author | huffman |
Tue, 02 Mar 2010 13:01:22 -0800 | |
changeset 35513 | 89eddccbb93d |
parent 35499 | 6acef0aea07d |
child 35514 | a2cfa413eaab |
permissions | -rw-r--r-- |
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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 *) |