--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/BNF/Tools/bnf_fp.ML Fri Sep 21 16:45:06 2012 +0200
@@ -0,0 +1,442 @@
+(* Title: HOL/BNF/Tools/bnf_fp.ML
+ Author: Dmitriy Traytel, TU Muenchen
+ Copyright 2012
+
+Shared library for the datatype and codatatype constructions.
+*)
+
+signature BNF_FP =
+sig
+ 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 corecsN: string
+ val ctorN: string
+ val ctor_dtorN: string
+ val ctor_dtor_unfoldsN: string
+ val ctor_dtor_corecsN: 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_foldsN: string
+ val ctor_recN: string
+ val ctor_recsN: string
+ val disc_unfold_iffN: string
+ val disc_unfoldsN: string
+ val disc_corec_iffN: string
+ val disc_corecsN: string
+ val dtorN: string
+ val dtor_coinductN: string
+ val dtor_unfoldN: string
+ val dtor_unfold_uniqueN: string
+ val dtor_unfoldsN: string
+ val dtor_corecN: string
+ val dtor_corecsN: string
+ val dtor_exhaustN: string
+ val dtor_ctorN: string
+ val dtor_injectN: string
+ val dtor_strong_coinductN: string
+ val exhaustN: string
+ val foldN: string
+ val foldsN: string
+ val hsetN: string
+ val hset_recN: string
+ val inductN: string
+ val injectN: string
+ val isNodeN: string
+ val lsbisN: string
+ val map_simpsN: string
+ val map_uniqueN: string
+ val min_algN: string
+ val morN: string
+ val nchotomyN: string
+ val recN: string
+ val recsN: string
+ val rel_coinductN: string
+ val rel_simpN: string
+ val rel_strong_coinductN: string
+ val rvN: string
+ val sel_unfoldsN: string
+ val sel_corecsN: string
+ val set_inclN: string
+ val set_set_inclN: string
+ val simpsN: string
+ val srel_coinductN: string
+ val srel_simpN: string
+ val srel_strong_coinductN: string
+ val strTN: string
+ val str_initN: string
+ val strongN: string
+ val sum_bdN: string
+ val sum_bdTN: string
+ val unfoldN: string
+ val unfoldsN: string
+ val uniqueN: string
+
+ val mk_exhaustN: string -> string
+ val mk_injectN: string -> string
+ val mk_nchotomyN: string -> string
+ val mk_set_simpsN: int -> string
+ val mk_set_minimalN: int -> string
+ val mk_set_inductN: int -> string
+
+ val mk_common_name: string list -> string
+
+ val split_conj_thm: thm -> thm list
+ val split_conj_prems: int -> thm -> thm
+
+ val retype_free: typ -> term -> term
+
+ val mk_sumTN: typ list -> typ
+ val mk_sumTN_balanced: typ list -> typ
+
+ val id_const: typ -> term
+ val id_abs: 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: (mixfix list -> (string * sort) list option -> binding list ->
+ typ list * typ list list -> BNF_Def.BNF list -> local_theory -> 'a) ->
+ binding list -> mixfix list -> (string * sort) list -> ((string * sort) * typ) list ->
+ local_theory -> BNF_Def.BNF list * 'a
+ val fp_bnf_cmd: (mixfix list -> (string * sort) list option -> binding list ->
+ typ list * typ list list -> BNF_Def.BNF list -> local_theory -> 'a) ->
+ binding list * (string list * string list) -> local_theory -> 'a
+end;
+
+structure BNF_FP : BNF_FP =
+struct
+
+open BNF_Comp
+open BNF_Def
+open BNF_Util
+
+val timing = true;
+fun time timer msg = (if timing
+ then warning (msg ^ ": " ^ ATP_Util.string_from_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 foldsN = foldN ^ "s"
+val unfoldN = unN ^ foldN
+val unfoldsN = unfoldN ^ "s"
+val uniqueN = "_unique"
+val simpsN = "simps"
+val ctorN = "ctor"
+val dtorN = "dtor"
+val ctor_foldN = ctorN ^ "_" ^ foldN
+val ctor_foldsN = ctor_foldN ^ "s"
+val dtor_unfoldN = dtorN ^ "_" ^ unfoldN
+val dtor_unfoldsN = dtor_unfoldN ^ "s"
+val ctor_fold_uniqueN = ctor_foldN ^ uniqueN
+val dtor_unfold_uniqueN = dtor_unfoldN ^ uniqueN
+val ctor_dtor_unfoldsN = ctorN ^ "_" ^ dtor_unfoldN ^ "s"
+val map_simpsN = mapN ^ "_" ^ simpsN
+val map_uniqueN = mapN ^ 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"
+fun mk_set_simpsN i = mk_setN i ^ "_" ^ simpsN
+fun mk_set_minimalN i = mk_setN i ^ "_minimal"
+fun mk_set_inductN i = mk_setN i ^ "_induct"
+
+val str_initN = "str_init"
+val recN = "rec"
+val recsN = recN ^ "s"
+val corecN = coN ^ recN
+val corecsN = corecN ^ "s"
+val ctor_recN = ctorN ^ "_" ^ recN
+val ctor_recsN = ctor_recN ^ "s"
+val dtor_corecN = dtorN ^ "_" ^ corecN
+val dtor_corecsN = dtor_corecN ^ "s"
+val ctor_dtor_corecsN = ctorN ^ "_" ^ dtor_corecN ^ "s"
+
+val ctor_dtorN = ctorN ^ "_" ^ dtorN
+val dtor_ctorN = dtorN ^ "_" ^ ctorN
+val nchotomyN = "nchotomy"
+fun mk_nchotomyN s = s ^ "_" ^ nchotomyN
+val injectN = "inject"
+fun mk_injectN s = s ^ "_" ^ injectN
+val exhaustN = "exhaust"
+fun mk_exhaustN s = s ^ "_" ^ exhaustN
+val ctor_injectN = mk_injectN ctorN
+val ctor_exhaustN = mk_exhaustN ctorN
+val dtor_injectN = mk_injectN dtorN
+val dtor_exhaustN = mk_exhaustN dtorN
+val inductN = "induct"
+val coinductN = coN ^ inductN
+val ctor_inductN = ctorN ^ "_" ^ inductN
+val ctor_induct2N = ctor_inductN ^ "2"
+val dtor_coinductN = dtorN ^ "_" ^ coinductN
+val rel_coinductN = relN ^ "_" ^ coinductN
+val srel_coinductN = srelN ^ "_" ^ coinductN
+val simpN = "_simp";
+val srel_simpN = srelN ^ simpN;
+val rel_simpN = relN ^ simpN;
+val strongN = "strong_"
+val dtor_strong_coinductN = dtorN ^ "_" ^ strongN ^ coinductN
+val rel_strong_coinductN = relN ^ "_" ^ strongN ^ coinductN
+val srel_strong_coinductN = srelN ^ "_" ^ strongN ^ coinductN
+val hsetN = "Hset"
+val hset_recN = hsetN ^ "_rec"
+val set_inclN = "set_incl"
+val set_set_inclN = "set_set_incl"
+
+val caseN = "case"
+val discN = "disc"
+val disc_unfoldsN = discN ^ "_" ^ unfoldsN
+val disc_corecsN = discN ^ "_" ^ corecsN
+val iffN = "_iff"
+val disc_unfold_iffN = discN ^ "_" ^ unfoldN ^ iffN
+val disc_corec_iffN = discN ^ "_" ^ corecN ^ iffN
+val selN = "sel"
+val sel_unfoldsN = selN ^ "_" ^ unfoldsN
+val sel_corecsN = selN ^ "_" ^ corecsN
+
+val mk_common_name = space_implode "_";
+
+fun retype_free T (Free (s, _)) = Free (s, T);
+
+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 id_abs T = Abs (Name.uu, T, Bound 0);
+
+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);
+
+(* 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;
+
+(* 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 lhss NONE Ass = Library.sort (Term_Ord.typ_ord o pairself TFree)
+ (subtract (op =) lhss (fold (fold (insert (op =))) Ass [])) @ lhss
+ | fp_sort lhss (SOME resBs) Ass =
+ (subtract (op =) lhss (filter (fn T => exists (fn Ts => member (op =) Ts T) Ass) resBs)) @ lhss;
+
+fun mk_fp_bnf timer construct resBs bs sort lhss bnfs deadss livess unfold_set lthy =
+ let
+ 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 = (case resBs of NONE => [] | SOME Ts => fold (subtract (op =)) Ass Ts);
+ val Ds = fold (fold Term.add_tfreesT) deadss [];
+
+ val _ = (case Library.inter (op =) Ds lhss of [] => ()
+ | A :: _ => error ("Nonadmissible 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 sort bnfs unfold_set lthy;
+
+ val Dss = map3 (append oo map o nth) livess kill_poss deadss;
+
+ val ((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 resBs bs (map TFree resDs, deadss) bnfs'' lthy'';
+
+ val timer = time (timer "FP construction in total");
+ in
+ timer; (bnfs'', res)
+ end;
+
+fun fp_bnf construct bs mixfixes resBs eqs lthy =
+ let
+ val timer = time (Timer.startRealTimer ());
+ val (lhss, rhss) = split_list eqs;
+ val sort = fp_sort lhss (SOME resBs);
+ fun qualify b = Binding.qualify true (Binding.name_of (Binding.prefix_name rawN b));
+ val ((bnfs, (Dss, Ass)), (unfold_set, lthy')) = apfst (apsnd split_list o split_list)
+ (fold_map2 (fn b => bnf_of_typ Smart_Inline (qualify b) sort) bs rhss
+ (empty_unfolds, lthy));
+ in
+ mk_fp_bnf timer (construct mixfixes) (SOME resBs) bs sort lhss bnfs Dss Ass unfold_set lthy'
+ end;
+
+fun fp_bnf_cmd construct (bs, (raw_lhss, raw_bnfs)) lthy =
+ let
+ val timer = time (Timer.startRealTimer ());
+ val lhss = map (dest_TFree o Syntax.read_typ lthy) raw_lhss;
+ val sort = fp_sort lhss NONE;
+ fun qualify b = Binding.qualify true (Binding.name_of (Binding.prefix_name rawN b));
+ val ((bnfs, (Dss, Ass)), (unfold_set, lthy')) = apfst (apsnd split_list o split_list)
+ (fold_map2 (fn b => fn rawT =>
+ (bnf_of_typ Smart_Inline (qualify b) sort (Syntax.read_typ lthy rawT)))
+ bs raw_bnfs (empty_unfolds, lthy));
+ in
+ snd (mk_fp_bnf timer
+ (construct (map (K NoSyn) bs)) NONE bs sort lhss bnfs Dss Ass unfold_set lthy')
+ end;
+
+end;