(* 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 T
val eqns: T -> string -> (thm * bool) list
val typ: T -> string -> (string * sort) list * typ
val all: T -> string list
val pretty: theory -> T -> Pretty.T
val make: theory -> string list
-> ((sort -> sort) * Sorts.algebra) * T
val eval_conv: theory
-> (term -> term * (((sort -> sort) * Sorts.algebra) -> T -> thm)) -> cterm -> thm
val eval_term: theory
-> (term -> term * (((sort -> sort) * Sorts.algebra) -> T -> 'a)) -> term -> 'a
end
structure Code_Wellsorted : CODE_WELLSORTED =
struct
(** the equation graph type **)
type T = (((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 complete_proper_sort thy =
Sign.complete_sort thy #> filter (can (AxClass.get_info 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, _) :: _) => (snd o Code_Unit.head_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 Code_Name.purify_tvar Code_Name.purify_var);
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 (proj_sort, algebra) 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 cs_rhss (arities, eqngr) =
let
val cs_rhss' = (map o apsnd o map) (styp_of NONE) cs_rhss;
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 is_proper_class = can (AxClass.get_info thy);
val (proj_sort, algebra) = Sorts.subalgebra pp is_proper_class
(AList.lookup (op =) arities') (Sign.classes_of thy);
val (rhss, eqngr') = Symtab.fold
(add_eqs thy (proj_sort, algebra) vardeps) eqntab ([], eqngr);
fun deps_of (c, rhs) = c ::
maps (dicts_of thy (proj_sort, 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 ((proj_sort, algebra), (arities', eqngr'')) end;
(** retrieval interfaces **)
fun proto_eval thy cterm_of evaluator_lift evaluator proto_ct arities_eqngr =
let
val ct = cterm_of proto_ct;
val _ = Sign.no_vars (Syntax.pp_global thy) (Thm.term_of ct);
val _ = Term.fold_types (Type.no_tvars #> K I) (Thm.term_of ct) ();
fun consts_of t =
fold_aterms (fn Const c_ty => cons c_ty | _ => I) t [];
val thm = Code.preprocess_conv thy ct;
val ct' = Thm.rhs_of thm;
val t' = Thm.term_of ct';
val (t'', evaluator_eqngr) = evaluator t';
val consts = map fst (consts_of t');
val consts' = consts_of t'';
val const_matches' = fold (fn (c, ty) =>
insert (op =) (c, Sign.const_typargs thy (c, ty))) consts' [];
val (algebra', arities_eqngr') =
extend_arities_eqngr thy consts const_matches' arities_eqngr;
in
(evaluator_lift (evaluator_eqngr algebra') thm (snd arities_eqngr'),
arities_eqngr')
end;
fun proto_eval_conv thy =
let
fun evaluator_lift evaluator thm1 eqngr =
let
val thm2 = evaluator eqngr;
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 proto_eval thy I evaluator_lift end;
fun proto_eval_term thy =
let
fun evaluator_lift evaluator _ eqngr = evaluator eqngr;
in proto_eval thy (Thm.cterm_of thy) evaluator_lift end;
structure Wellsorted = CodeDataFun
(
type T = ((string * class) * sort list) list * T;
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;
);
fun make thy cs = apsnd snd
(Wellsorted.change_yield thy (extend_arities_eqngr thy cs []));
fun eval_conv thy f =
fst o Wellsorted.change_yield thy o proto_eval_conv thy f;
fun eval_term thy f =
fst o Wellsorted.change_yield thy o proto_eval_term thy f;
(** diagnostic commands **)
fun code_depgr thy consts =
let
val (_, eqngr) = make thy consts;
val select = Graph.all_succs eqngr consts;
in
eqngr
|> not (null consts) ? Graph.subgraph (member (op =) select)
|> Graph.map_nodes ((apsnd o map o apfst) (AxClass.overload thy))
end;
fun code_thms thy = Pretty.writeln o pretty thy o code_depgr thy;
fun code_deps thy consts =
let
val eqngr = code_depgr thy consts;
val constss = Graph.strong_conn eqngr;
val mapping = Symtab.empty |> fold (fn consts => fold (fn const =>
Symtab.update (const, consts)) consts) constss;
fun succs consts = consts
|> maps (Graph.imm_succs eqngr)
|> subtract (op =) consts
|> map (the o Symtab.lookup mapping)
|> distinct (op =);
val conn = [] |> fold (fn consts => cons (consts, succs consts)) constss;
fun namify consts = map (Code_Unit.string_of_const thy) consts
|> commas;
val prgr = map (fn (consts, constss) =>
{ name = namify consts, ID = namify consts, dir = "", unfold = true,
path = "", parents = map namify constss }) conn;
in Present.display_graph prgr end;
local
structure P = OuterParse
and K = OuterKeyword
fun code_thms_cmd thy = code_thms thy o op @ o Code_Name.read_const_exprs thy;
fun code_deps_cmd thy = code_deps thy o op @ o Code_Name.read_const_exprs thy;
in
val _ =
OuterSyntax.improper_command "code_thms" "print system of code equations for code" OuterKeyword.diag
(Scan.repeat P.term_group
>> (fn cs => Toplevel.no_timing o Toplevel.unknown_theory
o Toplevel.keep ((fn thy => code_thms_cmd thy cs) o Toplevel.theory_of)));
val _ =
OuterSyntax.improper_command "code_deps" "visualize dependencies of code equations for code" OuterKeyword.diag
(Scan.repeat P.term_group
>> (fn cs => Toplevel.no_timing o Toplevel.unknown_theory
o Toplevel.keep ((fn thy => code_deps_cmd thy cs) o Toplevel.theory_of)));
end;
end; (*struct*)