(* Title: HOL/Codatatype/Tools/bnf_fp_util.ML
Author: Dmitriy Traytel, TU Muenchen
Copyright 2012
Shared library for the datatype and codatatype constructions.
*)
signature BNF_FP_UTIL =
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 coiterN: string
val coitersN: string
val corecN: string
val corecsN: string
val disc_coitersN: string
val disc_corecsN: string
val exhaustN: string
val fldN: string
val fld_exhaustN: string
val fld_induct2N: string
val fld_inductN: string
val fld_injectN: string
val fld_iterN: string
val fld_iter_uniqueN: string
val fld_itersN: string
val fld_recN: string
val fld_recsN: string
val fld_unfN: string
val fld_unf_coitersN: string
val fld_unf_corecsN: string
val hsetN: string
val hset_recN: string
val inductN: string
val injectN: string
val isNodeN: string
val iterN: string
val itersN: string
val lsbisN: string
val map_simpsN: string
val map_uniqueN: string
val min_algN: string
val morN: string
val nchotomyN: string
val pred_coinductN: string
val pred_coinduct_uptoN: string
val recN: string
val recsN: string
val rel_coinductN: string
val rel_coinduct_uptoN: string
val rvN: string
val sel_coitersN: string
val sel_corecsN: string
val set_inclN: string
val set_set_inclN: string
val simpsN: string
val strTN: string
val str_initN: string
val sum_bdN: string
val sum_bdTN: string
val unfN: string
val unf_coinductN: string
val unf_coinduct_uptoN: string
val unf_coiterN: string
val unf_coiter_uniqueN: string
val unf_coitersN: string
val unf_corecN: string
val unf_corecsN: string
val unf_exhaustN: string
val unf_fldN: string
val unf_injectN: string
val uniqueN: string
val uptoN: 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: binding list -> string
val split_conj_thm: thm -> thm list
val split_conj_prems: int -> thm -> thm
val retype_free: typ -> term -> term
val mk_predT: typ -> typ;
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 mk_tactics: 'a -> 'a -> 'a -> 'a list -> 'a -> 'a -> 'a list -> 'a -> 'a -> 'a list
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_Util : BNF_FP_UTIL =
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 algN = "alg"
val IITN = "IITN"
val iterN = "iter"
val itersN = iterN ^ "s"
val coiterN = coN ^ iterN
val coitersN = coiterN ^ "s"
val uniqueN = "_unique"
val simpsN = "simps"
val fldN = "fld"
val unfN = "unf"
val fld_iterN = fldN ^ "_" ^ iterN
val fld_itersN = fld_iterN ^ "s"
val unf_coiterN = unfN ^ "_" ^ coiterN
val unf_coitersN = unf_coiterN ^ "s"
val fld_iter_uniqueN = fld_iterN ^ uniqueN
val unf_coiter_uniqueN = unf_coiterN ^ uniqueN
val fld_unf_coitersN = fldN ^ "_" ^ unf_coiterN ^ "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 fld_recN = fldN ^ "_" ^ recN
val fld_recsN = fld_recN ^ "s"
val unf_corecN = unfN ^ "_" ^ corecN
val unf_corecsN = unf_corecN ^ "s"
val fld_unf_corecsN = fldN ^ "_" ^ unf_corecN ^ "s"
val fld_unfN = fldN ^ "_" ^ unfN
val unf_fldN = unfN ^ "_" ^ fldN
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 fld_injectN = mk_injectN fldN
val fld_exhaustN = mk_exhaustN fldN
val unf_injectN = mk_injectN unfN
val unf_exhaustN = mk_exhaustN unfN
val inductN = "induct"
val coinductN = coN ^ inductN
val fld_inductN = fldN ^ "_" ^ inductN
val fld_induct2N = fld_inductN ^ "2"
val unf_coinductN = unfN ^ "_" ^ coinductN
val rel_coinductN = relN ^ "_" ^ coinductN
val pred_coinductN = predN ^ "_" ^ coinductN
val uptoN = "upto"
val unf_coinduct_uptoN = unf_coinductN ^ "_" ^ uptoN
val rel_coinduct_uptoN = rel_coinductN ^ "_" ^ uptoN
val pred_coinduct_uptoN = pred_coinductN ^ "_" ^ uptoN
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_coitersN = discN ^ "_" ^ coitersN
val disc_corecsN = discN ^ "_" ^ corecsN
val selN = "sel"
val sel_coitersN = selN ^ "_" ^ coitersN
val sel_corecsN = selN ^ "_" ^ corecsN
val mk_common_name = space_implode "_" o map Binding.name_of;
fun mk_predT T = T --> HOLogic.boolT;
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;
fun mk_tactics mid mcomp mcong snat bdco bdinf sbd inbd wpull =
[mid, mcomp, mcong] @ snat @ [bdco, bdinf] @ sbd @ [inbd, wpull];
(* 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 lthy =
let
val name = mk_common_name 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', lthy'))) =
normalize_bnfs qualify Ass Ds sort bnfs unfold lthy;
val Dss = map3 (append oo map o nth) livess kill_poss deadss;
val ((bnfs'', deadss), lthy'') =
fold_map3 (seal_bnf unfold') (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, lthy')) = apfst (apsnd split_list o split_list)
(fold_map2 (fn b => bnf_of_typ Smart_Inline (qualify b) sort) bs rhss
(empty_unfold, lthy));
in
mk_fp_bnf timer (construct mixfixes) (SOME resBs) bs sort lhss bnfs Dss Ass unfold 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, 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_unfold, lthy));
in
snd (mk_fp_bnf timer (construct (map (K NoSyn) bs)) NONE bs sort lhss bnfs Dss Ass unfold lthy')
end;
end;