src/Pure/Tools/codegen_theorems.ML

tuned;

(*  Title:      Pure/Tools/codegen_theorems.ML
    ID:         $Id$
    Author:     Florian Haftmann, TU Muenchen

Theorems used for code generation.
*)

signature CODEGEN_THEOREMS =
sig
  val add_notify: ((string * typ) list option -> theory -> theory) -> theory -> theory;
  val add_preproc: (theory -> thm list -> thm list) -> theory -> theory;
  val add_fun_extr: (theory -> string * typ -> thm list) -> theory -> theory;
  val add_datatype_extr: (theory -> string
    -> (((string * sort) list * (string * typ list) list) * tactic) option)
    -> theory -> theory;
  val add_fun: thm -> theory -> theory;
  val del_fun: thm -> theory -> theory;
  val add_unfold: thm -> theory -> theory;
  val del_unfold: thm -> theory -> theory;
  val purge_defs: string * typ -> theory -> theory;
  val notify_dirty: theory -> theory;

  val extr_typ: theory -> thm -> typ;
  val rewrite_fun: thm list -> thm -> thm;
  val common_typ: theory -> (thm -> typ) -> thm list -> thm list;
  val preprocess: theory -> thm list -> thm list;

  val prove_freeness: theory -> tactic -> string
    -> (string * sort) list * (string * typ list) list -> thm list;

  type thmtab;
  val mk_thmtab: theory -> (string * typ) list -> thmtab;
  val get_sortalgebra: thmtab -> Sorts.algebra;
  val get_dtyp_of_cons: thmtab -> string * typ -> string option;
  val get_dtyp_spec: thmtab -> string
    -> ((string * sort) list * (string * typ list) list) option;
  val get_fun_thms: thmtab -> string * typ -> thm list;

  val pretty_funtab: theory -> thm list CodegenConsts.Consttab.table -> Pretty.T;
  val print_thms: theory -> unit;

  val init_obj: (thm * thm) * (thm * thm) -> theory -> theory;
  val debug: bool ref;
  val debug_msg: ('a -> string) -> 'a -> 'a;
end;

structure CodegenTheorems: CODEGEN_THEOREMS =
struct

(** preliminaries **)

(* diagnostics *)

val debug = ref false;
fun debug_msg f x = (if !debug then Output.tracing (f x) else (); x);


(* auxiliary *)

fun getf_first [] _ = NONE
  | getf_first (f::fs) x = case f x
     of NONE => getf_first fs x
      | y as SOME x => y;

fun getf_first_list [] x = []
  | getf_first_list (f::fs) x = case f x
     of [] => getf_first_list fs x
      | xs => xs;


(* object logic setup *)

structure CodegenTheoremsSetup = TheoryDataFun
(struct
  val name = "Pure/codegen_theorems_setup";
  type T = ((string * thm) * ((string * string) * (string * string))) option;
  val empty = NONE;
  val copy = I;
  val extend = I;
  fun merge pp = merge_opt (eq_pair (eq_pair (op =) eq_thm)
    (eq_pair (eq_pair (op =) (op =)) (eq_pair (op =) (op =)))) : T * T -> T;
  fun print thy data = ();
end);

val _ = Context.add_setup CodegenTheoremsSetup.init;

fun init_obj ((TrueI, FalseE), (conjI, atomize_eq)) thy =
  case CodegenTheoremsSetup.get thy
   of SOME _ => error "Code generator already set up for object logic"
    | NONE =>
        let
          fun strip_implies t = (Logic.strip_imp_prems t, Logic.strip_imp_concl t);
          fun dest_TrueI thm =
            Drule.plain_prop_of thm
            |> ObjectLogic.drop_judgment thy
            |> Term.dest_Const
            |> apsnd (
                  Term.dest_Type
                  #> fst
              );
          fun dest_FalseE thm =
            Drule.plain_prop_of thm
            |> Logic.dest_implies
            |> apsnd (
                 ObjectLogic.drop_judgment thy
                 #> Term.dest_Var
               )
            |> fst
            |> ObjectLogic.drop_judgment thy
            |> Term.dest_Const
            |> fst;
          fun dest_conjI thm =
            Drule.plain_prop_of thm
            |> strip_implies
            |> apfst (map (ObjectLogic.drop_judgment thy #> Term.dest_Var))
            |> apsnd (
                 ObjectLogic.drop_judgment thy
                 #> Term.strip_comb
                 #> apsnd (map Term.dest_Var)
                 #> apfst Term.dest_Const
               )
            |> (fn (v1, ((conj, _), v2)) => if v1 = v2 then conj else error "Wrong premise")
          fun dest_atomize_eq thm=
            Drule.plain_prop_of thm
            |> Logic.dest_equals
            |> apfst (
                 ObjectLogic.drop_judgment thy
                 #> Term.strip_comb
                 #> apsnd (map Term.dest_Var)
                 #> apfst Term.dest_Const
               )
            |> apsnd (
                 Logic.dest_equals
                 #> apfst Term.dest_Var
                 #> apsnd Term.dest_Var
               )
            |> (fn (((eq, _), v2), (v1a as (_, TVar (_, sort)), v1b)) =>
                 if [v1a, v1b] = v2 andalso sort = Sign.defaultS thy then eq else error "Wrong premise")
        in
          ((dest_TrueI TrueI, [dest_FalseE FalseE, dest_conjI conjI, dest_atomize_eq atomize_eq])
          handle _ => error "Bad code generator setup")
          |> (fn ((tr, b), [fl, con, eq]) => CodegenTheoremsSetup.put
               (SOME ((b, atomize_eq), ((tr, fl), (con, eq)))) thy)
        end;

fun get_obj thy =
  case CodegenTheoremsSetup.get thy
   of SOME ((b, atomize), x) => ((Type (b, []), atomize) ,x)
    | NONE => error "No object logic setup for code theorems";

fun mk_true thy =
  let
    val ((b, _), ((tr, fl), (con, eq))) = get_obj thy;
  in Const (tr, b) end;

fun mk_false thy =
  let
    val ((b, _), ((tr, fl), (con, eq))) = get_obj thy;
  in Const (fl, b) end;

fun mk_obj_conj thy (x, y) =
  let
    val ((b, _), ((tr, fl), (con, eq))) = get_obj thy;
  in Const (con, b --> b --> b) $ x $ y end;

fun mk_obj_eq thy (x, y) =
  let
    val ((b, _), ((tr, fl), (con, eq))) = get_obj thy;
  in Const (eq, fastype_of x --> fastype_of y --> b) $ x $ y end;

fun is_obj_eq thy c =
  let
    val ((b, _), ((tr, fl), (con, eq))) = get_obj thy;
  in c = eq end;

fun mk_func thy ((x, y), rhs) =
  Logic.mk_equals (
    (mk_obj_eq thy (x, y)),
    rhs
  );


(* theorem purification *)

fun err_thm msg thm =
  error (msg ^ ": " ^ string_of_thm thm);

val mk_rule =
  #mk o #mk_rews o snd o MetaSimplifier.rep_ss o Simplifier.simpset_of;

fun abs_norm thy thm =
  let
    fun expvars t =
      let
        val lhs = (fst o Logic.dest_equals) t;
        val tys = (fst o strip_type o fastype_of) lhs;
        val used = fold_aterms (fn Var ((v, _), _) => insert (op =) v | _ => I) lhs [];
        val vs = Name.invent_list used "x" (length tys);
      in
        map2 (fn v => fn ty => Var ((v, 0), ty)) vs tys
      end;
    fun expand ct thm =
      Thm.combination thm (Thm.reflexive ct);
    fun beta_norm thm =
      thm
      |> prop_of
      |> Logic.dest_equals
      |> fst
      |> cterm_of thy
      |> Thm.beta_conversion true
      |> Thm.symmetric
      |> (fn thm' => Thm.transitive thm' thm);
  in
    thm
    |> fold (expand o cterm_of thy) ((expvars o prop_of) thm)
    |> beta_norm
  end;

fun canonical_tvars thy thm =
  let
    fun mk_inst (v_i as (v, i), (v', sort)) (s as (maxidx, set, acc)) =
      if v = v' orelse member (op =) set v then s
        else let
          val ty = TVar (v_i, sort)
        in
          (maxidx + 1, v :: set,
            (ctyp_of thy ty, ctyp_of thy (TVar ((v', maxidx), sort))) :: acc)
        end;
    fun tvars_of thm = (fold_types o fold_atyps)
      (fn TVar (v_i as (v, i), sort) => cons (v_i, (CodegenNames.purify_var v, sort))
        | _ => I) (prop_of thm) [];
    val maxidx = Thm.maxidx_of thm + 1;
    val (_, _, inst) = fold mk_inst (tvars_of thm) (maxidx + 1, [], []);
  in Thm.instantiate (inst, []) thm end;

fun canonical_vars thy thm =
  let
    fun mk_inst (v_i as (v, i), (v', ty)) (s as (maxidx, set, acc)) =
      if v = v' orelse member (op =) set v then s
        else let
          val t = if i = ~1 then Free (v, ty) else Var (v_i, ty)
        in
          (maxidx + 1,  v :: set,
            (cterm_of thy t, cterm_of thy (Var ((v', maxidx), ty))) :: acc)
        end;
    fun vars_of thm = fold_aterms
      (fn Var (v_i as (v, i), ty) => cons (v_i, (CodegenNames.purify_var v, ty))
        | _ => I) (prop_of thm) [];
    val maxidx = Thm.maxidx_of thm + 1;
    val (_, _, inst) = fold mk_inst (vars_of thm) (maxidx + 1, [], []);
  in Thm.instantiate ([], inst) thm end;

fun drop_redundant thy eqs =
  let
    val matches = curry (Pattern.matches thy o
      pairself (fst o Logic.dest_equals o prop_of))
    fun drop eqs [] = eqs
      | drop eqs (eq::eqs') =
          drop (eq::eqs) (filter_out (matches eq) eqs')
  in drop [] eqs end;

fun drop_refl thy = filter_out (is_equal o Term.fast_term_ord o Logic.dest_equals
  o ObjectLogic.drop_judgment thy o Drule.plain_prop_of);

fun make_eq thy =
  let
    val ((_, atomize), _) = get_obj thy;
  in rewrite_rule [atomize] end;

fun dest_eq thy thm =
  case try (make_eq thy #> Drule.plain_prop_of
   #> ObjectLogic.drop_judgment thy #> Logic.dest_equals) thm
   of SOME eq => (eq, thm)
    | NONE => err_thm "Not an equation" thm;

fun dest_fun thy thm =
  let
    fun dest_fun' ((lhs, _), thm) =
      case try (dest_Const o fst o strip_comb) lhs
       of SOME (c, ty) => (c, (ty, thm))
        | NONE => err_thm "Not a function equation" thm;
  in
    thm
    |> dest_eq thy
    |> dest_fun'
  end;



(** theory data **)

(* data structures *)

structure Consttab = CodegenConsts.Consttab;

fun merge' eq (xys as (xs, ys)) =
  if eq_list eq (xs, ys) then (false, xs) else (true, merge eq xys);

fun alist_merge' eq_key eq (xys as (xs, ys)) =
  if eq_list (eq_pair eq_key eq) (xs, ys) then (false, xs) else (true, AList.merge eq_key eq xys);

fun list_consttab_join' eq (xyt as (xt, yt)) =
  let
    val xc = Consttab.keys xt;
    val yc = Consttab.keys yt;
    val zc = filter (member CodegenConsts.eq_const yc) xc;
    val wc = subtract (op =) zc xc @ subtract (op =) zc yc;
    fun same_thms c = if eq_list eq_thm ((the o Consttab.lookup xt) c, (the o Consttab.lookup yt) c)
      then NONE else SOME c;
  in (wc @ map_filter same_thms zc, Consttab.join (K (merge eq)) xyt) end;

datatype notify = Notify of (serial * ((string * typ) list option -> theory -> theory)) list;

val mk_notify = Notify;
fun map_notify f (Notify notify) = mk_notify (f notify);
fun merge_notify pp (Notify notify1, Notify notify2) =
  mk_notify (AList.merge (op =) (K true) (notify1, notify2));

datatype preproc = Preproc of {
  preprocs: (serial * (theory -> thm list -> thm list)) list,
  unfolds: thm list
};

fun mk_preproc (preprocs, unfolds) =
  Preproc { preprocs = preprocs, unfolds = unfolds };
fun map_preproc f (Preproc { preprocs, unfolds }) =
  mk_preproc (f (preprocs, unfolds));
fun merge_preproc _ (Preproc { preprocs = preprocs1, unfolds = unfolds1 },
  Preproc { preprocs = preprocs2, unfolds = unfolds2 }) =
    let
      val (dirty1, preprocs) = alist_merge' (op =) (K true) (preprocs1, preprocs2);
      val (dirty2, unfolds) = merge' eq_thm (unfolds1, unfolds2);
    in (dirty1 orelse dirty2, mk_preproc (preprocs, unfolds)) end;

datatype extrs = Extrs of {
  funs: (serial * (theory -> string * typ -> thm list)) list,
  datatypes: (serial * (theory -> string -> (((string * sort) list * (string * typ list) list) * tactic) option)) list
};

fun mk_extrs (funs, datatypes) =
  Extrs { funs = funs, datatypes = datatypes };
fun map_extrs f (Extrs { funs, datatypes }) =
  mk_extrs (f (funs, datatypes));
fun merge_extrs _ (Extrs { funs = funs1, datatypes = datatypes1 },
  Extrs { funs = funs2, datatypes = datatypes2 }) =
    let
      val (dirty1, funs) = alist_merge' (op =) (K true) (funs1, funs2);
      val (dirty2, datatypes) = alist_merge' (op =) (K true) (datatypes1, datatypes2);
    in (dirty1 orelse dirty2, mk_extrs (funs, datatypes)) end;

datatype funthms = Funthms of {
  dirty: string list,
  funs: thm list Consttab.table
};

fun mk_funthms (dirty, funs) =
  Funthms { dirty = dirty, funs = funs };
fun map_funthms f (Funthms { dirty, funs }) =
  mk_funthms (f (dirty, funs));
fun merge_funthms _ (Funthms { dirty = dirty1, funs = funs1 },
  Funthms { dirty = dirty2, funs = funs2 }) =
    let
      val (dirty3, funs) = list_consttab_join' eq_thm (funs1, funs2);
    in mk_funthms (merge (op =) (merge (op =) (dirty1, dirty2), map fst dirty3), funs) end;

datatype T = T of {
  dirty: bool,
  notify: notify,
  preproc: preproc,
  extrs: extrs,
  funthms: funthms
};

fun mk_T ((dirty, notify), (preproc, (extrs, funthms))) =
  T { dirty = dirty, notify = notify, preproc= preproc, extrs = extrs, funthms = funthms };
fun map_T f (T { dirty, notify, preproc, extrs, funthms }) =
  mk_T (f ((dirty, notify), (preproc, (extrs, funthms))));
fun merge_T pp (T { dirty = dirty1, notify = notify1, preproc = preproc1, extrs = extrs1, funthms = funthms1 },
  T { dirty = dirty2, notify = notify2, preproc = preproc2, extrs = extrs2, funthms = funthms2 }) =
    let
      val (dirty3, preproc) = merge_preproc pp (preproc1, preproc2);
      val (dirty4, extrs) = merge_extrs pp (extrs1, extrs2);
    in
      mk_T ((dirty1 orelse dirty2 orelse dirty3 orelse dirty4, merge_notify pp (notify1, notify2)),
        (preproc, (extrs, merge_funthms pp (funthms1, funthms2))))
    end;


(* setup *)

structure CodegenTheoremsData = TheoryDataFun
(struct
  val name = "Pure/codegen_theorems_data";
  type T = T;
  val empty = mk_T ((false, mk_notify []), (mk_preproc ([], []),
    (mk_extrs ([], []), mk_funthms ([], Consttab.empty))));
  val copy = I;
  val extend = I;
  val merge = merge_T;
  fun print (thy : theory) (data : T) =
    let
      val pretty_thm = ProofContext.pretty_thm (ProofContext.init thy);
      val funthms = (fn T { funthms, ... } => funthms) data;
      val funs = (Consttab.dest o (fn Funthms { funs, ... } => funs)) funthms;
      val preproc = (fn T { preproc, ... } => preproc) data;
      val unfolds = (fn Preproc { unfolds, ... } => unfolds) preproc;
    in
      (Pretty.writeln o Pretty.block o Pretty.fbreaks) ([
        Pretty.str "code generation theorems:",
        Pretty.str "function theorems:" ] @
          map (fn (c, thms) =>
            (Pretty.block o Pretty.fbreaks) (
              (Pretty.str o CodegenConsts.string_of_const thy) c  :: map pretty_thm (rev thms)
            )
          ) funs @ [
        Pretty.block (
          Pretty.str "inlined theorems:"
          :: Pretty.fbrk
          :: (Pretty.fbreaks o map pretty_thm) unfolds
      )])
    end;
end);

val _ = Context.add_setup CodegenTheoremsData.init;
val print_thms = CodegenTheoremsData.print;


(* accessors *)

local
  val the_preproc = (fn T { preproc = Preproc preproc, ... } => preproc) o CodegenTheoremsData.get;
  val the_extrs = (fn T { extrs = Extrs extrs, ... } => extrs) o CodegenTheoremsData.get;
  val the_funthms = (fn T { funthms = Funthms funthms, ... } => funthms) o CodegenTheoremsData.get;
in
  val is_dirty = (fn T { dirty = dirty, ... } => dirty) o CodegenTheoremsData.get;
  val the_dirty_consts = (fn { dirty = dirty, ... } => dirty) o the_funthms;
  val the_notify = (fn T { notify = Notify notify, ... } => map snd notify) o CodegenTheoremsData.get;
  val the_preprocs = (fn { preprocs, ... } => map snd preprocs) o the_preproc;
  val the_unfolds = (fn { unfolds, ... } => unfolds) o the_preproc;
  val the_funs_extrs = (fn { funs, ... } => map snd funs) o the_extrs;
  val the_datatypes_extrs = (fn { datatypes, ... } => map snd datatypes) o the_extrs;
  val the_funs = (fn { funs, ... } => funs) o the_funthms;
end (*local*);

val map_data = CodegenTheoremsData.map o map_T;

(* notifiers *)

fun all_typs thy c =
  let
    val c_tys = (map (pair c o #lhs o snd) o Defs.specifications_of (Theory.defs_of thy)) c;
  in (c, Sign.the_const_type thy c) :: map (CodegenConsts.typ_of_typinst thy) c_tys end;

fun add_notify f =
  map_data (fn ((dirty, notify), x) =>
    ((dirty, notify |> map_notify (cons (serial (), f))), x));

fun get_reset_dirty thy =
  let
    val dirty = is_dirty thy;
    val dirty_const = if dirty then [] else the_dirty_consts thy;
  in
    thy
    |> map_data (fn ((_, notify), (procs, (extrs, funthms))) =>
         ((false, notify), (procs, (extrs, funthms |> map_funthms (fn (_, funs) => ([], funs))))))
    |> pair (dirty, dirty_const)
  end;

fun notify_all c thy =
  thy
  |> get_reset_dirty
  |-> (fn (true, _) => fold (fn f => f NONE) (the_notify thy)
        | (false, cs) => let val cs' = case c of NONE => cs | SOME c => insert (op =) c cs
            in fold (fn f => f (SOME (maps (all_typs thy) cs'))) (the_notify thy) end);

fun notify_dirty thy =
  thy
  |> get_reset_dirty
  |-> (fn (true, _) => fold (fn f => f NONE) (the_notify thy)
        | (false, cs) => fold (fn f => f (SOME (maps (all_typs thy) cs))) (the_notify thy));


(* modifiers *)

fun add_preproc f =
  map_data (fn (x, (preproc, y)) =>
    (x, (preproc |> map_preproc (fn (preprocs, unfolds) => ((serial (), f) :: preprocs, unfolds)), y)))
  #> notify_all NONE;

fun add_fun_extr f =
  map_data (fn (x, (preproc, (extrs, funthms))) =>
    (x, (preproc, (extrs |> map_extrs (fn (funs, datatypes) =>
      ((serial (), f) :: funs, datatypes)), funthms))))
  #> notify_all NONE;

fun add_datatype_extr f =
  map_data (fn (x, (preproc, (extrs, funthms))) =>
    (x, (preproc, (extrs |> map_extrs (fn (funs, datatypes) =>
      (funs, (serial (), f) :: datatypes)), funthms))))
  #> notify_all NONE;

fun add_fun thm thy =
  case dest_fun thy thm
   of (c, (ty, _)) =>
    thy
    |> map_data (fn (x, (preproc, (extrs, funthms))) =>
        (x, (preproc, (extrs, funthms |> map_funthms (fn (dirty, funs) =>
          (dirty, funs |> Consttab.map_default (CodegenConsts.norminst_of_typ thy (c, ty), []) (cons thm)))))))
    |> notify_all (SOME c);

fun del_fun thm thy =
  case dest_fun thy thm
   of (c, (ty, _)) =>
    thy
    |> map_data (fn (x, (preproc, (extrs, funthms))) =>
        (x, (preproc, (extrs, funthms |> map_funthms (fn (dirty, funs) =>
          (dirty, funs |> Consttab.map_entry (CodegenConsts.norminst_of_typ thy (c, ty)) (remove eq_thm thm)))))))
    |> notify_all (SOME c);

fun add_unfold thm thy =
  thy
  |> tap (fn thy => dest_eq thy thm)
  |> map_data (fn (x, (preproc, y)) =>
       (x, (preproc |> map_preproc (fn (preprocs, unfolds) =>
         (preprocs, thm :: unfolds)), y)))
  |> notify_all NONE;

fun del_unfold thm =
  map_data (fn (x, (preproc, y)) =>
       (x, (preproc |> map_preproc (fn (preprocs, unfolds) =>
         (preprocs, remove eq_thm thm unfolds)), y)))
  #> notify_all NONE;

fun purge_defs (c, ty) thy =
  thy
  |> map_data (fn (x, (preproc, (extrs, funthms))) =>
      (x, (preproc, (extrs, funthms |> map_funthms (fn (dirty, funs) =>
        (dirty, funs |> Consttab.update (CodegenConsts.norminst_of_typ thy (c, ty), [])))))))
  |> notify_all (SOME c);



(** theorem handling **)

(* preprocessing *)

fun extr_typ thy thm = case dest_fun thy thm
 of (_, (ty, _)) => ty;

fun rewrite_fun rewrites thm =
  let
    val rewrite = Tactic.rewrite true rewrites;
    val (ct_eq, [ct_lhs, ct_rhs]) = (Drule.strip_comb o cprop_of) thm;
    val Const ("==", _) = term_of ct_eq;
    val (ct_f, ct_args) = Drule.strip_comb ct_lhs;
    val rhs' = rewrite ct_rhs;
    val args' = map rewrite ct_args;
    val lhs' = Thm.symmetric (fold (fn th1 => fn th2 => Thm.combination th2 th1)
      args' (Thm.reflexive ct_f));
  in
    Thm.transitive (Thm.transitive lhs' thm) rhs'
  end handle Bind => raise ERROR "rewrite_fun"

fun common_typ thy _ [] = []
  | common_typ thy _ [thm] = [thm]
  | common_typ thy extract_typ thms =
      let
        fun incr_thm thm max =
          let
            val thm' = incr_indexes max thm;
            val max' = (maxidx_of_typ o fastype_of o Drule.plain_prop_of) thm' + 1;
          in (thm', max') end;
        val (thms', maxidx) = fold_map incr_thm thms 0;
        val (ty1::tys) = map extract_typ thms;
        fun unify ty env = Sign.typ_unify thy (ty1, ty) env
          handle Type.TUNIFY =>
            error ("Type unificaton failed, while unifying function equations\n"
            ^ (cat_lines o map Display.string_of_thm) thms
            ^ "\nwith types\n"
            ^ (cat_lines o map (Sign.string_of_typ thy)) (ty1 :: tys));
        val (env, _) = fold unify tys (Vartab.empty, maxidx)
        val instT = Vartab.fold (fn (x_i, (sort, ty)) =>
          cons (Thm.ctyp_of thy (TVar (x_i, sort)), Thm.ctyp_of thy ty)) env [];
      in map (Thm.instantiate (instT, [])) thms end;

fun preprocess thy thms =
  let
    fun burrow_thms f [] = []
      | burrow_thms f thms =
          thms
          |> Conjunction.intr_list
          |> f
          |> Conjunction.elim_list;
    fun cmp_thms (thm1, thm2) =
      not (Sign.typ_instance thy (extr_typ thy thm1, extr_typ thy thm2));
    fun unvarify thms =
      #2 (#1 (Variable.import true thms (ProofContext.init thy)));
    val unfold_thms = map (make_eq thy) (the_unfolds thy);
  in
    thms
    |> map (make_eq thy)
    |> map (Thm.transfer thy)
    |> fold (fn f => f thy) (the_preprocs thy)
    |> map (rewrite_fun unfold_thms)
    |> debug_msg (fn _ => "[cg_thm] sorting")
    |> debug_msg (commas o map string_of_thm)
    |> sort (make_ord cmp_thms)
    |> debug_msg (fn _ => "[cg_thm] common_typ")
    |> debug_msg (commas o map string_of_thm)
    |> common_typ thy (extr_typ thy)
    |> debug_msg (fn _ => "[cg_thm] abs_norm")
    |> debug_msg (commas o map string_of_thm)
    |> map (abs_norm thy)
    |> drop_refl thy
    |> burrow_thms (
        debug_msg (fn _ => "[cg_thm] canonical tvars")
        #> debug_msg (string_of_thm)
        #> canonical_tvars thy
        #> debug_msg (fn _ => "[cg_thm] canonical vars")
        #> debug_msg (string_of_thm)
        #> canonical_vars thy
        #> debug_msg (fn _ => "[cg_thm] zero indices")
        #> debug_msg (string_of_thm)
        #> Drule.zero_var_indexes
       )
    |> drop_redundant thy
    |> debug_msg (fn _ => "[cg_thm] preprocessing done")
  end;


(* retrieval *)

fun get_funs thy (c, ty) =
  let
    val _ = debug_msg (fn _ => "[cg_thm] const (1) " ^ c ^ " :: " ^ Sign.string_of_typ thy ty) ()
    val postprocess_typ = case AxClass.class_of_param thy c
     of NONE => map_filter (fn (_, (ty', thm)) =>
          if Sign.typ_instance thy (ty, ty')
          then SOME thm else debug_msg (fn _ => "[cg_thm] dropping " ^ string_of_thm thm) NONE)
      | SOME _ => let
          (*FIXME make this more elegant*)
          val ty' = CodegenConsts.typ_of_classop thy (CodegenConsts.norminst_of_typ thy (c, ty));
          val ct = Thm.cterm_of thy (Const (c, ty'));
          val thm' = Thm.reflexive ct;
        in map (snd o snd) #> cons thm' #> common_typ thy (extr_typ thy) #> tl end;
    fun get_funs (c, ty) =
      (these o Consttab.lookup (the_funs thy) o CodegenConsts.norminst_of_typ thy) (c, ty)
      |> debug_msg (fn _ => "[cg_thm] trying funs")
      |> map (dest_fun thy)
      |> postprocess_typ;
    fun get_extr (c, ty) =
      getf_first_list (map (fn f => f thy) (the_funs_extrs thy)) (c, ty)
      |> debug_msg (fn _ => "[cg_thm] trying extr")
      |> map (dest_fun thy)
      |> postprocess_typ;
    fun get_spec (c, ty) =
      (CodegenConsts.find_def thy o CodegenConsts.norminst_of_typ thy) (c, ty)
      |> debug_msg (fn _ => "[cg_thm] trying spec")
      |> Option.mapPartial (fn ((_, name), _) => try (Thm.get_axiom_i thy) name)
      |> the_list
      |> map_filter (try (dest_fun thy))
      |> postprocess_typ;
  in
    getf_first_list [get_funs, get_extr, get_spec] (c, ty)
    |> debug_msg (fn _ => "[cg_thm] const (2) " ^ c ^ " :: " ^ Sign.string_of_typ thy ty)
    |> preprocess thy
  end;

fun prove_freeness thy tac dtco vs_cos =
  let
    val truh = mk_true thy;
    val fals = mk_false thy;
    fun mk_lhs vs ((co1, tys1), (co2, tys2)) =
      let
        val dty = Type (dtco, map TFree vs);
        val (xs1, xs2) = chop (length tys1) (Name.invent_list [] "a" (length tys1 + length tys2));
        val frees1 = map2 (fn x => fn ty => Free (x, ty)) xs1 tys1;
        val frees2 = map2 (fn x => fn ty => Free (x, ty)) xs2 tys2;
        fun zip_co co xs tys = list_comb (Const (co,
          tys ---> dty), map2 (fn x => fn ty => Free (x, ty)) xs tys);
      in
        ((frees1, frees2), (zip_co co1 xs1 tys1, zip_co co2 xs2 tys2))
      end;
    fun mk_rhs [] [] = truh
      | mk_rhs xs ys = foldr1 (mk_obj_conj thy) (map2 (curry (mk_obj_eq thy)) xs ys);
    fun mk_eq vs (args as ((co1, _), (co2, _))) (inj, dist) =
      if co1 = co2
        then let
          val ((fs1, fs2), lhs) = mk_lhs vs args;
          val rhs = mk_rhs fs1 fs2;
        in (mk_func thy (lhs, rhs) :: inj, dist) end
        else let
          val (_, lhs) = mk_lhs vs args;
        in (inj, mk_func thy (lhs, fals) :: dist) end;
    fun mk_eqs (vs, cos) =
      let val cos' = rev cos
      in (op @) (fold (mk_eq vs) (product cos' cos') ([], [])) end;
    val ts = (map (ObjectLogic.ensure_propT thy) o mk_eqs) vs_cos;
    fun prove t = if !quick_and_dirty then SkipProof.make_thm thy (Logic.varify t)
      else Goal.prove_global thy [] [] t (K tac);
  in map prove ts end;

fun get_datatypes thy dtco =
  let
    val _ = debug_msg (fn _ => "[cg_thm] datatype " ^ dtco) ()
  in
    case getf_first (map (fn f => f thy) (the_datatypes_extrs thy)) dtco
     of NONE => NONE
      | SOME (vs_cos, tac) => SOME (vs_cos, prove_freeness thy tac dtco vs_cos)
  end;

fun get_eq thy (c, ty) =
  if is_obj_eq thy c
  then case strip_type ty
   of (Type (tyco, _) :: _, _) =>
     (case get_datatypes thy tyco
       of SOME (_, thms) => thms
        | _ => [])
    | _ => []
  else [];

fun check_thms c thms =
  let
    fun check_head_lhs thm (lhs, rhs) =
      case strip_comb lhs
       of (Const (c', _), _) => if c' = c then ()
           else error ("Illegal function equation for " ^ quote c
             ^ ", actually defining " ^ quote c' ^ ": " ^ Display.string_of_thm thm)
        | _ => error ("Illegal function equation: " ^ Display.string_of_thm thm);
    fun check_vars_lhs thm (lhs, rhs) =
      if has_duplicates (op =)
          (fold_aterms (fn Free (v, _) => cons v | _ => I) lhs [])
      then error ("Repeated variables on left hand side of function equation:"
        ^ Display.string_of_thm thm)
      else ();
    fun check_vars_rhs thm (lhs, rhs) =
      if null (subtract (op =)
        (fold_aterms (fn Free (v, _) => cons v | _ => I) lhs [])
        (fold_aterms (fn Free (v, _) => cons v | _ => I) rhs []))
      then ()
      else error ("Free variables on right hand side of function equation:"
        ^ Display.string_of_thm thm)
    val tts = map (Logic.dest_equals o Logic.unvarify o Thm.prop_of) thms;
  in
    (map2 check_head_lhs thms tts; map2 check_vars_lhs thms tts;
      map2 check_vars_rhs thms tts; thms)
  end;

structure Consttab = CodegenConsts.Consttab;
type thmtab = (theory * (thm list Consttab.table
  * string Consttab.table)
  * (Sorts.algebra * ((string * sort) list * (string * typ list) list) Symtab.table));

fun thmtab_empty thy = (thy, (Consttab.empty, Consttab.empty),
  (ClassPackage.operational_algebra thy, Symtab.empty));

fun get_sortalgebra (_, _, (algebra, _)) =
  algebra;

fun get_dtyp_of_cons (thy, (_, dtcotab), _) =
  Consttab.lookup dtcotab o CodegenConsts.norminst_of_typ thy;

fun get_dtyp_spec (_, _, (_, dttab)) =
  Symtab.lookup dttab;

fun has_fun_thms (thy, (funtab, _), _) =
  is_some o Consttab.lookup funtab o CodegenConsts.norminst_of_typ thy;

fun get_fun_thms (thy, (funtab, _), _) (c_ty as (c, _)) =
  (check_thms c o these o Consttab.lookup funtab
    o CodegenConsts.norminst_of_typ thy) c_ty;

fun pretty_funtab thy funtab =
  funtab
  |> CodegenConsts.Consttab.dest
  |> map (fn (c, thms) =>
       (Pretty.block o Pretty.fbreaks) (
         (Pretty.str o CodegenConsts.string_of_const thy) c
         :: map Display.pretty_thm thms
       ))
  |> Pretty.chunks;

fun constrain_funtab thy funtab =
  let
    fun max k [] = k
      | max k (l::ls) = max (if k < l then l else k) ls;
    fun mk_consttyps funtab =
      CodegenConsts.Consttab.empty
      |> CodegenConsts.Consttab.fold (fn (c, thm :: _) =>
           CodegenConsts.Consttab.update_new (c, extr_typ thy thm) | (_, []) => I) funtab
    fun mk_typescheme_of typtab (c, ty) =
      CodegenConsts.Consttab.lookup typtab (CodegenConsts.norminst_of_typ thy (c, ty));
    fun incr_indices (c, thms) maxidx =
      let
        val thms' = map (Thm.incr_indexes maxidx) thms;
        val maxidx' = Int.max
          (maxidx, max ~1 (map Thm.maxidx_of thms') + 1);
      in (thms', maxidx') end;
    fun consts_of_eqs thms =
      let
        fun terms_of_eq thm =
          let
            val (lhs, rhs) = (Logic.dest_equals o Drule.plain_prop_of) thm
          in rhs :: (snd o strip_comb) lhs end;
      in (fold o fold_aterms) (fn Const c => insert (eq_pair (op =) (Type.eq_type Vartab.empty)) c | _ => I)
        (maps terms_of_eq thms) []
      end;
    val typscheme_of =
      mk_typescheme_of (mk_consttyps funtab);
    val tsig = Sign.tsig_of thy;
    fun unify_const (c, ty) (env, maxidx) =
      case typscheme_of (c, ty)
       of SOME ty_decl => let
            (*val _ = writeln "UNIFY";
            val _ = writeln (CodegenConsts.string_of_const_typ thy (c, ty))*)
            val ty_decl' = Logic.incr_tvar maxidx ty_decl;
            (*val _ = writeln "WITH";
            val _ = writeln (CodegenConsts.string_of_const_typ thy (c, ty_decl'))*)
            val maxidx' = Int.max (Term.maxidx_of_typ ty_decl' + 1, maxidx);
            (*val _ = writeln ("  " ^ string_of_int maxidx ^ " +> " ^ string_of_int maxidx');*)
          in Type.unify tsig (ty_decl', ty) (env, maxidx') end
        | NONE => (env, maxidx);
    fun apply_unifier unif [] = []
      | apply_unifier unif (thms as thm :: _) =
          let
            val ty = extr_typ thy thm;
            val ty' = Envir.norm_type unif ty;
            val env = Type.typ_match (Sign.tsig_of thy) (ty, ty') Vartab.empty;
            val inst = Thm.instantiate (Vartab.fold (fn (x_i, (sort, ty)) =>
              cons (Thm.ctyp_of thy (TVar (x_i, sort)), Thm.ctyp_of thy ty)) env [], []);
          in map (Drule.zero_var_indexes o inst) thms end;
(*     val _ = writeln "(1)";  *)
(*     val _ = (Pretty.writeln o pretty_funtab thy) funtab;  *)
    val (funtab', maxidx) =
      CodegenConsts.Consttab.fold_map incr_indices funtab 0;
(*     val _ = writeln "(2)";
 *     val _ = (Pretty.writeln o pretty_funtab thy) funtab';
 *)
    val (unif, _) =
      CodegenConsts.Consttab.fold (fold unify_const o consts_of_eqs o snd)
        funtab' (Vartab.empty, maxidx);
(*     val _ = writeln "(3)";  *)
    val funtab'' =
      CodegenConsts.Consttab.map (apply_unifier unif) funtab';
(*     val _ = writeln "(4)";
 *     val _ = (Pretty.writeln o pretty_funtab thy) funtab'';
 *)
  in funtab'' end;

fun mk_thmtab thy cs =
  let
    fun add_tycos (Type (tyco, tys)) = insert (op =) tyco #> fold add_tycos tys
      | add_tycos _ = I;
    fun consts_of ts =
      Consttab.empty
      |> (fold o fold_aterms)
           (fn Const c_ty => Consttab.update (CodegenConsts.norminst_of_typ thy c_ty, ())
             | _ => I) ts
      |> Consttab.keys;
    fun add_dtyps_of_type ty thmtab =
      let
        val tycos = add_tycos ty [];
        val tycos_new = filter (is_none o get_dtyp_spec thmtab) tycos;
        fun add_dtyp_spec dtco (dtyp_spec as (vs, cs)) ((thy, (funtab, dtcotab), (algebra, dttab))) =
          let
            fun mk_co (c, tys) =
              CodegenConsts.norminst_of_typ thy (c, Logic.varifyT (tys ---> Type (dtco, map TFree vs)));
          in
            (thy, (funtab, dtcotab |> fold (fn c_tys =>
              Consttab.update_new (mk_co c_tys, dtco)) cs),
              (algebra, dttab |> Symtab.update_new (dtco, dtyp_spec)))
          end;
      in
        thmtab
        |> fold (fn tyco => case get_datatypes thy tyco
             of SOME (dtyp_spec, _) => add_dtyp_spec tyco dtyp_spec
              | NONE => I) tycos_new
      end;
    fun known thmtab (c, ty) =
      is_some (get_dtyp_of_cons thmtab (c, ty)) orelse has_fun_thms thmtab (c, ty);
    fun add_funthms (c, ty) (thmtab as (thy, (funtab, dtcotab), algebra_dttab))=
      if known thmtab (c, ty) then thmtab
      else let
        val thms = get_funs thy (c, ty)
        val cs_dep = (consts_of o map Thm.prop_of) thms;
      in
        (thy, (funtab |> Consttab.update_new (CodegenConsts.norminst_of_typ thy (c, ty), thms)
        , dtcotab), algebra_dttab)
        |> fold add_c cs_dep
      end
    and add_c (c_tys as (c, tys)) thmtab =
      thmtab
      |> add_dtyps_of_type (snd (CodegenConsts.typ_of_typinst thy c_tys))
      |> fold (add_funthms o CodegenConsts.typ_of_typinst thy)
           (CodegenConsts.insts_of_classop thy c_tys);
  in
    thmtab_empty thy
    |> fold (add_c o CodegenConsts.norminst_of_typ thy) cs
    |> (fn (a, (funtab, b), c) => (a, (funtab |> constrain_funtab thy, b), c))
  end;



(** code attributes and setup **)

local
  fun add_simple_attribute (name, f) =
    (Codegen.add_attribute name o (Scan.succeed o Thm.declaration_attribute))
      (Context.map_theory o f);
in
  val _ = map (Context.add_setup o add_simple_attribute) [
    ("fun", add_fun),
    ("nofun", del_fun),
    ("unfold", (fn thm => Codegen.add_unfold thm #> add_unfold thm)),
    ("inline", add_unfold),
    ("noinline", del_unfold)
  ]
end; (*local*)

val _ = Context.add_setup (add_fun_extr get_eq);

end; (*struct*)