src/HOLCF/Tools/Domain/domain_axioms.ML
author huffman
Tue, 02 Mar 2010 13:01:22 -0800
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remove map_tab argument to calc_axioms
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(*  Title:      HOLCF/Tools/Domain/domain_axioms.ML
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    Author:     David von Oheimb
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Syntax generator for domain command.
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*)
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signature DOMAIN_AXIOMS =
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sig
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  val copy_of_dtyp :
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      string Symtab.table -> (int -> term) -> Datatype.dtyp -> term
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  val calc_axioms :
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      bool ->
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      Domain_Library.eq list -> int -> Domain_Library.eq ->
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      string * (string * term) list * (string * term) list
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  val add_axioms :
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      bool ->
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      ((string * typ list) *
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       (binding * (bool * binding option * typ) list * mixfix) list) list ->
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      Domain_Library.eq list -> theory -> theory
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end;
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structure Domain_Axioms : DOMAIN_AXIOMS =
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struct
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open Domain_Library;
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infixr 0 ===>;infixr 0 ==>;infix 0 == ; 
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infix 1 ===; infix 1 ~= ; infix 1 <<; infix 1 ~<<;
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infix 9 `   ; infix 9 `% ; infix 9 `%%; infixr 9 oo;
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(* FIXME: use theory data for this *)
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val copy_tab : string Symtab.table =
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    Symtab.make [(@{type_name "->"}, @{const_name "cfun_map"}),
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                 (@{type_name "++"}, @{const_name "ssum_map"}),
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                 (@{type_name "**"}, @{const_name "sprod_map"}),
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                 (@{type_name "*"}, @{const_name "cprod_map"}),
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                 (@{type_name "u"}, @{const_name "u_map"})];
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fun copy_of_dtyp tab r dt =
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    if Datatype_Aux.is_rec_type dt then copy tab r dt else ID
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and copy tab r (Datatype_Aux.DtRec i) = r i
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  | copy tab r (Datatype_Aux.DtTFree a) = ID
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  | copy tab r (Datatype_Aux.DtType (c, ds)) =
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    case Symtab.lookup tab c of
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      SOME f => list_ccomb (%%:f, map (copy_of_dtyp tab r) ds)
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    | NONE => (warning ("copy_of_dtyp: unknown type constructor " ^ c); ID);
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fun calc_axioms
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    (definitional : bool)
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    (eqs : eq list)
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    (n : int)
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    (eqn as ((dname,_),cons) : eq)
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    : string * (string * term) list * (string * term) list =
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  let
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(* ----- axioms and definitions concerning the isomorphism ------------------ *)
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    val dc_abs = %%:(dname^"_abs");
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    val dc_rep = %%:(dname^"_rep");
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    val x_name'= "x";
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    val x_name = idx_name eqs x_name' (n+1);
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    val dnam = Long_Name.base_name dname;
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    val abs_iso_ax = ("abs_iso", mk_trp(dc_rep`(dc_abs`%x_name') === %:x_name'));
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    val rep_iso_ax = ("rep_iso", mk_trp(dc_abs`(dc_rep`%x_name') === %:x_name'));
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(* ----- axiom and definitions concerning induction ------------------------- *)
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    val finite_def =
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        ("finite_def",
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         %%:(dname^"_finite") ==
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            mk_lam(x_name,
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                   mk_ex("n",(%%:(dname^"_take") $ Bound 0)`Bound 1 === Bound 1)));
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  in (dnam,
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      (if definitional then [] else [abs_iso_ax, rep_iso_ax]),
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      [finite_def])
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  end; (* let (calc_axioms) *)
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(* legacy type inference *)
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fun legacy_infer_term thy t =
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    singleton (Syntax.check_terms (ProofContext.init thy)) (Sign.intern_term thy t);
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fun legacy_infer_prop thy t = legacy_infer_term thy (TypeInfer.constrain propT t);
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fun infer_props thy = map (apsnd (legacy_infer_prop thy));
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fun add_axioms_i x = snd o PureThy.add_axioms (map (Thm.no_attributes o apfst Binding.name) x);
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fun add_axioms_infer axms thy = add_axioms_i (infer_props thy axms) thy;
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fun add_defs_i x = snd o (PureThy.add_defs false) (map (Thm.no_attributes o apfst Binding.name) x);
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fun add_defs_infer defs thy = add_defs_i (infer_props thy defs) thy;
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fun add_axioms definitional eqs' (eqs : eq list) thy' =
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  let
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    val dnames = map (fst o fst) eqs;
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    val x_name = idx_name dnames "x"; 
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    fun add_one (dnam, axs, dfs) =
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        Sign.add_path dnam
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          #> add_axioms_infer axs
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          #> Sign.parent_path;
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    val axs = mapn (calc_axioms definitional eqs) 0 eqs;
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    val thy = thy' |> fold add_one axs;
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    fun get_iso_info ((dname, tyvars), cons') =
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      let
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        fun opt_lazy (lazy,_,t) = if lazy then mk_uT t else t
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        fun prod     (_,args,_) =
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            case args of [] => oneT
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                       | _ => foldr1 mk_sprodT (map opt_lazy args);
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        val ax_abs_iso = PureThy.get_thm thy (dname ^ ".abs_iso");
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        val ax_rep_iso = PureThy.get_thm thy (dname ^ ".rep_iso");
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        val lhsT = Type(dname,tyvars);
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        val rhsT = foldr1 mk_ssumT (map prod cons');
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        val rep_const = Const(dname^"_rep", lhsT ->> rhsT);
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        val abs_const = Const(dname^"_abs", rhsT ->> lhsT);
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      in
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        {
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          absT = lhsT,
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          repT = rhsT,
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          abs_const = abs_const,
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          rep_const = rep_const,
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          abs_inverse = ax_abs_iso,
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          rep_inverse = ax_rep_iso
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        }
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      end;
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    val dom_binds = map (Binding.name o Long_Name.base_name) dnames;
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    val thy =
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        if definitional then thy
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        else snd (Domain_Isomorphism.define_take_functions
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                    (dom_binds ~~ map get_iso_info eqs') thy);
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    fun add_one' (dnam, axs, dfs) =
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        Sign.add_path dnam
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          #> add_defs_infer dfs
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          #> Sign.parent_path;
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    val thy = fold add_one' axs thy;
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    (* declare lub_take axioms *)
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    local
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      fun ax_lub_take dname =
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        let
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          val dnam : string = Long_Name.base_name dname;
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          val take_const = %%:(dname^"_take");
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          val lub = %%: @{const_name lub};
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          val image = %%: @{const_name image};
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          val UNIV = @{term "UNIV :: nat set"};
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          val lhs = lub $ (image $ take_const $ UNIV);
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          val ax = mk_trp (lhs === ID);
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        in
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          add_one (dnam, [("lub_take", ax)], [])
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        end
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    in
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      val thy =
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          if definitional then thy
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          else fold ax_lub_take dnames thy
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    end;
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  in
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    thy
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  end; (* let (add_axioms) *)
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end; (* struct *)