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

    Author:     Lukas Bulwahn, TU Muenchen

Prototype of an code generator for logic programming languages (a.k.a. Prolog)

*)

signature CODE_PROLOG =

sig

  datatype prolog_system = SWI_PROLOG | YAP

  type code_options =

    {ensure_groundness : bool,

     limited_types : (typ * int) list,

     limited_predicates : (string list * int) list,

     replacing : ((string * string) * string) list,

     manual_reorder : ((string * int) * int list) list}

  val set_ensure_groundness : code_options -> code_options

  val map_limit_predicates : ((string list * int) list -> (string list * int) list)

    -> code_options -> code_options

  val code_options_of : theory -> code_options 

  val map_code_options : (code_options -> code_options) -> theory -> theory

  datatype arith_op = Plus | Minus

  datatype prol_term = Var of string | Cons of string | AppF of string * prol_term list

    | Number of int | ArithOp of arith_op * prol_term list;

  datatype prem = Conj of prem list

    | Rel of string * prol_term list | NotRel of string * prol_term list

    | Eq of prol_term * prol_term | NotEq of prol_term * prol_term

    | ArithEq of prol_term * prol_term | NotArithEq of prol_term * prol_term

    | Ground of string * typ;

  type clause = ((string * prol_term list) * prem);

  type logic_program = clause list;

  type constant_table = (string * string) list

  val generate : Predicate_Compile_Aux.mode option * bool ->

    Proof.context -> string -> (logic_program * constant_table)

  val write_program : logic_program -> string

  val run : (Time.time * prolog_system) -> logic_program -> string -> string list -> int option -> prol_term list list

  val quickcheck : Proof.context -> term -> int -> term list option * (bool list * bool)

  val trace : bool Unsynchronized.ref

  val replace : ((string * string) * string) -> logic_program -> logic_program

end;

structure Code_Prolog : CODE_PROLOG =

struct

(* diagnostic tracing *)

val trace = Unsynchronized.ref false

fun tracing s = if !trace then Output.tracing s else () 

(* code generation options *)

type code_options =

  {ensure_groundness : bool,

   limited_types : (typ * int) list,

   limited_predicates : (string list * int) list,

   replacing : ((string * string) * string) list,

   manual_reorder : ((string * int) * int list) list}

fun set_ensure_groundness {ensure_groundness, limited_types, limited_predicates,

  replacing, manual_reorder} =

  {ensure_groundness = true, limited_types = limited_types,

   limited_predicates = limited_predicates, replacing = replacing,

   manual_reorder = manual_reorder}

fun map_limit_predicates f {ensure_groundness, limited_types, limited_predicates,

  replacing, manual_reorder} =

  {ensure_groundness = ensure_groundness, limited_types = limited_types,

   limited_predicates = f limited_predicates, replacing = replacing,

   manual_reorder = manual_reorder}

structure Options = Theory_Data

(

  type T = code_options

  val empty = {ensure_groundness = false,

    limited_types = [], limited_predicates = [], replacing = [], manual_reorder = []}

  val extend = I;

  fun merge

    ({ensure_groundness = ensure_groundness1, limited_types = limited_types1,

      limited_predicates = limited_predicates1, replacing = replacing1,

      manual_reorder = manual_reorder1},

     {ensure_groundness = ensure_groundness2, limited_types = limited_types2,

      limited_predicates = limited_predicates2, replacing = replacing2,

      manual_reorder = manual_reorder2}) =

    {ensure_groundness = ensure_groundness1 orelse ensure_groundness2,

     limited_types = AList.merge (op =) (K true) (limited_types1, limited_types2),

     limited_predicates = AList.merge (op =) (K true) (limited_predicates1, limited_predicates2),

     manual_reorder = AList.merge (op =) (K true) (manual_reorder1, manual_reorder2),

     replacing = Library.merge (op =) (replacing1, replacing2)};

);

val code_options_of = Options.get

val map_code_options = Options.map

(* system configuration *)

datatype prolog_system = SWI_PROLOG | YAP

fun string_of_system SWI_PROLOG = "swiprolog"

  | string_of_system YAP = "yap"

type system_configuration = {timeout : Time.time, prolog_system : prolog_system}

structure System_Config = Generic_Data

(

  type T = system_configuration

  val empty = {timeout = Time.fromSeconds 10, prolog_system = SWI_PROLOG}

  val extend = I;

  fun merge ({timeout = timeout1, prolog_system = prolog_system1},

        {timeout = timeout2, prolog_system = prolog_system2}) =

    {timeout = timeout1, prolog_system = prolog_system1}

)

(* general string functions *)

val first_upper = implode o nth_map 0 Symbol.to_ascii_upper o explode;

val first_lower = implode o nth_map 0 Symbol.to_ascii_lower o explode;

(* internal program representation *)

datatype arith_op = Plus | Minus

datatype prol_term = Var of string | Cons of string | AppF of string * prol_term list

  | Number of int | ArithOp of arith_op * prol_term list;

fun dest_Var (Var v) = v

fun add_vars (Var v) = insert (op =) v

  | add_vars (ArithOp (_, ts)) = fold add_vars ts

  | add_vars (AppF (_, ts)) = fold add_vars ts

  | add_vars _ = I

fun map_vars f (Var v) = Var (f v)

  | map_vars f (ArithOp (opr, ts)) = ArithOp (opr, map (map_vars f) ts)

  | map_vars f (AppF (fs, ts)) = AppF (fs, map (map_vars f) ts)

  | map_vars f t = t

fun maybe_AppF (c, []) = Cons c

  | maybe_AppF (c, xs) = AppF (c, xs)

fun is_Var (Var _) = true

  | is_Var _ = false

fun is_arith_term (Var _) = true

  | is_arith_term (Number _) = true

  | is_arith_term (ArithOp (_, operands)) = forall is_arith_term operands

  | is_arith_term _ = false

fun string_of_prol_term (Var s) = "Var " ^ s

  | string_of_prol_term (Cons s) = "Cons " ^ s

  | string_of_prol_term (AppF (f, args)) = f ^ "(" ^ commas (map string_of_prol_term args) ^ ")" 

  | string_of_prol_term (Number n) = "Number " ^ string_of_int n

datatype prem = Conj of prem list

  | Rel of string * prol_term list | NotRel of string * prol_term list

  | Eq of prol_term * prol_term | NotEq of prol_term * prol_term

  | ArithEq of prol_term * prol_term | NotArithEq of prol_term * prol_term

  | Ground of string * typ;

fun dest_Rel (Rel (c, ts)) = (c, ts)

fun map_term_prem f (Conj prems) = Conj (map (map_term_prem f) prems)

  | map_term_prem f (Rel (r, ts)) = Rel (r, map f ts)

  | map_term_prem f (NotRel (r, ts)) = NotRel (r, map f ts)

  | map_term_prem f (Eq (l, r)) = Eq (f l, f r)

  | map_term_prem f (NotEq (l, r)) = NotEq (f l, f r)

  | map_term_prem f (ArithEq (l, r)) = ArithEq (f l, f r)

  | map_term_prem f (NotArithEq (l, r)) = NotArithEq (f l, f r)

  | map_term_prem f (Ground (v, T)) = Ground (dest_Var (f (Var v)), T)

fun fold_prem_terms f (Conj prems) = fold (fold_prem_terms f) prems

  | fold_prem_terms f (Rel (_, ts)) = fold f ts

  | fold_prem_terms f (NotRel (_, ts)) = fold f ts

  | fold_prem_terms f (Eq (l, r)) = f l #> f r

  | fold_prem_terms f (NotEq (l, r)) = f l #> f r

  | fold_prem_terms f (ArithEq (l, r)) = f l #> f r

  | fold_prem_terms f (NotArithEq (l, r)) = f l #> f r

  | fold_prem_terms f (Ground (v, T)) = f (Var v)

type clause = ((string * prol_term list) * prem);

type logic_program = clause list;

(* translation from introduction rules to internal representation *)

fun mk_conform f empty avoid name =

  let

    fun dest_Char (Symbol.Char c) = c

    val name' = space_implode "" (map (dest_Char o Symbol.decode)

      (filter (fn s => Symbol.is_ascii_letter s orelse Symbol.is_ascii_digit s)

        (Symbol.explode name)))

    val name'' = f (if name' = "" then empty else name')

  in (if member (op =) avoid name'' then Name.variant avoid name'' else name'') end

(** constant table **)

type constant_table = (string * string) list

fun declare_consts consts constant_table =

  let

    fun update' c table =

      if AList.defined (op =) table c then table else

        let

          val c' = mk_conform first_lower "pred" (map snd table) (Long_Name.base_name c)

        in

          AList.update (op =) (c, c') table

        end

  in

    fold update' consts constant_table

  end

fun translate_const constant_table c =

  case AList.lookup (op =) constant_table c of

    SOME c' => c'

  | NONE => error ("No such constant: " ^ c)

fun inv_lookup _ [] _ = NONE

  | inv_lookup eq ((key, value)::xs) value' =

      if eq (value', value) then SOME key

      else inv_lookup eq xs value';

fun restore_const constant_table c =

  case inv_lookup (op =) constant_table c of

    SOME c' => c'

  | NONE => error ("No constant corresponding to "  ^ c)

(** translation of terms, literals, premises, and clauses **)

fun translate_arith_const @{const_name "Groups.plus_class.plus"} = SOME Plus

  | translate_arith_const @{const_name "Groups.minus_class.minus"} = SOME Minus

  | translate_arith_const _ = NONE

fun mk_nat_term constant_table n =

  let

    val zero = translate_const constant_table @{const_name "Groups.zero_class.zero"}

    val Suc = translate_const constant_table @{const_name "Suc"}

  in funpow n (fn t => AppF (Suc, [t])) (Cons zero) end

fun translate_term ctxt constant_table t =

  case try HOLogic.dest_number t of

    SOME (@{typ "int"}, n) => Number n

  | SOME (@{typ "nat"}, n) => mk_nat_term constant_table n

  | NONE =>

      (case strip_comb t of

        (Free (v, T), []) => Var v 

      | (Const (c, _), []) => Cons (translate_const constant_table c)

      | (Const (c, _), args) =>

        (case translate_arith_const c of

          SOME aop => ArithOp (aop, map (translate_term ctxt constant_table) args)

        | NONE =>                                                             

            AppF (translate_const constant_table c, map (translate_term ctxt constant_table) args))

      | _ => error ("illegal term for translation: " ^ Syntax.string_of_term ctxt t))

fun translate_literal ctxt constant_table t =

  case strip_comb t of

    (Const (@{const_name HOL.eq}, _), [l, r]) =>

      let

        val l' = translate_term ctxt constant_table l

        val r' = translate_term ctxt constant_table r

      in

        (if is_Var l' andalso is_arith_term r' andalso not (is_Var r') then ArithEq else Eq) (l', r')

      end

  | (Const (c, _), args) =>

      Rel (translate_const constant_table c, map (translate_term ctxt constant_table) args)

  | _ => error ("illegal literal for translation: " ^ Syntax.string_of_term ctxt t)

fun NegRel_of (Rel lit) = NotRel lit

  | NegRel_of (Eq eq) = NotEq eq

  | NegRel_of (ArithEq eq) = NotArithEq eq

fun mk_groundness_prems t = map Ground (Term.add_frees t [])

fun translate_prem ensure_groundness ctxt constant_table t =  

    case try HOLogic.dest_not t of

      SOME t =>

        if ensure_groundness then

          Conj (mk_groundness_prems t @ [NegRel_of (translate_literal ctxt constant_table t)])

        else

          NegRel_of (translate_literal ctxt constant_table t)

    | NONE => translate_literal ctxt constant_table t

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 (@{const_name Trueprop}, _) $ _ => Conv.arg_conv cv ct  

  | _ => raise Fail "Trueprop_conv"

fun preprocess_intro thy rule =

  Conv.fconv_rule

    (imp_prems_conv

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

    (Thm.transfer thy rule)

fun translate_intros ensure_groundness ctxt gr const constant_table =

  let

    val intros = map (preprocess_intro (ProofContext.theory_of ctxt)) (Graph.get_node gr const)

    val (intros', ctxt') = Variable.import_terms true (map prop_of intros) ctxt

    val constant_table' = declare_consts (fold Term.add_const_names intros' []) constant_table

    fun translate_intro intro =

      let

        val head = HOLogic.dest_Trueprop (Logic.strip_imp_concl intro)

        val prems = map HOLogic.dest_Trueprop (Logic.strip_imp_prems intro)

        val prems' = Conj (map (translate_prem ensure_groundness ctxt' constant_table') prems)

        val clause = (dest_Rel (translate_literal ctxt' constant_table' head), prems')

      in clause end

    val res = (map translate_intro intros', constant_table')

  in res end

fun depending_preds_of (key, intros) =

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

fun add_edges edges_of key G =

  let

    fun extend' key (G, visited) = 

      case try (Graph.get_node G) key of

          SOME v =>

            let

              val new_edges = filter (fn k => is_some (try (Graph.get_node G) k)) (edges_of (key, v))

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

                (subtract (op =) (key :: visited) new_edges) (G, key :: visited)

            in

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

            end

        | NONE => (G, visited)

  in

    fst (extend' key (G, []))

  end

fun print_intros ctxt gr consts =

  tracing (cat_lines (map (fn const =>

    "Constant " ^ const ^ "has intros:\n" ^

    cat_lines (map (Display.string_of_thm ctxt) (Graph.get_node gr const))) consts))

(* translation of moded predicates *)

(** generating graph of moded predicates **)

(* could be moved to Predicate_Compile_Core *)

fun requires_modes polarity cls =

  let

    fun req_mode_of pol (t, derivation) =

      (case fst (strip_comb t) of

        Const (c, _) => SOME (c, (pol, Predicate_Compile_Core.head_mode_of derivation))

      | _ => NONE)

    fun req (Predicate_Compile_Aux.Prem t, derivation) = req_mode_of polarity (t, derivation)

      | req (Predicate_Compile_Aux.Negprem t, derivation) = req_mode_of (not polarity) (t, derivation)

      | req _ = NONE

  in      

    maps (fn (_, prems) => map_filter req prems) cls

  end

structure Mode_Graph = Graph(type key = string * (bool * Predicate_Compile_Aux.mode)

  val ord = prod_ord fast_string_ord (prod_ord bool_ord Predicate_Compile_Aux.mode_ord));

fun mk_moded_clauses_graph ctxt scc gr =

  let

    val options = Predicate_Compile_Aux.default_options

    val mode_analysis_options =

      {use_random = true, reorder_premises = true, infer_pos_and_neg_modes = true}

    fun infer prednames (gr, (pos_modes, neg_modes, random)) =

      let

        val (lookup_modes, lookup_neg_modes, needs_random) =

          ((fn s => the (AList.lookup (op =) pos_modes s)),

           (fn s => the (AList.lookup (op =) neg_modes s)),

           (fn s => member (op =) (the (AList.lookup (op =) random s))))

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

          Predicate_Compile_Core.prepare_intrs options ctxt prednames

            (maps (Predicate_Compile_Core.intros_of ctxt) prednames)

        val ((moded_clauses, random'), _) =

          Predicate_Compile_Core.infer_modes mode_analysis_options options 

            (lookup_modes, lookup_neg_modes, needs_random) ctxt preds all_modes param_vs clauses

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

        val pos_modes' = map (apsnd (map_filter (fn (true, m) => SOME m | _ => NONE))) modes

        val neg_modes' = map (apsnd (map_filter (fn (false, m) => SOME m | _ => NONE))) modes

        val _ = tracing ("Inferred modes:\n" ^

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

            (fn (p, m) => Predicate_Compile_Aux.string_of_mode m ^ (if p then "pos" else "neg")) ms)) modes))

        val gr' = gr

          |> fold (fn (p, mps) => fold (fn (mode, cls) =>

                Mode_Graph.new_node ((p, mode), cls)) mps)

            moded_clauses

          |> fold (fn (p, mps) => fold (fn (mode, cls) => fold (fn req =>

              Mode_Graph.add_edge ((p, mode), req)) (requires_modes (fst mode) cls)) mps)

            moded_clauses

      in

        (gr', (AList.merge (op =) (op =) (pos_modes, pos_modes'),

          AList.merge (op =) (op =) (neg_modes, neg_modes'),

          AList.merge (op =) (op =) (random, random')))

      end

  in  

    fst (fold infer (rev scc) (Mode_Graph.empty, ([], [], []))) 

  end

fun declare_moded_predicate moded_preds table =

  let

    fun update' (p as (pred, (pol, mode))) table =

      if AList.defined (op =) table p then table else

        let

          val name = Long_Name.base_name pred ^ (if pol then "p" else "n")

            ^ Predicate_Compile_Aux.ascii_string_of_mode mode

          val p' = mk_conform first_lower "pred" (map snd table) name

        in

          AList.update (op =) (p, p') table

        end

  in

    fold update' moded_preds table

  end

fun mk_program ctxt moded_gr moded_preds (prog, (moded_pred_table, constant_table)) =

  let

    val moded_pred_table' = declare_moded_predicate moded_preds moded_pred_table

    fun mk_literal pol derivation constant_table' t =

      let

        val (p, args) = strip_comb t

        val mode = Predicate_Compile_Core.head_mode_of derivation 

        val name = fst (dest_Const p)

        val p' = the (AList.lookup (op =) moded_pred_table' (name, (pol, mode)))

        val args' = map (translate_term ctxt constant_table') args

      in

        Rel (p', args')

      end

    fun mk_prem pol (indprem, derivation) constant_table =

      case indprem of

        Predicate_Compile_Aux.Generator (s, T) => (Ground (s, T), constant_table)

      | _ =>

        declare_consts (Term.add_const_names (Predicate_Compile_Aux.dest_indprem indprem) []) constant_table

        |> (fn constant_table' =>

          (case indprem of Predicate_Compile_Aux.Negprem t =>

            NegRel_of (mk_literal (not pol) derivation constant_table' t)

          | _ =>

            mk_literal pol derivation constant_table' (Predicate_Compile_Aux.dest_indprem indprem), constant_table'))

    fun mk_clause pred_name pol (ts, prems) (prog, constant_table) =

    let

      val constant_table' = declare_consts (fold Term.add_const_names ts []) constant_table

      val args = map (translate_term ctxt constant_table') ts

      val (prems', constant_table'') = fold_map (mk_prem pol) prems constant_table'

    in

      (((pred_name, args), Conj prems') :: prog, constant_table'')

    end

    fun mk_clauses (pred, mode as (pol, _)) =

      let

        val clauses = Mode_Graph.get_node moded_gr (pred, mode)

        val pred_name = the (AList.lookup (op =) moded_pred_table' (pred, mode))

      in

        fold (mk_clause pred_name pol) clauses

      end

  in

    apsnd (pair moded_pred_table') (fold mk_clauses moded_preds (prog, constant_table))

  end

fun generate (use_modes, ensure_groundness) ctxt const =

  let 

    fun strong_conn_of gr keys =

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

    val gr = Predicate_Compile_Core.intros_graph_of ctxt

    val gr' = add_edges depending_preds_of const gr

    val scc = strong_conn_of gr' [const]

    val initial_constant_table = 

      declare_consts [@{const_name "Groups.zero_class.zero"}, @{const_name "Suc"}] []

  in

    case use_modes of

      SOME mode =>

        let

          val moded_gr = mk_moded_clauses_graph ctxt scc gr

          val moded_gr' = Mode_Graph.subgraph

            (member (op =) (Mode_Graph.all_succs moded_gr [(const, (true, mode))])) moded_gr

          val scc = Mode_Graph.strong_conn moded_gr' 

        in

          apfst rev (apsnd snd

            (fold (mk_program ctxt moded_gr') (rev scc) ([], ([], initial_constant_table))))

        end

      | NONE =>

        let 

          val _ = print_intros ctxt gr (flat scc)

          val constant_table = declare_consts (flat scc) initial_constant_table

        in

          apfst flat (fold_map (translate_intros ensure_groundness ctxt gr) (flat scc) constant_table)

        end

  end

(* implementation for fully enumerating predicates and

  for size-limited predicates for enumerating the values of a datatype upto a specific size *)

fun add_ground_typ (Conj prems) = fold add_ground_typ prems

  | add_ground_typ (Ground (_, T)) = insert (op =) T

  | add_ground_typ _ = I

fun mk_relname (Type (Tcon, Targs)) =

  first_lower (Long_Name.base_name Tcon) ^ space_implode "_" (map mk_relname Targs)

  | mk_relname _ = raise Fail "unexpected type"

fun mk_lim_relname T = "lim_" ^  mk_relname T

(* This is copied from "pat_completeness.ML" *)

fun inst_constrs_of thy (T as Type (name, _)) =

  map (fn (Cn,CT) =>

    Envir.subst_term_types (Sign.typ_match thy (body_type CT, T) Vartab.empty) (Const (Cn, CT)))

    (the (Datatype.get_constrs thy name))

  | inst_constrs_of thy T = raise TYPE ("inst_constrs_of", [T], [])

fun is_recursive_constr T (Const (constr_name, T')) = member (op =) (binder_types T') T

fun mk_ground_impl ctxt limited_types (T as Type (Tcon, Targs)) (seen, constant_table) =

  if member (op =) seen T then ([], (seen, constant_table))

  else

    let

      val (limited, size) = case AList.lookup (op =) limited_types T of

        SOME s => (true, s)

      | NONE => (false, 0)      

      val rel_name = (if limited then mk_lim_relname else mk_relname) T

      fun mk_impl (Const (constr_name, cT), recursive) (seen, constant_table) =

        let

          val constant_table' = declare_consts [constr_name] constant_table

          val Ts = binder_types cT

          val (rec_clauses, (seen', constant_table'')) =

            fold_map (mk_ground_impl ctxt limited_types) Ts (seen, constant_table')

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

          val lim_var =

            if limited then

              if recursive then [AppF ("suc", [Var "Lim"])]              

              else [Var "Lim"]

            else [] 

          fun mk_prem v T' =

            if limited andalso T' = T then Rel (mk_lim_relname T', [Var "Lim", v])

            else Rel (mk_relname T', [v])

          val clause =

            ((rel_name, lim_var @ [maybe_AppF (translate_const constant_table'' constr_name, vars)]),

             Conj (map2 mk_prem vars Ts))

        in

          (clause :: flat rec_clauses, (seen', constant_table''))

        end

      val constrs = inst_constrs_of (ProofContext.theory_of ctxt) T

      val constrs' = (constrs ~~ map (is_recursive_constr T) constrs)

        |> (fn cs => filter_out snd cs @ filter snd cs)

      val (clauses, constant_table') =

        apfst flat (fold_map mk_impl constrs' (T :: seen, constant_table))

      val size_term = funpow size (fn t => AppF ("suc", [t])) (Cons "zero")

    in

      ((if limited then

        cons ((mk_relname T, [Var "x"]), Rel (mk_lim_relname T, [size_term, Var "x"]))

      else I) clauses, constant_table')

    end

 | mk_ground_impl ctxt _ T (seen, constant_table) =

   raise Fail ("unexpected type :" ^ Syntax.string_of_typ ctxt T)

fun replace_ground (Conj prems) = Conj (map replace_ground prems)

  | replace_ground (Ground (x, T)) =

    Rel (mk_relname T, [Var x])  

  | replace_ground p = p

fun add_ground_predicates ctxt limited_types (p, constant_table) =

  let

    val ground_typs = fold (add_ground_typ o snd) p []

    val (grs, (_, constant_table')) = fold_map (mk_ground_impl ctxt limited_types) ground_typs ([], constant_table)

    val p' = map (apsnd replace_ground) p

  in

    ((flat grs) @ p', constant_table')

  end

(* make depth-limited version of predicate *)

fun mk_lim_rel_name rel_name = "lim_" ^ rel_name

fun mk_depth_limited rel_names ((rel_name, ts), prem) =

  let

    fun has_positive_recursive_prems (Conj prems) = exists has_positive_recursive_prems prems

      | has_positive_recursive_prems (Rel (rel, ts)) = member (op =) rel_names rel

      | has_positive_recursive_prems _ = false

    fun mk_lim_prem (Conj prems) = Conj (map mk_lim_prem prems)

      | mk_lim_prem (p as Rel (rel, ts)) =

        if member (op =) rel_names rel then Rel (mk_lim_rel_name rel, Var "Lim" :: ts) else p

      | mk_lim_prem p = p

  in

    if has_positive_recursive_prems prem then

      ((mk_lim_rel_name rel_name, (AppF ("suc", [Var "Lim"]))  :: ts), mk_lim_prem prem)

    else

      ((mk_lim_rel_name rel_name, (Var "Lim") :: ts), prem)

  end

fun add_limited_predicates limited_predicates =

  let                                     

    fun add (rel_names, limit) (p, constant_table) = 

      let

        val clauses = filter (fn ((rel, _), _) => member (op =) rel_names rel) p

        val clauses' = map (mk_depth_limited rel_names) clauses

        fun nat_term_of n = funpow n (fn t => AppF ("suc", [t])) (Cons "zero")

        fun mk_entry_clause rel_name =

          let

            val nargs = length (snd (fst

              (the (find_first (fn ((rel, _), _) => rel = rel_name) clauses))))

            val vars = map (fn i => Var ("x" ^ string_of_int i)) (1 upto nargs)        

          in

            (("limited_" ^ rel_name, vars), Rel ("lim_" ^ rel_name, nat_term_of limit :: vars))

          end

      in (p @ (map mk_entry_clause rel_names) @ clauses', constant_table) end

  in

    fold add limited_predicates

  end

(* replace predicates in clauses *)

(* replace (A, B, C) p = replace A by B in clauses of C *)

fun replace ((from, to), location) p =

  let

    fun replace_prem (Conj prems) = Conj (map replace_prem prems)

      | replace_prem (r as Rel (rel, ts)) =

          if rel = from then Rel (to, ts) else r

      | replace_prem r = r

  in

    map (fn ((rel, args), prem) => ((rel, args), (if rel = location then replace_prem else I) prem)) p

  end

(* reorder manually : reorder premises of ith clause of predicate p by a permutation perm *)

fun reorder_manually reorder p =

  let

    fun reorder' (clause as ((rel, args), prem)) seen =

      let

        val seen' = AList.map_default (op =) (rel, 0) (fn x => x + 1) seen

        val i = the (AList.lookup (op =) seen' rel)

        val perm = AList.lookup (op =) reorder (rel, i)

        val prem' = (case perm of 

          SOME p => (case prem of Conj prems => Conj (map (nth prems) p) | _ => prem)

        | NONE => prem)

      in (((rel, args), prem'), seen') end

  in

    fst (fold_map reorder' p [])

  end

(* rename variables to prolog-friendly names *)

fun rename_vars_term renaming = map_vars (fn v => the (AList.lookup (op =) renaming v))

fun rename_vars_prem renaming = map_term_prem (rename_vars_term renaming)

fun is_prolog_conform v =

  forall (fn s => Symbol.is_ascii_letter s orelse Symbol.is_ascii_digit s) (Symbol.explode v)

fun mk_renaming v renaming =

  (v, mk_conform first_upper "Var" (map snd renaming) v) :: renaming

fun rename_vars_clause ((rel, args), prem) =

  let

    val vars = fold_prem_terms add_vars prem (fold add_vars args [])

    val renaming = fold mk_renaming vars []

  in ((rel, map (rename_vars_term renaming) args), rename_vars_prem renaming prem) end

val rename_vars_program = map rename_vars_clause

(* code printer *)

fun write_arith_op Plus = "+"

  | write_arith_op Minus = "-"

fun write_term (Var v) = v

  | write_term (Cons c) = c

  | write_term (AppF (f, args)) = f ^ "(" ^ space_implode ", " (map write_term args) ^ ")"

  | write_term (ArithOp (oper, [a1, a2])) = write_term a1 ^ " " ^ write_arith_op oper ^ " " ^ write_term a2

  | write_term (Number n) = string_of_int n

fun write_rel (pred, args) =

  pred ^ "(" ^ space_implode ", " (map write_term args) ^ ")" 

fun write_prem (Conj prems) = space_implode ", " (map write_prem prems)

  | write_prem (Rel p) = write_rel p  

  | write_prem (NotRel p) = "not(" ^ write_rel p ^ ")"

  | write_prem (Eq (l, r)) = write_term l ^ " = " ^ write_term r

  | write_prem (NotEq (l, r)) = write_term l ^ " \\= " ^ write_term r

  | write_prem (ArithEq (l, r)) = write_term l ^ " is " ^ write_term r

  | write_prem (NotArithEq (l, r)) = write_term l ^ " =\\= " ^ write_term r

  | write_prem _ = raise Fail "Not a valid prolog premise"

fun write_clause (head, prem) =

  write_rel head ^ (if prem = Conj [] then "." else " :- " ^ write_prem prem ^ ".")

fun write_program p =

  cat_lines (map write_clause p) 

(* query templates *)

(** query and prelude for swi-prolog **)

fun swi_prolog_query_first rel vnames =

  "eval :- once("  ^ rel ^ "(" ^ space_implode ", " vnames ^ ")),\n" ^

  "writef('" ^ space_implode ";" (map (fn v => v ^ " = %w") vnames) ^

  "\\n', [" ^ space_implode ", " vnames ^ "]).\n"

fun swi_prolog_query_firstn n rel vnames =

  "eval :- findnsols(" ^ string_of_int n ^ ", (" ^ space_implode ", " vnames ^ "), " ^

    rel ^ "(" ^ space_implode ", " vnames ^ "), Sols), writelist(Sols).\n" ^

    "writelist([]).\n" ^

    "writelist([(" ^ space_implode ", " vnames ^ ")|T]) :- " ^

    "writef('" ^ space_implode ";" (map (fn v => v ^ " = %w") vnames) ^

    "\\n', [" ^ space_implode ", " vnames ^ "]), writelist(T).\n"

val swi_prolog_prelude =

  "#!/usr/bin/swipl -q -t main -f\n\n" ^

  ":- use_module(library('dialect/ciao/aggregates')).\n" ^

  ":- style_check(-singleton).\n" ^

  ":- style_check(-discontiguous).\n" ^ 	

  ":- style_check(-atom).\n\n" ^

  "main :- catch(eval, E, (print_message(error, E), fail)), halt.\n" ^

  "main :- halt(1).\n"

(** query and prelude for yap **)

fun yap_query_first rel vnames =

  "eval :- once(" ^ rel ^ "(" ^ space_implode ", " vnames ^ ")),\n" ^

  "format('" ^ space_implode ";" (map (fn v => v ^ " = ~w") vnames) ^

  "\\n', [" ^ space_implode ", " vnames ^ "]).\n"

val yap_prelude =

  "#!/usr/bin/yap -L\n\n" ^

  ":- initialization(eval).\n"

(* system-dependent query, prelude and invocation *)

fun query system nsols = 

  case system of

    SWI_PROLOG =>

      (case nsols of NONE => swi_prolog_query_first | SOME n => swi_prolog_query_firstn n)

  | YAP =>

      case nsols of NONE => yap_query_first | SOME n =>

        error "No support for querying multiple solutions in the prolog system yap"

fun prelude system =

  case system of SWI_PROLOG => swi_prolog_prelude | YAP => yap_prelude

fun invoke system file_name =

  let

    val env_var =

      (case system of SWI_PROLOG => "EXEC_SWIPL"| YAP => "EXEC_YAP")

    val prog = getenv env_var

    val cmd =

      case system of SWI_PROLOG => prog ^ " -f " | YAP => prog ^ " -L "

  in

    if prog = "" then

      (warning (env_var ^ " not set; could not execute code for " ^ string_of_system system); "")

    else fst (bash_output (cmd ^ file_name))

  end

(* parsing prolog solution *)

val scan_number =

  Scan.many1 Symbol.is_ascii_digit

val scan_atom =

  Scan.many1 (fn s => Symbol.is_ascii_lower s orelse Symbol.is_ascii_digit s orelse Symbol.is_ascii_quasi s)

val scan_var =

  Scan.many1

    (fn s => Symbol.is_ascii_upper s orelse Symbol.is_ascii_digit s orelse Symbol.is_ascii_quasi s)

val scan_ident =

  Scan.repeat (Scan.one

    (fn s => Symbol.is_ascii_letter s orelse Symbol.is_ascii_digit s orelse Symbol.is_ascii_quasi s))

fun dest_Char (Symbol.Char s) = s

val string_of = concat o map (dest_Char o Symbol.decode)

val is_atom_ident = forall Symbol.is_ascii_lower

val is_var_ident =

  forall (fn s => Symbol.is_ascii_upper s orelse Symbol.is_ascii_digit s orelse Symbol.is_ascii_quasi s)

fun int_of_symbol_list xs = fold (fn x => fn s => s * 10 + (ord x - ord "0")) xs 0

fun scan_terms xs = (((scan_term --| $$ ",") ::: scan_terms)

  || (scan_term >> single)) xs

and scan_term xs =

  ((scan_number >> (Number o int_of_symbol_list))

  || (scan_var >> (Var o string_of))

  || ((scan_atom -- ($$ "(" |-- scan_terms --| $$ ")"))

    >> (fn (f, ts) => AppF (string_of f, ts)))

  || (scan_atom >> (Cons o string_of))) xs

val parse_term = fst o Scan.finite Symbol.stopper

    (Scan.error (!! (fn _ => raise Fail "parsing prolog output failed")) scan_term)

  o explode

fun parse_solutions sol =

  let

    fun dest_eq s = case space_explode "=" s of

        (l :: r :: []) => parse_term (unprefix " " r)

      | _ => raise Fail "unexpected equation in prolog output"

    fun parse_solution s = map dest_eq (space_explode ";" s)

    val sols = case space_explode "\n" sol of [] => [] | s => fst (split_last s)  

  in

    map parse_solution sols

  end 

(* calling external interpreter and getting results *)

fun run (timeout, system) p query_rel vnames nsols =

  let

    val p' = rename_vars_program p

    val _ = tracing "Renaming variable names..."

    val renaming = fold mk_renaming vnames [] 

    val vnames' = map (fn v => the (AList.lookup (op =) renaming v)) vnames

    val prog = prelude system ^ query system nsols query_rel vnames' ^ write_program p'

    val _ = tracing ("Generated prolog program:\n" ^ prog)

    val solution = TimeLimit.timeLimit timeout (fn prog => Cache_IO.with_tmp_file "prolog_file" (fn prolog_file =>

      (File.write prolog_file prog; invoke system (Path.implode prolog_file)))) prog

    val _ = tracing ("Prolog returned solution(s):\n" ^ solution)

    val tss = parse_solutions solution

  in

    tss

  end

(* restoring types in terms *)

fun restore_term ctxt constant_table (Var s, T) = Free (s, T)

  | restore_term ctxt constant_table (Number n, @{typ "int"}) = HOLogic.mk_number @{typ "int"} n

  | restore_term ctxt constant_table (Number n, _) = raise (Fail "unexpected type for number") 

  | restore_term ctxt constant_table (Cons s, T) = Const (restore_const constant_table s, T)

  | restore_term ctxt constant_table (AppF (f, args), T) =

    let

      val thy = ProofContext.theory_of ctxt

      val c = restore_const constant_table f

      val cT = Sign.the_const_type thy c

      val (argsT, resT) = strip_type cT

      val subst = Sign.typ_match thy (resT, T) Vartab.empty

      val argsT' = map (Envir.subst_type subst) argsT

    in

      list_comb (Const (c, Envir.subst_type subst cT),

        map (restore_term ctxt constant_table) (args ~~ argsT'))

    end

(* values command *)

val preprocess_options = Predicate_Compile_Aux.Options {

  expected_modes = NONE,

  proposed_modes = [],

  proposed_names = [],

  show_steps = false,

  show_intermediate_results = false,

  show_proof_trace = false,

  show_modes = false,

  show_mode_inference = false,

  show_compilation = false,

  show_caught_failures = false,

  show_invalid_clauses = false,

  skip_proof = true,

  no_topmost_reordering = false,

  function_flattening = true,

  specialise = false,

  fail_safe_function_flattening = false,

  no_higher_order_predicate = [],

  inductify = false,

  detect_switches = true,

  compilation = Predicate_Compile_Aux.Pred

}

fun values ctxt soln t_compr =

  let

    val options = code_options_of (ProofContext.theory_of ctxt)

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

      | _ => error ("Not a set comprehension: " ^ Syntax.string_of_term ctxt 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 = rev (map2 (curry Free) output_names Ts)

    val body = subst_bounds (output_frees, body)

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

      case strip_comb body of

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

      | (head, _) => error ("Not a constant: " ^ Syntax.string_of_term ctxt head)

    val vnames =

      case try (map (fst o dest_Free)) all_args of

        SOME vs => vs

      | NONE => error ("Not only free variables in " ^ commas (map (Syntax.string_of_term ctxt) all_args))

    val _ = tracing "Preprocessing specification..."

    val T = Sign.the_const_type (ProofContext.theory_of ctxt) name

    val t = Const (name, T)

    val thy' =

      Theory.copy (ProofContext.theory_of ctxt)

      |> Predicate_Compile.preprocess preprocess_options t

    val ctxt' = ProofContext.init_global thy'

    val _ = tracing "Generating prolog program..."

    val (p, constant_table) = generate (NONE, #ensure_groundness options) ctxt' name (* FIXME *)

      |> (if #ensure_groundness options then

          add_ground_predicates ctxt' (#limited_types options)

        else I)

      |> add_limited_predicates (#limited_predicates options)

      |> apfst (fold replace (#replacing options))

      |> apfst (reorder_manually (#manual_reorder options))

    val _ = tracing "Running prolog program..."

    val system_config = System_Config.get (Context.Proof ctxt)

    val tss = run (#timeout system_config, #prolog_system system_config)

      p (translate_const constant_table name) (map first_upper vnames) soln

    val _ = tracing "Restoring terms..."

    val empty = Const("Orderings.bot_class.bot", fastype_of t_compr)

    fun mk_insert x S =

      Const (@{const_name "Set.insert"}, fastype_of x --> fastype_of S --> fastype_of S) $ x $ S 

    fun mk_set_compr in_insert [] xs =

       rev ((Free ("...", fastype_of t_compr)) ::

        (if null in_insert then xs else (fold mk_insert in_insert empty) :: xs))

      | mk_set_compr in_insert (t :: ts) xs =

        let

          val frees = Term.add_frees t []

        in

          if null frees then

            mk_set_compr (t :: in_insert) ts xs

          else

            let

              val uu as (uuN, uuT) = singleton (Variable.variant_frees ctxt' [t]) ("uu", fastype_of t)

              val set_compr =

                HOLogic.mk_Collect (uuN, uuT, fold (fn (s, T) => fn t => HOLogic.mk_exists (s, T, t))

                  frees (HOLogic.mk_conj (HOLogic.mk_eq (Free uu, t), @{term "True"})))

            in

              mk_set_compr [] ts

                (set_compr :: (if null in_insert then xs else (fold mk_insert in_insert empty) :: xs))  

            end

        end

  in

      foldl1 (HOLogic.mk_binop @{const_name sup}) (mk_set_compr []

        (map (fn ts => HOLogic.mk_tuple (map (restore_term ctxt' constant_table) (ts ~~ Ts))) tss) [])

  end

fun values_cmd print_modes soln raw_t state =

  let

    val ctxt = Toplevel.context_of state

    val t = Syntax.read_term ctxt raw_t

    val t' = values ctxt soln t

    val ty' = Term.type_of t'

    val ctxt' = Variable.auto_fixes t' ctxt

    val _ = tracing "Printing terms..."

    val p = Print_Mode.with_modes print_modes (fn () =>

      Pretty.block [Pretty.quote (Syntax.pretty_term ctxt' t'), Pretty.fbrk,

        Pretty.str "::", Pretty.brk 1, Pretty.quote (Syntax.pretty_typ ctxt' ty')]) ();

  in Pretty.writeln p end;

(* renewing the values command for Prolog queries *)

val opt_print_modes =

  Scan.optional (Parse.$$$ "(" |-- Parse.!!! (Scan.repeat1 Parse.xname --| Parse.$$$ ")")) [];

val _ = Outer_Syntax.improper_command "values" "enumerate and print comprehensions" Keyword.diag

  (opt_print_modes -- Scan.optional (Parse.nat >> SOME) NONE -- Parse.term

   >> (fn ((print_modes, soln), t) => Toplevel.keep

        (values_cmd print_modes soln t))); (*FIXME does not preserve the previous functionality*)

(* quickcheck generator *)

(* FIXME: large copy of Predicate_Compile_Quickcheck - refactor out commons *)

fun strip_imp_prems (Const(@{const_name HOL.implies}, _) $ A $ B) = A :: strip_imp_prems B

  | strip_imp_prems _ = [];

fun strip_imp_concl (Const(@{const_name HOL.implies}, _) $ A $ B) = strip_imp_concl B

  | strip_imp_concl A = A : term;

fun strip_horn A = (strip_imp_prems A, strip_imp_concl A);

fun quickcheck ctxt t size =

  let

    val options = code_options_of (ProofContext.theory_of ctxt)

    val thy = Theory.copy (ProofContext.theory_of ctxt)

    val (vs, t') = strip_abs t

    val vs' = Variable.variant_frees ctxt [] vs

    val Ts = map snd vs'

    val t'' = subst_bounds (map Free (rev vs'), t')

    val (prems, concl) = strip_horn t''

    val constname = "quickcheck"

    val full_constname = Sign.full_bname thy constname

    val constT = Ts ---> @{typ bool}

    val thy1 = Sign.add_consts_i [(Binding.name constname, constT, NoSyn)] thy

    val const = Const (full_constname, constT)

    val t = Logic.list_implies

      (map HOLogic.mk_Trueprop (prems @ [HOLogic.mk_not concl]),

       HOLogic.mk_Trueprop (list_comb (Const (full_constname, constT), map Free vs')))

    val tac = fn _ => Skip_Proof.cheat_tac thy1

    val intro = Goal.prove (ProofContext.init_global thy1) (map fst vs') [] t tac

    val thy2 = Context.theory_map (Predicate_Compile_Alternative_Defs.add_thm intro) thy1

    val thy3 = Predicate_Compile.preprocess preprocess_options const thy2

    val ctxt' = ProofContext.init_global thy3

    val _ = tracing "Generating prolog program..."