(*  Title:      Tools/Code/code_preproc.ML

    Author:     Florian Haftmann, TU Muenchen

Preprocessing code equations into a well-sorted system

in a graph with explicit dependencies.

*)

signature CODE_PREPROC =

sig

  val map_pre: (simpset -> simpset) -> theory -> theory

  val map_post: (simpset -> simpset) -> theory -> theory

  val add_unfold: thm -> theory -> theory

  val add_functrans: string * (theory -> (thm * bool) list -> (thm * bool) list option) -> theory -> theory

  val del_functrans: string -> theory -> theory

  val simple_functrans: (theory -> thm list -> thm list option)

    -> theory -> (thm * bool) list -> (thm * bool) list option

  val preprocess_functrans: theory -> (thm * bool) list -> (thm * bool) list

  val print_codeproc: theory -> unit

  type code_algebra

  type code_graph

  val cert: code_graph -> string -> Code.cert

  val sortargs: code_graph -> string -> sort list

  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

    -> (code_algebra -> code_graph -> (string * sort) list -> term -> cterm -> thm) -> cterm -> thm

  val eval: theory -> ((term -> term) -> 'a -> 'a)

    -> (code_algebra -> code_graph -> (string * sort) list -> term -> 'a) -> term -> 'a

  val pre_post_conv: theory -> (cterm -> thm) -> cterm -> thm

  val setup: theory -> theory

end

structure Code_Preproc : CODE_PREPROC =

struct

(** preprocessor administration **)

(* theory data *)

datatype thmproc = Thmproc of {

  pre: simpset,

  post: simpset,

  functrans: (string * (serial * (theory -> (thm * bool) list -> (thm * bool) list option))) list

};

fun make_thmproc ((pre, post), functrans) =

  Thmproc { pre = pre, post = post, functrans = functrans };

fun map_thmproc f (Thmproc { pre, post, functrans }) =

  make_thmproc (f ((pre, post), functrans));

fun merge_thmproc (Thmproc { pre = pre1, post = post1, functrans = functrans1 },

  Thmproc { pre = pre2, post = post2, functrans = functrans2 }) =

    let

      val pre = Simplifier.merge_ss (pre1, pre2);

      val post = Simplifier.merge_ss (post1, post2);

      val functrans = AList.merge (op =) (eq_fst (op =)) (functrans1, functrans2)

        handle AList.DUP => error ("Duplicate function transformer");

    in make_thmproc ((pre, post), functrans) end;

structure Code_Preproc_Data = Theory_Data

(

  type T = thmproc;

  val empty = make_thmproc ((Simplifier.empty_ss, Simplifier.empty_ss), []);

  val extend = I;

  val merge = merge_thmproc;

);

fun the_thmproc thy = case Code_Preproc_Data.get thy

 of Thmproc x => x;

fun delete_force msg key xs =

  if AList.defined (op =) xs key then AList.delete (op =) key xs

  else error ("No such " ^ msg ^ ": " ^ quote key);

fun map_data f = Code.purge_data

  #> (Code_Preproc_Data.map o map_thmproc) f;

val map_pre_post = map_data o apfst;

val map_pre = map_pre_post o apfst;

val map_post = map_pre_post o apsnd;

val add_unfold = map_pre o MetaSimplifier.add_simp;

val del_unfold = map_pre o MetaSimplifier.del_simp;

val add_post = map_post o MetaSimplifier.add_simp;

val del_post = map_post o MetaSimplifier.del_simp;

fun add_unfold_post raw_thm thy =

  let

    val thm = Local_Defs.meta_rewrite_rule (ProofContext.init_global thy) raw_thm;

    val thm_sym = Thm.symmetric thm;

  in

    thy |> map_pre_post (fn (pre, post) =>

      (pre |> MetaSimplifier.add_simp thm, post |> MetaSimplifier.del_simp thm_sym))

  end;

fun add_functrans (name, f) = (map_data o apsnd)

  (AList.update (op =) (name, (serial (), f)));

fun del_functrans name = (map_data o apsnd)

  (delete_force "function transformer" name);

(* post- and preprocessing *)

fun trans_conv_rule conv thm = Thm.transitive thm ((conv o Thm.rhs_of) thm);

fun eqn_conv conv ct =

  let

    fun lhs_conv ct = if can Thm.dest_comb ct

      then Conv.combination_conv lhs_conv conv ct

      else Conv.all_conv ct;

  in Conv.combination_conv (Conv.arg_conv lhs_conv) conv ct end;

val rewrite_eqn = Conv.fconv_rule o eqn_conv o Simplifier.rewrite;

fun term_of_conv thy f =

  Thm.cterm_of thy

  #> f

  #> Thm.prop_of

  #> Logic.dest_equals

  #> snd;

fun preprocess_functrans thy = 

  let

    val functrans = (map (fn (_, (_, f)) => f thy) o #functrans

      o the_thmproc) thy;

  in perhaps (perhaps_loop (perhaps_apply functrans)) end;

fun preprocess thy =

  let

    val pre = (Simplifier.global_context thy o #pre o the_thmproc) thy;

  in

    preprocess_functrans thy

    #> (map o apfst) (rewrite_eqn pre)

  end;

fun preprocess_conv thy ct =

  let

    val pre = (Simplifier.global_context thy o #pre o the_thmproc) thy;

  in

    ct

    |> Simplifier.rewrite pre

    |> trans_conv_rule (AxClass.unoverload_conv thy)

  end;

fun postprocess_conv thy ct =

  let

    val post = (Simplifier.global_context thy o #post o the_thmproc) thy;

  in

    ct

    |> AxClass.overload_conv thy

    |> trans_conv_rule (Simplifier.rewrite post)

  end;

fun postprocess_term thy = term_of_conv thy (postprocess_conv thy);

fun print_codeproc thy =

  let

    val ctxt = ProofContext.init_global thy;

    val pre = (#pre o the_thmproc) thy;

    val post = (#post o the_thmproc) thy;

    val functrans = (map fst o #functrans o the_thmproc) thy;

  in

    (Pretty.writeln o Pretty.chunks) [

      Pretty.block [

        Pretty.str "preprocessing simpset:",

        Pretty.fbrk,

        Simplifier.pretty_ss ctxt pre

      ],

      Pretty.block [

        Pretty.str "postprocessing simpset:",

        Pretty.fbrk,

        Simplifier.pretty_ss ctxt post

      ],

      Pretty.block (

        Pretty.str "function transformers:"

        :: Pretty.fbrk

        :: (Pretty.fbreaks o map Pretty.str) functrans

      )

    ]

  end;

fun simple_functrans f thy eqns = case f thy (map fst eqns)

 of SOME thms' => SOME (map (rpair (forall snd eqns)) thms')

  | NONE => NONE;

(** sort algebra and code equation graph types **)

type code_algebra = (sort -> sort) * Sorts.algebra;

type code_graph = ((string * sort) list * Code.cert) Graph.T;

fun cert eqngr = snd o Graph.get_node eqngr;

fun sortargs eqngr = map snd o 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.string_of_const thy)

  |> sort (string_ord o pairself fst)

  |> map (fn (s, cert) => (Pretty.block o Pretty.fbreaks) (Pretty.str s :: Code.pretty_cert thy cert))

  |> 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);

(* 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 =

  Graph(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 * Code.cert) 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, cert) => ((lhs, []), cert)

    | NONE => let

        val cert = Code.get_cert thy (preprocess thy) c;

        val (lhs, rhss) = Code.typargs_deps_of_cert thy cert;

      in ((lhs, rhss), cert) 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 super_classes = 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, (super_classes, 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 (ensure_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 new_tyco_styps vardeps_data =

  let

    val (old_tyco_stypss, classes) = Vargraph.get_node (fst vardeps_data) c_k;

  in if member (op =) old_tyco_stypss new_tyco_styps then vardeps_data

  else

    vardeps_data

    |> (apfst o Vargraph.map_node c_k o apfst) (cons new_tyco_styps)

    |> fold (ensure_typmatch_inst thy arities eqngr new_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 ensure_typmatch_inst thy arities eqngr (tyco, styps) class vardeps_data =

  if can (Sign.arity_sorts thy tyco) [class]

  then vardeps_data

    |> ensure_inst thy arities eqngr (class, tyco)

    |> fold_index (fn (k, styp) =>

         ensure_typmatch thy arities eqngr styp (Inst (class, tyco), k)) styps

  else vardeps_data (*permissive!*)

and ensure_inst thy arities eqngr (inst as (class, tyco)) (vardeps_data as (_, (_, insts))) =

  if member (op =) insts inst then vardeps_data

  else let

    val (classess, (super_classes, 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 super_class => ensure_inst thy arities eqngr (super_class, tyco)) super_classes

    |> fold (ensure_fun thy arities eqngr) inst_params

    |> fold_index (fn (k, classes) =>

         add_classes thy arities eqngr (Inst (class, tyco), k) classes

         #> fold (fn super_class =>

             add_dep thy arities eqngr (Inst (super_class, tyco), k)

             (Inst (class, tyco), k)) super_classes

         #> fold (fn inst_param =>

             add_dep thy arities eqngr (Fun inst_param, k)

             (Inst (class, tyco), k)

             ) inst_params

         ) classess

  end

and ensure_typmatch thy arities eqngr (Tyco tyco_styps) c_k vardeps_data =

      vardeps_data

      |> add_styp thy arities eqngr c_k tyco_styps

  | ensure_typmatch thy arities eqngr (Var c_k') c_k vardeps_data =

      vardeps_data

      |> add_dep thy arities eqngr c_k c_k'

  | ensure_typmatch thy arities eqngr Free c_k vardeps_data =

      vardeps_data

and ensure_rhs thy arities eqngr (c', styps) vardeps_data =

  vardeps_data

  |> ensure_fun thy arities eqngr c'

  |> fold_index (fn (k, styp) =>

       ensure_typmatch thy arities eqngr styp (Fun c', k)) styps

and ensure_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 (ensure_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 algebra

      { class_relation = K 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_range (fn k => (snd o Vargraph.get_node vardeps) (Inst (class, tyco), k))

      (Sign.arity_number thy tyco));

fun add_cert thy vardeps (c, (proto_lhs, proto_cert)) (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 cert = Code.constrain_cert thy (map snd lhs) proto_cert;

    val (vs, rhss') = Code.typargs_deps_of_cert thy cert;

    val eqngr' = Graph.new_node (c, (vs, cert)) eqngr;

  in (map (pair c) rhss' @ rhss, eqngr') end;

fun extend_arities_eqngr thy cs ts (arities, (eqngr : code_graph)) =

  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 (ensure_fun thy arities eqngr) cs

      |> fold (ensure_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_cert thy vardeps) eqntab ([], eqngr);

    fun deps_of (c, rhs) = c :: maps (dicts_of thy algebra)

      (rhs ~~ sortargs 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 for preprocessed arities and code equations **)

structure Wellsorted = Code_Data

(

  type T = ((string * class) * sort list) list * code_graph;

  val empty = ([], Graph.empty);

);

(** retrieval and evaluation interfaces **)

fun obtain thy cs ts = apsnd snd

  (Wellsorted.change_yield thy (extend_arities_eqngr thy cs ts));

fun gen_eval thy cterm_of conclude_evaluation 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 = 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 (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 = 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_global thy)) [thm1, thm2, thm3])

      end;

  in gen_eval thy I conclude_evaluation end;

fun eval thy postproc evaluator = gen_eval thy (Thm.cterm_of thy)

  (K o postproc (postprocess_term thy)) (simple_evaluator evaluator);

fun pre_post_conv thy conv = (preprocess_conv thy) then_conv conv then_conv (postprocess_conv thy);

(** setup **)

val setup = 

  let

    fun mk_attribute f = Thm.declaration_attribute (fn thm => Context.mapping (f thm) I);

    fun add_del_attribute_parser add del =

      Attrib.add_del (mk_attribute add) (mk_attribute del);

    fun both f g thm = f thm #> g thm;

  in

    Attrib.setup @{binding code_unfold} (add_del_attribute_parser 

       (both Codegen.add_unfold add_unfold) (both Codegen.del_unfold del_unfold))

        "preprocessing equations for code generators"

    #> Attrib.setup @{binding code_inline} (add_del_attribute_parser add_unfold del_unfold)

        "preprocessing equations for code generator"

    #> Attrib.setup @{binding code_post} (add_del_attribute_parser add_post del_post)

        "postprocessing equations for code generator"

    #> Attrib.setup @{binding code_unfold_post} (Scan.succeed (mk_attribute add_unfold_post))

        "pre- and postprocessing equations for code generator"

  end;

val _ =

  Outer_Syntax.improper_command "print_codeproc" "print code preprocessor setup"

  Keyword.diag (Scan.succeed

      (Toplevel.no_timing o Toplevel.unknown_theory o Toplevel.keep

        (print_codeproc o Toplevel.theory_of)));

end; (*struct*)