resBs;
val Ds = fold (fold Term.add_tfreesT) deadss [];
val _ = (case Library.inter (op =) Ds lhss of [] => ()
| A :: _ => error ("Inadmissible type recursion (cannot take fixed point of dead type \
\variable " ^ quote (Syntax.string_of_typ lthy (TFree A)) ^ ")"));
val timer = time (timer "Construction of BNFs");
val ((kill_poss, _), (bnfs', (unfold_set', lthy'))) =
normalize_bnfs qualify Ass Ds fp_sort bnfs unfold_set lthy;
val Dss = map3 (append oo map o nth) livess kill_poss deadss;
val ((pre_bnfs, deadss), lthy'') =
fold_map3 (seal_bnf unfold_set') (map (Binding.prefix_name preN) bs) Dss bnfs' lthy'
|>> split_list;
val timer = time (timer "Normalization & sealing of BNFs");
val res = construct_fp bs resBs (map TFree resDs, deadss) pre_bnfs lthy'';
val timer = time (timer "FP construction in total");
in
timer; (pre_bnfs, res)
end;
end;