(* 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
type code_options =
{ensure_groundness : bool,
limit_globally : int option,
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
val prolog_system: string Config.T
val prolog_timeout: real Config.T
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 : Proof.context -> logic_program -> (string * prol_term list) ->
string list -> int option -> prol_term list list
val active : bool Config.T
val test_goals :
Proof.context -> bool -> (string * typ) list -> (term * term list) list ->
Quickcheck.result list
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,
limit_globally : int option,
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, limit_globally, limited_types, limited_predicates,
replacing, manual_reorder} =
{ensure_groundness = true, limit_globally = limit_globally, limited_types = limited_types,
limited_predicates = limited_predicates, replacing = replacing,
manual_reorder = manual_reorder}
fun map_limit_predicates f {ensure_groundness, limit_globally, limited_types, limited_predicates,
replacing, manual_reorder} =
{ensure_groundness = ensure_groundness, limit_globally = limit_globally,
limited_types = limited_types, limited_predicates = f limited_predicates,
replacing = replacing, manual_reorder = manual_reorder}
fun merge_global_limit (NONE, NONE) = NONE
| merge_global_limit (NONE, SOME n) = SOME n
| merge_global_limit (SOME n, NONE) = SOME n
| merge_global_limit (SOME n, SOME m) = SOME (Int.max (n, m)) (* FIXME odd merge *)
structure Options = Theory_Data
(
type T = code_options
val empty = {ensure_groundness = false, limit_globally = NONE,
limited_types = [], limited_predicates = [], replacing = [], manual_reorder = []}
val extend = I;
fun merge
({ensure_groundness = ensure_groundness1, limit_globally = limit_globally1,
limited_types = limited_types1, limited_predicates = limited_predicates1,
replacing = replacing1, manual_reorder = manual_reorder1},
{ensure_groundness = ensure_groundness2, limit_globally = limit_globally2,
limited_types = limited_types2, limited_predicates = limited_predicates2,
replacing = replacing2, manual_reorder = manual_reorder2}) =
{ensure_groundness = ensure_groundness1 orelse ensure_groundness2 (* FIXME odd merge *),
limit_globally = merge_global_limit (limit_globally1, limit_globally2),
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"
val prolog_system = Attrib.setup_config_string @{binding prolog_system} (K "swiprolog")
fun get_prolog_system ctxt =
(case Config.get ctxt prolog_system of
"swiprolog" => SWI_PROLOG
| "yap" => YAP
| name => error ("Bad prolog system: " ^ quote name ^ " (\"swiprolog\" or \"yap\" expected)"))
val prolog_timeout = Attrib.setup_config_real @{binding prolog_timeout} (K 10.0)
fun get_prolog_timeout ctxt = seconds (Config.get ctxt prolog_timeout)
(* 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 singleton (Name.variant_list 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 (Name.enforce_case false) "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 (@{const_name Pure.imp}, _) $ _ $ _ =>
Conv.combination_conv (Conv.arg_conv cv) (imp_prems_conv cv) ct
| _ => Conv.all_conv ct)
fun preprocess_intro thy rule =
Conv.fconv_rule
(imp_prems_conv
(HOLogic.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 (Proof_Context.theory_of ctxt)) (Graph.get_node gr const)
val (intros', ctxt') = Variable.import_terms true (map Thm.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
in
(map translate_intro intros', constant_table')
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_generators = 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 (Core_Data.intros_of ctxt) prednames)
val ((moded_clauses, random'), _) =
Mode_Inference.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 (Name.enforce_case false) "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.restrict (member (op =) (Graph.all_succs gr keys)) gr)
val gr = Core_Data.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.restrict
(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)) =
Name.enforce_case false (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
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 = Function_Lib.inst_constrs_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 nat_term_of n = funpow n (fn t => AppF ("suc", [t])) (Cons "zero")
fun add_limited_predicates limited_predicates (p, constant_table) =
let
fun add (rel_names, limit) p =
let
val clauses = filter (fn ((rel, _), _) => member (op =) rel_names rel) p
val clauses' = map (mk_depth_limited rel_names) clauses
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') end
in
(fold add limited_predicates p, constant_table)
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' ((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 mk_renaming v renaming =
(v, mk_conform (Name.enforce_case true) "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
(* limit computation globally by some threshold *)
fun limit_globally limit const_name (p, constant_table) =
let
val rel_names = fold (fn ((r, _), _) => insert (op =) r) p []
val p' = map (mk_depth_limited rel_names) p
val rel_name = translate_const constant_table const_name
val nargs = length (snd (fst
(the (find_first (fn ((rel, _), _) => rel = rel_name) p))))
val vars = map (fn i => Var ("x" ^ string_of_int i)) (1 upto nargs)
val entry_clause = ((rel_name, vars), Rel ("lim_" ^ rel_name, nat_term_of limit :: vars))
val p'' = filter_out (fn ((rel, _), _) => rel = rel_name) p
in
(entry_clause :: p' @ p'', constant_table)
end
(* post processing of generated prolog program *)
fun post_process ctxt (options: code_options) const_name (p, constant_table) =
(p, constant_table)
|> (case #limit_globally options of
SOME limit => limit_globally limit const_name
| NONE => I)
|> (if #ensure_groundness options then
add_ground_predicates ctxt (#limited_types options)
else I)
|> tap (fn _ => tracing "Adding limited predicates...")
|> add_limited_predicates (#limited_predicates options)
|> tap (fn _ => tracing "Replacing predicates...")
|> apfst (fold replace (#replacing options))
|> apfst (reorder_manually (#manual_reorder options))
|> apfst (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, args) vnames =
"eval :- once(" ^ rel ^ "(" ^ space_implode ", " (map write_term args) ^ ")),\n" ^
"writef('" ^ space_implode ";" (map (fn v => v ^ " = %w") vnames) ^
"\\n', [" ^ space_implode ", " vnames ^ "]).\n"
fun swi_prolog_query_firstn n (rel, args) vnames =
"eval :- findnsols(" ^ string_of_int n ^ ", (" ^ space_implode ", " vnames ^ "), " ^
rel ^ "(" ^ space_implode ", " (map write_term args) ^ "), Sols), writelist(Sols).\n" ^
"writelist([]).\n" ^
"writelist([(" ^ space_implode ", " vnames ^ ")|SolutionTail]) :- " ^
"writef('" ^ space_implode ";" (map (fn v => v ^ " = %w") vnames) ^
"\\n', [" ^ space_implode ", " vnames ^ "]), writelist(SolutionTail).\n"
val swi_prolog_prelude =
":- 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, args) vnames =
"eval :- once(" ^ rel ^ "(" ^ space_implode ", " (map write_term args) ^ ")),\n" ^
"format('" ^ space_implode ";" (map (fn v => v ^ " = ~w") vnames) ^
"\\n', [" ^ space_implode ", " vnames ^ "]).\n"
val yap_prelude =
":- 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 =
let
val (env_var, cmd) =
(case system of
SWI_PROLOG => ("ISABELLE_SWIPL", "\"$ISABELLE_SWIPL\" -q -t main -f ")
| YAP => ("ISABELLE_YAP", "\"$ISABELLE_YAP\" -L "))
in
if getenv env_var = "" then
(warning (env_var ^ " not set; could not execute code for " ^ string_of_system system); "")
else
(case Isabelle_System.bash_output (cmd ^ File.shell_path file) of
(out, 0) => out
| (_, rc) =>
error ("Error caused by prolog system " ^ env_var ^
": return code " ^ string_of_int rc))
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)
fun dest_Char (Symbol.Char s) = s
val string_of = implode o map (dest_Char o Symbol.decode)
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 raw_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 ctxt p (query_rel, args) vnames nsols =
let
val timeout = get_prolog_timeout ctxt
val system = get_prolog_system ctxt
val renaming = fold mk_renaming (fold add_vars args vnames) []
val vnames' = map (fn v => the (AList.lookup (op =) renaming v)) vnames
val args' = map (rename_vars_term renaming) args
val prog = prelude system ^ query system nsols (query_rel, args') vnames' ^ write_program p
val _ = tracing ("Generated prolog program:\n" ^ prog)
val solution = TimeLimit.timeLimit timeout (fn prog =>
Isabelle_System.with_tmp_file "prolog_file" "" (fn prolog_file =>
(File.write prolog_file prog; invoke system 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 = Proof_Context.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
(* restore numerals in natural numbers *)
fun restore_nat_numerals t =
if fastype_of t = @{typ nat} andalso is_some (try HOLogic.dest_nat t) then
HOLogic.mk_number @{typ nat} (HOLogic.dest_nat t)
else
(case t of
t1 $ t2 => restore_nat_numerals t1 $ restore_nat_numerals t2
| t => t)
(* 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,
smart_depth_limiting = true,
compilation = Predicate_Compile_Aux.Pred
}
fun values ctxt soln t_compr =
let
val options = code_options_of (Proof_Context.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 _ = tracing "Preprocessing specification..."
val T = Sign.the_const_type (Proof_Context.theory_of ctxt) name
val t = Const (name, T)
val thy' =
Proof_Context.theory_of ctxt
|> Predicate_Compile.preprocess preprocess_options t
val ctxt' = Proof_Context.init_global thy'
val _ = tracing "Generating prolog program..."
val (p, constant_table) = generate (NONE, #ensure_groundness options) ctxt' name (* FIXME *)
|> post_process ctxt' options name
val constant_table' = declare_consts (fold Term.add_const_names all_args []) constant_table
val args' = map (translate_term ctxt constant_table') all_args
val _ = tracing "Running prolog program..."
val tss = run ctxt p (translate_const constant_table' name, args') output_names soln
val _ = tracing "Restoring terms..."
val empty = Const(@{const_name 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 ("dots", fastype_of t_compr)) :: (* FIXME proper name!? *)
(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_nat_numerals o 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..."
in
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')]) ()
end |> Pretty.writeln
(* values command for Prolog queries *)
val opt_print_modes =
Scan.optional (@{keyword "("} |-- Parse.!!! (Scan.repeat1 Parse.xname --| @{keyword ")"})) []
val _ =
Outer_Syntax.command @{command_keyword values_prolog}
"enumerate and print comprehensions"
(opt_print_modes -- Scan.optional (Parse.nat >> SOME) NONE -- Parse.term
>> (fn ((print_modes, soln), t) => Toplevel.keep (values_cmd print_modes soln t)))
(* quickcheck generator *)
(* FIXME: a small clone of Predicate_Compile_Quickcheck - maybe refactor out commons *)
val active = Attrib.setup_config_bool @{binding quickcheck_prolog_active} (K true)
fun test_term ctxt (t, eval_terms) =
let
val t' = fold_rev absfree (Term.add_frees t []) t
val options = code_options_of (Proof_Context.theory_of ctxt)
val thy = Proof_Context.theory_of ctxt
val ((((full_constname, constT), vs'), intro), thy1) =
Predicate_Compile_Aux.define_quickcheck_predicate t' thy
val thy2 =
Context.theory_map (Named_Theorems.add_thm @{named_theorems code_pred_def} intro) thy1
val thy3 = Predicate_Compile.preprocess preprocess_options (Const (full_constname, constT)) thy2
val ctxt' = Proof_Context.init_global thy3
val _ = tracing "Generating prolog program..."
val (p, constant_table) = generate (NONE, true) ctxt' full_constname
|> post_process ctxt' (set_ensure_groundness options) full_constname
val _ = tracing "Running prolog program..."
val tss =
run ctxt p (translate_const constant_table full_constname, map (Var o fst) vs')
(map fst vs') (SOME 1)
val _ = tracing "Restoring terms..."
val counterexample =
(case tss of
[ts] => SOME (map (restore_term ctxt' constant_table) (ts ~~ map snd vs'))
| _ => NONE)
in
Quickcheck.Result
{counterexample =
Option.map (pair true o curry (op ~~) (Term.add_free_names t [])) counterexample,
evaluation_terms = Option.map (K []) counterexample,
timings = [],
reports = []}
end
fun test_goals ctxt _ insts goals =
let
val correct_inst_goals = Quickcheck_Common.instantiate_goals ctxt insts goals
in
Quickcheck_Common.collect_results (test_term ctxt) (maps (map snd) correct_inst_goals) []
end
end