(*  Title:      Pure/Isar/code.ML

    ID:         $Id$

    Author:     Florian Haftmann, TU Muenchen

Abstract executable content of theory.  Management of data dependent on

executable content.  Cache assumes non-concurrent processing of a single theory.

*)

signature CODE =

sig

  val add_func: thm -> theory -> theory

  val add_liberal_func: thm -> theory -> theory

  val add_default_func: thm -> theory -> theory

  val add_default_func_attr: Attrib.src

  val del_func: thm -> theory -> theory

  val del_funcs: string -> theory -> theory

  val add_funcl: string * thm list Susp.T -> theory -> theory

  val add_inline: thm -> theory -> theory

  val del_inline: thm -> theory -> theory

  val add_inline_proc: string * (theory -> cterm list -> thm list) -> theory -> theory

  val del_inline_proc: string -> theory -> theory

  val add_preproc: string * (theory -> thm list -> thm list) -> theory -> theory

  val del_preproc: string -> theory -> theory

  val add_post: thm -> theory -> theory

  val del_post: thm -> theory -> theory

  val add_datatype: (string * typ) list -> theory -> theory

  val add_datatype_cmd: string list -> theory -> theory

  val type_interpretation:

    (string * ((string * sort) list * (string * typ list) list)

      -> theory -> theory) -> theory -> theory

  val add_case: thm -> theory -> theory

  val add_undefined: string -> theory -> theory

  val coregular_algebra: theory -> Sorts.algebra

  val operational_algebra: theory -> (sort -> sort) * Sorts.algebra

  val these_funcs: theory -> string -> thm list

  val get_datatype: theory -> string -> ((string * sort) list * (string * typ list) list)

  val get_datatype_of_constr: theory -> string -> string option

  val get_case_data: theory -> string -> (int * string list) option

  val is_undefined: theory -> string -> bool

  val default_typ: theory -> string -> typ

  val preprocess_conv: cterm -> thm

  val preprocess_term: theory -> term -> term

  val postprocess_conv: cterm -> thm

  val postprocess_term: theory -> term -> term

  val add_attribute: string * (Args.T list -> attribute * Args.T list) -> theory -> theory

  val print_codesetup: theory -> unit

end;

signature CODE_DATA_ARGS =

sig

  type T

  val empty: T

  val merge: Pretty.pp -> T * T -> T

  val purge: theory option -> string list option -> T -> T

end;

signature CODE_DATA =

sig

  type T

  val get: theory -> T

  val change: theory -> (T -> T) -> T

  val change_yield: theory -> (T -> 'a * T) -> 'a * T

end;

signature PRIVATE_CODE =

sig

  include CODE

  val declare_data: Object.T -> (Pretty.pp -> Object.T * Object.T -> Object.T)

    -> (theory option -> string list option -> Object.T -> Object.T) -> serial

  val get_data: serial * ('a -> Object.T) * (Object.T -> 'a)

    -> theory -> 'a

  val change_data: serial * ('a -> Object.T) * (Object.T -> 'a)

    -> theory -> ('a -> 'a) -> 'a

  val change_yield_data: serial * ('a -> Object.T) * (Object.T -> 'a)

    -> theory -> ('a -> 'b * 'a) -> 'b * 'a

end;

structure Code : PRIVATE_CODE =

struct

(** code attributes **)

structure CodeAttr = TheoryDataFun (

  type T = (string * (Args.T list -> attribute * Args.T list)) list;

  val empty = [];

  val copy = I;

  val extend = I;

  fun merge _ = AList.merge (op =) (K true);

);

fun add_attribute (attr as (name, _)) =

  let

    fun add_parser ("", parser) attrs = attrs @ [("", parser)]

      | add_parser (name, parser) attrs = (name, Args.$$$ name |-- parser) :: attrs;

    fun error "" = error ("Code attribute already declared")

      | error name = error ("Code attribute " ^ name ^ " already declared")

  in CodeAttr.map (fn attrs => if AList.defined (op =) attrs name

    then error name else add_parser attr attrs)

  end;

val _ =

  let

    val code_attr = Attrib.syntax (Scan.peek (fn context =>

      List.foldr op || Scan.fail (map snd (CodeAttr.get (Context.theory_of context)))));

  in

    Context.>> (Context.map_theory

      (Attrib.add_attributes

        [("code", code_attr, "declare theorems for code generation")]))

  end;

(** certificate theorems **)

fun string_of_lthms r = case Susp.peek r

 of SOME thms => (map Display.string_of_thm o rev) thms

  | NONE => ["[...]"];

fun pretty_lthms ctxt r = case Susp.peek r

 of SOME thms => map (ProofContext.pretty_thm ctxt) thms

  | NONE => [Pretty.str "[...]"];

fun certificate thy f r =

  case Susp.peek r

   of SOME thms => (Susp.value o f thy) thms

    | NONE => let

        val thy_ref = Theory.check_thy thy;

      in Susp.delay (fn () => (f (Theory.deref thy_ref) o Susp.force) r) end;

(** logical and syntactical specification of executable code **)

(* pairs of (selected, deleted) defining equations *)

type sdthms = thm list Susp.T * thm list;

fun add_drop_redundant thm (sels, dels) =

  let

    val thy = Thm.theory_of_thm thm;

    val args_of = snd o strip_comb o fst o Logic.dest_equals o Thm.plain_prop_of;

    val args = args_of thm;

    fun matches [] _ = true

      | matches (Var _ :: xs) [] = matches xs []

      | matches (_ :: _) [] = false

      | matches (x :: xs) (y :: ys) = Pattern.matches thy (x, y) andalso matches xs ys;

    fun drop thm' = not (matches args (args_of thm'))

      orelse (warning ("Code generator: dropping redundant defining equation\n" ^ Display.string_of_thm thm'); false);

    val (keeps, drops) = List.partition drop sels;

  in (thm :: keeps, dels |> remove Thm.eq_thm_prop thm |> fold (insert Thm.eq_thm_prop) drops) end;

fun add_thm thm (sels, dels) =

  apfst Susp.value (add_drop_redundant thm (Susp.force sels, dels));

fun add_lthms lthms (sels, []) =

      (Susp.delay (fn () => fold add_drop_redundant

        (Susp.force lthms) (Susp.force sels, []) |> fst), [])

        (*FIXME*)

  | add_lthms lthms (sels, dels) =

      fold add_thm (Susp.force lthms) (sels, dels);

fun del_thm thm (sels, dels) =

  (Susp.value (remove Thm.eq_thm_prop thm (Susp.force sels)), thm :: dels);

fun del_thms (sels, dels) =

  let

    val all_sels = Susp.force sels;

  in (Susp.value [], rev all_sels @ dels) end;

fun pretty_sdthms ctxt (sels, _) = pretty_lthms ctxt sels;

(* fundamental melting operations *)

fun melt _ ([], []) = (false, [])

  | melt _ ([], ys) = (true, ys)

  | melt eq (xs, ys) = fold_rev

      (fn y => fn (t, xs) => (t orelse not (member eq xs y), insert eq y xs)) ys (false, xs);

fun melt_alist 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);

val melt_thms = melt Thm.eq_thm_prop;

fun melt_lthms (r1, r2) =

  if Susp.same (r1, r2)

    then (false, r1)

  else case Susp.peek r1

   of SOME [] => (true, r2)

    | _ => case Susp.peek r2

       of SOME [] => (true, r1)

        | _ => (apsnd (Susp.delay o K)) (melt_thms (Susp.force r1, Susp.force r2));

fun melt_sdthms ((sels1, dels1), (sels2, dels2)) =

  let

    val (dels_t, dels) = melt_thms (dels1, dels2);

  in if dels_t

    then let

      val (_, sels) = melt_thms

        (subtract Thm.eq_thm_prop dels2 (Susp.force sels1), Susp.force sels2);

      val (_, dels) = melt_thms

        (subtract Thm.eq_thm_prop (Susp.force sels2) dels1, dels2);

    in (true, ((Susp.delay o K) sels, dels)) end

    else let

      val (sels_t, sels) = melt_lthms (sels1, sels2);

    in (sels_t, (sels, dels)) end

  end;

(* specification data *)

fun melt_funcs tabs =

  let

    val tab' = Symtab.join (fn _ => fn ((_, a), (_, b)) => melt_sdthms (a, b)) tabs;

    val touched = Symtab.fold (fn (c, (true, _)) => insert (op =) c | _ => I) tab' [];

  in (touched, tab') end;

val eq_string = op = : string * string -> bool;

fun eq_dtyp ((vs1, cs1), (vs2, cs2)) = 

  gen_eq_set (eq_pair eq_string (gen_eq_set eq_string)) (vs1, vs2)

    andalso gen_eq_set (eq_fst eq_string) (cs1, cs2);

fun melt_dtyps (tabs as (tab1, tab2)) =

  let

    val tycos1 = Symtab.keys tab1;

    val tycos2 = Symtab.keys tab2;

    val tycos' = filter (member eq_string tycos2) tycos1;

    val touched = not (gen_eq_set (op =) (tycos1, tycos2)

      andalso gen_eq_set (eq_pair (op =) eq_dtyp)

      (AList.make (the o Symtab.lookup tab1) tycos',

       AList.make (the o Symtab.lookup tab2) tycos'));

    fun join _ (cos as (_, cos2)) = if eq_dtyp cos

      then raise Symtab.SAME else cos2;

  in (touched, Symtab.join join tabs) end;

fun melt_cases ((cases1, undefs1), (cases2, undefs2)) =

  let

    val touched1 = subtract (op =) (Symtab.keys cases1) (Symtab.keys cases2)

      @ subtract (op =) (Symtab.keys cases2) (Symtab.keys cases1);

    val touched2 = subtract (op =) (Symtab.keys undefs1) (Symtab.keys undefs2)

      @ subtract (op =) (Symtab.keys undefs2) (Symtab.keys undefs1);

    val touched = fold (insert (op =)) touched1 touched2;

  in

    (touched, (Symtab.merge (K true) (cases1, cases2),

      Symtab.merge (K true) (undefs1, undefs2)))

  end;

datatype spec = Spec of {

  funcs: (bool * sdthms) Symtab.table,

  dtyps: ((string * sort) list * (string * typ list) list) Symtab.table,

  cases: (int * string list) Symtab.table * unit Symtab.table

};

fun mk_spec (funcs, (dtyps, cases)) =

  Spec { funcs = funcs, dtyps = dtyps, cases = cases };

fun map_spec f (Spec { funcs = funcs, dtyps = dtyps, cases = cases }) =

  mk_spec (f (funcs, (dtyps, cases)));

fun melt_spec (Spec { funcs = funcs1, dtyps = dtyps1, cases = cases1 },

  Spec { funcs = funcs2, dtyps = dtyps2, cases = cases2 }) =

  let

    val (touched_funcs, funcs) = melt_funcs (funcs1, funcs2);

    val (touched_dtyps, dtyps) = melt_dtyps (dtyps1, dtyps2);

    val (touched_cases, cases) = melt_cases (cases1, cases2);

    val touched = if touched_dtyps then NONE else

      SOME (fold (insert (op =)) touched_cases touched_funcs);

  in (touched, mk_spec (funcs, (dtyps, cases))) end;

(* pre- and postprocessor *)

datatype thmproc = Thmproc of {

  inlines: thm list,

  inline_procs: (string * (serial * (theory -> cterm list -> thm list))) list,

  preprocs: (string * (serial * (theory -> thm list -> thm list))) list,

  posts: thm list

};

fun mk_thmproc (((inlines, inline_procs), preprocs), posts) =

  Thmproc { inlines = inlines, inline_procs = inline_procs, preprocs = preprocs,

    posts = posts };

fun map_thmproc f (Thmproc { inlines, inline_procs, preprocs, posts }) =

  mk_thmproc (f (((inlines, inline_procs), preprocs), posts));

fun melt_thmproc (Thmproc { inlines = inlines1, inline_procs = inline_procs1,

    preprocs = preprocs1, posts = posts1 },

  Thmproc { inlines = inlines2, inline_procs = inline_procs2,

      preprocs = preprocs2, posts= posts2 }) =

    let

      val (touched1, inlines) = melt_thms (inlines1, inlines2);

      val (touched2, inline_procs) = melt_alist (op =) (eq_fst (op =)) (inline_procs1, inline_procs2);

      val (touched3, preprocs) = melt_alist (op =) (eq_fst (op =)) (preprocs1, preprocs2);

      val (_, posts) = melt_thms (posts1, posts2);

    in (touched1 orelse touched2 orelse touched3,

      mk_thmproc (((inlines, inline_procs), preprocs), posts)) end;

datatype exec = Exec of {

  thmproc: thmproc,

  spec: spec

};

fun mk_exec (thmproc, spec) =

  Exec { thmproc = thmproc, spec = spec };

fun map_exec f (Exec { thmproc = thmproc, spec = spec }) =

  mk_exec (f (thmproc, spec));

fun melt_exec (Exec { thmproc = thmproc1, spec = spec1 },

  Exec { thmproc = thmproc2, spec = spec2 }) =

  let

    val (touched', thmproc) = melt_thmproc (thmproc1, thmproc2);

    val (touched_cs, spec) = melt_spec (spec1, spec2);

    val touched = if touched' then NONE else touched_cs;

  in (touched, mk_exec (thmproc, spec)) end;

val empty_exec = mk_exec (mk_thmproc ((([], []), []), []),

  mk_spec (Symtab.empty, (Symtab.empty, (Symtab.empty, Symtab.empty))));

fun the_thmproc (Exec { thmproc = Thmproc x, ...}) = x;

fun the_spec (Exec { spec = Spec x, ...}) = x;

val the_funcs = #funcs o the_spec;

val the_dtyps = #dtyps o the_spec;

val the_cases = #cases o the_spec;

val map_thmproc = map_exec o apfst o map_thmproc;

val map_funcs = map_exec o apsnd o map_spec o apfst;

val map_dtyps = map_exec o apsnd o map_spec o apsnd o apfst;

val map_cases = map_exec o apsnd o map_spec o apsnd o apsnd;

(* data slots dependent on executable content *)

(*private copy avoids potential conflict of table exceptions*)

structure Datatab = TableFun(type key = int val ord = int_ord);

local

type kind = {

  empty: Object.T,

  merge: Pretty.pp -> Object.T * Object.T -> Object.T,

  purge: theory option -> string list option -> Object.T -> Object.T

};

val kinds = ref (Datatab.empty: kind Datatab.table);

val kind_keys = ref ([]: serial list);

fun invoke f k = case Datatab.lookup (! kinds) k

 of SOME kind => f kind

  | NONE => sys_error "Invalid code data identifier";

in

fun declare_data empty merge purge =

  let

    val k = serial ();

    val kind = {empty = empty, merge = merge, purge = purge};

    val _ = change kinds (Datatab.update (k, kind));

    val _ = change kind_keys (cons k);

  in k end;

fun invoke_empty k = invoke (fn kind => #empty kind) k;

fun invoke_merge_all pp = Datatab.join

  (invoke (fn kind => #merge kind pp));

fun invoke_purge_all thy_opt cs =

  fold (fn k => Datatab.map_entry k

    (invoke (fn kind => #purge kind thy_opt cs) k)) (! kind_keys);

end; (*local*)

(** theory store **)

local

type data = Object.T Datatab.table;

structure CodeData = TheoryDataFun

(

  type T = exec * data ref;

  val empty = (empty_exec, ref Datatab.empty : data ref);

  fun copy (exec, data) = (exec, ref (! data));

  val extend = copy;

  fun merge pp ((exec1, data1), (exec2, data2)) =

    let

      val (touched, exec) = melt_exec (exec1, exec2);

      val data1' = invoke_purge_all NONE touched (! data1);

      val data2' = invoke_purge_all NONE touched (! data2);

      val data = invoke_merge_all pp (data1', data2');

    in (exec, ref data) end;

);

val _ = Context.>> (Context.map_theory CodeData.init);

fun thy_data f thy = f ((snd o CodeData.get) thy);

fun get_ensure_init kind data_ref =

  case Datatab.lookup (! data_ref) kind

   of SOME x => x

    | NONE => let val y = invoke_empty kind

        in (change data_ref (Datatab.update (kind, y)); y) end;

in

(* access to executable content *)

val the_exec = fst o CodeData.get;

fun map_exec_purge touched f thy =

  CodeData.map (fn (exec, data) => 

    (f exec, ref (invoke_purge_all (SOME thy) touched (! data)))) thy;

(* access to data dependent on abstract executable content *)

fun get_data (kind, _, dest) = thy_data (get_ensure_init kind #> dest);

fun change_data (kind, mk, dest) =

  let

    fun chnge data_ref f =

      let

        val data = get_ensure_init kind data_ref;

        val data' = f (dest data);

      in (change data_ref (Datatab.update (kind, mk data')); data') end;

  in thy_data chnge end;

fun change_yield_data (kind, mk, dest) =

  let

    fun chnge data_ref f =

      let

        val data = get_ensure_init kind data_ref;

        val (x, data') = f (dest data);

      in (x, (change data_ref (Datatab.update (kind, mk data')); data')) end;

  in thy_data chnge end;

end; (*local*)

(* print executable content *)

fun print_codesetup thy =

  let

    val ctxt = ProofContext.init thy;

    val exec = the_exec thy;

    fun pretty_func (s, lthms) =

      (Pretty.block o Pretty.fbreaks) (

        Pretty.str s :: pretty_sdthms ctxt lthms

      );

    fun pretty_dtyp (s, []) =

          Pretty.str s

      | pretty_dtyp (s, cos) =

          (Pretty.block o Pretty.breaks) (

            Pretty.str s

            :: Pretty.str "="

            :: separate (Pretty.str "|") (map (fn (c, []) => Pretty.str c

                 | (c, tys) =>

                     (Pretty.block o Pretty.breaks)

                        (Pretty.str (CodeUnit.string_of_const thy c)

                          :: Pretty.str "of"

                          :: map (Pretty.quote o Syntax.pretty_typ_global thy) tys)) cos)

          );

    val inlines = (#inlines o the_thmproc) exec;

    val posts = (#posts o the_thmproc) exec;

    val inline_procs = (map fst o #inline_procs o the_thmproc) exec;

    val preprocs = (map fst o #preprocs o the_thmproc) exec;

    val funs = the_funcs exec

      |> Symtab.dest

      |> (map o apsnd) snd

      |> (map o apfst) (CodeUnit.string_of_const thy)

      |> sort (string_ord o pairself fst);

    val dtyps = the_dtyps exec

      |> Symtab.dest

      |> map (fn (dtco, (vs, cos)) =>

          (Syntax.string_of_typ_global thy (Type (dtco, map TFree vs)), cos))

      |> sort (string_ord o pairself fst)

  in

    (Pretty.writeln o Pretty.chunks) [

      Pretty.block (

        Pretty.str "defining equations:"

        :: Pretty.fbrk

        :: (Pretty.fbreaks o map pretty_func) funs

      ),

      Pretty.block (

        Pretty.str "inlining theorems:"

        :: Pretty.fbrk

        :: (Pretty.fbreaks o map (ProofContext.pretty_thm ctxt)) inlines

      ),

      Pretty.block (

        Pretty.str "inlining procedures:"

        :: Pretty.fbrk

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

      ),

      Pretty.block (

        Pretty.str "preprocessors:"

        :: Pretty.fbrk

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

      ),

      Pretty.block (

        Pretty.str "postprocessor theorems:"

        :: Pretty.fbrk

        :: (Pretty.fbreaks o map (ProofContext.pretty_thm ctxt)) posts

      ),

      Pretty.block (

        Pretty.str "datatypes:"

        :: Pretty.fbrk

        :: (Pretty.fbreaks o map pretty_dtyp) dtyps

      )

    ]

  end;

(** theorem transformation and certification **)

fun common_typ_funcs [] = []

  | common_typ_funcs [thm] = [thm]

  | common_typ_funcs (thms as thm :: _) =

      let

        val thy = Thm.theory_of_thm thm;

        fun incr_thm thm max =

          let

            val thm' = incr_indexes max thm;

            val max' = Thm.maxidx_of thm' + 1;

          in (thm', max') end;

        val (thms', maxidx) = fold_map incr_thm thms 0;

        val ty1 :: tys = map (snd o CodeUnit.head_func) thms';

        fun unify ty env = Sign.typ_unify thy (ty1, ty) env

          handle Type.TUNIFY =>

            error ("Type unificaton failed, while unifying defining equations\n"

            ^ (cat_lines o map Display.string_of_thm) thms

            ^ "\nwith types\n"

            ^ (cat_lines o map (CodeUnit.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 const_of_func thy = AxClass.unoverload_const thy o CodeUnit.head_func;

fun certify_const thy const thms =

  let

    fun cert thm = if const = const_of_func thy thm

      then thm else error ("Wrong head of defining equation,\nexpected constant "

        ^ CodeUnit.string_of_const thy const ^ "\n" ^ Display.string_of_thm thm)

  in map cert thms end;

(** operational sort algebra and class discipline **)

local

fun aggr_neutr f y [] = y

  | aggr_neutr f y (x::xs) = aggr_neutr f (f y x) xs;

fun aggregate f [] = NONE

  | aggregate f (x::xs) = SOME (aggr_neutr f x xs);

fun inter_sorts algebra =

  aggregate (map2 (curry (Sorts.inter_sort algebra)));

fun specific_constraints thy (class, tyco) =

  let

    val vs = Name.invents Name.context "" (Sign.arity_number thy tyco);

    val classparams = (map fst o these o try (#params o AxClass.get_info thy)) class;

    val funcs = classparams

      |> map_filter (fn c => try (AxClass.param_of_inst thy) (c, tyco))

      |> map (Symtab.lookup ((the_funcs o the_exec) thy))

      |> (map o Option.map) (Susp.force o fst o snd)

      |> maps these

      |> map (Thm.transfer thy)

    fun sorts_of [Type (_, tys)] = map (snd o dest_TVar) tys

      | sorts_of tys = map (snd o dest_TVar) tys;

    val sorts = map (sorts_of o Sign.const_typargs thy o CodeUnit.head_func) funcs;

  in sorts end;

fun weakest_constraints thy algebra (class, tyco) =

  let

    val all_superclasses = Sorts.complete_sort algebra [class];

  in case inter_sorts algebra (maps (fn class => specific_constraints thy (class, tyco)) all_superclasses)

   of SOME sorts => sorts

    | NONE => Sorts.mg_domain algebra tyco [class]

  end;

fun strongest_constraints thy algebra (class, tyco) =

  let

    val all_subclasses = class :: Graph.all_preds ((#classes o Sorts.rep_algebra) algebra) [class];

    val inst_subclasses = filter (can (Sorts.mg_domain algebra tyco) o single) all_subclasses;

  in case inter_sorts algebra (maps (fn class => specific_constraints thy (class, tyco)) inst_subclasses)

   of SOME sorts => sorts

    | NONE => replicate

        (Sign.arity_number thy tyco) (Sorts.minimize_sort algebra (Sorts.all_classes algebra))

  end;

fun get_algebra thy (class, tyco) =

  let

    val base_algebra = Sign.classes_of thy;

  in if can (Sorts.mg_domain base_algebra tyco) [class]

    then base_algebra

    else let

      val superclasses = Sorts.super_classes base_algebra class;

      val sorts = inter_sorts base_algebra

          (map_filter (fn class => try (Sorts.mg_domain base_algebra tyco) [class]) superclasses)

        |> the_default (replicate (Sign.arity_number thy tyco) [])

    in

      base_algebra

      |> Sorts.add_arities (Syntax.pp_global thy) (tyco, [(class, sorts)])

    end

  end;

fun gen_classparam_typ constr thy class (c, tyco) = 

  let

    val algebra = get_algebra thy (class, tyco);

    val cs = these (try (#params o AxClass.get_info thy) class);

    val SOME ty = AList.lookup (op =) cs c;

    val sort_args = Name.names (Name.declare Name.aT Name.context) Name.aT

      (constr thy algebra (class, tyco));

    val ty_inst = Type (tyco, map TFree sort_args);

  in Logic.varifyT (map_type_tfree (K ty_inst) ty) end;

fun retrieve_algebra thy operational =

  Sorts.subalgebra (Syntax.pp_global thy) operational

    (weakest_constraints thy (Sign.classes_of thy))

    (Sign.classes_of thy);

in

fun coregular_algebra thy = retrieve_algebra thy (K true) |> snd;

fun operational_algebra thy =

  let

    fun add_iff_operational class =

      can (AxClass.get_info thy) class ? cons class;

    val operational_classes = fold add_iff_operational (Sign.all_classes thy) []

  in retrieve_algebra thy (member (op =) operational_classes) end;

val classparam_weakest_typ = gen_classparam_typ weakest_constraints;

val classparam_strongest_typ = gen_classparam_typ strongest_constraints;

fun assert_func_typ thm =

  let

    val thy = Thm.theory_of_thm thm;

    fun check_typ_classparam tyco (c, thm) =

          let

            val SOME class = AxClass.class_of_param thy c;

            val (_, ty) = CodeUnit.head_func thm;

            val ty_decl = classparam_weakest_typ thy class (c, tyco);

            val ty_strongest = classparam_strongest_typ thy class (c, tyco);

            fun constrain thm = 

              let

                val max = Thm.maxidx_of thm + 1;

                val ty_decl' = Logic.incr_tvar max ty_decl;

                val (_, ty') = CodeUnit.head_func thm;

                val (env, _) = Sign.typ_unify thy (ty_decl', ty') (Vartab.empty, max);

                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 Thm.instantiate (instT, []) thm end;

          in if Sign.typ_instance thy (ty_strongest, ty)

            then if Sign.typ_instance thy (ty, ty_decl)

            then thm

            else (warning ("Constraining type\n" ^ CodeUnit.string_of_typ thy ty

              ^ "\nof defining equation\n"

              ^ Display.string_of_thm thm

              ^ "\nto permitted most general type\n"

              ^ CodeUnit.string_of_typ thy ty_decl);

              constrain thm)

            else CodeUnit.bad_thm ("Type\n" ^ CodeUnit.string_of_typ thy ty

              ^ "\nof defining equation\n"

              ^ Display.string_of_thm thm

              ^ "\nis incompatible with permitted least general type\n"

              ^ CodeUnit.string_of_typ thy ty_strongest)

          end;

    fun check_typ_fun (c, thm) =

      let

        val (_, ty) = CodeUnit.head_func thm;

        val ty_decl = Sign.the_const_type thy c;

      in if Sign.typ_equiv thy (Type.strip_sorts ty_decl, Type.strip_sorts ty)

        then thm

        else CodeUnit.bad_thm ("Type\n" ^ CodeUnit.string_of_typ thy ty

           ^ "\nof defining equation\n"

           ^ Display.string_of_thm thm

           ^ "\nis incompatible with declared function type\n"

           ^ CodeUnit.string_of_typ thy ty_decl)

      end;

    fun check_typ (c, thm) =

      case AxClass.inst_of_param thy c

       of SOME (c, tyco) => check_typ_classparam tyco (c, thm)

        | NONE => check_typ_fun (c, thm);

  in check_typ (const_of_func thy thm, thm) end;

val mk_func = CodeUnit.error_thm (assert_func_typ o CodeUnit.mk_func);

val mk_liberal_func = CodeUnit.warning_thm (assert_func_typ o CodeUnit.mk_func);

val mk_default_func = CodeUnit.try_thm (assert_func_typ o CodeUnit.mk_func);

end;

(** interfaces and attributes **)

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 get_datatype thy tyco =

  case Symtab.lookup ((the_dtyps o the_exec) thy) tyco

   of SOME spec => spec

    | NONE => Sign.arity_number thy tyco

        |> Name.invents Name.context Name.aT

        |> map (rpair [])

        |> rpair [];

fun get_datatype_of_constr thy c =

  case (snd o strip_type o Sign.the_const_type thy) c

   of Type (tyco, _) => if member (op =)

       ((the_default [] o Option.map (map fst o snd) o Symtab.lookup ((the_dtyps o the_exec) thy)) tyco) c

       then SOME tyco else NONE

    | _ => NONE;

fun get_constr_typ thy c =

  case get_datatype_of_constr thy c

   of SOME tyco => let

          val (vs, cos) = get_datatype thy tyco;

          val SOME tys = AList.lookup (op =) cos c;

          val ty = tys ---> Type (tyco, map TFree vs);

        in SOME (Logic.varifyT ty) end

    | NONE => NONE;

val get_case_data = Symtab.lookup o fst o the_cases o the_exec;

val is_undefined = Symtab.defined o snd o the_cases o the_exec;

fun add_func thm thy =

  let

    val func = mk_func thm;

    val c = const_of_func thy func;

    val _ = if (is_some o AxClass.class_of_param thy) c

      then error ("Rejected polymorphic equation for overloaded constant:\n"

        ^ Display.string_of_thm thm)

      else ();

    val _ = if (is_some o get_datatype_of_constr thy) c

      then error ("Rejected equation for datatype constructor:\n"

        ^ Display.string_of_thm func)

      else ();

  in

    (map_exec_purge (SOME [c]) o map_funcs) (Symtab.map_default

      (c, (false, (Susp.value [], []))) (apsnd (add_thm func))) thy

  end;

fun add_liberal_func thm thy =

  case mk_liberal_func thm

   of SOME func => let

          val c = const_of_func thy func

        in if (is_some o AxClass.class_of_param thy) c

          orelse (is_some o get_datatype_of_constr thy) c

          then thy

          else map_exec_purge (SOME [c]) (map_funcs

            (Symtab.map_default

              (c, (false, (Susp.value [], []))) (apsnd (add_thm func)))) thy

        end

    | NONE => thy;

fun add_default_func thm thy =

  case mk_default_func thm

   of SOME func => let

          val c = const_of_func thy func

        in if (is_some o AxClass.class_of_param thy) c

          orelse (is_some o get_datatype_of_constr thy) c

          then thy

          else map_exec_purge (SOME [c]) (map_funcs

          (Symtab.map_default

            (c, (false, (Susp.value [], []))) (apsnd (add_thm func)))) thy

        end

    | NONE => thy;

fun del_func thm thy =

  case mk_liberal_func thm

   of SOME func => let

          val c = const_of_func thy func;

        in map_exec_purge (SOME [c]) (map_funcs

          (Symtab.map_entry c (apsnd (del_thm func)))) thy

        end

    | NONE => thy;

fun del_funcs const = map_exec_purge (SOME [const])

  (map_funcs (Symtab.map_entry const (apsnd del_thms)));

fun add_funcl (const, lthms) thy =

  let

    val lthms' = certificate thy (fn thy => certify_const thy const) lthms;

      (*FIXME must check compatibility with sort algebra;

        alas, naive checking results in non-termination!*)

  in

    map_exec_purge (SOME [const])

      (map_funcs (Symtab.map_default (const, (false, (Susp.value [], [])))

      (apsnd (add_lthms lthms')))) thy

  end;

val add_default_func_attr = Attrib.internal (fn _ => Thm.declaration_attribute

  (fn thm => Context.mapping (add_default_func thm) I));

structure TypeInterpretation = InterpretationFun(type T = string * serial val eq = eq_snd (op =) : T * T -> bool);

fun add_datatype raw_cs thy =

  let

    val cs = map (fn c_ty as (_, ty) => (AxClass.unoverload_const thy c_ty, ty)) raw_cs;

    val (tyco, vs_cos) = CodeUnit.constrset_of_consts thy cs;

    val cs' = map fst (snd vs_cos);

    val purge_cs = case Symtab.lookup ((the_dtyps o the_exec) thy) tyco

     of SOME (vs, cos) => if null cos then NONE else SOME (cs' @ map fst cos)

      | NONE => NONE;

  in

    thy

    |> map_exec_purge purge_cs (map_dtyps (Symtab.update (tyco, vs_cos))

        #> map_funcs (fold (Symtab.delete_safe o fst) cs))

    |> TypeInterpretation.data (tyco, serial ())

  end;

fun type_interpretation f =  TypeInterpretation.interpretation

  (fn (tyco, _) => fn thy => f (tyco, get_datatype thy tyco) thy);

fun add_datatype_cmd raw_cs thy =

  let

    val cs = map (CodeUnit.read_bare_const thy) raw_cs;

  in add_datatype cs thy end;

fun add_case thm thy =

  let

    val entry as (c, _) = CodeUnit.case_cert thm;

  in

    (map_exec_purge (SOME [c]) o map_cases o apfst) (Symtab.update entry) thy

  end;

fun add_undefined c thy =

  (map_exec_purge (SOME [c]) o map_cases o apsnd) (Symtab.update (c, ())) thy;

fun add_inline thm thy =

  (map_exec_purge NONE o map_thmproc o apfst o apfst o apfst)

    (insert Thm.eq_thm_prop (CodeUnit.error_thm CodeUnit.mk_rew thm)) thy;

        (*fully applied in order to get right context for mk_rew!*)

fun del_inline thm thy =

  (map_exec_purge NONE o map_thmproc o apfst o apfst o apfst)

    (remove Thm.eq_thm_prop (CodeUnit.error_thm CodeUnit.mk_rew thm)) thy;

        (*fully applied in order to get right context for mk_rew!*)

fun add_inline_proc (name, f) =

  (map_exec_purge NONE o map_thmproc o apfst o apfst o apsnd)

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

fun del_inline_proc name =

  (map_exec_purge NONE o map_thmproc o apfst o apfst o apsnd)

    (delete_force "inline procedure" name);

fun add_preproc (name, f) =

  (map_exec_purge NONE o map_thmproc o apfst o apsnd)

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

fun del_preproc name =

  (map_exec_purge NONE o map_thmproc o apfst o apsnd)

    (delete_force "preprocessor" name);

fun add_post thm thy =

  (map_exec_purge NONE o map_thmproc o apsnd)

    (insert Thm.eq_thm_prop (CodeUnit.error_thm CodeUnit.mk_rew thm)) thy;

        (*fully applied in order to get right context for mk_rew!*)

fun del_post thm thy =

  (map_exec_purge NONE o map_thmproc o apsnd)

    (remove Thm.eq_thm_prop (CodeUnit.error_thm CodeUnit.mk_rew thm)) thy;

        (*fully applied in order to get right context for mk_rew!*)

val _ = Context.>> (Context.map_theory

  (let

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

    fun add_simple_attribute (name, f) =

      add_attribute (name, Scan.succeed (mk_attribute f));

    fun add_del_attribute (name, (add, del)) =

      add_attribute (name, Args.del |-- Scan.succeed (mk_attribute del)

        || Scan.succeed (mk_attribute add))

  in

    TypeInterpretation.init

    #> add_del_attribute ("func", (add_func, del_func))

    #> add_del_attribute ("inline", (add_inline, del_inline))

    #> add_del_attribute ("post", (add_post, del_post))

  end));

(** post- and preprocessing **)

local

fun gen_apply_inline_proc prep post thy f x =

  let

    val cts = prep x;

    val rews = map CodeUnit.assert_rew (f thy cts);

  in post rews x end;

val apply_inline_proc = gen_apply_inline_proc (maps

  ((fn [args, rhs] => rhs :: (snd o Drule.strip_comb) args) o snd o Drule.strip_comb o Thm.cprop_of))

  (fn rews => map (CodeUnit.rewrite_func rews));

val apply_inline_proc_cterm = gen_apply_inline_proc single

  (MetaSimplifier.rewrite false);

fun apply_preproc thy f [] = []

  | apply_preproc thy f (thms as (thm :: _)) =

      let

        val const = const_of_func thy thm;

        val thms' = f thy thms;

      in certify_const thy const thms' end;

fun rhs_conv conv thm =

  let

    val thm' = (conv o Thm.rhs_of) thm;

  in Thm.transitive thm thm' end

fun term_of_conv thy f =

  Thm.cterm_of thy

  #> f

  #> Thm.prop_of

  #> Logic.dest_equals

  #> snd;

in

fun preprocess thy thms =

  thms

  |> fold (fn (_, (_, f)) => apply_preproc thy f) ((#preprocs o the_thmproc o the_exec) thy)

  |> map (CodeUnit.rewrite_func ((#inlines o the_thmproc o the_exec) thy))

  |> fold (fn (_, (_, f)) => apply_inline_proc thy f) ((#inline_procs o the_thmproc o the_exec) thy)

(*FIXME - must check: rewrite rule, defining equation, proper constant |> map (snd o check_func false thy) *)

  |> common_typ_funcs

  |> map (AxClass.unoverload thy);

fun preprocess_conv ct =

  let

    val thy = Thm.theory_of_cterm ct;

  in

    ct

    |> MetaSimplifier.rewrite false ((#inlines o the_thmproc o the_exec) thy)

    |> fold (fn (_, (_, f)) => rhs_conv (apply_inline_proc_cterm thy f))

        ((#inline_procs o the_thmproc o the_exec) thy)

    |> rhs_conv (AxClass.unoverload_conv thy)

  end;

fun preprocess_term thy = term_of_conv thy preprocess_conv;

fun postprocess_conv ct =

  let

    val thy = Thm.theory_of_cterm ct;

  in

    ct

    |> AxClass.overload_conv thy

    |> rhs_conv (MetaSimplifier.rewrite false ((#posts o the_thmproc o the_exec) thy))

  end;

fun postprocess_term thy = term_of_conv thy postprocess_conv;

end; (*local*)

fun default_typ_proto thy c = case AxClass.inst_of_param thy c

 of SOME (c, tyco) => classparam_weakest_typ thy ((the o AxClass.class_of_param thy) c)

      (c, tyco) |> SOME

  | NONE => (case AxClass.class_of_param thy c

     of SOME class => SOME (Term.map_type_tvar

          (K (TVar ((Name.aT, 0), [class]))) (Sign.the_const_type thy c))

      | NONE => get_constr_typ thy c);

local

fun get_funcs thy const =

  Symtab.lookup ((the_funcs o the_exec) thy) const

  |> Option.map (Susp.force o fst o snd)

  |> these

  |> map (Thm.transfer thy);

in

fun these_funcs thy const =

  let

    fun drop_refl thy = filter_out (is_equal o Term.fast_term_ord o Logic.dest_equals

      o ObjectLogic.drop_judgment thy o Thm.plain_prop_of);

  in

    get_funcs thy const

    |> preprocess thy

    |> drop_refl thy

  end;

fun default_typ thy c = case default_typ_proto thy c

 of SOME ty => ty

  | NONE => (case get_funcs thy c

     of thm :: _ => snd (CodeUnit.head_func (AxClass.unoverload thy thm))

      | [] => Sign.the_const_type thy c);

end; (*local*)