(* 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}
val options : code_options ref
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 : code_options -> Proof.context -> string -> (logic_program * constant_table)
val write_program : logic_program -> string
val run : logic_program -> string -> string list -> int option -> prol_term list list
val trace : bool Unsynchronized.ref
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}
val options = Unsynchronized.ref {ensure_groundness = false};
(* 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 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)
type clause = ((string * prol_term list) * prem);
type logic_program = clause list;
(* translation from introduction rules to internal representation *)
(** constant table **)
type constant_table = (string * string) list
(* assuming no clashing *)
fun mk_constant_table consts =
AList.make (first_lower o Long_Name.base_name) consts
fun declare_consts consts constant_table =
fold (fn c => AList.update (op =) (c, first_lower (Long_Name.base_name c))) consts constant_table
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 translate_term ctxt constant_table t =
case try HOLogic.dest_number t of
SOME (@{typ "int"}, n) => Number 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 "op ="}, _), [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 options ctxt constant_table t =
case try HOLogic.dest_not t of
SOME t =>
if #ensure_groundness options 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 options 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 options 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
val preprocess_options = Predicate_Compile_Aux.Options {
expected_modes = NONE,
proposed_modes = NONE,
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,
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 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 generate options 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 constant_table = mk_constant_table (flat scc)
in
apfst flat (fold_map (translate_intros options ctxt gr) (flat scc) constant_table)
end
(* add implementation for ground predicates *)
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"
(* 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 mk_ground_impl ctxt (T as Type (Tcon, Targs)) (seen, constant_table) =
if member (op =) seen T then ([], (seen, constant_table))
else
let
val rel_name = mk_relname T
fun mk_impl (Const (constr_name, T)) (seen, constant_table) =
let
val constant_table' = declare_consts [constr_name] constant_table
val (rec_clauses, (seen', constant_table'')) =
fold_map (mk_ground_impl ctxt) (binder_types T) (seen, constant_table')
val vars = map (fn i => Var ("x" ^ string_of_int i)) (1 upto (length (binder_types T)))
fun mk_prem v T = Rel (mk_relname T, [v])
val clause =
((rel_name, [maybe_AppF (translate_const constant_table'' constr_name, vars)]),
Conj (map2 mk_prem vars (binder_types T)))
in
(clause :: flat rec_clauses, (seen', constant_table''))
end
val constrs = inst_constrs_of (ProofContext.theory_of ctxt) T
in apfst flat (fold_map mk_impl constrs (T :: seen, 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 (p, constant_table) =
let
val ground_typs = fold (add_ground_typ o snd) p []
val (grs, (_, constant_table')) = fold_map (mk_ground_impl ctxt) ground_typs ([], constant_table)
val p' = map (apsnd replace_ground) p
in
((flat grs) @ p', constant_table')
end
(* code printer *)
fun write_arith_op Plus = "+"
| write_arith_op Minus = "-"
fun write_term (Var v) = first_upper 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
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 **)
fun 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 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 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"
(* 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)
in
map parse_solution (fst (split_last (space_explode "\n" sol)))
end
(* calling external interpreter and getting results *)
fun run p query_rel vnames nsols =
let
val cmd = Path.named_root
val query = case nsols of NONE => query_first | SOME n => query_firstn n
val prog = prelude ^ query query_rel vnames ^ write_program p
val _ = tracing ("Generated prolog program:\n" ^ prog)
val prolog_file = File.tmp_path (Path.basic "prolog_file")
val _ = File.write prolog_file prog
val (solution, _) = bash_output ("/usr/local/bin/swipl -f " ^ File.shell_path prolog_file)
val _ = tracing ("Prolog returned solution(s):\n" ^ solution)
val tss = parse_solutions solution
in
tss
end
(* values command *)
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
fun values ctxt soln t_compr =
let
val options = !options
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 ctxt' = ProofContext.theory (Context.copy_thy) ctxt
val thy' = Predicate_Compile.preprocess preprocess_options t (ProofContext.theory_of ctxt')
val ctxt'' = ProofContext.init_global thy'
val _ = tracing "Generating prolog program..."
val (p, constant_table) = generate options ctxt'' name
|> (if #ensure_groundness options then add_ground_predicates ctxt'' else I)
val _ = tracing "Running prolog program..."
val tss = run 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*)
end;