(* Title: HOL/Tools/Metis/metis_generate.ML
Author: Jia Meng, Cambridge University Computer Laboratory and NICTA
Author: Kong W. Susanto, Cambridge University Computer Laboratory
Author: Lawrence C. Paulson, Cambridge University Computer Laboratory
Author: Jasmin Blanchette, TU Muenchen
Translation of HOL to FOL for Metis.
*)
signature METIS_GENERATE =
sig
type type_enc = ATP_Problem_Generate.type_enc
datatype isa_thm =
Isa_Reflexive_or_Trivial |
Isa_Lambda_Lifted |
Isa_Raw of thm
val metis_equal : string
val metis_predicator : string
val metis_app_op : string
val metis_systematic_type_tag : string
val metis_ad_hoc_type_tag : string
val metis_generated_var_prefix : string
val trace : bool Config.T
val verbose : bool Config.T
val trace_msg : Proof.context -> (unit -> string) -> unit
val verbose_warning : Proof.context -> string -> unit
val metis_name_table : ((string * int) * ((type_enc -> string) * bool)) list
val reveal_old_skolem_terms : (string * term) list -> term -> term
val reveal_lam_lifted : (string * term) list -> term -> term
val prepare_metis_problem :
Proof.context -> type_enc -> string -> thm list -> thm list
-> int Symtab.table * (Metis_Thm.thm * isa_thm) list
* (unit -> (string * int) list)
* ((string * term) list * (string * term) list)
end
structure Metis_Generate : METIS_GENERATE =
struct
open ATP_Problem
open ATP_Problem_Generate
val metis_equal = "="
val metis_predicator = "{}"
val metis_app_op = Metis_Name.toString Metis_Term.appName
val metis_systematic_type_tag =
Metis_Name.toString Metis_Term.hasTypeFunctionName
val metis_ad_hoc_type_tag = "**"
val metis_generated_var_prefix = "_"
val trace = Attrib.setup_config_bool @{binding metis_trace} (K false)
val verbose = Attrib.setup_config_bool @{binding metis_verbose} (K true)
fun trace_msg ctxt msg = if Config.get ctxt trace then tracing (msg ()) else ()
fun verbose_warning ctxt msg =
if Config.get ctxt verbose then warning ("Metis: " ^ msg) else ()
val metis_name_table =
[((tptp_equal, 2), (K metis_equal, false)),
((tptp_old_equal, 2), (K metis_equal, false)),
((prefixed_predicator_name, 1), (K metis_predicator, false)),
((prefixed_app_op_name, 2), (K metis_app_op, false)),
((prefixed_type_tag_name, 2),
(fn type_enc =>
if level_of_type_enc type_enc = All_Types then metis_systematic_type_tag
else metis_ad_hoc_type_tag, true))]
fun old_skolem_const_name i j num_T_args =
old_skolem_const_prefix ^ Long_Name.separator ^
(space_implode Long_Name.separator (map string_of_int [i, j, num_T_args]))
fun conceal_old_skolem_terms i old_skolems t =
if exists_Const (curry (op =) @{const_name Meson.skolem} o fst) t then
let
fun aux old_skolems
(t as (Const (@{const_name Meson.skolem}, Type (_, [_, T])) $ _)) =
let
val (old_skolems, s) =
if i = ~1 then
(old_skolems, @{const_name undefined})
else case AList.find (op aconv) old_skolems t of
s :: _ => (old_skolems, s)
| [] =>
let
val s = old_skolem_const_name i (length old_skolems)
(length (Term.add_tvarsT T []))
in ((s, t) :: old_skolems, s) end
in (old_skolems, Const (s, T)) end
| aux old_skolems (t1 $ t2) =
let
val (old_skolems, t1) = aux old_skolems t1
val (old_skolems, t2) = aux old_skolems t2
in (old_skolems, t1 $ t2) end
| aux old_skolems (Abs (s, T, t')) =
let val (old_skolems, t') = aux old_skolems t' in
(old_skolems, Abs (s, T, t'))
end
| aux old_skolems t = (old_skolems, t)
in aux old_skolems t end
else
(old_skolems, t)
fun reveal_old_skolem_terms old_skolems =
map_aterms (fn t as Const (s, _) =>
if String.isPrefix old_skolem_const_prefix s then
AList.lookup (op =) old_skolems s |> the
|> map_types (map_type_tvar (K dummyT))
else
t
| t => t)
fun reveal_lam_lifted lambdas =
map_aterms (fn t as Const (s, _) =>
if String.isPrefix lam_lifted_prefix s then
case AList.lookup (op =) lambdas s of
SOME t =>
Const (@{const_name Metis.lambda}, dummyT)
$ map_types (map_type_tvar (K dummyT))
(reveal_lam_lifted lambdas t)
| NONE => t
else
t
| t => t)
(* ------------------------------------------------------------------------- *)
(* Logic maps manage the interface between HOL and first-order logic. *)
(* ------------------------------------------------------------------------- *)
datatype isa_thm =
Isa_Reflexive_or_Trivial |
Isa_Lambda_Lifted |
Isa_Raw of thm
val proxy_defs = map (fst o snd o snd) proxy_table
val prepare_helper =
Meson.make_meta_clause #> rewrite_rule (map safe_mk_meta_eq proxy_defs)
fun metis_term_from_atp type_enc (ATerm (s, tms)) =
if is_tptp_variable s then
Metis_Term.Var (Metis_Name.fromString s)
else
(case AList.lookup (op =) metis_name_table (s, length tms) of
SOME (f, swap) => (f type_enc, swap)
| NONE => (s, false))
|> (fn (s, swap) =>
Metis_Term.Fn (Metis_Name.fromString s,
tms |> map (metis_term_from_atp type_enc)
|> swap ? rev))
fun metis_atom_from_atp type_enc (AAtom tm) =
(case metis_term_from_atp type_enc tm of
Metis_Term.Fn x => x
| _ => raise Fail "non CNF -- expected function")
| metis_atom_from_atp _ _ = raise Fail "not CNF -- expected atom"
fun metis_literal_from_atp type_enc (AConn (ANot, [phi])) =
(false, metis_atom_from_atp type_enc phi)
| metis_literal_from_atp type_enc phi =
(true, metis_atom_from_atp type_enc phi)
fun metis_literals_from_atp type_enc (AConn (AOr, phis)) =
maps (metis_literals_from_atp type_enc) phis
| metis_literals_from_atp type_enc phi = [metis_literal_from_atp type_enc phi]
fun metis_axiom_from_atp type_enc clauses (Formula (ident, _, phi, _, _)) =
let
fun some isa =
SOME (phi |> metis_literals_from_atp type_enc
|> Metis_LiteralSet.fromList
|> Metis_Thm.axiom, isa)
in
if String.isPrefix tags_sym_formula_prefix ident then
Isa_Reflexive_or_Trivial |> some
else if String.isPrefix conjecture_prefix ident then
NONE
else if String.isPrefix helper_prefix ident then
case (String.isSuffix typed_helper_suffix ident,
space_explode "_" ident) of
(needs_fairly_sound, _ :: const :: j :: _) =>
nth (AList.lookup (op =) helper_table (const, needs_fairly_sound)
|> the)
(the (Int.fromString j) - 1)
|> snd |> prepare_helper
|> Isa_Raw |> some
| _ => raise Fail ("malformed helper identifier " ^ quote ident)
else case try (unprefix fact_prefix) ident of
SOME s =>
let val s = s |> space_explode "_" |> tl |> space_implode "_"
in
case Int.fromString s of
SOME j =>
Meson.make_meta_clause (snd (nth clauses j)) |> Isa_Raw |> some
| NONE =>
if String.isPrefix lam_fact_prefix (unascii_of s) then
Isa_Lambda_Lifted |> some
else
raise Fail ("malformed fact identifier " ^ quote ident)
end
| NONE => TrueI |> Isa_Raw |> some
end
| metis_axiom_from_atp _ _ _ = raise Fail "not CNF -- expected formula"
fun eliminate_lam_wrappers (Const (@{const_name Metis.lambda}, _) $ t) =
eliminate_lam_wrappers t
| eliminate_lam_wrappers (t $ u) =
eliminate_lam_wrappers t $ eliminate_lam_wrappers u
| eliminate_lam_wrappers (Abs (s, T, t)) =
Abs (s, T, eliminate_lam_wrappers t)
| eliminate_lam_wrappers t = t
(* Function to generate metis clauses, including comb and type clauses *)
fun prepare_metis_problem ctxt type_enc lam_trans conj_clauses fact_clauses =
let
val (conj_clauses, fact_clauses) =
if polymorphism_of_type_enc type_enc = Raw_Polymorphic then
(conj_clauses, fact_clauses)
else
conj_clauses @ fact_clauses
|> map (pair 0)
|> rpair (ctxt |> Config.put Monomorph.keep_partial_instances false)
|-> Monomorph.monomorph atp_schematic_consts_of
|> fst |> chop (length conj_clauses)
|> pairself (maps (map (zero_var_indexes o snd)))
val num_conjs = length conj_clauses
(* Pretend every clause is a "simp" rule, to guide the term ordering. *)
val clauses =
map2 (fn j => pair (Int.toString j, (Local, Simp)))
(0 upto num_conjs - 1) conj_clauses @
map2 (fn j => pair (Int.toString (num_conjs + j), (Local, Simp)))
(0 upto length fact_clauses - 1) fact_clauses
val (old_skolems, props) =
fold_rev (fn (name, th) => fn (old_skolems, props) =>
th |> prop_of |> Logic.strip_imp_concl
|> conceal_old_skolem_terms (length clauses) old_skolems
||> (lam_trans = liftingN orelse lam_trans = lam_liftingN)
? eliminate_lam_wrappers
||> (fn prop => (name, prop) :: props))
clauses ([], [])
(*
val _ =
tracing ("PROPS:\n" ^
cat_lines (map (Syntax.string_of_term ctxt o snd) props))
*)
val lam_trans = if lam_trans = combsN then no_lamsN else lam_trans
val (atp_problem, _, _, lifted, sym_tab) =
prepare_atp_problem ctxt CNF Hypothesis type_enc Metis lam_trans false
false false [] @{prop False} props
(*
val _ = tracing ("ATP PROBLEM: " ^
cat_lines (lines_for_atp_problem CNF atp_problem))
*)
(* "rev" is for compatibility with existing proof scripts. *)
val axioms =
atp_problem
|> maps (map_filter (metis_axiom_from_atp type_enc clauses) o snd) |> rev
fun ord_info () = atp_problem_term_order_info atp_problem
in (sym_tab, axioms, ord_info, (lifted, old_skolems)) end
end;