(*  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;

    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) eqngr [];

  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*)