(*  Title:      HOL/Tools/Predicate_Compile/predicate_compile_core.ML

     Author:     Lukas Bulwahn, TU Muenchen

 A compiler from predicates specified by intro/elim rules to equations.

 *)

 signature PREDICATE_COMPILE_CORE =

 sig

   val setup : theory -> theory

   val code_pred : Predicate_Compile_Aux.options -> string -> Proof.context -> Proof.state

   val code_pred_cmd : Predicate_Compile_Aux.options -> string -> Proof.context -> Proof.state

   val values_cmd : string list -> Predicate_Compile_Aux.mode option list option

     -> (string option * (Predicate_Compile_Aux.compilation * int list))

     -> int -> string -> Toplevel.state -> unit

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

   val register_intros : string * thm list -> theory -> theory

   val is_registered : theory -> string -> bool

   val function_name_of : Predicate_Compile_Aux.compilation -> theory

     -> string -> Predicate_Compile_Aux.mode -> string

   val predfun_intro_of: theory -> string -> Predicate_Compile_Aux.mode -> thm

   val predfun_elim_of: theory -> string -> Predicate_Compile_Aux.mode -> thm

   val all_preds_of : theory -> string list

   val modes_of: Predicate_Compile_Aux.compilation

     -> theory -> string -> Predicate_Compile_Aux.mode list

   val all_modes_of : Predicate_Compile_Aux.compilation

     -> theory -> (string * Predicate_Compile_Aux.mode list) list

   val all_random_modes_of : theory -> (string * Predicate_Compile_Aux.mode list) list

   val intros_of : theory -> string -> thm list

   val add_intro : thm -> theory -> theory

   val set_elim : thm -> theory -> theory

   val preprocess_intro : theory -> thm -> thm

   val print_stored_rules : theory -> unit

   val print_all_modes : Predicate_Compile_Aux.compilation -> theory -> unit

   val mk_casesrule : Proof.context -> term -> thm list -> term

   val eval_ref : (unit -> term Predicate.pred) option Unsynchronized.ref

   val random_eval_ref : (unit -> int * int -> term Predicate.pred * (int * int))

     option Unsynchronized.ref

   val dseq_eval_ref : (unit -> term DSequence.dseq) option Unsynchronized.ref

   val random_dseq_eval_ref : (unit -> int -> int -> int * int -> term DSequence.dseq * (int * int))

     option Unsynchronized.ref

   val code_pred_intro_attrib : attribute

   (* used by Quickcheck_Generator *) 

   (* temporary for testing of the compilation *)

   datatype compilation_funs = CompilationFuns of {

     mk_predT : typ -> typ,

     dest_predT : typ -> typ,

     mk_bot : typ -> term,

     mk_single : term -> term,

     mk_bind : term * term -> term,

     mk_sup : term * term -> term,

     mk_if : term -> term,

     mk_not : term -> term,

     mk_map : typ -> typ -> term -> term -> term

   };

   val pred_compfuns : compilation_funs

   val randompred_compfuns : compilation_funs

   val add_equations : Predicate_Compile_Aux.options -> string list -> theory -> theory

   val add_random_dseq_equations : Predicate_Compile_Aux.options -> string list -> theory -> theory

   val mk_tracing : string -> term -> term

 end;

 structure Predicate_Compile_Core : PREDICATE_COMPILE_CORE =

 struct

 open Predicate_Compile_Aux;

 (** auxiliary **)

 (* debug stuff *)

 fun print_tac s = Seq.single;

 fun print_tac' options s = 

   if show_proof_trace options then Tactical.print_tac s else Seq.single;

 fun debug_tac msg = Seq.single; (* (fn st => (Output.tracing msg; Seq.single st)); *)

 fun assert b = if not b then error "Assertion failed" else warning "Assertion holds"

 datatype assertion = Max_number_of_subgoals of int

 fun assert_tac (Max_number_of_subgoals i) st =

   if (nprems_of st <= i) then Seq.single st

   else error ("assert_tac: Numbers of subgoals mismatch at goal state :"

     ^ "\n" ^ Pretty.string_of (Pretty.chunks

       (Goal_Display.pretty_goals_without_context (! Goal_Display.goals_limit) st)));

 (** fundamentals **)

 (* syntactic operations *)

 fun mk_eq (x, xs) =

   let fun mk_eqs _ [] = []

         | mk_eqs a (b::cs) =

             HOLogic.mk_eq (Free (a, fastype_of b), b) :: mk_eqs a cs

   in mk_eqs x xs end;

 fun mk_scomp (t, u) =

   let

     val T = fastype_of t

     val U = fastype_of u

     val [A] = binder_types T

     val D = body_type U                   

   in 

     Const (@{const_name "scomp"}, T --> U --> A --> D) $ t $ u

   end;

 fun dest_funT (Type ("fun",[S, T])) = (S, T)

   | dest_funT T = raise TYPE ("dest_funT", [T], [])

 fun mk_fun_comp (t, u) =

   let

     val (_, B) = dest_funT (fastype_of t)

     val (C, A) = dest_funT (fastype_of u)

   in

     Const(@{const_name "Fun.comp"}, (A --> B) --> (C --> A) --> C --> B) $ t $ u

   end;

 fun dest_randomT (Type ("fun", [@{typ Random.seed},

   Type ("*", [Type ("*", [T, @{typ "unit => Code_Evaluation.term"}]) ,@{typ Random.seed}])])) = T

   | dest_randomT T = raise TYPE ("dest_randomT", [T], [])

 fun mk_tracing s t =

   Const(@{const_name Code_Evaluation.tracing},

     @{typ String.literal} --> (fastype_of t) --> (fastype_of t)) $ (HOLogic.mk_literal s) $ t

 val strip_intro_concl = (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl o prop_of)

 (* derivation trees for modes of premises *)

 datatype mode_derivation = Mode_App of mode_derivation * mode_derivation | Context of mode

   | Mode_Pair of mode_derivation * mode_derivation | Term of mode

 fun string_of_derivation (Mode_App (m1, m2)) =

   "App (" ^ string_of_derivation m1 ^ ", " ^ string_of_derivation m2 ^ ")"

   | string_of_derivation (Mode_Pair (m1, m2)) =

   "Pair (" ^ string_of_derivation m1 ^ ", " ^ string_of_derivation m2 ^ ")"

   | string_of_derivation (Term m) = "Term (" ^ string_of_mode m ^ ")"

   | string_of_derivation (Context m) = "Context (" ^ string_of_mode m ^ ")"

 fun strip_mode_derivation deriv =

   let

     fun strip (Mode_App (deriv1, deriv2)) ds = strip deriv1 (deriv2 :: ds)

       | strip deriv ds = (deriv, ds)

   in

     strip deriv []

   end

 fun mode_of (Context m) = m

   | mode_of (Term m) = m

   | mode_of (Mode_App (d1, d2)) =

     (case mode_of d1 of Fun (m, m') =>

         (if m = mode_of d2 then m' else error "mode_of")

       | _ => error "mode_of2")

   | mode_of (Mode_Pair (d1, d2)) =

     Pair (mode_of d1, mode_of d2)

 fun head_mode_of deriv = mode_of (fst (strip_mode_derivation deriv))

 fun param_derivations_of deriv =

   let

     val (_, argument_derivs) = strip_mode_derivation deriv

     fun param_derivation (Mode_Pair (m1, m2)) =

         param_derivation m1 @ param_derivation m2

       | param_derivation (Term _) = []

       | param_derivation m = [m]

   in

     maps param_derivation argument_derivs

   end

 fun collect_context_modes (Mode_App (m1, m2)) =

       collect_context_modes m1 @ collect_context_modes m2

   | collect_context_modes (Mode_Pair (m1, m2)) =

       collect_context_modes m1 @ collect_context_modes m2

   | collect_context_modes (Context m) = [m]

   | collect_context_modes (Term _) = []

 (* representation of inferred clauses with modes *)

 type moded_clause = term list * (indprem * mode_derivation) list

 type 'a pred_mode_table = (string * (mode * 'a) list) list

 (* book-keeping *)

 datatype predfun_data = PredfunData of {

   definition : thm,

   intro : thm,

   elim : thm

 };

 fun rep_predfun_data (PredfunData data) = data;

 fun mk_predfun_data (definition, intro, elim) =

   PredfunData {definition = definition, intro = intro, elim = elim}

 datatype pred_data = PredData of {

   intros : thm list,

   elim : thm option,

   function_names : (compilation * (mode * string) list) list,

   predfun_data : (mode * predfun_data) list,

   needs_random : mode list

 };

 fun rep_pred_data (PredData data) = data;

 fun mk_pred_data ((intros, elim), (function_names, predfun_data, needs_random)) =

   PredData {intros = intros, elim = elim,

     function_names = function_names, predfun_data = predfun_data, needs_random = needs_random}

 fun map_pred_data f (PredData {intros, elim, function_names, predfun_data, needs_random}) =

   mk_pred_data (f ((intros, elim), (function_names, predfun_data, needs_random)))

 fun eq_option eq (NONE, NONE) = true

   | eq_option eq (SOME x, SOME y) = eq (x, y)

   | eq_option eq _ = false

 fun eq_pred_data (PredData d1, PredData d2) = 

   eq_list (Thm.eq_thm) (#intros d1, #intros d2) andalso

   eq_option (Thm.eq_thm) (#elim d1, #elim d2)

 structure PredData = Theory_Data

 (

   type T = pred_data Graph.T;

   val empty = Graph.empty;

   val extend = I;

   val merge = Graph.merge eq_pred_data;

 );

 (* queries *)

 fun lookup_pred_data thy name =

   Option.map rep_pred_data (try (Graph.get_node (PredData.get thy)) name)

 fun the_pred_data thy name = case lookup_pred_data thy name

  of NONE => error ("No such predicate " ^ quote name)  

   | SOME data => data;

 val is_registered = is_some oo lookup_pred_data

 val all_preds_of = Graph.keys o PredData.get

 fun intros_of thy = map (Thm.transfer thy) o #intros o the_pred_data thy

 fun the_elim_of thy name = case #elim (the_pred_data thy name)

  of NONE => error ("No elimination rule for predicate " ^ quote name)

   | SOME thm => Thm.transfer thy thm 

 val has_elim = is_some o #elim oo the_pred_data;

 fun function_names_of compilation thy name =

   case AList.lookup (op =) (#function_names (the_pred_data thy name)) compilation of

     NONE => error ("No " ^ string_of_compilation compilation

       ^ "functions defined for predicate " ^ quote name)

   | SOME fun_names => fun_names

 fun function_name_of compilation thy name mode =

   case AList.lookup (op =) (function_names_of compilation thy name) mode of

     NONE => error ("No " ^ string_of_compilation compilation

       ^ "function defined for mode " ^ string_of_mode mode ^ " of predicate " ^ quote name)

   | SOME function_name => function_name

 fun modes_of compilation thy name = map fst (function_names_of compilation thy name)

 fun all_modes_of compilation thy =

   map_filter (fn name => Option.map (pair name) (try (modes_of compilation thy) name))

     (all_preds_of thy)

 val all_random_modes_of = all_modes_of Random

 fun defined_functions compilation thy name =

   AList.defined (op =) (#function_names (the_pred_data thy name)) compilation

 fun lookup_predfun_data thy name mode =

   Option.map rep_predfun_data

     (AList.lookup (op =) (#predfun_data (the_pred_data thy name)) mode)

 fun the_predfun_data thy name mode =

   case lookup_predfun_data thy name mode of

     NONE => error ("No function defined for mode " ^ string_of_mode mode ^

       " of predicate " ^ name)

   | SOME data => data;

 val predfun_definition_of = #definition ooo the_predfun_data

 val predfun_intro_of = #intro ooo the_predfun_data

 val predfun_elim_of = #elim ooo the_predfun_data

 (* diagnostic display functions *)

 fun print_modes options thy modes =

   if show_modes options then

     tracing ("Inferred modes:\n" ^

       cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map

         string_of_mode ms)) modes))

   else ()

 fun print_pred_mode_table string_of_entry thy pred_mode_table =

   let

     fun print_mode pred (mode, entry) =  "mode : " ^ string_of_mode mode

       ^ string_of_entry pred mode entry

     fun print_pred (pred, modes) =

       "predicate " ^ pred ^ ": " ^ cat_lines (map (print_mode pred) modes)

     val _ = tracing (cat_lines (map print_pred pred_mode_table))

   in () end;

 fun string_of_prem thy (Prem t) =

     (Syntax.string_of_term_global thy t) ^ "(premise)"

   | string_of_prem thy (Negprem t) =

     (Syntax.string_of_term_global thy (HOLogic.mk_not t)) ^ "(negative premise)"

   | string_of_prem thy (Sidecond t) =

     (Syntax.string_of_term_global thy t) ^ "(sidecondition)"

   | string_of_prem thy _ = error "string_of_prem: unexpected input"

 fun string_of_clause thy pred (ts, prems) =

   (space_implode " --> "

   (map (string_of_prem thy) prems)) ^ " --> " ^ pred ^ " "

    ^ (space_implode " " (map (Syntax.string_of_term_global thy) ts))

 fun print_compiled_terms options thy =

   if show_compilation options then

     print_pred_mode_table (fn _ => fn _ => Syntax.string_of_term_global thy) thy

   else K ()

 fun print_stored_rules thy =

   let

     val preds = (Graph.keys o PredData.get) thy

     fun print pred () = let

       val _ = writeln ("predicate: " ^ pred)

       val _ = writeln ("introrules: ")

       val _ = fold (fn thm => fn u => writeln (Display.string_of_thm_global thy thm))

         (rev (intros_of thy pred)) ()

     in

       if (has_elim thy pred) then

         writeln ("elimrule: " ^ Display.string_of_thm_global thy (the_elim_of thy pred))

       else

         writeln ("no elimrule defined")

     end

   in

     fold print preds ()

   end;

 fun print_all_modes compilation thy =

   let

     val _ = writeln ("Inferred modes:")

     fun print (pred, modes) u =

       let

         val _ = writeln ("predicate: " ^ pred)

         val _ = writeln ("modes: " ^ (commas (map string_of_mode modes)))

       in u end

   in

     fold print (all_modes_of compilation thy) ()

   end

 (* validity checks *)

 (* EXPECTED MODE and PROPOSED_MODE are largely the same; define a clear semantics for those! *)

 fun check_expected_modes preds options modes =

   case expected_modes options of

     SOME (s, ms) => (case AList.lookup (op =) modes s of

       SOME modes =>

         let

           val modes' = modes

         in

           if not (eq_set eq_mode (ms, modes')) then

             error ("expected modes were not inferred:\n"

             ^ "  inferred modes for " ^ s ^ ": " ^ commas (map string_of_mode modes')  ^ "\n"

             ^ "  expected modes for " ^ s ^ ": " ^ commas (map string_of_mode ms))

           else ()

         end

       | NONE => ())

   | NONE => ()

 fun check_proposed_modes preds options modes extra_modes errors =

   case proposed_modes options of

     SOME (s, ms) => (case AList.lookup (op =) modes s of

       SOME inferred_ms =>

         let

           val preds_without_modes = map fst (filter (null o snd) (modes @ extra_modes))

           val modes' = inferred_ms

         in

           if not (eq_set eq_mode (ms, modes')) then

             error ("expected modes were not inferred:\n"

             ^ "  inferred modes for " ^ s ^ ": " ^ commas (map string_of_mode modes')  ^ "\n"

             ^ "  expected modes for " ^ s ^ ": " ^ commas (map string_of_mode ms) ^ "\n"

             ^ "For the following clauses, the following modes could not be inferred: " ^ "\n"

             ^ cat_lines errors ^

             (if not (null preds_without_modes) then

               "\n" ^ "No mode inferred for the predicates " ^ commas preds_without_modes

             else ""))

           else ()

         end

       | NONE => ())

   | NONE => ()

 (* importing introduction rules *)

 fun unify_consts thy cs intr_ts =

   (let

      val add_term_consts_2 = fold_aterms (fn Const c => insert (op =) c | _ => I);

      fun varify (t, (i, ts)) =

        let val t' = map_types (Logic.incr_tvar (i + 1)) (#2 (Type.varify [] t))

        in (maxidx_of_term t', t'::ts) end;

      val (i, cs') = List.foldr varify (~1, []) cs;

      val (i', intr_ts') = List.foldr varify (i, []) intr_ts;

      val rec_consts = fold add_term_consts_2 cs' [];

      val intr_consts = fold add_term_consts_2 intr_ts' [];

      fun unify (cname, cT) =

        let val consts = map snd (filter (fn c => fst c = cname) intr_consts)

        in fold (Sign.typ_unify thy) ((replicate (length consts) cT) ~~ consts) end;

      val (env, _) = fold unify rec_consts (Vartab.empty, i');

      val subst = map_types (Envir.norm_type env)

    in (map subst cs', map subst intr_ts')

    end) handle Type.TUNIFY =>

      (warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts));

 fun import_intros inp_pred [] ctxt =

   let

     val ([outp_pred], ctxt') = Variable.import_terms true [inp_pred] ctxt

     val T = fastype_of outp_pred

     (* TODO: put in a function for this next line! *)

     val paramTs = ho_argsT_of (hd (all_modes_of_typ T)) (binder_types T)

     val (param_names, ctxt'') = Variable.variant_fixes

       (map (fn i => "p" ^ (string_of_int i)) (1 upto (length paramTs))) ctxt'

     val params = map2 (curry Free) param_names paramTs

   in

     (((outp_pred, params), []), ctxt')

   end

   | import_intros inp_pred (th :: ths) ctxt =

     let

       val ((_, [th']), ctxt') = Variable.import true [th] ctxt

       val thy = ProofContext.theory_of ctxt'

       val (pred, args) = strip_intro_concl th'

       val T = fastype_of pred

       val ho_args = ho_args_of (hd (all_modes_of_typ T)) args

       fun subst_of (pred', pred) =

         let

           val subst = Sign.typ_match thy (fastype_of pred', fastype_of pred) Vartab.empty

         in map (fn (indexname, (s, T)) => ((indexname, s), T)) (Vartab.dest subst) end

       fun instantiate_typ th =

         let

           val (pred', _) = strip_intro_concl th

           val _ = if not (fst (dest_Const pred) = fst (dest_Const pred')) then

             error "Trying to instantiate another predicate" else ()

         in Thm.certify_instantiate (subst_of (pred', pred), []) th end;

       fun instantiate_ho_args th =

         let

           val (_, args') = (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl o prop_of) th

           val ho_args' = map dest_Var (ho_args_of (hd (all_modes_of_typ T)) args')

         in Thm.certify_instantiate ([], ho_args' ~~ ho_args) th end

       val outp_pred =

         Term_Subst.instantiate (subst_of (inp_pred, pred), []) inp_pred

       val ((_, ths'), ctxt1) =

         Variable.import false (map (instantiate_typ #> instantiate_ho_args) ths) ctxt'

     in

       (((outp_pred, ho_args), th' :: ths'), ctxt1)

     end

 (* generation of case rules from user-given introduction rules *)

 fun mk_args2 (Type ("*", [T1, T2])) st =

     let

       val (t1, st') = mk_args2 T1 st

       val (t2, st'') = mk_args2 T2 st'

     in

       (HOLogic.mk_prod (t1, t2), st'')

     end

   | mk_args2 (T as Type ("fun", _)) (params, ctxt) = 

     let

       val (S, U) = strip_type T

     in

       if U = HOLogic.boolT then

         (hd params, (tl params, ctxt))

       else

         let

           val ([x], ctxt') = Variable.variant_fixes ["x"] ctxt

         in

           (Free (x, T), (params, ctxt'))

         end

     end

   | mk_args2 T (params, ctxt) =

     let

       val ([x], ctxt') = Variable.variant_fixes ["x"] ctxt

     in

       (Free (x, T), (params, ctxt'))

     end

 fun mk_casesrule ctxt pred introrules =

   let

     val (((pred, params), intros_th), ctxt1) = import_intros pred introrules ctxt

     val intros = map prop_of intros_th

     val ([propname], ctxt2) = Variable.variant_fixes ["thesis"] ctxt1

     val prop = HOLogic.mk_Trueprop (Free (propname, HOLogic.boolT))

     val argsT = binder_types (fastype_of pred)

     val (argvs, _) = fold_map mk_args2 argsT (params, ctxt2)

     fun mk_case intro =

       let

         val (_, args) = (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl) intro

         val prems = Logic.strip_imp_prems intro

         val eqprems = map2 (HOLogic.mk_Trueprop oo (curry HOLogic.mk_eq)) argvs args

         val frees = (fold o fold_aterms)

           (fn t as Free _ =>

               if member (op aconv) params t then I else insert (op aconv) t

            | _ => I) (args @ prems) []

       in fold Logic.all frees (Logic.list_implies (eqprems @ prems, prop)) end

     val assm = HOLogic.mk_Trueprop (list_comb (pred, argvs))

     val cases = map mk_case intros

   in Logic.list_implies (assm :: cases, prop) end;

 (** preprocessing rules **)

 fun imp_prems_conv cv ct =

   case Thm.term_of ct of

     Const ("==>", _) $ _ $ _ => Conv.combination_conv (Conv.arg_conv cv) (imp_prems_conv cv) ct

   | _ => Conv.all_conv ct

 fun Trueprop_conv cv ct =

   case Thm.term_of ct of

     Const ("Trueprop", _) $ _ => Conv.arg_conv cv ct  

   | _ => error "Trueprop_conv"

 fun preprocess_intro thy rule =

   Conv.fconv_rule

     (imp_prems_conv

       (Trueprop_conv (Conv.try_conv (Conv.rewr_conv (Thm.symmetric @{thm Predicate.eq_is_eq})))))

     (Thm.transfer thy rule)

 fun preprocess_elim thy elimrule =

   let

     fun replace_eqs (Const ("Trueprop", _) $ (Const ("op =", T) $ lhs $ rhs)) =

        HOLogic.mk_Trueprop (Const (@{const_name Predicate.eq}, T) $ lhs $ rhs)

      | replace_eqs t = t

     val ctxt = ProofContext.init thy

     val ((_, [elimrule]), ctxt') = Variable.import false [elimrule] ctxt

     val prems = Thm.prems_of elimrule

     val nargs = length (snd (strip_comb (HOLogic.dest_Trueprop (hd prems))))

     fun preprocess_case t =

       let

        val params = Logic.strip_params t

        val (assums1, assums2) = chop nargs (Logic.strip_assums_hyp t)

        val assums_hyp' = assums1 @ (map replace_eqs assums2)

       in

        list_all (params, Logic.list_implies (assums_hyp', Logic.strip_assums_concl t))

       end

     val cases' = map preprocess_case (tl prems)

     val elimrule' = Logic.list_implies ((hd prems) :: cases', Thm.concl_of elimrule)

     val bigeq = (Thm.symmetric (Conv.implies_concl_conv

       (MetaSimplifier.rewrite true [@{thm Predicate.eq_is_eq}])

         (cterm_of thy elimrule')))

     val tac = (fn _ => Skip_Proof.cheat_tac thy)    

     val eq = Goal.prove ctxt' [] [] (Logic.mk_equals ((Thm.prop_of elimrule), elimrule')) tac

   in

     Thm.equal_elim eq elimrule |> singleton (Variable.export ctxt' ctxt)

   end;

 fun expand_tuples_elim th = th

 val no_compilation = ([], [], [])

 fun fetch_pred_data thy name =

   case try (Inductive.the_inductive (ProofContext.init thy)) name of

     SOME (info as (_, result)) => 

       let

         fun is_intro_of intro =

           let

             val (const, _) = strip_comb (HOLogic.dest_Trueprop (concl_of intro))

           in (fst (dest_Const const) = name) end;      

         val intros =

           (map (expand_tuples thy #> preprocess_intro thy) (filter is_intro_of (#intrs result)))

         val index = find_index (fn s => s = name) (#names (fst info))

         val pre_elim = nth (#elims result) index

         val pred = nth (#preds result) index

         (*val elim = singleton (Inductive_Set.codegen_preproc thy) (preprocess_elim thy nparams 

           (expand_tuples_elim pre_elim))*)

         val elim =

           (Drule.export_without_context o Skip_Proof.make_thm thy)

           (mk_casesrule (ProofContext.init thy) pred intros)

       in

         mk_pred_data ((intros, SOME elim), no_compilation)

       end

   | NONE => error ("No such predicate: " ^ quote name)

 fun add_predfun_data name mode data =

   let

     val add = (apsnd o apsnd3) (cons (mode, mk_predfun_data data))

   in PredData.map (Graph.map_node name (map_pred_data add)) end

 fun is_inductive_predicate thy name =

   is_some (try (Inductive.the_inductive (ProofContext.init thy)) name)

 fun depending_preds_of thy (key, value) =

   let

     val intros = (#intros o rep_pred_data) value

   in

     fold Term.add_const_names (map Thm.prop_of intros) []

       |> filter (fn c => (not (c = key)) andalso

         (is_inductive_predicate thy c orelse is_registered thy c))

   end;

 fun add_intro thm thy =

   let

     val (name, T) = dest_Const (fst (strip_intro_concl thm))

     fun cons_intro gr =

      case try (Graph.get_node gr) name of

        SOME pred_data => Graph.map_node name (map_pred_data

          (apfst (fn (intros, elim) => (intros @ [thm], elim)))) gr

      | NONE => Graph.new_node (name, mk_pred_data (([thm], NONE), no_compilation)) gr

   in PredData.map cons_intro thy end

 fun set_elim thm =

   let

     val (name, _) = dest_Const (fst 

       (strip_comb (HOLogic.dest_Trueprop (hd (prems_of thm)))))

     fun set (intros, _) = (intros, SOME thm)

   in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end

 fun register_predicate (constname, pre_intros, pre_elim) thy =

   let

     val intros = map (preprocess_intro thy) pre_intros

     val elim = preprocess_elim thy pre_elim

   in

     if not (member (op =) (Graph.keys (PredData.get thy)) constname) then

       PredData.map

         (Graph.new_node (constname,

           mk_pred_data ((intros, SOME elim), no_compilation))) thy

     else thy

   end

 fun register_intros (constname, pre_intros) thy =

   let

     val T = Sign.the_const_type thy constname

     fun constname_of_intro intr = fst (dest_Const (fst (strip_intro_concl intr)))

     val _ = if not (forall (fn intr => constname_of_intro intr = constname) pre_intros) then

       error ("register_intros: Introduction rules of different constants are used\n" ^

         "expected rules for " ^ constname ^ ", but received rules for " ^

           commas (map constname_of_intro pre_intros))

       else ()

     val pred = Const (constname, T)

     val pre_elim = 

       (Drule.export_without_context o Skip_Proof.make_thm thy)

       (mk_casesrule (ProofContext.init thy) pred pre_intros)

   in register_predicate (constname, pre_intros, pre_elim) thy end

 fun defined_function_of compilation pred =

   let

     val set = (apsnd o apfst3) (cons (compilation, []))

   in

     PredData.map (Graph.map_node pred (map_pred_data set))

   end

 fun set_function_name compilation pred mode name =

   let

     val set = (apsnd o apfst3)

       (AList.map_default (op =) (compilation, [(mode, name)]) (cons (mode, name)))

   in

     PredData.map (Graph.map_node pred (map_pred_data set))

   end

 fun set_needs_random name modes =

   let

     val set = (apsnd o aptrd3) (K modes)

   in

     PredData.map (Graph.map_node name (map_pred_data set))

   end

 (* datastructures and setup for generic compilation *)

 datatype compilation_funs = CompilationFuns of {

   mk_predT : typ -> typ,

   dest_predT : typ -> typ,

   mk_bot : typ -> term,

   mk_single : term -> term,

   mk_bind : term * term -> term,

   mk_sup : term * term -> term,

   mk_if : term -> term,

   mk_not : term -> term,

   mk_map : typ -> typ -> term -> term -> term

 };

 fun mk_predT (CompilationFuns funs) = #mk_predT funs

 fun dest_predT (CompilationFuns funs) = #dest_predT funs

 fun mk_bot (CompilationFuns funs) = #mk_bot funs

 fun mk_single (CompilationFuns funs) = #mk_single funs

 fun mk_bind (CompilationFuns funs) = #mk_bind funs

 fun mk_sup (CompilationFuns funs) = #mk_sup funs

 fun mk_if (CompilationFuns funs) = #mk_if funs

 fun mk_not (CompilationFuns funs) = #mk_not funs

 fun mk_map (CompilationFuns funs) = #mk_map funs

 structure PredicateCompFuns =

 struct

 fun mk_predT T = Type (@{type_name Predicate.pred}, [T])

 fun dest_predT (Type (@{type_name Predicate.pred}, [T])) = T

   | dest_predT T = raise TYPE ("dest_predT", [T], []);

 fun mk_bot T = Const (@{const_name Orderings.bot}, mk_predT T);

 fun mk_single t =

   let val T = fastype_of t

   in Const(@{const_name Predicate.single}, T --> mk_predT T) $ t end;

 fun mk_bind (x, f) =

   let val T as Type ("fun", [_, U]) = fastype_of f

   in

     Const (@{const_name Predicate.bind}, fastype_of x --> T --> U) $ x $ f

   end;

 val mk_sup = HOLogic.mk_binop @{const_name sup};

 fun mk_if cond = Const (@{const_name Predicate.if_pred},

   HOLogic.boolT --> mk_predT HOLogic.unitT) $ cond;

 fun mk_not t = let val T = mk_predT HOLogic.unitT

   in Const (@{const_name Predicate.not_pred}, T --> T) $ t end

 fun mk_Enum f =

   let val T as Type ("fun", [T', _]) = fastype_of f

   in

     Const (@{const_name Predicate.Pred}, T --> mk_predT T') $ f    

   end;

 fun mk_Eval (f, x) =

   let

     val T = fastype_of x

   in

     Const (@{const_name Predicate.eval}, mk_predT T --> T --> HOLogic.boolT) $ f $ x

   end;

 fun dest_Eval (Const (@{const_name Predicate.eval}, _) $ f $ x) = (f, x)

 fun mk_map T1 T2 tf tp = Const (@{const_name Predicate.map},

   (T1 --> T2) --> mk_predT T1 --> mk_predT T2) $ tf $ tp;

 val compfuns = CompilationFuns {mk_predT = mk_predT, dest_predT = dest_predT, mk_bot = mk_bot,

   mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if, mk_not = mk_not,

   mk_map = mk_map};

 end;

 structure RandomPredCompFuns =

 struct

 fun mk_randompredT T =

   @{typ Random.seed} --> HOLogic.mk_prodT (PredicateCompFuns.mk_predT T, @{typ Random.seed})

 fun dest_randompredT (Type ("fun", [@{typ Random.seed}, Type (@{type_name "*"},

   [Type (@{type_name "Predicate.pred"}, [T]), @{typ Random.seed}])])) = T

   | dest_randompredT T = raise TYPE ("dest_randompredT", [T], []);

 fun mk_bot T = Const(@{const_name Quickcheck.empty}, mk_randompredT T)

 fun mk_single t =

   let               

     val T = fastype_of t

   in

     Const (@{const_name Quickcheck.single}, T --> mk_randompredT T) $ t

   end;

 fun mk_bind (x, f) =

   let

     val T as (Type ("fun", [_, U])) = fastype_of f

   in

     Const (@{const_name Quickcheck.bind}, fastype_of x --> T --> U) $ x $ f

   end

 val mk_sup = HOLogic.mk_binop @{const_name Quickcheck.union}

 fun mk_if cond = Const (@{const_name Quickcheck.if_randompred},

   HOLogic.boolT --> mk_randompredT HOLogic.unitT) $ cond;

 fun mk_not t = let val T = mk_randompredT HOLogic.unitT

   in Const (@{const_name Quickcheck.not_randompred}, T --> T) $ t end

 fun mk_map T1 T2 tf tp = Const (@{const_name Quickcheck.map},

   (T1 --> T2) --> mk_randompredT T1 --> mk_randompredT T2) $ tf $ tp

 val compfuns = CompilationFuns {mk_predT = mk_randompredT, dest_predT = dest_randompredT,

     mk_bot = mk_bot, mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if,

     mk_not = mk_not, mk_map = mk_map};

 end;

 structure DSequence_CompFuns =

 struct

 fun mk_dseqT T = Type ("fun", [@{typ code_numeral}, Type ("fun", [@{typ bool},

   Type (@{type_name Option.option}, [Type  ("Lazy_Sequence.lazy_sequence", [T])])])])

 fun dest_dseqT (Type ("fun", [@{typ code_numeral}, Type ("fun", [@{typ bool},

   Type (@{type_name Option.option}, [Type ("Lazy_Sequence.lazy_sequence", [T])])])])) = T

   | dest_dseqT T = raise TYPE ("dest_dseqT", [T], []);

 fun mk_bot T = Const ("DSequence.empty", mk_dseqT T);

 fun mk_single t =

   let val T = fastype_of t

   in Const("DSequence.single", T --> mk_dseqT T) $ t end;

 fun mk_bind (x, f) =

   let val T as Type ("fun", [_, U]) = fastype_of f

   in

     Const ("DSequence.bind", fastype_of x --> T --> U) $ x $ f

   end;

 val mk_sup = HOLogic.mk_binop "DSequence.union";

 fun mk_if cond = Const ("DSequence.if_seq",

   HOLogic.boolT --> mk_dseqT HOLogic.unitT) $ cond;

 fun mk_not t = let val T = mk_dseqT HOLogic.unitT

   in Const ("DSequence.not_seq", T --> T) $ t end

 fun mk_map T1 T2 tf tp = Const ("DSequence.map",

   (T1 --> T2) --> mk_dseqT T1 --> mk_dseqT T2) $ tf $ tp

 val compfuns = CompilationFuns {mk_predT = mk_dseqT, dest_predT = dest_dseqT,

     mk_bot = mk_bot, mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if,

     mk_not = mk_not, mk_map = mk_map}

 end;

 structure Random_Sequence_CompFuns =

 struct

 fun mk_random_dseqT T =

   @{typ code_numeral} --> @{typ code_numeral} --> @{typ Random.seed} -->

     HOLogic.mk_prodT (DSequence_CompFuns.mk_dseqT T, @{typ Random.seed})

 fun dest_random_dseqT (Type ("fun", [@{typ code_numeral}, Type ("fun", [@{typ code_numeral},

   Type ("fun", [@{typ Random.seed},

   Type (@{type_name "*"}, [T, @{typ Random.seed}])])])])) = DSequence_CompFuns.dest_dseqT T

   | dest_random_dseqT T = raise TYPE ("dest_random_dseqT", [T], []);

 fun mk_bot T = Const ("Random_Sequence.empty", mk_random_dseqT T);

 fun mk_single t =

   let val T = fastype_of t

   in Const("Random_Sequence.single", T --> mk_random_dseqT T) $ t end;

 fun mk_bind (x, f) =

   let

     val T as Type ("fun", [_, U]) = fastype_of f

   in

     Const ("Random_Sequence.bind", fastype_of x --> T --> U) $ x $ f

   end;

 val mk_sup = HOLogic.mk_binop "Random_Sequence.union";

 fun mk_if cond = Const ("Random_Sequence.if_random_dseq",

   HOLogic.boolT --> mk_random_dseqT HOLogic.unitT) $ cond;

 fun mk_not t = let val T = mk_random_dseqT HOLogic.unitT

   in Const ("Random_Sequence.not_random_dseq", T --> T) $ t end

 fun mk_map T1 T2 tf tp = Const ("Random_Sequence.map",

   (T1 --> T2) --> mk_random_dseqT T1 --> mk_random_dseqT T2) $ tf $ tp

 val compfuns = CompilationFuns {mk_predT = mk_random_dseqT, dest_predT = dest_random_dseqT,

     mk_bot = mk_bot, mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if,

     mk_not = mk_not, mk_map = mk_map}

 end;

 fun mk_random T =

   let

     val random = Const ("Quickcheck.random_class.random",

       @{typ code_numeral} --> @{typ Random.seed} -->

         HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed}))

   in

     Const ("Random_Sequence.Random", (@{typ code_numeral} --> @{typ Random.seed} -->

       HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed})) -->

       Random_Sequence_CompFuns.mk_random_dseqT T) $ random

   end;

 (* for external use with interactive mode *)

 val pred_compfuns = PredicateCompFuns.compfuns

 val randompred_compfuns = Random_Sequence_CompFuns.compfuns;

 (* function types and names of different compilations *)

 fun funT_of compfuns mode T =

   let

     val Ts = binder_types T

     val (inTs, outTs) = split_map_modeT (fn m => fn T => (SOME (funT_of compfuns m T), NONE)) mode Ts

   in

     inTs ---> (mk_predT compfuns (HOLogic.mk_tupleT outTs))

   end;

 (** mode analysis **)

 fun is_constrt thy =

   let

     val cnstrs = flat (maps

       (map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd)

       (Symtab.dest (Datatype.get_all thy)));

     fun check t = (case strip_comb t of

         (Free _, []) => true

       | (Const (s, T), ts) => (case (AList.lookup (op =) cnstrs s, body_type T) of

             (SOME (i, Tname), Type (Tname', _)) =>

               length ts = i andalso Tname = Tname' andalso forall check ts

           | _ => false)

       | _ => false)

   in check end;

 (*** check if a type is an equality type (i.e. doesn't contain fun)

   FIXME this is only an approximation ***)

 fun is_eqT (Type (s, Ts)) = s <> "fun" andalso forall is_eqT Ts

   | is_eqT _ = true;

 fun term_vs tm = fold_aterms (fn Free (x, T) => cons x | _ => I) tm [];

 val terms_vs = distinct (op =) o maps term_vs;

 (** collect all Frees in a term (with duplicates!) **)

 fun term_vTs tm =

   fold_aterms (fn Free xT => cons xT | _ => I) tm [];

 fun subsets i j =

   if i <= j then

     let

       fun merge xs [] = xs

         | merge [] ys = ys

         | merge (x::xs) (y::ys) = if length x >= length y then x::merge xs (y::ys)

             else y::merge (x::xs) ys;

       val is = subsets (i+1) j

     in merge (map (fn ks => i::ks) is) is end

   else [[]];

 fun print_failed_mode options thy modes p m rs is =

   if show_mode_inference options then

     let

       val _ = tracing ("Clauses " ^ commas (map (fn i => string_of_int (i + 1)) is) ^ " of " ^

         p ^ " violates mode " ^ string_of_mode m)

     in () end

   else ()

 fun error_of p m is =

   ("  Clauses " ^ commas (map (fn i => string_of_int (i + 1)) is) ^ " of " ^

         p ^ " violates mode " ^ string_of_mode m)

 fun is_all_input mode =

   let

     fun is_all_input' (Fun _) = true

       | is_all_input' (Pair (m1, m2)) = is_all_input' m1 andalso is_all_input' m2

       | is_all_input' Input = true

       | is_all_input' Output = false

   in

     forall is_all_input' (strip_fun_mode mode)

   end

 fun all_input_of T =

   let

     val (Ts, U) = strip_type T

     fun input_of (Type ("*", [T1, T2])) = Pair (input_of T1, input_of T2)

       | input_of _ = Input

   in

     if U = HOLogic.boolT then

       fold_rev (curry Fun) (map input_of Ts) Bool

     else

       error "all_input_of: not a predicate"

   end

 fun partial_hd [] = NONE

   | partial_hd (x :: xs) = SOME x

 fun term_vs tm = fold_aterms (fn Free (x, T) => cons x | _ => I) tm [];

 val terms_vs = distinct (op =) o maps term_vs;

 fun input_mode T =

   let

     val (Ts, U) = strip_type T

   in

     fold_rev (curry Fun) (map (K Input) Ts) Input

   end

 fun output_mode T =

   let

     val (Ts, U) = strip_type T

   in

     fold_rev (curry Fun) (map (K Output) Ts) Output

   end

 fun is_invertible_function thy (Const (f, _)) = is_constr thy f

   | is_invertible_function thy _ = false

 fun non_invertible_subterms thy (Free _) = []

   | non_invertible_subterms thy t = 

   case (strip_comb t) of (f, args) =>

     if is_invertible_function thy f then

       maps (non_invertible_subterms thy) args

     else

       [t]

 fun collect_non_invertible_subterms thy (f as Free _) (names, eqs) = (f, (names, eqs))

   | collect_non_invertible_subterms thy t (names, eqs) =

     case (strip_comb t) of (f, args) =>

       if is_invertible_function thy f then

           let

             val (args', (names', eqs')) =

               fold_map (collect_non_invertible_subterms thy) args (names, eqs)

           in

             (list_comb (f, args'), (names', eqs'))

           end

         else

           let

             val s = Name.variant names "x"

             val v = Free (s, fastype_of t)

           in

             (v, (s :: names, HOLogic.mk_eq (v, t) :: eqs))

           end

 (*

   if is_constrt thy t then (t, (names, eqs)) else

     let

       val s = Name.variant names "x"

       val v = Free (s, fastype_of t)

     in (v, (s::names, HOLogic.mk_eq (v, t)::eqs)) end;

 *)

 fun is_possible_output thy vs t =

   forall

     (fn t => is_eqT (fastype_of t) andalso forall (member (op =) vs) (term_vs t))

       (non_invertible_subterms thy t)

 fun vars_of_destructable_term thy (Free (x, _)) = [x]

   | vars_of_destructable_term thy t =

   case (strip_comb t) of (f, args) =>

     if is_invertible_function thy f then

       maps (vars_of_destructable_term thy) args

     else

       []

 fun is_constructable thy vs t = forall (member (op =) vs) (term_vs t)

 fun missing_vars vs t = subtract (op =) vs (term_vs t)

 fun derivations_of thy modes vs t Input = 

     [(Term Input, missing_vars vs t)]

   | derivations_of thy modes vs t Output =

     if is_possible_output thy vs t then [(Term Output, [])] else []

   | derivations_of thy modes vs (Const ("Pair", _) $ t1 $ t2) (Pair (m1, m2)) =

     map_product

       (fn (m1, mvars1) => fn (m2, mvars2) => (Mode_Pair (m1, m2), union (op =) mvars1 mvars2))

         (derivations_of thy modes vs t1 m1) (derivations_of thy modes vs t2 m2)

   | derivations_of thy modes vs t m =

     (case try (all_derivations_of thy modes vs) t of

       SOME derivs => filter (fn (d, mvars) => mode_of d = m) derivs

     | NONE => (if is_all_input m then [(Context m, [])] else []))

 and all_derivations_of thy modes vs (Const ("Pair", _) $ t1 $ t2) =

   let

     val derivs1 = all_derivations_of thy modes vs t1

     val derivs2 = all_derivations_of thy modes vs t2

   in

     map_product

       (fn (m1, mvars1) => fn (m2, mvars2) => (Mode_Pair (m1, m2), union (op =) mvars1 mvars2))

         derivs1 derivs2

   end

   | all_derivations_of thy modes vs (t1 $ t2) =

   let

     val derivs1 = all_derivations_of thy modes vs t1

   in

     maps (fn (d1, mvars1) =>

       case mode_of d1 of

         Fun (m', _) => map (fn (d2, mvars2) =>

           (Mode_App (d1, d2), union (op =) mvars1 mvars2)) (derivations_of thy modes vs t2 m')

         | _ => error "Something went wrong") derivs1

   end

   | all_derivations_of thy modes vs (Const (s, T)) =

     (case (AList.lookup (op =) modes s) of

       SOME ms => map (fn m => (Context m, [])) ms

     | NONE => error ("No mode for constant " ^ s))

   | all_derivations_of _ modes vs (Free (x, _)) =

     (case (AList.lookup (op =) modes x) of

       SOME ms => map (fn m => (Context m , [])) ms

     | NONE => error ("No mode for parameter variable " ^ x))

   | all_derivations_of _ modes vs _ = error "all_derivations_of"

 fun rev_option_ord ord (NONE, NONE) = EQUAL

   | rev_option_ord ord (NONE, SOME _) = GREATER

   | rev_option_ord ord (SOME _, NONE) = LESS

   | rev_option_ord ord (SOME x, SOME y) = ord (x, y)

 fun term_of_prem (Prem t) = t

   | term_of_prem (Negprem t) = t

   | term_of_prem (Sidecond t) = t

 fun random_mode_in_deriv modes t deriv =

   case try dest_Const (fst (strip_comb t)) of

     SOME (s, _) =>

       (case AList.lookup (op =) modes s of

         SOME ms =>

           (case AList.lookup (op =) ms (head_mode_of deriv) of

             SOME r => r

           | NONE => false)

       | NONE => false)

   | NONE => false

 fun number_of_output_positions mode =

   let

     val args = strip_fun_mode mode

     fun contains_output (Fun _) = false

       | contains_output Input = false

       | contains_output Output = true

       | contains_output (Pair (m1, m2)) = contains_output m1 orelse contains_output m2

   in

     length (filter contains_output args)

   end

 fun lex_ord ord1 ord2 (x, x') =

   case ord1 (x, x') of

     EQUAL => ord2 (x, x')

   | ord => ord

 fun deriv_ord2' thy modes t1 t2 ((deriv1, mvars1), (deriv2, mvars2)) =

   let

     fun mvars_ord ((t1, deriv1, mvars1), (t2, deriv2, mvars2)) =

       int_ord (length mvars1, length mvars2)

     fun random_mode_ord ((t1, deriv1, mvars1), (t2, deriv2, mvars2)) =

       int_ord (if random_mode_in_deriv modes t1 deriv1 then 1 else 0,

         if random_mode_in_deriv modes t1 deriv1 then 1 else 0)

     fun output_mode_ord ((t1, deriv1, mvars1), (t2, deriv2, mvars2)) =

       int_ord (number_of_output_positions (head_mode_of deriv1),

         number_of_output_positions (head_mode_of deriv2))

   in

     lex_ord mvars_ord (lex_ord random_mode_ord output_mode_ord)

       ((t1, deriv1, mvars1), (t2, deriv2, mvars2))

   end

 fun deriv_ord2 thy modes t = deriv_ord2' thy modes t t

 fun deriv_ord ((deriv1, mvars1), (deriv2, mvars2)) =

   int_ord (length mvars1, length mvars2)

 fun premise_ord thy modes ((prem1, a1), (prem2, a2)) =

   rev_option_ord (deriv_ord2' thy modes (term_of_prem prem1) (term_of_prem prem2)) (a1, a2)

 fun print_mode_list modes =

   tracing ("modes: " ^ (commas (map (fn (s, ms) => s ^ ": " ^

     commas (map (fn (m, r) => string_of_mode m ^ (if r then " random " else " not ")) ms)) modes)))

 fun select_mode_prem' thy modes vs ps =

   let

     val modes' = map (fn (s, ms) => (s, map fst ms)) modes

   in

     partial_hd (sort (premise_ord thy modes) (ps ~~ map

     (fn Prem t =>

       partial_hd

         (sort (deriv_ord2 thy modes t) (all_derivations_of thy modes' vs t))

      | Sidecond t => SOME (Context Bool, missing_vars vs t)

      | Negprem t =>

          partial_hd

           (sort (deriv_ord2 thy modes t) (filter (fn (d, missing_vars) => is_all_input (head_mode_of d))

              (all_derivations_of thy modes' vs t)))

      | p => error (string_of_prem thy p))

     ps))

   end

 fun check_mode_clause' use_random thy param_vs modes mode (ts, ps) =

   let

     val vTs = distinct (op =) (fold Term.add_frees (map term_of_prem ps) (fold Term.add_frees ts []))

     val modes' = modes @ (param_vs ~~ map (fn x => [(x, false)]) (ho_arg_modes_of mode))

     val (in_ts, out_ts) = split_mode mode ts    

     val in_vs = maps (vars_of_destructable_term thy) in_ts

     val out_vs = terms_vs out_ts

     fun check_mode_prems acc_ps rnd vs [] = SOME (acc_ps, vs, rnd)

       | check_mode_prems acc_ps rnd vs ps =

         (case select_mode_prem' thy modes' vs ps of

           SOME (p, SOME (deriv, [])) => check_mode_prems ((p, deriv) :: acc_ps) rnd (*TODO: uses random? *)

             (case p of

                 Prem t => union (op =) vs (term_vs t)

               | Sidecond t => vs

               | Negprem t => union (op =) vs (term_vs t)

               | _ => error "I do not know")

             (filter_out (equal p) ps)

         | SOME (p, SOME (deriv, missing_vars)) =>

           if use_random then

             check_mode_prems ((p, deriv) :: (map

               (fn v => (Generator (v, the (AList.lookup (op =) vTs v)), Term Output)) missing_vars)

                 @ acc_ps) true

             (case p of

                 Prem t => union (op =) vs (term_vs t)

               | Sidecond t => union (op =) vs (term_vs t)

               | Negprem t => union (op =) vs (term_vs t)

               | _ => error "I do not know")

             (filter_out (equal p) ps)

           else NONE

         | SOME (p, NONE) => NONE

         | NONE => NONE)

   in

     case check_mode_prems [] false in_vs ps of

       NONE => NONE

     | SOME (acc_ps, vs, rnd) =>

       if forall (is_constructable thy vs) (in_ts @ out_ts) then

         SOME (ts, rev acc_ps, rnd)

       else

         if use_random then

           let

             val generators = map

               (fn v => (Generator (v, the (AList.lookup (op =) vTs v)), Term Output))

                 (subtract (op =) vs (terms_vs out_ts))

           in

             SOME (ts, rev (generators @ acc_ps), true)

           end

         else

           NONE

   end

 datatype result = Success of bool | Error of string

 fun check_modes_pred' use_random options thy param_vs clauses modes (p, ms) =

   let

     fun split xs =

       let

         fun split' [] (ys, zs) = (rev ys, rev zs)

           | split' ((m, Error z) :: xs) (ys, zs) = split' xs (ys, z :: zs)

           | split' ((m, Success rnd) :: xs) (ys, zs) = split' xs ((m, rnd) :: ys, zs)

        in

          split' xs ([], [])

        end

     val rs = these (AList.lookup (op =) clauses p)

     fun check_mode m =

       let

         val res = map (check_mode_clause' use_random thy param_vs modes m) rs

       in

         case find_indices is_none res of

           [] => Success (exists (fn SOME (_, _, true) => true | _ => false) res)

         | is => (print_failed_mode options thy modes p m rs is; Error (error_of p m is))

       end

     val res = map (fn (m, _) => (m, check_mode m)) ms

     val (ms', errors) = split res

   in

     ((p, ms'), errors)

   end;

 fun get_modes_pred' use_random thy param_vs clauses modes (p, ms) =

   let

     val rs = these (AList.lookup (op =) clauses p)

   in

     (p, map (fn (m, rnd) =>

       (m, map ((fn (ts, ps, rnd) => (ts, ps)) o the o check_mode_clause' use_random thy param_vs modes m) rs)) ms)

   end;

 fun fixp f x =

   let val y = f x

   in if x = y then x else fixp f y end;

 fun fixp_with_state f (x, state) =

   let

     val (y, state') = f (x, state)

   in

     if x = y then (y, state') else fixp_with_state f (y, state')

   end

 fun infer_modes use_random options preds extra_modes param_vs clauses thy =

   let

     val all_modes = map (fn (s, T) => (s, map (rpair false) (all_modes_of_typ T))) preds

     fun needs_random s m = (m, member (op =) (#needs_random (the_pred_data thy s)) m)

     val extra_modes = map (fn (s, ms) => (s, map (needs_random s) ms)) extra_modes

     val (modes, errors) =

       fixp_with_state (fn (modes, errors) =>

         let

           val res = map

             (check_modes_pred' use_random options thy param_vs clauses (modes @ extra_modes)) modes

         in (map fst res, errors @ maps snd res) end)

           (all_modes, [])

     val thy' = fold (fn (s, ms) => if member (op =) (map fst preds) s then

       set_needs_random s (map fst (filter (fn (_, rnd) => rnd = true) ms)) else I) modes thy

   in

     ((map (get_modes_pred' use_random thy param_vs clauses (modes @ extra_modes)) modes, errors), thy')

   end;

 (* term construction *)

 fun mk_v (names, vs) s T = (case AList.lookup (op =) vs s of

       NONE => (Free (s, T), (names, (s, [])::vs))

     | SOME xs =>

         let

           val s' = Name.variant names s;

           val v = Free (s', T)

         in

           (v, (s'::names, AList.update (op =) (s, v::xs) vs))

         end);

 fun distinct_v (Free (s, T)) nvs = mk_v nvs s T

   | distinct_v (t $ u) nvs =

       let

         val (t', nvs') = distinct_v t nvs;

         val (u', nvs'') = distinct_v u nvs';

       in (t' $ u', nvs'') end

   | distinct_v x nvs = (x, nvs);

 (** specific rpred functions -- move them to the correct place in this file *)

 fun mk_Eval_of additional_arguments ((x, T), NONE) names = (x, names)

   | mk_Eval_of additional_arguments ((x, T), SOME mode) names =

   let

     val Ts = binder_types T

     fun mk_split_lambda [] t = lambda (Free (Name.variant names "x", HOLogic.unitT)) t

       | mk_split_lambda [x] t = lambda x t

       | mk_split_lambda xs t =

       let

         fun mk_split_lambda' (x::y::[]) t = HOLogic.mk_split (lambda x (lambda y t))

           | mk_split_lambda' (x::xs) t = HOLogic.mk_split (lambda x (mk_split_lambda' xs t))

       in

         mk_split_lambda' xs t

       end;

     fun mk_arg (i, T) =

       let

         val vname = Name.variant names ("x" ^ string_of_int i)

         val default = Free (vname, T)

       in 

         case AList.lookup (op =) mode i of

           NONE => (([], [default]), [default])

         | SOME NONE => (([default], []), [default])

         | SOME (SOME pis) =>

           case HOLogic.strip_tupleT T of

             [] => error "pair mode but unit tuple" (*(([default], []), [default])*)

           | [_] => error "pair mode but not a tuple" (*(([default], []), [default])*)

           | Ts =>

             let

               val vnames = Name.variant_list names

                 (map (fn j => "x" ^ string_of_int i ^ "p" ^ string_of_int j)

                   (1 upto length Ts))

               val args = map2 (curry Free) vnames Ts

               fun split_args (i, arg) (ins, outs) =

                 if member (op =) pis i then

                   (arg::ins, outs)

                 else

                   (ins, arg::outs)

               val (inargs, outargs) = fold_rev split_args ((1 upto length Ts) ~~ args) ([], [])

               fun tuple args = if null args then [] else [HOLogic.mk_tuple args]

             in ((tuple inargs, tuple outargs), args) end

       end

     val (inoutargs, args) = split_list (map mk_arg (1 upto (length Ts) ~~ Ts))

     val (inargs, outargs) = pairself flat (split_list inoutargs)

     val r = PredicateCompFuns.mk_Eval 

       (list_comb (x, inargs @ additional_arguments), HOLogic.mk_tuple outargs)

     val t = fold_rev mk_split_lambda args r

   in

     (t, names)

   end;

 structure Comp_Mod =

 struct

 datatype comp_modifiers = Comp_Modifiers of

 {

   compilation : compilation,

   function_name_prefix : string,

   compfuns : compilation_funs,

   additional_arguments : string list -> term list,

   wrap_compilation : compilation_funs -> string -> typ -> mode -> term list -> term -> term,

   transform_additional_arguments : indprem -> term list -> term list

 }

 fun dest_comp_modifiers (Comp_Modifiers c) = c

 val compilation = #compilation o dest_comp_modifiers

 val function_name_prefix = #function_name_prefix o dest_comp_modifiers

 val compfuns = #compfuns o dest_comp_modifiers

 val funT_of = funT_of o compfuns

 val additional_arguments = #additional_arguments o dest_comp_modifiers

 val wrap_compilation = #wrap_compilation o dest_comp_modifiers

 val transform_additional_arguments = #transform_additional_arguments o dest_comp_modifiers

 end;

 (* TODO: uses param_vs -- change necessary for compilation with new modes *)

 fun compile_arg compilation_modifiers compfuns additional_arguments thy param_vs iss arg = 

   let

     fun map_params (t as Free (f, T)) =

       if member (op =) param_vs f then

         case (AList.lookup (op =) (param_vs ~~ iss) f) of

           SOME is =>

             let

               val _ = error "compile_arg: A parameter in a input position -- do we have a test case?"

               val T' = Comp_Mod.funT_of compilation_modifiers is T

             in t(*fst (mk_Eval_of additional_arguments ((Free (f, T'), T), is) [])*) end

         | NONE => t

       else t

       | map_params t = t

     in map_aterms map_params arg end

 fun compile_match compilation_modifiers compfuns additional_arguments

   param_vs iss thy eqs eqs' out_ts success_t =

   let

     val eqs'' = maps mk_eq eqs @ eqs'

     val eqs'' =

       map (compile_arg compilation_modifiers compfuns additional_arguments thy param_vs iss) eqs''

     val names = fold Term.add_free_names (success_t :: eqs'' @ out_ts) [];

     val name = Name.variant names "x";

     val name' = Name.variant (name :: names) "y";

     val T = HOLogic.mk_tupleT (map fastype_of out_ts);

     val U = fastype_of success_t;

     val U' = dest_predT compfuns U;

     val v = Free (name, T);

     val v' = Free (name', T);

   in

     lambda v (fst (Datatype.make_case

       (ProofContext.init thy) Datatype_Case.Quiet [] v

       [(HOLogic.mk_tuple out_ts,

         if null eqs'' then success_t

         else Const (@{const_name HOL.If}, HOLogic.boolT --> U --> U --> U) $

           foldr1 HOLogic.mk_conj eqs'' $ success_t $

             mk_bot compfuns U'),

        (v', mk_bot compfuns U')]))

   end;

 fun compile_expr compilation_modifiers compfuns thy (t, deriv) additional_arguments =

   let

     fun expr_of (t, deriv) =

       (case (t, deriv) of

         (t, Term Input) => SOME t

       | (t, Term Output) => NONE

       | (Const (name, T), Context mode) =>

         SOME (Const (function_name_of (Comp_Mod.compilation compilation_modifiers) thy name mode,

           Comp_Mod.funT_of compilation_modifiers mode T))

       | (Free (s, T), Context m) =>

         SOME (Free (s, Comp_Mod.funT_of compilation_modifiers m T))

       | (t, Context m) =>

         let

           val bs = map (pair "x") (binder_types (fastype_of t))

           val bounds = map Bound (rev (0 upto (length bs) - 1))

         in SOME (list_abs (bs, mk_if compfuns (list_comb (t, bounds)))) end

       | (Const ("Pair", _) $ t1 $ t2, Mode_Pair (d1, d2)) =>

         (case (expr_of (t1, d1), expr_of (t2, d2)) of

           (NONE, NONE) => NONE

         | (NONE, SOME t) => SOME t

         | (SOME t, NONE) => SOME t

         | (SOME t1, SOME t2) => SOME (HOLogic.mk_prod (t1, t2)))

       | (t1 $ t2, Mode_App (deriv1, deriv2)) =>

         (case (expr_of (t1, deriv1), expr_of (t2, deriv2)) of

           (SOME t, NONE) => SOME t

          | (SOME t, SOME u) => SOME (t $ u)

          | _ => error "something went wrong here!"))

   in

     the (expr_of (t, deriv))

   end

 fun compile_clause compilation_modifiers compfuns thy all_vs param_vs additional_arguments

   mode inp (ts, moded_ps) =

   let

     val iss = ho_arg_modes_of mode

     val compile_match = compile_match compilation_modifiers compfuns

       additional_arguments param_vs iss thy

     val (in_ts, out_ts) = split_mode mode ts;

     val (in_ts', (all_vs', eqs)) =

       fold_map (collect_non_invertible_subterms thy) in_ts (all_vs, []);

     fun compile_prems out_ts' vs names [] =

           let

             val (out_ts'', (names', eqs')) =

               fold_map (collect_non_invertible_subterms thy) out_ts' (names, []);

             val (out_ts''', (names'', constr_vs)) = fold_map distinct_v

               out_ts'' (names', map (rpair []) vs);

           in

             compile_match constr_vs (eqs @ eqs') out_ts'''

               (mk_single compfuns (HOLogic.mk_tuple out_ts))

           end

       | compile_prems out_ts vs names ((p, deriv) :: ps) =

           let

             val vs' = distinct (op =) (flat (vs :: map term_vs out_ts));

             val (out_ts', (names', eqs)) =

               fold_map (collect_non_invertible_subterms thy) out_ts (names, [])

             val (out_ts'', (names'', constr_vs')) = fold_map distinct_v

               out_ts' ((names', map (rpair []) vs))

             val mode = head_mode_of deriv

             val additional_arguments' =

               Comp_Mod.transform_additional_arguments compilation_modifiers p additional_arguments

             val (compiled_clause, rest) = case p of

                Prem t =>

                  let

                    val u =

                      compile_expr compilation_modifiers compfuns thy

                        (t, deriv) additional_arguments'

                    val (_, out_ts''') = split_mode mode (snd (strip_comb t))

                    val rest = compile_prems out_ts''' vs' names'' ps

                  in

                    (u, rest)

                  end

              | Negprem t =>

                  let

                    val u = mk_not compfuns

                      (compile_expr compilation_modifiers compfuns thy

                        (t, deriv) additional_arguments')

                    val (_, out_ts''') = split_mode mode (snd (strip_comb t))

                    val rest = compile_prems out_ts''' vs' names'' ps

                  in

                    (u, rest)

                  end

              | Sidecond t =>

                  let

                    val t = compile_arg compilation_modifiers compfuns additional_arguments

                      thy param_vs iss t

                    val rest = compile_prems [] vs' names'' ps;

                  in

                    (mk_if compfuns t, rest)

                  end

              | Generator (v, T) =>

                  let

                    val u = mk_random T

                    val rest = compile_prems [Free (v, T)]  vs' names'' ps;

                  in

                    (u, rest)

                  end

           in

             compile_match constr_vs' eqs out_ts''

               (mk_bind compfuns (compiled_clause, rest))

           end

     val prem_t = compile_prems in_ts' param_vs all_vs' moded_ps;

   in

     mk_bind compfuns (mk_single compfuns inp, prem_t)

   end

 fun compile_pred compilation_modifiers thy all_vs param_vs s T mode moded_cls =

   let

     (* TODO: val additional_arguments = Comp_Mod.additional_arguments compilation_modifiers

       (all_vs @ param_vs)

     *)

     val compfuns = Comp_Mod.compfuns compilation_modifiers

     fun is_param_type (T as Type ("fun",[_ , T'])) =

       is_some (try (dest_predT compfuns) T) orelse is_param_type T'

       | is_param_type T = is_some (try (dest_predT compfuns) T)

     val additional_arguments = []

     val (inpTs, outTs) = split_map_modeT (fn m => fn T => (SOME (funT_of compfuns m T), NONE)) mode

       (binder_types T)

     val predT = mk_predT compfuns (HOLogic.mk_tupleT outTs)

     val funT = Comp_Mod.funT_of compilation_modifiers mode T

     val (in_ts, _) = fold_map (fold_map_aterms_prodT (curry HOLogic.mk_prod)

       (fn T => fn (param_vs, names) =>

         if is_param_type T then

           (Free (hd param_vs, T), (tl param_vs, names))

         else

           let

             val new = Name.variant names "x"

           in (Free (new, T), (param_vs, new :: names)) end)) inpTs

         (param_vs, (all_vs @ param_vs))

     val in_ts' = map_filter (map_filter_prod

       (fn t as Free (x, _) => if member (op =) param_vs x then NONE else SOME t | t => SOME t)) in_ts

     val cl_ts =

       map (compile_clause compilation_modifiers compfuns

         thy all_vs param_vs additional_arguments mode (HOLogic.mk_tuple in_ts')) moded_cls;

     val compilation = Comp_Mod.wrap_compilation compilation_modifiers compfuns

       s T mode additional_arguments

       (if null cl_ts then

         mk_bot compfuns (HOLogic.mk_tupleT outTs)

       else foldr1 (mk_sup compfuns) cl_ts)

     val fun_const =

       Const (function_name_of (Comp_Mod.compilation compilation_modifiers) thy s mode, funT)

   in

     HOLogic.mk_Trueprop

       (HOLogic.mk_eq (list_comb (fun_const, in_ts @ additional_arguments), compilation))

   end;

 (* special setup for simpset *)                  

 val HOL_basic_ss' = HOL_basic_ss addsimps (@{thms HOL.simp_thms} @ [@{thm Pair_eq}])

   setSolver (mk_solver "all_tac_solver" (fn _ => fn _ => all_tac))

   setSolver (mk_solver "True_solver" (fn _ => rtac @{thm TrueI}))

 (* Definition of executable functions and their intro and elim rules *)

 fun print_arities arities = tracing ("Arities:\n" ^

   cat_lines (map (fn (s, (ks, k)) => s ^ ": " ^

     space_implode " -> " (map

       (fn NONE => "X" | SOME k' => string_of_int k')

         (ks @ [SOME k]))) arities));

 fun split_lambda (x as Free _) t = lambda x t

   | split_lambda (Const ("Pair", _) $ t1 $ t2) t =

     HOLogic.mk_split (split_lambda t1 (split_lambda t2 t))

   | split_lambda (Const ("Product_Type.Unity", _)) t = Abs ("x", HOLogic.unitT, t)

   | split_lambda t _ = raise (TERM ("split_lambda", [t]))

 fun strip_split_abs (Const ("split", _) $ t) = strip_split_abs t

   | strip_split_abs (Abs (_, _, t)) = strip_split_abs t

   | strip_split_abs t = t

 fun mk_args is_eval (Pair (m1, m2), Type ("*", [T1, T2])) names =

     let

       val (t1, names') = mk_args is_eval (m1, T1) names

       val (t2, names'') = mk_args is_eval (m2, T2) names'

     in

       (HOLogic.mk_prod (t1, t2), names'')

     end

   | mk_args is_eval ((m as Fun _), T) names =

     let

       val funT = funT_of PredicateCompFuns.compfuns m T

       val x = Name.variant names "x"

       val (args, _) = fold_map (mk_args is_eval) (strip_fun_mode m ~~ binder_types T) (x :: names)

       val (inargs, outargs) = split_map_mode (fn _ => fn t => (SOME t, NONE)) m args

       val t = fold_rev split_lambda args (PredicateCompFuns.mk_Eval

         (list_comb (Free (x, funT), inargs), HOLogic.mk_tuple outargs))

     in

       (if is_eval then t else Free (x, funT), x :: names)

     end

   | mk_args is_eval (_, T) names =

     let

       val x = Name.variant names "x"

     in

       (Free (x, T), x :: names)

     end

 fun create_intro_elim_rule mode defthm mode_id funT pred thy =

   let

     val funtrm = Const (mode_id, funT)

     val Ts = binder_types (fastype_of pred)

     val (args, argnames) = fold_map (mk_args true) (strip_fun_mode mode ~~ Ts) []

     fun strip_eval _ t =

       let

         val t' = strip_split_abs t

         val (r, _) = PredicateCompFuns.dest_Eval t'

       in (SOME (fst (strip_comb r)), NONE) end

     val (inargs, outargs) = split_map_mode strip_eval mode args

     val eval_hoargs = ho_args_of mode args

     val hoargTs = ho_argsT_of mode Ts

     val hoarg_names' =

       Name.variant_list argnames ((map (fn i => "x" ^ string_of_int i)) (1 upto (length hoargTs)))

     val hoargs' = map2 (curry Free) hoarg_names' hoargTs

     val args' = replace_ho_args mode hoargs' args

     val predpropI = HOLogic.mk_Trueprop (list_comb (pred, args'))

     val predpropE = HOLogic.mk_Trueprop (list_comb (pred, args))

     val param_eqs = map2 (HOLogic.mk_Trueprop oo (curry HOLogic.mk_eq)) eval_hoargs hoargs'

     val funpropE = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, inargs),

                     if null outargs then Free("y", HOLogic.unitT) else HOLogic.mk_tuple outargs))

     val funpropI = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, inargs),

                      HOLogic.mk_tuple outargs))

     val introtrm = Logic.list_implies (predpropI :: param_eqs, funpropI)

     val simprules = [defthm, @{thm eval_pred},

       @{thm "split_beta"}, @{thm "fst_conv"}, @{thm "snd_conv"}, @{thm pair_collapse}]

     val unfolddef_tac = Simplifier.asm_full_simp_tac (HOL_basic_ss addsimps simprules) 1

     val introthm = Goal.prove (ProofContext.init thy)

       (argnames @ hoarg_names' @ ["y"]) [] introtrm (fn _ => unfolddef_tac)

     val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT));

     val elimtrm = Logic.list_implies ([funpropE, Logic.mk_implies (predpropE, P)], P)

     val elimthm = Goal.prove (ProofContext.init thy)

       (argnames @ ["y", "P"]) [] elimtrm (fn _ => unfolddef_tac)

   in

     (introthm, elimthm)

   end

 fun create_constname_of_mode options thy prefix name T mode = 

   let

     val system_proposal = prefix ^ (Long_Name.base_name name)

       ^ "_" ^ ascii_string_of_mode mode

     val name = the_default system_proposal (proposed_names options name mode)

   in

     Sign.full_bname thy name

   end;

 fun create_definitions options preds (name, modes) thy =

   let

     val compfuns = PredicateCompFuns.compfuns

     val T = AList.lookup (op =) preds name |> the

     fun create_definition mode thy =

       let

         val mode_cname = create_constname_of_mode options thy "" name T mode

         val mode_cbasename = Long_Name.base_name mode_cname

         val funT = funT_of compfuns mode T

         val (args, _) = fold_map (mk_args true) ((strip_fun_mode mode) ~~ (binder_types T)) []

         fun strip_eval m t =

           let

             val t' = strip_split_abs t

             val (r, _) = PredicateCompFuns.dest_Eval t'

           in (SOME (fst (strip_comb r)), NONE) end

         val (inargs, outargs) = split_map_mode strip_eval mode args

         val predterm = fold_rev split_lambda inargs

           (PredicateCompFuns.mk_Enum (split_lambda (HOLogic.mk_tuple outargs)

             (list_comb (Const (name, T), args))))

         val lhs = Const (mode_cname, funT)

         val def = Logic.mk_equals (lhs, predterm)

         val ([definition], thy') = thy |>

           Sign.add_consts_i [(Binding.name mode_cbasename, funT, NoSyn)] |>

           PureThy.add_defs false [((Binding.name (mode_cbasename ^ "_def"), def), [])]

         val (intro, elim) =

           create_intro_elim_rule mode definition mode_cname funT (Const (name, T)) thy'

         in thy'

           |> set_function_name Pred name mode mode_cname

           |> add_predfun_data name mode (definition, intro, elim)

           |> PureThy.store_thm (Binding.name (mode_cbasename ^ "I"), intro) |> snd

           |> PureThy.store_thm (Binding.name (mode_cbasename ^ "E"), elim)  |> snd

           |> Theory.checkpoint

         end;

   in

     thy |> defined_function_of Pred name |> fold create_definition modes

   end;

 fun define_functions comp_modifiers compfuns options preds (name, modes) thy =

   let

     val T = AList.lookup (op =) preds name |> the

     fun create_definition mode thy =

       let

         val function_name_prefix = Comp_Mod.function_name_prefix comp_modifiers

         val mode_cname = create_constname_of_mode options thy function_name_prefix name T mode

         val funT = Comp_Mod.funT_of comp_modifiers mode T

       in

         thy |> Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)]

         |> set_function_name (Comp_Mod.compilation comp_modifiers) name mode mode_cname

       end;

   in

     thy

     |> defined_function_of (Comp_Mod.compilation comp_modifiers) name

     |> fold create_definition modes

   end;

 (* Proving equivalence of term *)

 fun is_Type (Type _) = true

   | is_Type _ = false

 (* returns true if t is an application of an datatype constructor *)

 (* which then consequently would be splitted *)

 (* else false *)

 fun is_constructor thy t =

   if (is_Type (fastype_of t)) then

     (case Datatype.get_info thy ((fst o dest_Type o fastype_of) t) of

       NONE => false

     | SOME info => (let

       val constr_consts = maps (fn (_, (_, _, constrs)) => map fst constrs) (#descr info)

       val (c, _) = strip_comb t

       in (case c of

         Const (name, _) => name mem_string constr_consts

         | _ => false) end))

   else false

 (* MAJOR FIXME:  prove_params should be simple

  - different form of introrule for parameters ? *)

 fun prove_param options thy t deriv =

   let

     val  (f, args) = strip_comb (Envir.eta_contract t)

     val mode = head_mode_of deriv

     val param_derivations = param_derivations_of deriv

     val ho_args = ho_args_of mode args

     val f_tac = case f of

       Const (name, T) => simp_tac (HOL_basic_ss addsimps 

          ([@{thm eval_pred}, (predfun_definition_of thy name mode),

          @{thm "split_eta"}, @{thm "split_beta"}, @{thm "fst_conv"},

          @{thm "snd_conv"}, @{thm pair_collapse}, @{thm "Product_Type.split_conv"}])) 1

     | Free _ => TRY (rtac @{thm refl} 1)

     | Abs _ => error "prove_param: No valid parameter term"

   in

     REPEAT_DETERM (rtac @{thm ext} 1)

     THEN print_tac' options "prove_param"

     THEN f_tac

     THEN print_tac' options "after simplification in prove_args"

     THEN (REPEAT_DETERM (atac 1))

     THEN (EVERY (map2 (prove_param options thy) ho_args param_derivations))

   end

 fun prove_expr options thy (premposition : int) (t, deriv) =

   case strip_comb t of

     (Const (name, T), args) =>

       let

         val mode = head_mode_of deriv

         val introrule = predfun_intro_of thy name mode

         val param_derivations = param_derivations_of deriv

         val ho_args = ho_args_of mode args

       in

         print_tac' options "before intro rule:"

         (* for the right assumption in first position *)

         THEN rotate_tac premposition 1

         THEN debug_tac (Display.string_of_thm (ProofContext.init thy) introrule)

         THEN rtac introrule 1

         THEN print_tac' options "after intro rule"

         (* work with parameter arguments *)

         THEN atac 1

         THEN print_tac' options "parameter goal"

         THEN (EVERY (map2 (prove_param options thy) ho_args param_derivations))

         THEN (REPEAT_DETERM (atac 1))

       end

   | _ =>

     asm_full_simp_tac

       (HOL_basic_ss' addsimps [@{thm "split_eta"}, @{thm "split_beta"}, @{thm "fst_conv"},

          @{thm "snd_conv"}, @{thm pair_collapse}]) 1

     THEN (atac 1)

     THEN print_tac' options "after prove parameter call"

 fun SOLVED tac st = FILTER (fn st' => nprems_of st' = nprems_of st - 1) tac st;

 fun SOLVEDALL tac st = FILTER (fn st' => nprems_of st' = 0) tac st

 fun check_format thy st =

   let

     val concl' = Logic.strip_assums_concl (hd (prems_of st))

     val concl = HOLogic.dest_Trueprop concl'

     val expr = fst (strip_comb (fst (PredicateCompFuns.dest_Eval concl)))

     fun valid_expr (Const (@{const_name Predicate.bind}, _)) = true

       | valid_expr (Const (@{const_name Predicate.single}, _)) = true

       | valid_expr _ = false

   in

     if valid_expr expr then

       ((*tracing "expression is valid";*) Seq.single st)

     else

       ((*tracing "expression is not valid";*) Seq.empty) (*error "check_format: wrong format"*)

   end

 fun prove_match options thy (out_ts : term list) =

   let

     fun get_case_rewrite t =

       if (is_constructor thy t) then let

         val case_rewrites = (#case_rewrites (Datatype.the_info thy

           ((fst o dest_Type o fastype_of) t)))

         in case_rewrites @ maps get_case_rewrite (snd (strip_comb t)) end

       else []

     val simprules = @{thm "unit.cases"} :: @{thm "prod.cases"} :: maps get_case_rewrite out_ts

   (* replace TRY by determining if it necessary - are there equations when calling compile match? *)

   in

      (* make this simpset better! *)

     asm_full_simp_tac (HOL_basic_ss' addsimps simprules) 1

     THEN print_tac' options "after prove_match:"

     THEN (DETERM (TRY (EqSubst.eqsubst_tac (ProofContext.init thy) [0] [@{thm HOL.if_P}] 1

            THEN (REPEAT_DETERM (rtac @{thm conjI} 1 THEN (SOLVED (asm_simp_tac HOL_basic_ss' 1))))

            THEN print_tac' options "if condition to be solved:"

            THEN (SOLVED (asm_simp_tac HOL_basic_ss' 1 THEN print_tac' options "after if simp; in SOLVED:"))

            THEN check_format thy

            THEN print_tac' options "after if simplification - a TRY block")))

     THEN print_tac' options "after if simplification"

   end;

 (* corresponds to compile_fun -- maybe call that also compile_sidecond? *)

 fun prove_sidecond thy modes t =

   let

     fun preds_of t nameTs = case strip_comb t of 

       (f as Const (name, T), args) =>

         if AList.defined (op =) modes name then (name, T) :: nameTs

           else fold preds_of args nameTs

       | _ => nameTs

     val preds = preds_of t []

     val defs = map

       (fn (pred, T) => predfun_definition_of thy pred

         (all_input_of T))

         preds

   in 

     (* remove not_False_eq_True when simpset in prove_match is better *)

     simp_tac (HOL_basic_ss addsimps

       (@{thms HOL.simp_thms} @ (@{thm not_False_eq_True} :: @{thm eval_pred} :: defs))) 1 

     (* need better control here! *)

   end

 fun prove_clause options thy nargs modes mode (_, clauses) (ts, moded_ps) =

   let

     val (in_ts, clause_out_ts) = split_mode mode ts;

     fun prove_prems out_ts [] =

       (prove_match options thy out_ts)

       THEN print_tac' options "before simplifying assumptions"

       THEN asm_full_simp_tac HOL_basic_ss' 1

       THEN print_tac' options "before single intro rule"

       THEN (rtac (if null clause_out_ts then @{thm singleI_unit} else @{thm singleI}) 1)

     | prove_prems out_ts ((p, deriv) :: ps) =

       let

         val premposition = (find_index (equal p) clauses) + nargs

         val mode = head_mode_of deriv

         val rest_tac =

           rtac @{thm bindI} 1

           THEN (case p of Prem t =>

             let

               val (_, us) = strip_comb t

               val (_, out_ts''') = split_mode mode us

               val rec_tac = prove_prems out_ts''' ps

             in

               print_tac' options "before clause:"

               (*THEN asm_simp_tac HOL_basic_ss 1*)

               THEN print_tac' options "before prove_expr:"

               THEN prove_expr options thy premposition (t, deriv)

               THEN print_tac' options "after prove_expr:"

               THEN rec_tac

             end

           | Negprem t =>

             let

               val (t, args) = strip_comb t

               val (_, out_ts''') = split_mode mode args

               val rec_tac = prove_prems out_ts''' ps

               val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE)

               val param_derivations = param_derivations_of deriv

               val params = ho_args_of mode args

             in

               print_tac' options "before prove_neg_expr:"

               THEN full_simp_tac (HOL_basic_ss addsimps

                 [@{thm split_eta}, @{thm split_beta}, @{thm fst_conv},

                  @{thm snd_conv}, @{thm pair_collapse}, @{thm Product_Type.split_conv}]) 1

               THEN (if (is_some name) then

                   print_tac' options ("before unfolding definition " ^

                     (Display.string_of_thm_global thy

                       (predfun_definition_of thy (the name) mode)))

                   THEN simp_tac (HOL_basic_ss addsimps

                     [predfun_definition_of thy (the name) mode]) 1

                   THEN rtac @{thm not_predI} 1

                   THEN print_tac' options "after applying rule not_predI"

                   THEN full_simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True},

                     @{thm split_eta}, @{thm split_beta}, @{thm fst_conv},

                     @{thm snd_conv}, @{thm pair_collapse}, @{thm Product_Type.split_conv}]) 1

                   THEN (REPEAT_DETERM (atac 1))

                   THEN (EVERY (map2 (prove_param options thy) params param_derivations))

                   THEN (REPEAT_DETERM (atac 1))

                 else

                   rtac @{thm not_predI'} 1)

                   THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1

               THEN rec_tac

             end

           | Sidecond t =>

            rtac @{thm if_predI} 1

            THEN print_tac' options "before sidecond:"

            THEN prove_sidecond thy modes t

            THEN print_tac' options "after sidecond:"

            THEN prove_prems [] ps)

       in (prove_match options thy out_ts)

           THEN rest_tac

       end;

     val prems_tac = prove_prems in_ts moded_ps

   in

     print_tac' options "Proving clause..."

     THEN rtac @{thm bindI} 1

     THEN rtac @{thm singleI} 1

     THEN prems_tac

   end;

 fun select_sup 1 1 = []

   | select_sup _ 1 = [rtac @{thm supI1}]

   | select_sup n i = (rtac @{thm supI2})::(select_sup (n - 1) (i - 1));

 fun prove_one_direction options thy clauses preds modes pred mode moded_clauses =

   let

     val T = the (AList.lookup (op =) preds pred)

     val nargs = length (binder_types T)

     val pred_case_rule = the_elim_of thy pred

   in

     REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"}))

     THEN print_tac' options "before applying elim rule"

     THEN etac (predfun_elim_of thy pred mode) 1

     THEN etac pred_case_rule 1

     THEN (EVERY (map

            (fn i => EVERY' (select_sup (length moded_clauses) i) i) 

              (1 upto (length moded_clauses))))

     THEN (EVERY (map2 (prove_clause options thy nargs modes mode) clauses moded_clauses))

     THEN print_tac' options "proved one direction"

   end;

 (** Proof in the other direction **)

 fun prove_match2 thy out_ts = let

   fun split_term_tac (Free _) = all_tac

     | split_term_tac t =

       if (is_constructor thy t) then let

         val info = Datatype.the_info thy ((fst o dest_Type o fastype_of) t)

         val num_of_constrs = length (#case_rewrites info)

         (* special treatment of pairs -- because of fishing *)

         val split_rules = case (fst o dest_Type o fastype_of) t of

           "*" => [@{thm prod.split_asm}] 

           | _ => PureThy.get_thms thy (((fst o dest_Type o fastype_of) t) ^ ".split_asm")

         val (_, ts) = strip_comb t

       in

         (print_tac ("Term " ^ (Syntax.string_of_term_global thy t) ^ 

           "splitting with rules \n" ^

         commas (map (Display.string_of_thm_global thy) split_rules)))

         THEN TRY ((Splitter.split_asm_tac split_rules 1)

         THEN (print_tac "after splitting with split_asm rules")

         (* THEN (Simplifier.asm_full_simp_tac HOL_basic_ss 1)

           THEN (DETERM (TRY (etac @{thm Pair_inject} 1)))*)

           THEN (REPEAT_DETERM_N (num_of_constrs - 1)

             (etac @{thm botE} 1 ORELSE etac @{thm botE} 2)))

         THEN (assert_tac (Max_number_of_subgoals 2))

         THEN (EVERY (map split_term_tac ts))

       end

     else all_tac

   in

     split_term_tac (HOLogic.mk_tuple out_ts)

     THEN (DETERM (TRY ((Splitter.split_asm_tac [@{thm "split_if_asm"}] 1)

     THEN (etac @{thm botE} 2))))

   end

 (* VERY LARGE SIMILIRATIY to function prove_param 

 -- join both functions

 *)

 (* TODO: remove function *)

 fun prove_param2 thy t deriv =

   let

     val (f, args) = strip_comb (Envir.eta_contract t)

     val mode = head_mode_of deriv

     val param_derivations = param_derivations_of deriv

     val ho_args = ho_args_of mode args

     val f_tac = case f of

         Const (name, T) => full_simp_tac (HOL_basic_ss addsimps 

            (@{thm eval_pred}::(predfun_definition_of thy name mode)

            :: @{thm "Product_Type.split_conv"}::[])) 1

       | Free _ => all_tac

       | _ => error "prove_param2: illegal parameter term"

   in

     print_tac "before simplification in prove_args:"

     THEN f_tac

     THEN print_tac "after simplification in prove_args"

     THEN EVERY (map2 (prove_param2 thy) ho_args param_derivations)

   end

 fun prove_expr2 thy (t, deriv) = 

   (case strip_comb t of

       (Const (name, T), args) =>

         let

           val mode = head_mode_of deriv

           val param_derivations = param_derivations_of deriv

           val ho_args = ho_args_of mode args

         in

           etac @{thm bindE} 1

           THEN (REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"})))

           THEN print_tac "prove_expr2-before"

           THEN (debug_tac (Syntax.string_of_term_global thy

             (prop_of (predfun_elim_of thy name mode))))

           THEN (etac (predfun_elim_of thy name mode) 1)

           THEN print_tac "prove_expr2"

           THEN (EVERY (map2 (prove_param2 thy) ho_args param_derivations))

           THEN print_tac "finished prove_expr2"

         end

       | _ => etac @{thm bindE} 1)

 (* FIXME: what is this for? *)

 (* replace defined by has_mode thy pred *)

 (* TODO: rewrite function *)

 fun prove_sidecond2 thy modes t = let

   fun preds_of t nameTs = case strip_comb t of 

     (f as Const (name, T), args) =>

       if AList.defined (op =) modes name then (name, T) :: nameTs

         else fold preds_of args nameTs

     | _ => nameTs

   val preds = preds_of t []

   val defs = map

     (fn (pred, T) => predfun_definition_of thy pred 

       (all_input_of T))

       preds

   in

    (* only simplify the one assumption *)

    full_simp_tac (HOL_basic_ss' addsimps @{thm eval_pred} :: defs) 1 

    (* need better control here! *)

    THEN print_tac "after sidecond2 simplification"

    end

 fun prove_clause2 thy modes pred mode (ts, ps) i =

   let

     val pred_intro_rule = nth (intros_of thy pred) (i - 1)

     val (in_ts, clause_out_ts) = split_mode mode ts;

     fun prove_prems2 out_ts [] =

       print_tac "before prove_match2 - last call:"

       THEN prove_match2 thy out_ts

       THEN print_tac "after prove_match2 - last call:"

       THEN (etac @{thm singleE} 1)

       THEN (REPEAT_DETERM (etac @{thm Pair_inject} 1))

       THEN (asm_full_simp_tac HOL_basic_ss' 1)

       THEN (REPEAT_DETERM (etac @{thm Pair_inject} 1))

       THEN (asm_full_simp_tac HOL_basic_ss' 1)

       THEN SOLVED (print_tac "state before applying intro rule:"

       THEN (rtac pred_intro_rule 1)

       (* How to handle equality correctly? *)

       THEN (print_tac "state before assumption matching")

       THEN (REPEAT (atac 1 ORELSE 

          (CHANGED (asm_full_simp_tac (HOL_basic_ss' addsimps

            [@{thm split_eta}, @{thm "split_beta"}, @{thm "fst_conv"},

              @{thm "snd_conv"}, @{thm pair_collapse}]) 1)

           THEN print_tac "state after simp_tac:"))))

     | prove_prems2 out_ts ((p, deriv) :: ps) =

       let

         val mode = head_mode_of deriv

         val rest_tac = (case p of

           Prem t =>

           let

             val (_, us) = strip_comb t

             val (_, out_ts''') = split_mode mode us

             val rec_tac = prove_prems2 out_ts''' ps

           in

             (prove_expr2 thy (t, deriv)) THEN rec_tac

           end

         | Negprem t =>

           let

             val (_, args) = strip_comb t

             val (_, out_ts''') = split_mode mode args

             val rec_tac = prove_prems2 out_ts''' ps

             val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE)

             val param_derivations = param_derivations_of deriv

             val ho_args = ho_args_of mode args

           in

             print_tac "before neg prem 2"

             THEN etac @{thm bindE} 1

             THEN (if is_some name then

                 full_simp_tac (HOL_basic_ss addsimps

                   [predfun_definition_of thy (the name) mode]) 1

                 THEN etac @{thm not_predE} 1

                 THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1

                 THEN (EVERY (map2 (prove_param2 thy) ho_args param_derivations))

               else

                 etac @{thm not_predE'} 1)

             THEN rec_tac

           end 

         | Sidecond t =>

           etac @{thm bindE} 1

           THEN etac @{thm if_predE} 1

           THEN prove_sidecond2 thy modes t 

           THEN prove_prems2 [] ps)

       in print_tac "before prove_match2:"

          THEN prove_match2 thy out_ts

          THEN print_tac "after prove_match2:"

          THEN rest_tac

       end;

     val prems_tac = prove_prems2 in_ts ps 

   in

     print_tac "starting prove_clause2"

     THEN etac @{thm bindE} 1

     THEN (etac @{thm singleE'} 1)

     THEN (TRY (etac @{thm Pair_inject} 1))

     THEN print_tac "after singleE':"

     THEN prems_tac

   end;

 fun prove_other_direction options thy modes pred mode moded_clauses =

   let

     fun prove_clause clause i =

       (if i < length moded_clauses then etac @{thm supE} 1 else all_tac)

       THEN (prove_clause2 thy modes pred mode clause i)

   in

     (DETERM (TRY (rtac @{thm unit.induct} 1)))

      THEN (REPEAT_DETERM (CHANGED (rewtac @{thm split_paired_all})))

      THEN (rtac (predfun_intro_of thy pred mode) 1)

      THEN (REPEAT_DETERM (rtac @{thm refl} 2))

      THEN (if null moded_clauses then

          etac @{thm botE} 1

        else EVERY (map2 prove_clause moded_clauses (1 upto (length moded_clauses))))

   end;

 (** proof procedure **)

 fun prove_pred options thy clauses preds modes pred mode (moded_clauses, compiled_term) =

   let

     val ctxt = ProofContext.init thy

     val clauses = case AList.lookup (op =) clauses pred of SOME rs => rs | NONE => []

   in

     Goal.prove ctxt (Term.add_free_names compiled_term []) [] compiled_term

       (if not (skip_proof options) then

         (fn _ =>

         rtac @{thm pred_iffI} 1

         THEN print_tac' options "after pred_iffI"

         THEN prove_one_direction options thy clauses preds modes pred mode moded_clauses

         THEN print_tac' options "proved one direction"

         THEN prove_other_direction options thy modes pred mode moded_clauses

         THEN print_tac' options "proved other direction")

       else (fn _ => Skip_Proof.cheat_tac thy))

   end;

 (* composition of mode inference, definition, compilation and proof *)

 (** auxillary combinators for table of preds and modes **)

 fun map_preds_modes f preds_modes_table =

   map (fn (pred, modes) =>

     (pred, map (fn (mode, value) => (mode, f pred mode value)) modes)) preds_modes_table

 fun join_preds_modes table1 table2 =

   map_preds_modes (fn pred => fn mode => fn value =>

     (value, the (AList.lookup (op =) (the (AList.lookup (op =) table2 pred)) mode))) table1

 fun maps_modes preds_modes_table =

   map (fn (pred, modes) =>

     (pred, map (fn (mode, value) => value) modes)) preds_modes_table

 fun compile_preds comp_modifiers thy all_vs param_vs preds moded_clauses =

   map_preds_modes (fn pred => compile_pred comp_modifiers thy all_vs param_vs pred

       (the (AList.lookup (op =) preds pred))) moded_clauses

 fun prove options thy clauses preds modes moded_clauses compiled_terms =

   map_preds_modes (prove_pred options thy clauses preds modes)

     (join_preds_modes moded_clauses compiled_terms)

 fun prove_by_skip options thy _ _ _ _ compiled_terms =

   map_preds_modes

     (fn pred => fn mode => fn t => Drule.export_without_context (Skip_Proof.make_thm thy t))

     compiled_terms

 (* preparation of introduction rules into special datastructures *)

 fun dest_prem thy params t =

   (case strip_comb t of

     (v as Free _, ts) => if member (op =) params v then Prem t else Sidecond t

   | (c as Const (@{const_name Not}, _), [t]) => (case dest_prem thy params t of

       Prem t => Negprem t

     | Negprem _ => error ("Double negation not allowed in premise: " ^

         Syntax.string_of_term_global thy (c $ t)) 

     | Sidecond t => Sidecond (c $ t))

   | (c as Const (s, _), ts) =>

     if is_registered thy s then Prem t else Sidecond t

   | _ => Sidecond t)

 fun prepare_intrs options compilation thy prednames intros =

   let

     val intrs = map prop_of intros

     val preds = map (fn c => Const (c, Sign.the_const_type thy c)) prednames

     val (preds, intrs) = unify_consts thy preds intrs

     val ([preds, intrs], _) = fold_burrow (Variable.import_terms false) [preds, intrs]

       (ProofContext.init thy)

     val preds = map dest_Const preds

     val extra_modes =

       all_modes_of compilation thy |> filter_out (fn (name, _) => member (op =) prednames name)

     val all_vs = terms_vs intrs

     val params =

       case intrs of

         [] =>

           let

             val T = snd (hd preds)

             val paramTs =

               ho_argsT_of (hd (all_modes_of_typ T)) (binder_types T)

             val param_names = Name.variant_list [] (map (fn i => "p" ^ string_of_int i)

               (1 upto length paramTs))

           in

             map2 (curry Free) param_names paramTs

           end

       | (intr :: _) => maps extract_params

           (snd (strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl intr))))

     val param_vs = map (fst o dest_Free) params

     fun add_clause intr clauses =

       let

         val (Const (name, T), ts) = strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl intr))

         val prems = map (dest_prem thy params o HOLogic.dest_Trueprop) (Logic.strip_imp_prems intr)

       in

         AList.update op = (name, these (AList.lookup op = clauses name) @

           [(ts, prems)]) clauses

       end;

     val clauses = fold add_clause intrs []

   in

     (preds, all_vs, param_vs, extra_modes, clauses)

   end;

 (* sanity check of introduction rules *)

 (* TODO: rethink check with new modes *)

 (*

 fun check_format_of_intro_rule thy intro =

   let

     val concl = Logic.strip_imp_concl (prop_of intro)

     val (p, args) = strip_comb (HOLogic.dest_Trueprop concl)

     val params = fst (chop (nparams_of thy (fst (dest_Const p))) args)

     fun check_arg arg = case HOLogic.strip_tupleT (fastype_of arg) of

       (Ts as _ :: _ :: _) =>

         if length (HOLogic.strip_tuple arg) = length Ts then

           true

         else

           error ("Format of introduction rule is invalid: tuples must be expanded:"

           ^ (Syntax.string_of_term_global thy arg) ^ " in " ^

           (Display.string_of_thm_global thy intro)) 

       | _ => true

     val prems = Logic.strip_imp_prems (prop_of intro)

     fun check_prem (Prem t) = forall check_arg args

       | check_prem (Negprem t) = forall check_arg args

       | check_prem _ = true

   in

     forall check_arg args andalso

     forall (check_prem o dest_prem thy params o HOLogic.dest_Trueprop) prems

   end

 *)

 (*

 fun check_intros_elim_match thy prednames =

   let

     fun check predname =

       let

         val intros = intros_of thy predname

         val elim = the_elim_of thy predname

         val nparams = nparams_of thy predname

         val elim' =

           (Drule.export_without_context o Skip_Proof.make_thm thy)

           (mk_casesrule (ProofContext.init thy) nparams intros)

       in

         if not (Thm.equiv_thm (elim, elim')) then

           error "Introduction and elimination rules do not match!"

         else true

       end

   in forall check prednames end

 *)

 (* create code equation *)

 fun add_code_equations thy preds result_thmss =

   let

     fun add_code_equation (predname, T) (pred, result_thms) =

       let

         val full_mode = fold_rev (curry Fun) (map (K Input) (binder_types T)) Bool

       in

         if member (op =) (modes_of Pred thy predname) full_mode then

           let

             val Ts = binder_types T

             val arg_names = Name.variant_list []

               (map (fn i => "x" ^ string_of_int i) (1 upto length Ts))

             val args = map2 (curry Free) arg_names Ts

             val predfun = Const (function_name_of Pred thy predname full_mode,

               Ts ---> PredicateCompFuns.mk_predT @{typ unit})

             val rhs = @{term Predicate.holds} $ (list_comb (predfun, args))

             val eq_term = HOLogic.mk_Trueprop

               (HOLogic.mk_eq (list_comb (Const (predname, T), args), rhs))

             val def = predfun_definition_of thy predname full_mode

             val tac = fn _ => Simplifier.simp_tac

               (HOL_basic_ss addsimps [def, @{thm holds_eq}, @{thm eval_pred}]) 1

             val eq = Goal.prove (ProofContext.init thy) arg_names [] eq_term tac

           in

             (pred, result_thms @ [eq])

           end

         else

           (pred, result_thms)

       end

   in

     map2 add_code_equation preds result_thmss

   end

 (** main function of predicate compiler **)

 datatype steps = Steps of

   {

   define_functions : options -> (string * typ) list -> string * mode list -> theory -> theory,

   infer_modes : options -> (string * typ) list -> (string * mode list) list

     -> string list -> (string * (term list * indprem list) list) list

     -> theory -> ((moded_clause list pred_mode_table * string list) * theory),

   prove : options -> theory -> (string * (term list * indprem list) list) list

     -> (string * typ) list -> (string * mode list) list

     -> moded_clause list pred_mode_table -> term pred_mode_table -> thm pred_mode_table,

   add_code_equations : theory -> (string * typ) list

     -> (string * thm list) list -> (string * thm list) list,

   comp_modifiers : Comp_Mod.comp_modifiers,

   qname : bstring

   }

 fun add_equations_of steps options prednames thy =

   let

     fun dest_steps (Steps s) = s

     val _ = print_step options

       ("Starting predicate compiler for predicates " ^ commas prednames ^ "...")

       (*val _ = check_intros_elim_match thy prednames*)

       (*val _ = map (check_format_of_intro_rule thy) (maps (intros_of thy) prednames)*)

     val compilation = Comp_Mod.compilation (#comp_modifiers (dest_steps steps))

     val (preds, all_vs, param_vs, extra_modes, clauses) =

       prepare_intrs options compilation thy prednames (maps (intros_of thy) prednames)

     val _ = print_step options "Infering modes..."

     val ((moded_clauses, errors), thy') =

       #infer_modes (dest_steps steps) options preds extra_modes param_vs clauses thy

     val modes = map (fn (p, mps) => (p, map fst mps)) moded_clauses

     val _ = check_expected_modes preds options modes

     val _ = check_proposed_modes preds options modes extra_modes errors

     val _ = print_modes options thy' modes

     val _ = print_step options "Defining executable functions..."

     val thy'' = fold (#define_functions (dest_steps steps) options preds) modes thy'

       |> Theory.checkpoint

     val _ = print_step options "Compiling equations..."

     val compiled_terms =

       compile_preds (#comp_modifiers (dest_steps steps)) thy'' all_vs param_vs preds moded_clauses

     val _ = print_compiled_terms options thy'' compiled_terms

     val _ = print_step options "Proving equations..."

     val result_thms = #prove (dest_steps steps) options thy'' clauses preds (extra_modes @ modes)

       moded_clauses compiled_terms

     val result_thms' = #add_code_equations (dest_steps steps) thy'' preds

       (maps_modes result_thms)

     val qname = #qname (dest_steps steps)

     val attrib = fn thy => Attrib.attribute_i thy (Attrib.internal (K (Thm.declaration_attribute

       (fn thm => Context.mapping (Code.add_eqn thm) I))))

     val thy''' = fold (fn (name, result_thms) => fn thy => snd (PureThy.add_thmss

       [((Binding.qualify true (Long_Name.base_name name) (Binding.name qname), result_thms),

         [attrib thy ])] thy))

       result_thms' thy'' |> Theory.checkpoint

   in

     thy'''

   end

 fun extend' value_of edges_of key (G, visited) =

   let

     val (G', v) = case try (Graph.get_node G) key of

         SOME v => (G, v)

       | NONE => (Graph.new_node (key, value_of key) G, value_of key)

     val (G'', visited') = fold (extend' value_of edges_of)

       (subtract (op =) visited (edges_of (key, v)))

       (G', key :: visited)

   in

     (fold (Graph.add_edge o (pair key)) (edges_of (key, v)) G'', visited')

   end;

 fun extend value_of edges_of key G = fst (extend' value_of edges_of key (G, [])) 

 fun gen_add_equations steps options names thy =

   let

     fun dest_steps (Steps s) = s

     val defined = defined_functions (Comp_Mod.compilation (#comp_modifiers (dest_steps steps)))

     val thy' = thy

       |> PredData.map (fold (extend (fetch_pred_data thy) (depending_preds_of thy)) names)

       |> Theory.checkpoint;

     fun strong_conn_of gr keys =

       Graph.strong_conn (Graph.subgraph (member (op =) (Graph.all_succs gr keys)) gr)

     val scc = strong_conn_of (PredData.get thy') names

     val thy'' = fold_rev

       (fn preds => fn thy =>

         if not (forall (defined thy) preds) then

           add_equations_of steps options preds thy

         else thy)

       scc thy' |> Theory.checkpoint

   in thy'' end

 (*

 val depth_limited_comp_modifiers = Comp_Mod.Comp_Modifiers

   {

   compilation = Depth_Limited,

   function_name_of = function_name_of Depth_Limited,

   set_function_name = set_function_name Depth_Limited,

   funT_of = depth_limited_funT_of : (compilation_funs -> mode -> typ -> typ),

   function_name_prefix = "depth_limited_",

   additional_arguments = fn names =>

     let

       val [depth_name, polarity_name] = Name.variant_list names ["depth", "polarity"]

     in [Free (polarity_name, @{typ "bool"}), Free (depth_name, @{typ "code_numeral"})] end,

   wrap_compilation =

     fn compfuns => fn s => fn T => fn mode => fn additional_arguments => fn compilation =>

     let

       val [polarity, depth] = additional_arguments

       val (_, Ts2) = chop (length (fst mode)) (binder_types T)

       val (_, Us2) = split_smodeT (snd mode) Ts2

       val T' = mk_predT compfuns (HOLogic.mk_tupleT Us2)

       val if_const = Const (@{const_name "If"}, @{typ bool} --> T' --> T' --> T')

       val full_mode = null Us2

     in

       if_const $ HOLogic.mk_eq (depth, @{term "0 :: code_numeral"})

         $ (if_const $ polarity $ mk_bot compfuns (dest_predT compfuns T')

           $ (if full_mode then mk_single compfuns HOLogic.unit else

             Const (@{const_name undefined}, T')))

         $ compilation

     end,

   transform_additional_arguments =

     fn prem => fn additional_arguments =>

     let

       val [polarity, depth] = additional_arguments

       val polarity' = (case prem of Prem _ => I | Negprem _ => HOLogic.mk_not | _ => I) polarity

       val depth' =

         Const ("Algebras.minus", @{typ "code_numeral => code_numeral => code_numeral"})

           $ depth $ Const ("Algebras.one", @{typ "Code_Numeral.code_numeral"})

     in [polarity', depth'] end

   }

 val random_comp_modifiers = Comp_Mod.Comp_Modifiers

   {

   compilation = Random,

   function_name_of = function_name_of Random,

   set_function_name = set_function_name Random,

   function_name_prefix = "random_",

   funT_of = K random_function_funT_of : (compilation_funs -> mode -> typ -> typ),

   additional_arguments = fn names => [Free (Name.variant names "size", @{typ code_numeral})],

   wrap_compilation = K (K (K (K (K I))))

     : (compilation_funs -> string -> typ -> mode -> term list -> term -> term),

   transform_additional_arguments = K I : (indprem -> term list -> term list)

   }

 *)

 (* different instantiantions of the predicate compiler *)

 val predicate_comp_modifiers = Comp_Mod.Comp_Modifiers

   {

   compilation = Pred,

   function_name_prefix = "",

   compfuns = PredicateCompFuns.compfuns,

   additional_arguments = K [],

   wrap_compilation = K (K (K (K (K I))))

    : (compilation_funs -> string -> typ -> mode -> term list -> term -> term),

   transform_additional_arguments = K I : (indprem -> term list -> term list)

   }

 val add_equations = gen_add_equations

   (Steps {infer_modes = infer_modes false,

   define_functions = create_definitions,

   prove = prove,

   add_code_equations = add_code_equations,

   comp_modifiers = predicate_comp_modifiers,

   qname = "equation"})

 val annotated_comp_modifiers = Comp_Mod.Comp_Modifiers

   {

   compilation = Annotated,

   function_name_prefix = "annotated_",

   compfuns = PredicateCompFuns.compfuns,

   additional_arguments = K [],

   wrap_compilation =

     fn compfuns => fn s => fn T => fn mode => fn additional_arguments => fn compilation =>

       mk_tracing ("calling predicate " ^ s ^

         " with mode " ^ string_of_mode mode) compilation,

   transform_additional_arguments = K I : (indprem -> term list -> term list)

   }

 val dseq_comp_modifiers = Comp_Mod.Comp_Modifiers

   {

   compilation = DSeq,

   function_name_prefix = "dseq_",

   compfuns = DSequence_CompFuns.compfuns,

   additional_arguments = K [],

   wrap_compilation = K (K (K (K (K I))))

    : (compilation_funs -> string -> typ -> mode -> term list -> term -> term),

   transform_additional_arguments = K I : (indprem -> term list -> term list)

   }

 val random_dseq_comp_modifiers = Comp_Mod.Comp_Modifiers

   {

   compilation = Random_DSeq,

   function_name_prefix = "random_dseq_",

   compfuns = Random_Sequence_CompFuns.compfuns,

   additional_arguments = K [],

   wrap_compilation = K (K (K (K (K I))))

    : (compilation_funs -> string -> typ -> mode -> term list -> term -> term),

   transform_additional_arguments = K I : (indprem -> term list -> term list)

   }

 (*

 val add_depth_limited_equations = gen_add_equations

   (Steps {infer_modes = infer_modes,

   define_functions = define_functions depth_limited_comp_modifiers PredicateCompFuns.compfuns,

   compile_preds = compile_preds depth_limited_comp_modifiers PredicateCompFuns.compfuns,

   prove = prove_by_skip,

   add_code_equations = K (K I),

   defined = defined_functions Depth_Limited,

   qname = "depth_limited_equation"})

 *)

 val add_annotated_equations = gen_add_equations

   (Steps {infer_modes = infer_modes false,

   define_functions = define_functions annotated_comp_modifiers PredicateCompFuns.compfuns,

   prove = prove_by_skip,

   add_code_equations = K (K I),

   comp_modifiers = annotated_comp_modifiers,

   qname = "annotated_equation"})

 (*

 val add_quickcheck_equations = gen_add_equations

   (Steps {infer_modes = infer_modes_with_generator,

   define_functions = define_functions random_comp_modifiers RandomPredCompFuns.compfuns,

   compile_preds = compile_preds random_comp_modifiers RandomPredCompFuns.compfuns,

   prove = prove_by_skip,

   add_code_equations = K (K I),

   defined = defined_functions Random,

   qname = "random_equation"})

 *)

 val add_dseq_equations = gen_add_equations

   (Steps {infer_modes = infer_modes false,

   define_functions = define_functions dseq_comp_modifiers DSequence_CompFuns.compfuns,

   prove = prove_by_skip,

   add_code_equations = K (K I),

   comp_modifiers = dseq_comp_modifiers,

   qname = "dseq_equation"})

 val add_random_dseq_equations = gen_add_equations

   (Steps {infer_modes = infer_modes true,

   define_functions = define_functions random_dseq_comp_modifiers Random_Sequence_CompFuns.compfuns,

   prove = prove_by_skip,

   add_code_equations = K (K I),

   comp_modifiers = random_dseq_comp_modifiers,

   qname = "random_dseq_equation"})

 (** user interface **)

 (* code_pred_intro attribute *)

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

 val code_pred_intro_attrib = attrib add_intro;

 (*FIXME

 - Naming of auxiliary rules necessary?

 *)

 val setup = PredData.put (Graph.empty) #>

   Attrib.setup @{binding code_pred_intro} (Scan.succeed (attrib add_intro))

     "adding alternative introduction rules for code generation of inductive predicates"

 (* TODO: make Theory_Data to Generic_Data & remove duplication of local theory and theory *)

 fun generic_code_pred prep_const options raw_const lthy =

   let

     val thy = ProofContext.theory_of lthy

     val const = prep_const thy raw_const

     val lthy' = Local_Theory.theory (PredData.map

         (extend (fetch_pred_data thy) (depending_preds_of thy) const)) lthy

       |> Local_Theory.checkpoint

     val thy' = ProofContext.theory_of lthy'

     val preds = Graph.all_succs (PredData.get thy') [const] |> filter_out (has_elim thy')

     fun mk_cases const =

       let

         val T = Sign.the_const_type thy const

         val pred = Const (const, T)

         val intros = intros_of thy' const

       in mk_casesrule lthy' pred intros end  

     val cases_rules = map mk_cases preds

     val cases =

       map (fn case_rule => Rule_Cases.Case {fixes = [],

         assumes = [("", Logic.strip_imp_prems case_rule)],

         binds = [], cases = []}) cases_rules

     val case_env = map2 (fn p => fn c => (Long_Name.base_name p, SOME c)) preds cases

     val lthy'' = lthy'

       |> fold Variable.auto_fixes cases_rules 

       |> ProofContext.add_cases true case_env

     fun after_qed thms goal_ctxt =

       let

         val global_thms = ProofContext.export goal_ctxt

           (ProofContext.init (ProofContext.theory_of goal_ctxt)) (map the_single thms)

       in

         goal_ctxt |> Local_Theory.theory (fold set_elim global_thms #>

           ((case compilation options of

              Pred => add_equations

            | DSeq => add_dseq_equations

            | Random_DSeq => add_random_dseq_equations

            | compilation => error ("Compilation not supported")

            (*| Random => (fn opt => fn cs => add_equations opt cs #> add_quickcheck_equations opt cs)

            | Depth_Limited => add_depth_limited_equations

            | Annotated => add_annotated_equations*)

            ) options [const]))

       end

   in

     Proof.theorem_i NONE after_qed (map (single o (rpair [])) cases_rules) lthy''

   end;

 val code_pred = generic_code_pred (K I);

 val code_pred_cmd = generic_code_pred Code.read_const

 (* transformation for code generation *)

 val eval_ref = Unsynchronized.ref (NONE : (unit -> term Predicate.pred) option);

 val random_eval_ref =

   Unsynchronized.ref (NONE : (unit -> int * int -> term Predicate.pred * (int * int)) option);

 val dseq_eval_ref = Unsynchronized.ref (NONE : (unit -> term DSequence.dseq) option);

 val random_dseq_eval_ref =

   Unsynchronized.ref (NONE : (unit -> int -> int -> int * int -> term DSequence.dseq * (int * int)) option);

 (*FIXME turn this into an LCF-guarded preprocessor for comprehensions*)

 fun analyze_compr thy compfuns param_user_modes (compilation, arguments) t_compr =

   let

     val all_modes_of = all_modes_of compilation

     val split = case t_compr of (Const (@{const_name Collect}, _) $ t) => t

       | _ => error ("Not a set comprehension: " ^ Syntax.string_of_term_global thy t_compr);

     val (body, Ts, fp) = HOLogic.strip_psplits split;

     val output_names = Name.variant_list (Term.add_free_names body [])

       (map (fn i => "x" ^ string_of_int i) (1 upto length Ts))

     val output_frees = map2 (curry Free) output_names (rev Ts)

     val body = subst_bounds (output_frees, body)

     val T_compr = HOLogic.mk_ptupleT fp Ts

     val output_tuple = HOLogic.mk_ptuple fp T_compr (rev output_frees)

     val (pred as Const (name, T), all_args) = strip_comb body

   in

     if defined_functions compilation thy name then

       let

         fun extract_mode (Const ("Pair", _) $ t1 $ t2) = Pair (extract_mode t1, extract_mode t2)

           | extract_mode (Free (x, _)) = if member (op =) output_names x then Output else Input

           | extract_mode _ = Input