author | haftmann |
Fri, 26 Sep 2008 09:10:02 +0200 | |
changeset 28370 | 37f56e6e702d |
parent 28361 | 232fcbba2e4e |
child 28394 | b9c8e3a12a98 |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/function_package/size.ML |
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ID: $Id$ |
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Author: Stefan Berghofer, Florian Haftmann, TU Muenchen |
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Size functions for datatypes. |
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*) |
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signature SIZE = |
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sig |
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val size_thms: theory -> string -> thm list |
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val setup: theory -> theory |
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end; |
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structure Size: SIZE = |
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struct |
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open DatatypeAux; |
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structure SizeData = TheoryDataFun |
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( |
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type T = (string * thm list) Symtab.table; |
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val empty = Symtab.empty; |
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val copy = I |
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val extend = I |
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fun merge _ = Symtab.merge (K true); |
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); |
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val lookup_size = SizeData.get #> Symtab.lookup; |
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fun plus (t1, t2) = Const ("HOL.plus_class.plus", |
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HOLogic.natT --> HOLogic.natT --> HOLogic.natT) $ t1 $ t2; |
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||
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fun size_of_type f g h (T as Type (s, Ts)) = |
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(case f s of |
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SOME t => SOME t |
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| NONE => (case g s of |
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SOME size_name => |
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SOME (list_comb (Const (size_name, |
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map (fn U => U --> HOLogic.natT) Ts @ [T] ---> HOLogic.natT), |
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map (size_of_type' f g h) Ts)) |
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| NONE => NONE)) |
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| size_of_type f g h (TFree (s, _)) = h s |
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and size_of_type' f g h T = (case size_of_type f g h T of |
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NONE => Abs ("x", T, HOLogic.zero) |
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| SOME t => t); |
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fun is_poly thy (DtType (name, dts)) = |
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(case DatatypePackage.get_datatype thy name of |
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NONE => false |
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| SOME _ => exists (is_poly thy) dts) |
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| is_poly _ _ = true; |
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fun constrs_of thy name = |
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let |
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val {descr, index, ...} = DatatypePackage.the_datatype thy name |
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val SOME (_, _, constrs) = AList.lookup op = descr index |
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in constrs end; |
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val app = curry (list_comb o swap); |
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fun prove_size_thms (info : datatype_info) new_type_names thy = |
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let |
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val {descr, alt_names, sorts, rec_names, rec_rewrites, induction, ...} = info; |
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val l = length new_type_names; |
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val alt_names' = (case alt_names of |
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NONE => replicate l NONE | SOME names => map SOME names); |
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val descr' = List.take (descr, l); |
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val (rec_names1, rec_names2) = chop l rec_names; |
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val recTs = get_rec_types descr sorts; |
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val (recTs1, recTs2) = chop l recTs; |
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val (_, (_, paramdts, _)) :: _ = descr; |
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val paramTs = map (typ_of_dtyp descr sorts) paramdts; |
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val ((param_size_fs, param_size_fTs), f_names) = paramTs |> |
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map (fn T as TFree (s, _) => |
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let |
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val name = "f" ^ implode (tl (explode s)); |
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val U = T --> HOLogic.natT |
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in |
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(((s, Free (name, U)), U), name) |
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end) |> split_list |>> split_list; |
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val param_size = AList.lookup op = param_size_fs; |
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val extra_rewrites = descr |> map (#1 o snd) |> distinct op = |> |
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List.mapPartial (Option.map snd o lookup_size thy) |> flat; |
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val extra_size = Option.map fst o lookup_size thy; |
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val (((size_names, size_fns), def_names), def_names') = |
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recTs1 ~~ alt_names' |> |
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map (fn (T as Type (s, _), optname) => |
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let |
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val s' = the_default (Sign.base_name s) optname ^ "_size"; |
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val s'' = Sign.full_name thy s' |
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in |
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(s'', |
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(list_comb (Const (s'', param_size_fTs @ [T] ---> HOLogic.natT), |
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map snd param_size_fs), |
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(s' ^ "_def", s' ^ "_overloaded_def"))) |
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end) |> split_list ||>> split_list ||>> split_list; |
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val overloaded_size_fns = map HOLogic.size_const recTs1; |
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(* instantiation for primrec combinator *) |
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fun size_of_constr b size_ofp ((_, cargs), (_, cargs')) = |
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let |
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val Ts = map (typ_of_dtyp descr sorts) cargs; |
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val k = length (filter is_rec_type cargs); |
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val (ts, _, _) = fold_rev (fn ((dt, dt'), T) => fn (us, i, j) => |
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if is_rec_type dt then (Bound i :: us, i + 1, j + 1) |
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else |
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(if b andalso is_poly thy dt' then |
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case size_of_type (K NONE) extra_size size_ofp T of |
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NONE => us | SOME sz => sz $ Bound j :: us |
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else us, i, j + 1)) |
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(cargs ~~ cargs' ~~ Ts) ([], 0, k); |
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val t = |
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if null ts andalso (not b orelse not (exists (is_poly thy) cargs')) |
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then HOLogic.zero |
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else foldl1 plus (ts @ [HOLogic.Suc_zero]) |
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in |
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foldr (fn (T, t') => Abs ("x", T, t')) t (Ts @ replicate k HOLogic.natT) |
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end; |
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||
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val fs = maps (fn (_, (name, _, constrs)) => |
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map (size_of_constr true param_size) (constrs ~~ constrs_of thy name)) descr; |
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val fs' = maps (fn (n, (name, _, constrs)) => |
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map (size_of_constr (l <= n) (K NONE)) (constrs ~~ constrs_of thy name)) descr; |
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val fTs = map fastype_of fs; |
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val (rec_combs1, rec_combs2) = chop l (map (fn (T, rec_name) => |
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Const (rec_name, fTs @ [T] ---> HOLogic.natT)) |
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(recTs ~~ rec_names)); |
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fun define_overloaded (def_name, eq) lthy = |
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let |
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val (Free (c, _), rhs) = (Logic.dest_equals o Syntax.check_term lthy) eq; |
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val ((_, (_, thm)), lthy') = lthy |> LocalTheory.define Thm.definitionK |
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((Name.binding c, NoSyn), ((Name.binding def_name, []), rhs)); |
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val ctxt_thy = ProofContext.init (ProofContext.theory_of lthy'); |
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val thm' = singleton (ProofContext.export lthy' ctxt_thy) thm; |
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in (thm', lthy') end; |
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val ((size_def_thms, size_def_thms'), thy') = |
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thy |
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|> Sign.add_consts_i (map (fn (s, T) => |
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(Sign.base_name s, param_size_fTs @ [T] ---> HOLogic.natT, NoSyn)) |
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(size_names ~~ recTs1)) |
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|> PureThy.add_defs false |
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(map (Thm.no_attributes o apsnd (Logic.mk_equals o apsnd (app fs))) |
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(def_names ~~ (size_fns ~~ rec_combs1))) |
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||> TheoryTarget.instantiation |
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(map (#1 o snd) descr', map dest_TFree paramTs, [HOLogic.class_size]) |
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||>> fold_map define_overloaded |
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(def_names' ~~ map Logic.mk_equals (overloaded_size_fns ~~ map (app fs') rec_combs1)) |
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||> Class.prove_instantiation_instance (K (Class.intro_classes_tac [])) |
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||> LocalTheory.exit |
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||> ProofContext.theory_of; |
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val ctxt = ProofContext.init thy'; |
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val simpset1 = HOL_basic_ss addsimps @{thm add_0} :: @{thm add_0_right} :: |
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size_def_thms @ size_def_thms' @ rec_rewrites @ extra_rewrites; |
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val xs = map (fn i => "x" ^ string_of_int i) (1 upto length recTs2); |
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|
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fun mk_unfolded_size_eq tab size_ofp fs (p as (x, T), r) = |
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HOLogic.mk_eq (app fs r $ Free p, |
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the (size_of_type tab extra_size size_ofp T) $ Free p); |
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|
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fun prove_unfolded_size_eqs size_ofp fs = |
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if null recTs2 then [] |
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else split_conj_thm (SkipProof.prove ctxt xs [] |
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(HOLogic.mk_Trueprop (mk_conj (replicate l HOLogic.true_const @ |
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map (mk_unfolded_size_eq (AList.lookup op = |
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(new_type_names ~~ map (app fs) rec_combs1)) size_ofp fs) |
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(xs ~~ recTs2 ~~ rec_combs2)))) |
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(fn _ => (indtac induction xs THEN_ALL_NEW asm_simp_tac simpset1) 1)); |
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|
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val unfolded_size_eqs1 = prove_unfolded_size_eqs param_size fs; |
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val unfolded_size_eqs2 = prove_unfolded_size_eqs (K NONE) fs'; |
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|
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(* characteristic equations for size functions *) |
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fun gen_mk_size_eq p size_of size_ofp size_const T (cname, cargs) = |
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let |
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val Ts = map (typ_of_dtyp descr sorts) cargs; |
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val tnames = Name.variant_list f_names (DatatypeProp.make_tnames Ts); |
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val ts = List.mapPartial (fn (sT as (s, T), dt) => |
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Option.map (fn sz => sz $ Free sT) |
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(if p dt then size_of_type size_of extra_size size_ofp T |
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else NONE)) (tnames ~~ Ts ~~ cargs) |
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in |
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HOLogic.mk_Trueprop (HOLogic.mk_eq |
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(size_const $ list_comb (Const (cname, Ts ---> T), |
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map2 (curry Free) tnames Ts), |
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if null ts then HOLogic.zero |
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else foldl1 plus (ts @ [HOLogic.Suc_zero]))) |
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end; |
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|
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val simpset2 = HOL_basic_ss addsimps |
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rec_rewrites @ size_def_thms @ unfolded_size_eqs1; |
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val simpset3 = HOL_basic_ss addsimps |
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rec_rewrites @ size_def_thms' @ unfolded_size_eqs2; |
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|
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fun prove_size_eqs p size_fns size_ofp simpset = |
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maps (fn (((_, (_, _, constrs)), size_const), T) => |
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map (fn constr => standard (SkipProof.prove ctxt [] [] |
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(gen_mk_size_eq p (AList.lookup op = (new_type_names ~~ size_fns)) |
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size_ofp size_const T constr) |
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(fn _ => simp_tac simpset 1))) constrs) |
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(descr' ~~ size_fns ~~ recTs1); |
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208 |
|
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val size_eqns = prove_size_eqs (is_poly thy') size_fns param_size simpset2 @ |
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210 |
prove_size_eqs is_rec_type overloaded_size_fns (K NONE) simpset3; |
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211 |
|
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val ([size_thms], thy'') = PureThy.add_thmss |
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[(("size", size_eqns), |
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214 |
[Simplifier.simp_add, Thm.declaration_attribute |
28370 | 215 |
(fn thm => Context.mapping (Code.add_default_eqn thm) I)])] thy' |
24710 | 216 |
|
217 |
in |
|
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SizeData.map (fold (Symtab.update_new o apsnd (rpair size_thms)) |
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219 |
(new_type_names ~~ size_names)) thy'' |
24710 | 220 |
end; |
221 |
||
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222 |
fun add_size_thms (new_type_names as name :: _) thy = |
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let |
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val info as {descr, alt_names, ...} = DatatypePackage.the_datatype thy name; |
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225 |
val prefix = NameSpace.map_base (K (space_implode "_" |
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226 |
(the_default (map Sign.base_name new_type_names) alt_names))) name; |
24710 | 227 |
val no_size = exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists (fn dt => |
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is_rec_type dt andalso not (null (fst (strip_dtyp dt)))) cargs) constrs) descr |
24710 | 229 |
in if no_size then thy |
230 |
else |
|
231 |
thy |
|
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232 |
|> Sign.root_path |
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233 |
|> Sign.add_path prefix |
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234 |
|> Theory.checkpoint |
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235 |
|> prove_size_thms info new_type_names |
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236 |
|> Sign.restore_naming thy |
24710 | 237 |
end; |
238 |
||
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239 |
val size_thms = snd oo (the oo lookup_size); |
24710 | 240 |
|
24711 | 241 |
val setup = DatatypePackage.interpretation add_size_thms; |
24710 | 242 |
|
243 |
end; |