(* Title: Tools/code/code_funcgr.ML
ID: $Id$
Author: Florian Haftmann, TU Muenchen
Retrieving, well-sorting and structuring defining equations in graph
with explicit dependencies.
*)
signature CODE_FUNCGR =
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_Funcgr : CODE_FUNCGR =
struct
(** the graph type **)
type T = (((string * sort) list * typ) * (thm * bool) list) Graph.T;
fun eqns funcgr =
these o Option.map snd o try (Graph.get_node funcgr);
fun typ funcgr =
fst o Graph.get_node funcgr;
fun all funcgr = Graph.keys funcgr;
fun pretty thy funcgr =
AList.make (snd o Graph.get_node funcgr) (Graph.keys funcgr)
|> (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;
(** generic combinators **)
fun fold_consts f thms =
thms
|> maps (op :: o swap o apfst (snd o strip_comb) o Logic.dest_equals o Thm.plain_prop_of)
|> (fold o fold_aterms) (fn Const c => f c | _ => I);
fun consts_of (const, []) = []
| consts_of (const, thms as _ :: _) =
let
fun the_const (c, _) = if c = const then I else insert (op =) c
in fold_consts the_const (map fst thms) [] end;
(** graph algorithm **)
(* some nonsense -- FIXME *)
fun lhs_rhss_of thy c =
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, _) = case eqns of [] => Code.default_typscheme thy c
| ((thm, _) :: _) => (snd o Code_Unit.head_eqn thy) thm;
val rhss = fold_consts (fn (c, ty) =>
insert (op =) (c, Sign.const_typargs thy (c, Logic.unvarifyT ty))) (map fst eqns) [];
in (lhs, rhss) end;
fun inst_params thy tyco class =
map (fn (c, _) => AxClass.param_of_inst thy (c, tyco))
((#params o AxClass.get_info thy) class);
fun complete_proper_sort thy sort =
Sign.complete_sort thy sort |> filter (can (AxClass.get_info thy));
fun minimal_proper_sort thy sort =
complete_proper_sort thy sort |> Sign.minimize_sort thy;
fun dicts_of thy algebra (T, sort) =
let
fun class_relation (x, _) _ = x;
fun type_constructor tyco xs class =
inst_params thy tyco class @ (maps o maps) fst xs;
fun type_variable (TFree (_, sort)) = map (pair []) 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, minimal_proper_sort thy sort)
handle Sorts.CLASS_ERROR _ => [] (*permissive!*))
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;
type vardeps = const list * ((string * styp list) list * class list) Vargraph.T;
(* computing instantiations -- FIXME does not consider existing things *)
fun add_classes thy c_k new_classes vardeps =
let
val _ = tracing "add_classes";
val (styps, old_classes) = Vargraph.get_node (snd vardeps) c_k;
val diff_classes = new_classes |> subtract (op =) old_classes;
in if null diff_classes then vardeps
else let
val c_ks = Vargraph.imm_succs (snd vardeps) c_k |> insert (op =) c_k;
in
vardeps
|> (apsnd o Vargraph.map_node c_k o apsnd) (append diff_classes)
|> fold (fn styp => fold (add_typmatch_inst thy styp) new_classes) styps
|> fold (fn c_k => add_classes thy c_k diff_classes) c_ks
end end
and add_styp thy c_k tyco_styps vardeps =
let
val _ = tracing "add_styp";
val (old_styps, classes) = Vargraph.get_node (snd vardeps) c_k;
in if member (op =) old_styps tyco_styps then vardeps
else
vardeps
|> (apsnd o Vargraph.map_node c_k o apfst) (cons tyco_styps)
|> fold (add_typmatch_inst thy tyco_styps) classes
end
and add_dep thy c_k c_k' vardeps =
let
val _ = tracing ("add_dep " ^ makestring c_k ^ " -> " ^ makestring c_k');
val (_, classes) = Vargraph.get_node (snd vardeps) c_k;
in
vardeps
|> add_classes thy c_k' classes
|> apsnd (Vargraph.add_edge (c_k, c_k'))
end
and add_typmatch_inst thy (tyco, styps) class vardeps = if can (Sign.arity_sorts thy tyco) [class]
then vardeps
|> tap (fn _ => tracing "add_typmatch_inst")
|> assert thy (Inst (class, tyco))
|> fold_index (fn (k, styp) =>
add_typmatch thy styp (Inst (class, tyco), k)) styps
else vardeps (*permissive!*)
and add_typmatch thy (Var c_k') c_k vardeps =
vardeps
|> tap (fn _ => tracing "add_typmatch (Inst)")
|> add_dep thy c_k c_k'
| add_typmatch thy (Tyco tyco_styps) c_k vardeps =
vardeps
|> tap (fn _ => tracing "add_typmatch (Tyco)")
|> add_styp thy c_k tyco_styps
and add_inst thy (class, tyco) vardeps =
let
val _ = tracing ("add_inst " ^ tyco ^ "::" ^ class);
val superclasses = complete_proper_sort thy
(Sign.super_classes thy class);
val classess = map (complete_proper_sort thy)
(Sign.arity_sorts thy tyco [class]);
val inst_params = inst_params thy tyco class;
in
vardeps
|> fold (fn superclass => assert thy (Inst (superclass, tyco))) superclasses
|> fold (assert thy o Fun) inst_params
|> fold_index (fn (k, classes) =>
apsnd (Vargraph.default_node ((Inst (class, tyco), k), ([] ,[])))
#> add_classes thy (Inst (class, tyco), k) classes
#> fold (fn superclass =>
add_dep thy (Inst (superclass, tyco), k)
(Inst (class, tyco), k)) superclasses
#> fold (fn inst_param =>
add_dep thy (Fun inst_param, k)
(Inst (class, tyco), k)
) inst_params
) classess
end
and add_const thy c vardeps =
let
val _ = tracing "add_const";
val (lhs, rhss) = lhs_rhss_of thy c;
fun styp_of (Type (tyco, tys)) = Tyco (tyco, map styp_of tys)
| styp_of (TFree (v, _)) = Var (Fun c, find_index (fn (v', _) => v = v') lhs);
val rhss' = (map o apsnd o map) styp_of rhss;
in
vardeps
|> fold_index (fn (k, (_, sort)) =>
apsnd (Vargraph.default_node ((Fun c, k), ([] ,[])))
#> add_classes thy (Fun c, k) (complete_proper_sort thy sort)) lhs
|> fold (assert thy o Fun o fst) rhss'
|> fold (fn (c', styps) => fold_index (fn (k', styp) =>
add_typmatch thy styp (Fun c', k')) styps) rhss'
end
and assert thy c (vardeps as (asserted, _)) =
if member (op =) asserted c then vardeps
else case c
of Fun const => vardeps |> apfst (cons c) |> add_const thy const
| Inst inst => vardeps |> apfst (cons c) |> add_inst thy inst;
(* applying instantiations *)
fun algebra_of thy vardeps =
let
val pp = Syntax.pp_global thy;
val thy_algebra = Sign.classes_of thy;
val is_proper = can (AxClass.get_info thy);
val arities = Vargraph.fold (fn ((Fun _, _), _) => I
| ((Inst (class, tyco), k), ((_, classes), _)) =>
AList.map_default (op =)
((tyco, class), replicate (Sign.arity_number thy tyco) [])
(nth_map k (K classes))) vardeps [];
val classrels = Sorts.classrels_of thy_algebra
|> filter (is_proper o fst)
|> (map o apsnd) (filter is_proper);
fun add_arity (tyco, class) = case AList.lookup (op =) arities (tyco, class)
of SOME sorts => Sorts.add_arities pp (tyco, [(class, sorts)])
| NONE => if Sign.arity_number thy tyco = 0
then (tracing (tyco ^ "::" ^ class); Sorts.add_arities pp (tyco, [(class, [])]))
else I;
val instances = Sorts.instances_of thy_algebra
|> filter (is_proper o snd)
in
Sorts.empty_algebra
|> fold (Sorts.add_class pp) classrels
|> fold add_arity instances
end;
fun add_eqs thy algebra vardeps c gr =
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 (vs, _) = case eqns of [] => Code.default_typscheme thy c
| ((thm, _) :: _) => (snd o Code_Unit.head_eqn thy) thm;
val inst = Vartab.empty |> fold_index (fn (k, (v, _)) =>
Vartab.update ((v, 0), snd (Vargraph.get_node vardeps (Fun c, k)))) vs;
val eqns' = eqns
|> (map o apfst) (Code_Unit.inst_thm thy inst);
val tyscm = case eqns' of [] => Code.default_typscheme thy c
| ((thm, _) :: _) => (snd o Code_Unit.head_eqn thy) thm;
val _ = tracing ("tyscm " ^ makestring (map snd (fst tyscm)));
val rhss = fold_consts (fn (c, ty) =>
insert (op =) (c, Sign.const_typargs thy (c, Logic.unvarifyT ty))) (map fst eqns') [];
in
gr
|> Graph.new_node (c, (tyscm, eqns'))
|> fold (fn (c', Ts) => ensure_eqs_dep thy algebra vardeps c c'
#-> (fn (vs, _) =>
fold2 (ensure_match thy algebra vardeps c) Ts (map snd vs))) rhss
|> pair tyscm
end
and ensure_match thy algebra vardeps c T sort gr =
gr
|> fold (fn c' => ensure_eqs_dep thy algebra vardeps c c' #> snd)
(dicts_of thy algebra (T, sort))
and ensure_eqs_dep thy algebra vardeps c c' gr =
gr
|> ensure_eqs thy algebra vardeps c'
||> Graph.add_edge (c, c')
and ensure_eqs thy algebra vardeps c gr =
case try (Graph.get_node gr) c
of SOME (tyscm, _) => (tyscm, gr)
| NONE => add_eqs thy algebra vardeps c gr;
fun extend_graph thy cs gr =
let
val _ = tracing ("extending with " ^ commas cs);
val _ = tracing "obtaining instantiations";
val (_, vardeps) = fold (assert thy o Fun) cs ([], Vargraph.empty)
val _ = tracing "obtaining algebra";
val algebra = algebra_of thy vardeps;
val _ = tracing "obtaining equations";
val (_, gr) = fold_map (ensure_eqs thy algebra vardeps) cs gr;
val _ = tracing "sort projection";
val minimal_proper_sort = fn sort => sort
|> Sorts.complete_sort (Sign.classes_of thy)
|> filter (can (AxClass.get_info thy))
|> Sorts.minimize_sort algebra;
in ((minimal_proper_sort, algebra), gr) end;
(** retrieval interfaces **)
fun proto_eval thy cterm_of evaluator_lift evaluator proto_ct funcgr =
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 consts = map fst (consts_of t');
val (algebra', funcgr') = extend_graph thy consts funcgr;
val (t'', evaluator_funcgr) = evaluator t';
val consts' = consts_of t'';
val const_matches = fold (fn (c, ty) =>
insert (op =) (Sign.const_typargs thy (c, Logic.unvarifyT ty), c)) consts' [];
val typ_matches = maps (fn (tys, c) => tys ~~ map snd (fst (fst (Graph.get_node funcgr' c))))
const_matches;
val dicts = maps (dicts_of thy (snd algebra')) typ_matches;
val (algebra'', funcgr'') = extend_graph thy dicts funcgr';
in (evaluator_lift (evaluator_funcgr algebra'') thm funcgr'', funcgr'') end;
fun proto_eval_conv thy =
let
fun evaluator_lift evaluator thm1 funcgr =
let
val thm2 = evaluator funcgr;
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 _ funcgr = evaluator funcgr;
in proto_eval thy (Thm.cterm_of thy) evaluator_lift end;
structure Funcgr = CodeDataFun
(
type T = T;
val empty = Graph.empty;
fun purge _ cs funcgr =
Graph.del_nodes ((Graph.all_preds funcgr
o filter (can (Graph.get_node funcgr))) cs) funcgr;
);
fun make thy = Funcgr.change_yield thy o extend_graph thy;
fun eval_conv thy f =
fst o Funcgr.change_yield thy o proto_eval_conv thy f;
fun eval_term thy f =
fst o Funcgr.change_yield thy o proto_eval_term thy f;
(** diagnostic commands **)
fun code_depgr thy consts =
let
val (_, gr) = make thy consts;
val select = Graph.all_succs gr consts;
in
gr
|> 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 gr = code_depgr thy consts;
fun mk_entry (const, (_, (_, parents))) =
let
val name = Code_Unit.string_of_const thy const;
val nameparents = map (Code_Unit.string_of_const thy) parents;
in { name = name, ID = name, dir = "", unfold = true,
path = "", parents = nameparents }
end;
val prgr = Graph.fold ((fn x => fn xs => xs @ [x]) o mk_entry) gr [];
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 defining 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 defining 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*)