--- a/src/Tools/code/code_wellsorted.ML Tue May 12 17:09:36 2009 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,342 +0,0 @@
-(* Title: Tools/code/code_wellsorted.ML
- Author: Florian Haftmann, TU Muenchen
-
-Producing well-sorted systems of code equations in a graph
-with explicit dependencies -- the Waisenhaus algorithm.
-*)
-
-signature CODE_WELLSORTED =
-sig
- type code_algebra
- type code_graph
- val eqns: code_graph -> string -> (thm * bool) list
- val typ: code_graph -> string -> (string * sort) list * typ
- val all: code_graph -> string list
- val pretty: theory -> code_graph -> Pretty.T
- val obtain: theory -> string list -> term list -> code_algebra * code_graph
- val eval_conv: theory -> (sort -> sort)
- -> (code_algebra -> code_graph -> (string * sort) list -> term -> cterm -> thm) -> cterm -> thm
- val eval: theory -> (sort -> sort) -> ((term -> term) -> 'a -> 'a)
- -> (code_algebra -> code_graph -> (string * sort) list -> term -> 'a) -> term -> 'a
-end
-
-structure Code_Wellsorted : CODE_WELLSORTED =
-struct
-
-(** the algebra and code equation graph types **)
-
-type code_algebra = (sort -> sort) * Sorts.algebra;
-type code_graph = (((string * sort) list * typ) * (thm * bool) list) Graph.T;
-
-fun eqns eqngr = these o Option.map snd o try (Graph.get_node eqngr);
-fun typ eqngr = fst o Graph.get_node eqngr;
-fun all eqngr = Graph.keys eqngr;
-
-fun pretty thy eqngr =
- AList.make (snd o Graph.get_node eqngr) (Graph.keys eqngr)
- |> (map o apfst) (Code_Unit.string_of_const thy)
- |> sort (string_ord o pairself fst)
- |> map (fn (s, thms) =>
- (Pretty.block o Pretty.fbreaks) (
- Pretty.str s
- :: map (Display.pretty_thm o fst) thms
- ))
- |> Pretty.chunks;
-
-
-(** the Waisenhaus algorithm **)
-
-(* auxiliary *)
-
-fun is_proper_class thy = can (AxClass.get_info thy);
-
-fun complete_proper_sort thy =
- Sign.complete_sort thy #> filter (is_proper_class thy);
-
-fun inst_params thy tyco =
- map (fn (c, _) => AxClass.param_of_inst thy (c, tyco))
- o maps (#params o AxClass.get_info thy);
-
-fun consts_of thy eqns = [] |> (fold o fold o fold_aterms)
- (fn Const (c, ty) => insert (op =) (c, Sign.const_typargs thy (c, Logic.unvarifyT ty)) | _ => I)
- (map (op :: o swap o apfst (snd o strip_comb) o Logic.dest_equals o Thm.plain_prop_of o fst) eqns);
-
-fun tyscm_rhss_of thy c eqns =
- let
- val tyscm = case eqns of [] => Code.default_typscheme thy c
- | ((thm, _) :: _) => Code_Unit.typscheme_eqn thy thm;
- val rhss = consts_of thy eqns;
- in (tyscm, rhss) end;
-
-
-(* data structures *)
-
-datatype const = Fun of string | Inst of class * string;
-
-fun const_ord (Fun c1, Fun c2) = fast_string_ord (c1, c2)
- | const_ord (Inst class_tyco1, Inst class_tyco2) =
- prod_ord fast_string_ord fast_string_ord (class_tyco1, class_tyco2)
- | const_ord (Fun _, Inst _) = LESS
- | const_ord (Inst _, Fun _) = GREATER;
-
-type var = const * int;
-
-structure Vargraph =
- GraphFun(type key = var val ord = prod_ord const_ord int_ord);
-
-datatype styp = Tyco of string * styp list | Var of var | Free;
-
-fun styp_of c_lhs (Type (tyco, tys)) = Tyco (tyco, map (styp_of c_lhs) tys)
- | styp_of c_lhs (TFree (v, _)) = case c_lhs
- of SOME (c, lhs) => Var (Fun c, find_index (fn (v', _) => v = v') lhs)
- | NONE => Free;
-
-type vardeps_data = ((string * styp list) list * class list) Vargraph.T
- * (((string * sort) list * (thm * bool) list) Symtab.table
- * (class * string) list);
-
-val empty_vardeps_data : vardeps_data =
- (Vargraph.empty, (Symtab.empty, []));
-
-
-(* retrieving equations and instances from the background context *)
-
-fun obtain_eqns thy eqngr c =
- case try (Graph.get_node eqngr) c
- of SOME ((lhs, _), eqns) => ((lhs, []), [])
- | NONE => let
- val eqns = Code.these_eqns thy c
- |> burrow_fst (Code_Unit.norm_args thy)
- |> burrow_fst (Code_Unit.norm_varnames thy);
- val ((lhs, _), rhss) = tyscm_rhss_of thy c eqns;
- in ((lhs, rhss), eqns) end;
-
-fun obtain_instance thy arities (inst as (class, tyco)) =
- case AList.lookup (op =) arities inst
- of SOME classess => (classess, ([], []))
- | NONE => let
- val all_classes = complete_proper_sort thy [class];
- val superclasses = remove (op =) class all_classes
- val classess = map (complete_proper_sort thy)
- (Sign.arity_sorts thy tyco [class]);
- val inst_params = inst_params thy tyco all_classes;
- in (classess, (superclasses, inst_params)) end;
-
-
-(* computing instantiations *)
-
-fun add_classes thy arities eqngr c_k new_classes vardeps_data =
- let
- val (styps, old_classes) = Vargraph.get_node (fst vardeps_data) c_k;
- val diff_classes = new_classes |> subtract (op =) old_classes;
- in if null diff_classes then vardeps_data
- else let
- val c_ks = Vargraph.imm_succs (fst vardeps_data) c_k |> insert (op =) c_k;
- in
- vardeps_data
- |> (apfst o Vargraph.map_node c_k o apsnd) (append diff_classes)
- |> fold (fn styp => fold (assert_typmatch_inst thy arities eqngr styp) new_classes) styps
- |> fold (fn c_k => add_classes thy arities eqngr c_k diff_classes) c_ks
- end end
-and add_styp thy arities eqngr c_k tyco_styps vardeps_data =
- let
- val (old_styps, classes) = Vargraph.get_node (fst vardeps_data) c_k;
- in if member (op =) old_styps tyco_styps then vardeps_data
- else
- vardeps_data
- |> (apfst o Vargraph.map_node c_k o apfst) (cons tyco_styps)
- |> fold (assert_typmatch_inst thy arities eqngr tyco_styps) classes
- end
-and add_dep thy arities eqngr c_k c_k' vardeps_data =
- let
- val (_, classes) = Vargraph.get_node (fst vardeps_data) c_k;
- in
- vardeps_data
- |> add_classes thy arities eqngr c_k' classes
- |> apfst (Vargraph.add_edge (c_k, c_k'))
- end
-and assert_typmatch_inst thy arities eqngr (tyco, styps) class vardeps_data =
- if can (Sign.arity_sorts thy tyco) [class]
- then vardeps_data
- |> assert_inst thy arities eqngr (class, tyco)
- |> fold_index (fn (k, styp) =>
- assert_typmatch thy arities eqngr styp (Inst (class, tyco), k)) styps
- else vardeps_data (*permissive!*)
-and assert_inst thy arities eqngr (inst as (class, tyco)) (vardeps_data as (_, (_, insts))) =
- if member (op =) insts inst then vardeps_data
- else let
- val (classess, (superclasses, inst_params)) =
- obtain_instance thy arities inst;
- in
- vardeps_data
- |> (apsnd o apsnd) (insert (op =) inst)
- |> fold_index (fn (k, _) =>
- apfst (Vargraph.new_node ((Inst (class, tyco), k), ([] ,[])))) classess
- |> fold (fn superclass => assert_inst thy arities eqngr (superclass, tyco)) superclasses
- |> fold (assert_fun thy arities eqngr) inst_params
- |> fold_index (fn (k, classes) =>
- add_classes thy arities eqngr (Inst (class, tyco), k) classes
- #> fold (fn superclass =>
- add_dep thy arities eqngr (Inst (superclass, tyco), k)
- (Inst (class, tyco), k)) superclasses
- #> fold (fn inst_param =>
- add_dep thy arities eqngr (Fun inst_param, k)
- (Inst (class, tyco), k)
- ) inst_params
- ) classess
- end
-and assert_typmatch thy arities eqngr (Tyco tyco_styps) c_k vardeps_data =
- vardeps_data
- |> add_styp thy arities eqngr c_k tyco_styps
- | assert_typmatch thy arities eqngr (Var c_k') c_k vardeps_data =
- vardeps_data
- |> add_dep thy arities eqngr c_k c_k'
- | assert_typmatch thy arities eqngr Free c_k vardeps_data =
- vardeps_data
-and assert_rhs thy arities eqngr (c', styps) vardeps_data =
- vardeps_data
- |> assert_fun thy arities eqngr c'
- |> fold_index (fn (k, styp) =>
- assert_typmatch thy arities eqngr styp (Fun c', k)) styps
-and assert_fun thy arities eqngr c (vardeps_data as (_, (eqntab, _))) =
- if Symtab.defined eqntab c then vardeps_data
- else let
- val ((lhs, rhss), eqns) = obtain_eqns thy eqngr c;
- val rhss' = (map o apsnd o map) (styp_of (SOME (c, lhs))) rhss;
- in
- vardeps_data
- |> (apsnd o apfst) (Symtab.update_new (c, (lhs, eqns)))
- |> fold_index (fn (k, _) =>
- apfst (Vargraph.new_node ((Fun c, k), ([] ,[])))) lhs
- |> fold_index (fn (k, (_, sort)) =>
- add_classes thy arities eqngr (Fun c, k) (complete_proper_sort thy sort)) lhs
- |> fold (assert_rhs thy arities eqngr) rhss'
- end;
-
-
-(* applying instantiations *)
-
-fun dicts_of thy (proj_sort, algebra) (T, sort) =
- let
- fun class_relation (x, _) _ = x;
- fun type_constructor tyco xs class =
- inst_params thy tyco (Sorts.complete_sort algebra [class])
- @ (maps o maps) fst xs;
- fun type_variable (TFree (_, sort)) = map (pair []) (proj_sort sort);
- in
- flat (Sorts.of_sort_derivation (Syntax.pp_global thy) algebra
- { class_relation = class_relation, type_constructor = type_constructor,
- type_variable = type_variable } (T, proj_sort sort)
- handle Sorts.CLASS_ERROR _ => [] (*permissive!*))
- end;
-
-fun add_arity thy vardeps (class, tyco) =
- AList.default (op =)
- ((class, tyco), map (fn k => (snd o Vargraph.get_node vardeps) (Inst (class, tyco), k))
- (0 upto Sign.arity_number thy tyco - 1));
-
-fun add_eqs thy vardeps (c, (proto_lhs, proto_eqns)) (rhss, eqngr) =
- if can (Graph.get_node eqngr) c then (rhss, eqngr)
- else let
- val lhs = map_index (fn (k, (v, _)) =>
- (v, snd (Vargraph.get_node vardeps (Fun c, k)))) proto_lhs;
- val inst_tab = Vartab.empty |> fold (fn (v, sort) =>
- Vartab.update ((v, 0), sort)) lhs;
- val eqns = proto_eqns
- |> (map o apfst) (Code_Unit.inst_thm thy inst_tab);
- val (tyscm, rhss') = tyscm_rhss_of thy c eqns;
- val eqngr' = Graph.new_node (c, (tyscm, eqns)) eqngr;
- in (map (pair c) rhss' @ rhss, eqngr') end;
-
-fun extend_arities_eqngr thy cs ts (arities, eqngr) =
- let
- val cs_rhss = (fold o fold_aterms) (fn Const (c_ty as (c, _)) =>
- insert (op =) (c, (map (styp_of NONE) o Sign.const_typargs thy) c_ty) | _ => I) ts [];
- val (vardeps, (eqntab, insts)) = empty_vardeps_data
- |> fold (assert_fun thy arities eqngr) cs
- |> fold (assert_rhs thy arities eqngr) cs_rhss;
- val arities' = fold (add_arity thy vardeps) insts arities;
- val pp = Syntax.pp_global thy;
- val algebra = Sorts.subalgebra pp (is_proper_class thy)
- (AList.lookup (op =) arities') (Sign.classes_of thy);
- val (rhss, eqngr') = Symtab.fold (add_eqs thy vardeps) eqntab ([], eqngr);
- fun deps_of (c, rhs) = c :: maps (dicts_of thy algebra)
- (rhs ~~ (map snd o fst o fst o Graph.get_node eqngr') c);
- val eqngr'' = fold (fn (c, rhs) => fold
- (curry Graph.add_edge c) (deps_of rhs)) rhss eqngr';
- in (algebra, (arities', eqngr'')) end;
-
-
-(** store **)
-
-structure Wellsorted = CodeDataFun
-(
- type T = ((string * class) * sort list) list * code_graph;
- val empty = ([], Graph.empty);
- fun purge thy cs (arities, eqngr) =
- let
- val del_cs = ((Graph.all_preds eqngr
- o filter (can (Graph.get_node eqngr))) cs);
- val del_arities = del_cs
- |> map_filter (AxClass.inst_of_param thy)
- |> maps (fn (c, tyco) =>
- (map (rpair tyco) o Sign.complete_sort thy o the_list
- o AxClass.class_of_param thy) c);
- val arities' = fold (AList.delete (op =)) del_arities arities;
- val eqngr' = Graph.del_nodes del_cs eqngr;
- in (arities', eqngr') end;
-);
-
-
-(** retrieval interfaces **)
-
-fun obtain thy cs ts = apsnd snd
- (Wellsorted.change_yield thy (extend_arities_eqngr thy cs ts));
-
-fun prepare_sorts_typ prep_sort
- = map_type_tfree (fn (v, sort) => TFree (v, prep_sort sort));
-
-fun prepare_sorts prep_sort (Const (c, ty)) =
- Const (c, prepare_sorts_typ prep_sort ty)
- | prepare_sorts prep_sort (t1 $ t2) =
- prepare_sorts prep_sort t1 $ prepare_sorts prep_sort t2
- | prepare_sorts prep_sort (Abs (v, ty, t)) =
- Abs (v, prepare_sorts_typ prep_sort ty, prepare_sorts prep_sort t)
- | prepare_sorts _ (t as Bound _) = t;
-
-fun gen_eval thy cterm_of conclude_evaluation prep_sort evaluator proto_ct =
- let
- val pp = Syntax.pp_global thy;
- val ct = cterm_of proto_ct;
- val _ = (Sign.no_frees pp o map_types (K dummyT) o Sign.no_vars pp)
- (Thm.term_of ct);
- val thm = Code.preprocess_conv thy ct;
- val ct' = Thm.rhs_of thm;
- val t' = Thm.term_of ct';
- val vs = Term.add_tfrees t' [];
- val consts = fold_aterms
- (fn Const (c, _) => insert (op =) c | _ => I) t' [];
-
- val t'' = prepare_sorts prep_sort t';
- val (algebra', eqngr') = obtain thy consts [t''];
- in conclude_evaluation (evaluator algebra' eqngr' vs t'' ct') thm end;
-
-fun simple_evaluator evaluator algebra eqngr vs t ct =
- evaluator algebra eqngr vs t;
-
-fun eval_conv thy =
- let
- fun conclude_evaluation thm2 thm1 =
- let
- val thm3 = Code.postprocess_conv thy (Thm.rhs_of thm2);
- in
- Thm.transitive thm1 (Thm.transitive thm2 thm3) handle THM _ =>
- error ("could not construct evaluation proof:\n"
- ^ (cat_lines o map Display.string_of_thm) [thm1, thm2, thm3])
- end;
- in gen_eval thy I conclude_evaluation end;
-
-fun eval thy prep_sort postproc evaluator = gen_eval thy (Thm.cterm_of thy)
- (K o postproc (Code.postprocess_term thy)) prep_sort (simple_evaluator evaluator);
-
-end; (*struct*)