--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Tools/repdef.ML Fri Nov 13 15:31:20 2009 -0800
@@ -0,0 +1,181 @@
+(* Title: HOLCF/Tools/repdef.ML
+ Author: Brian Huffman
+
+Defining representable domains using algebraic deflations.
+*)
+
+signature REPDEF =
+sig
+ type rep_info =
+ { emb_def: thm, prj_def: thm, approx_def: thm, REP: thm }
+
+ val add_repdef: bool -> binding option -> binding * string list * mixfix ->
+ term -> (binding * binding) option -> theory ->
+ (Typedef.info * Pcpodef.cpo_info * Pcpodef.pcpo_info * rep_info) * theory
+
+ val repdef_cmd: (bool * binding) * (binding * string list * mixfix) * string
+ * (binding * binding) option -> theory -> theory
+end;
+
+structure Repdef :> REPDEF =
+struct
+
+(** type definitions **)
+
+type rep_info =
+ { emb_def: thm, prj_def: thm, approx_def: thm, REP: thm };
+
+(* building terms *)
+
+fun adm_const T = Const (@{const_name adm}, (T --> HOLogic.boolT) --> HOLogic.boolT);
+fun mk_adm (x, T, P) = adm_const T $ absfree (x, T, P);
+
+fun below_const T = Const (@{const_name below}, T --> T --> HOLogic.boolT);
+
+val natT = @{typ nat};
+val udomT = @{typ udom};
+fun alg_deflT T = Type (@{type_name alg_defl}, [T]);
+fun cfunT (T, U) = Type (@{type_name "->"}, [T, U]);
+fun emb_const T = Const (@{const_name emb}, cfunT (T, udomT));
+fun prj_const T = Const (@{const_name prj}, cfunT (udomT, T));
+fun approx_const T = Const (@{const_name approx}, natT --> cfunT (T, T));
+
+fun LAM_const (T, U) = Const (@{const_name Abs_CFun}, (T --> U) --> cfunT (T, U));
+fun APP_const (T, U) = Const (@{const_name Rep_CFun}, cfunT (T, U) --> (T --> U));
+fun cast_const T = Const (@{const_name cast}, cfunT (alg_deflT T, cfunT (T, T)));
+fun mk_cast (t, x) =
+ APP_const (udomT, udomT)
+ $ (APP_const (alg_deflT udomT, cfunT (udomT, udomT)) $ cast_const udomT $ t)
+ $ x;
+
+(* manipulating theorems *)
+
+(* proving class instances *)
+
+fun declare_type_name a =
+ Variable.declare_constraints (Logic.mk_type (TFree (a, dummyS)));
+
+fun gen_add_repdef
+ (prep_term: Proof.context -> 'a -> term)
+ (def: bool)
+ (name: binding)
+ (typ as (t, vs, mx) : binding * string list * mixfix)
+ (raw_defl: 'a)
+ (opt_morphs: (binding * binding) option)
+ (thy: theory)
+ : (Typedef.info * Pcpodef.cpo_info * Pcpodef.pcpo_info * rep_info) * theory =
+ let
+ val _ = Theory.requires thy "Representable" "repdefs";
+ val ctxt = ProofContext.init thy;
+
+ (*rhs*)
+ val defl = prep_term (ctxt |> fold declare_type_name vs) raw_defl;
+ val deflT = Term.fastype_of defl;
+ val _ = if deflT = @{typ "udom alg_defl"} then ()
+ else error ("Not type udom alg_defl: " ^ quote (Syntax.string_of_typ ctxt deflT));
+ val rhs_tfrees = Term.add_tfrees defl [];
+
+ (*lhs*)
+ val defS = Sign.defaultS thy;
+ val lhs_tfrees = map (fn v => (v, the_default defS (AList.lookup (op =) rhs_tfrees v))) vs;
+ val lhs_sorts = map snd lhs_tfrees;
+ val tname = Binding.map_name (Syntax.type_name mx) t;
+ val full_tname = Sign.full_name thy tname;
+ val newT = Type (full_tname, map TFree lhs_tfrees);
+
+ (*morphisms*)
+ val morphs = opt_morphs
+ |> the_default (Binding.prefix_name "Rep_" name, Binding.prefix_name "Abs_" name);
+
+ (*set*)
+ val in_defl = @{term "in_deflation :: udom => udom alg_defl => bool"};
+ val set = HOLogic.Collect_const udomT $ Abs ("x", udomT, in_defl $ Bound 0 $ defl);
+
+ (*pcpodef*)
+ val tac1 = rtac @{thm CollectI} 1 THEN rtac @{thm bottom_in_deflation} 1;
+ val tac2 = rtac @{thm adm_mem_Collect_in_deflation} 1;
+ val ((info, cpo_info, pcpo_info), thy2) = thy
+ |> Pcpodef.add_pcpodef def (SOME name) typ set (SOME morphs) (tac1, tac2);
+
+ (*definitions*)
+ val Rep_const = Const (#Rep_name info, newT --> udomT);
+ val Abs_const = Const (#Abs_name info, udomT --> newT);
+ val emb_eqn = Logic.mk_equals (emb_const newT, LAM_const (newT, udomT) $ Rep_const);
+ val prj_eqn = Logic.mk_equals (prj_const newT, LAM_const (udomT, newT) $
+ Abs ("x", udomT, Abs_const $ mk_cast (defl, Bound 0)));
+ val repdef_approx_const =
+ Const (@{const_name repdef_approx}, (newT --> udomT) --> (udomT --> newT)
+ --> alg_deflT udomT --> natT --> cfunT (newT, newT));
+ val approx_eqn = Logic.mk_equals (approx_const newT,
+ repdef_approx_const $ Rep_const $ Abs_const $ defl);
+
+ (*instantiate class rep*)
+ val name_def = Binding.suffix_name "_def" name;
+ val ([emb_ldef, prj_ldef, approx_ldef], lthy3) = thy2
+ |> Theory_Target.instantiation ([full_tname], lhs_tfrees, @{sort rep})
+ |> fold_map Specification.definition
+ [ (NONE, ((Binding.prefix_name "emb_" name_def, []), emb_eqn))
+ , (NONE, ((Binding.prefix_name "prj_" name_def, []), prj_eqn))
+ , (NONE, ((Binding.prefix_name "approx_" name_def, []), approx_eqn)) ]
+ |>> map (snd o snd);
+ val ctxt_thy = ProofContext.init (ProofContext.theory_of lthy3);
+ val [emb_def, prj_def, approx_def] =
+ ProofContext.export lthy3 ctxt_thy [emb_ldef, prj_ldef, approx_ldef];
+ val typedef_thms =
+ [#type_definition info, #below_def cpo_info, emb_def, prj_def, approx_def];
+ val thy4 = lthy3
+ |> Class.prove_instantiation_instance
+ (K (Tactic.rtac (@{thm typedef_rep_class} OF typedef_thms) 1))
+ |> LocalTheory.exit_global;
+
+ (*other theorems*)
+ val typedef_thms' = map (Thm.transfer thy4)
+ [#type_definition info, #below_def cpo_info, emb_def, prj_def];
+ val ([REP_thm], thy5) = thy4
+ |> Sign.add_path (Binding.name_of name)
+ |> PureThy.add_thms
+ [((Binding.prefix_name "REP_" name,
+ Drule.standard (@{thm typedef_REP} OF typedef_thms')), [])]
+ ||> Sign.parent_path;
+
+ val rep_info =
+ { emb_def = emb_def, prj_def = prj_def, approx_def = approx_def, REP = REP_thm };
+ in
+ ((info, cpo_info, pcpo_info, rep_info), thy5)
+ end
+ handle ERROR msg =>
+ cat_error msg ("The error(s) above occurred in repdef " ^ quote (Binding.str_of name));
+
+fun add_repdef def opt_name typ defl opt_morphs thy =
+ let
+ val name = the_default (#1 typ) opt_name;
+ in
+ gen_add_repdef Syntax.check_term def name typ defl opt_morphs thy
+ end;
+
+fun repdef_cmd ((def, name), typ, A, morphs) =
+ snd o gen_add_repdef Syntax.read_term def name typ A morphs;
+
+(** outer syntax **)
+
+local structure P = OuterParse and K = OuterKeyword in
+
+val repdef_decl =
+ Scan.optional (P.$$$ "(" |--
+ ((P.$$$ "open" >> K false) -- Scan.option P.binding || P.binding >> (fn s => (true, SOME s)))
+ --| P.$$$ ")") (true, NONE) --
+ (P.type_args -- P.binding) -- P.opt_infix -- (P.$$$ "=" |-- P.term) --
+ Scan.option (P.$$$ "morphisms" |-- P.!!! (P.binding -- P.binding));
+
+fun mk_repdef ((((((def, opt_name), (vs, t)), mx), A), morphs)) =
+ repdef_cmd
+ ((def, the_default (Binding.map_name (Syntax.type_name mx) t) opt_name), (t, vs, mx), A, morphs);
+
+val _ =
+ OuterSyntax.command "repdef" "HOLCF definition of representable domains" K.thy_goal
+ (repdef_decl >>
+ (Toplevel.print oo (Toplevel.theory o mk_repdef)));
+
+end;
+
+end;