ensure type class predicates are generated in symbol declarations (for "poly_preds" and similar)
(* Title: HOL/Tools/Metis/metis_translate.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_TRANSLATE =
sig
type name = string * string
datatype type_literal =
TyLitVar of name * name |
TyLitFree of name * name
datatype arLit =
TConsLit of name * name * name list |
TVarLit of name * name
datatype arity_clause =
ArityClause of {name: string, conclLit: arLit, premLits: arLit list}
datatype class_rel_clause =
ClassRelClause of {name: string, subclass: name, superclass: name}
datatype combterm =
CombConst of name * typ * typ list (* Const and Free *) |
CombVar of name * typ |
CombApp of combterm * combterm
datatype fol_literal = FOLLiteral of bool * combterm
datatype mode = FO | HO | FT
type metis_problem =
{axioms: (Metis_Thm.thm * thm) list,
tfrees: type_literal list,
old_skolems: (string * term) list}
val metis_generated_var_prefix : string
val type_tag_name : string
val bound_var_prefix : string
val schematic_var_prefix: string
val fixed_var_prefix: string
val tvar_prefix: string
val tfree_prefix: string
val const_prefix: string
val type_const_prefix: string
val class_prefix: string
val new_skolem_const_prefix : string
val proxify_const : string -> (string * string) option
val invert_const: string -> string
val unproxify_const: string -> string
val ascii_of: string -> string
val unascii_of: string -> string
val strip_prefix_and_unascii: string -> string -> string option
val make_bound_var : string -> string
val make_schematic_var : string * int -> string
val make_fixed_var : string -> string
val make_schematic_type_var : string * int -> string
val make_fixed_type_var : string -> string
val make_fixed_const : string -> string
val make_fixed_type_const : string -> string
val make_type_class : string -> string
val num_type_args: theory -> string -> int
val new_skolem_var_name_from_const : string -> string
val type_literals_for_types : typ list -> type_literal list
val make_class_rel_clauses :
theory -> class list -> class list -> class_rel_clause list
val make_arity_clauses :
theory -> string list -> class list -> class list * arity_clause list
val combtyp_of : combterm -> typ
val strip_combterm_comb : combterm -> combterm * combterm list
val atyps_of : typ -> typ list
val combterm_from_term :
theory -> (string * typ) list -> term -> combterm * typ list
val reveal_old_skolem_terms : (string * term) list -> term -> term
val tfree_classes_of_terms : term list -> string list
val tvar_classes_of_terms : term list -> string list
val type_consts_of_terms : theory -> term list -> string list
val string_of_mode : mode -> string
val metis_helpers : (string * (bool * thm list)) list
val prepare_metis_problem :
mode -> Proof.context -> bool -> thm list -> thm list list
-> mode * metis_problem
end
structure Metis_Translate : METIS_TRANSLATE =
struct
val metis_generated_var_prefix = "_"
val type_tag_name = "ti"
val bound_var_prefix = "B_"
val schematic_var_prefix = "V_"
val fixed_var_prefix = "v_"
val tvar_prefix = "T_";
val tfree_prefix = "t_";
val const_prefix = "c_";
val type_const_prefix = "tc_";
val class_prefix = "class_";
val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
val old_skolem_const_prefix = skolem_const_prefix ^ "o"
val new_skolem_const_prefix = skolem_const_prefix ^ "n"
fun union_all xss = fold (union (op =)) xss []
val metis_proxies =
[("c_False", (@{const_name False}, ("fFalse", @{const_name Metis.fFalse}))),
("c_True", (@{const_name True}, ("fTrue", @{const_name Metis.fTrue}))),
("c_Not", (@{const_name Not}, ("fNot", @{const_name Metis.fNot}))),
("c_conj", (@{const_name conj}, ("fconj", @{const_name Metis.fconj}))),
("c_disj", (@{const_name disj}, ("fdisj", @{const_name Metis.fdisj}))),
("c_implies", (@{const_name implies},
("fimplies", @{const_name Metis.fimplies}))),
("equal", (@{const_name HOL.eq}, ("fequal", @{const_name Metis.fequal})))]
val proxify_const = AList.lookup (op =) metis_proxies #> Option.map snd
(* Readable names for the more common symbolic functions. Do not mess with the
table unless you know what you are doing. *)
val const_trans_table =
[(@{type_name Product_Type.prod}, "prod"),
(@{type_name Sum_Type.sum}, "sum"),
(@{const_name False}, "False"),
(@{const_name True}, "True"),
(@{const_name Not}, "Not"),
(@{const_name conj}, "conj"),
(@{const_name disj}, "disj"),
(@{const_name implies}, "implies"),
(@{const_name HOL.eq}, "equal"),
(@{const_name If}, "If"),
(@{const_name Set.member}, "member"),
(@{const_name Meson.COMBI}, "COMBI"),
(@{const_name Meson.COMBK}, "COMBK"),
(@{const_name Meson.COMBB}, "COMBB"),
(@{const_name Meson.COMBC}, "COMBC"),
(@{const_name Meson.COMBS}, "COMBS")]
|> Symtab.make
|> fold (Symtab.update o swap o snd o snd) metis_proxies
(* Invert the table of translations between Isabelle and Metis. *)
val const_trans_table_inv =
const_trans_table |> Symtab.dest |> map swap |> Symtab.make
val const_trans_table_unprox =
Symtab.empty
|> fold (fn (_, (isa, (_, metis))) => Symtab.update (metis, isa))
metis_proxies
val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
(*Escaping of special characters.
Alphanumeric characters are left unchanged.
The character _ goes to __
Characters in the range ASCII space to / go to _A to _P, respectively.
Other characters go to _nnn where nnn is the decimal ASCII code.*)
val A_minus_space = Char.ord #"A" - Char.ord #" ";
fun stringN_of_int 0 _ = ""
| stringN_of_int k n = stringN_of_int (k-1) (n div 10) ^ string_of_int (n mod 10);
fun ascii_of_c c =
if Char.isAlphaNum c then String.str c
else if c = #"_" then "__"
else if #" " <= c andalso c <= #"/"
then "_" ^ String.str (Char.chr (Char.ord c + A_minus_space))
else ("_" ^ stringN_of_int 3 (Char.ord c)) (*fixed width, in case more digits follow*)
val ascii_of = String.translate ascii_of_c;
(** Remove ASCII armouring from names in proof files **)
(*We don't raise error exceptions because this code can run inside the watcher.
Also, the errors are "impossible" (hah!)*)
fun unascii_aux rcs [] = String.implode(rev rcs)
| unascii_aux rcs [#"_"] = unascii_aux (#"_"::rcs) [] (*ERROR*)
(*Three types of _ escapes: __, _A to _P, _nnn*)
| unascii_aux rcs (#"_" :: #"_" :: cs) = unascii_aux (#"_"::rcs) cs
| unascii_aux rcs (#"_" :: c :: cs) =
if #"A" <= c andalso c<= #"P" (*translation of #" " to #"/"*)
then unascii_aux (Char.chr(Char.ord c - A_minus_space) :: rcs) cs
else
let val digits = List.take (c::cs, 3) handle Subscript => []
in
case Int.fromString (String.implode digits) of
NONE => unascii_aux (c:: #"_"::rcs) cs (*ERROR*)
| SOME n => unascii_aux (Char.chr n :: rcs) (List.drop (cs, 2))
end
| unascii_aux rcs (c::cs) = unascii_aux (c::rcs) cs
val unascii_of = unascii_aux [] o String.explode
(* If string s has the prefix s1, return the result of deleting it,
un-ASCII'd. *)
fun strip_prefix_and_unascii s1 s =
if String.isPrefix s1 s then
SOME (unascii_of (String.extract (s, size s1, NONE)))
else
NONE
(*Remove the initial ' character from a type variable, if it is present*)
fun trim_type_var s =
if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)
else raise Fail ("trim_type: Malformed type variable encountered: " ^ s)
fun ascii_of_indexname (v,0) = ascii_of v
| ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ string_of_int i;
fun make_bound_var x = bound_var_prefix ^ ascii_of x
fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
fun make_schematic_type_var (x,i) =
tvar_prefix ^ (ascii_of_indexname (trim_type_var x,i));
fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x));
fun lookup_const c =
case Symtab.lookup const_trans_table c of
SOME c' => c'
| NONE => ascii_of c
(* HOL.eq MUST BE "equal" because it's built into ATPs. *)
fun make_fixed_const @{const_name HOL.eq} = "equal"
| make_fixed_const c = const_prefix ^ lookup_const c
fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
fun make_type_class clas = class_prefix ^ ascii_of clas;
(* The number of type arguments of a constant, zero if it's monomorphic. For
(instances of) Skolem pseudoconstants, this information is encoded in the
constant name. *)
fun num_type_args thy s =
if String.isPrefix skolem_const_prefix s then
s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
else
(s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
fun new_skolem_var_name_from_const s =
let val ss = s |> space_explode Long_Name.separator in
nth ss (length ss - 2)
end
(**** Definitions and functions for FOL clauses for TPTP format output ****)
type name = string * string
(**** Isabelle FOL clauses ****)
(* The first component is the type class; the second is a TVar or TFree. *)
datatype type_literal =
TyLitVar of name * name |
TyLitFree of name * name
(*Make literals for sorted type variables*)
fun sorts_on_typs_aux (_, []) = []
| sorts_on_typs_aux ((x,i), s::ss) =
let val sorts = sorts_on_typs_aux ((x,i), ss)
in
if s = "HOL.type" then sorts
else if i = ~1 then TyLitFree (`make_type_class s, `make_fixed_type_var x) :: sorts
else TyLitVar (`make_type_class s, (make_schematic_type_var (x,i), x)) :: sorts
end;
fun sorts_on_typs (TFree (a,s)) = sorts_on_typs_aux ((a,~1),s)
| sorts_on_typs (TVar (v,s)) = sorts_on_typs_aux (v,s);
(*Given a list of sorted type variables, return a list of type literals.*)
fun type_literals_for_types Ts =
fold (union (op =)) (map sorts_on_typs Ts) []
(** make axiom and conjecture clauses. **)
(**** Isabelle arities ****)
datatype arLit =
TConsLit of name * name * name list |
TVarLit of name * name
datatype arity_clause =
ArityClause of {name: string, conclLit: arLit, premLits: arLit list}
fun gen_TVars 0 = []
| gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1);
fun pack_sort(_,[]) = []
| pack_sort(tvar, "HOL.type"::srt) = pack_sort (tvar, srt) (*IGNORE sort "type"*)
| pack_sort(tvar, cls::srt) =
(`make_type_class cls, (tvar, tvar)) :: pack_sort (tvar, srt)
(*Arity of type constructor tcon :: (arg1,...,argN)res*)
fun make_axiom_arity_clause (tcons, name, (cls,args)) =
let
val tvars = gen_TVars (length args)
val tvars_srts = ListPair.zip (tvars, args)
in
ArityClause {name = name,
conclLit = TConsLit (`make_type_class cls,
`make_fixed_type_const tcons,
tvars ~~ tvars),
premLits = map TVarLit (union_all (map pack_sort tvars_srts))}
end
(**** Isabelle class relations ****)
datatype class_rel_clause =
ClassRelClause of {name: string, subclass: name, superclass: name}
(*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)
fun class_pairs _ [] _ = []
| class_pairs thy subs supers =
let
val class_less = Sorts.class_less (Sign.classes_of thy)
fun add_super sub super = class_less (sub, super) ? cons (sub, super)
fun add_supers sub = fold (add_super sub) supers
in fold add_supers subs [] end
fun make_class_rel_clause (sub,super) =
ClassRelClause {name = sub ^ "_" ^ super,
subclass = `make_type_class sub,
superclass = `make_type_class super}
fun make_class_rel_clauses thy subs supers =
map make_class_rel_clause (class_pairs thy subs supers);
(** Isabelle arities **)
fun arity_clause _ _ (_, []) = []
| arity_clause seen n (tcons, ("HOL.type",_)::ars) = (*ignore*)
arity_clause seen n (tcons,ars)
| arity_clause seen n (tcons, (ar as (class,_)) :: ars) =
if member (op =) seen class then (*multiple arities for the same tycon, class pair*)
make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class ^ "_" ^ string_of_int n, ar) ::
arity_clause seen (n+1) (tcons,ars)
else
make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class, ar) ::
arity_clause (class::seen) n (tcons,ars)
fun multi_arity_clause [] = []
| multi_arity_clause ((tcons, ars) :: tc_arlists) =
arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
(*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy
provided its arguments have the corresponding sorts.*)
fun type_class_pairs thy tycons classes =
let val alg = Sign.classes_of thy
fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
fun add_class tycon class =
cons (class, domain_sorts tycon class)
handle Sorts.CLASS_ERROR _ => I
fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
in map try_classes tycons end;
(*Proving one (tycon, class) membership may require proving others, so iterate.*)
fun iter_type_class_pairs _ _ [] = ([], [])
| iter_type_class_pairs thy tycons classes =
let val cpairs = type_class_pairs thy tycons classes
val newclasses = union_all (union_all (union_all (map (map #2 o #2) cpairs)))
|> subtract (op =) classes |> subtract (op =) HOLogic.typeS
val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
in (union (op =) classes' classes, union (op =) cpairs' cpairs) end;
fun make_arity_clauses thy tycons classes =
let val (classes', cpairs) = iter_type_class_pairs thy tycons classes
in (classes', multi_arity_clause cpairs) end;
datatype combterm =
CombConst of name * typ * typ list (* Const and Free *) |
CombVar of name * typ |
CombApp of combterm * combterm
datatype fol_literal = FOLLiteral of bool * combterm
(*********************************************************************)
(* convert a clause with type Term.term to a clause with type clause *)
(*********************************************************************)
fun combtyp_of (CombConst (_, T, _)) = T
| combtyp_of (CombVar (_, T)) = T
| combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
(*gets the head of a combinator application, along with the list of arguments*)
fun strip_combterm_comb u =
let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
| stripc x = x
in stripc(u,[]) end
fun atyps_of T = fold_atyps (insert (op =)) T []
fun new_skolem_const_name s num_T_args =
[new_skolem_const_prefix, s, string_of_int num_T_args]
|> space_implode Long_Name.separator
(* Converts a term (with combinators) into a combterm. Also accumulates sort
infomation. *)
fun combterm_from_term thy bs (P $ Q) =
let
val (P', P_atomics_Ts) = combterm_from_term thy bs P
val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
| combterm_from_term thy _ (Const (c, T)) =
let
val tvar_list =
(if String.isPrefix old_skolem_const_prefix c then
[] |> Term.add_tvarsT T |> map TVar
else
(c, T) |> Sign.const_typargs thy)
val c' = CombConst (`make_fixed_const c, T, tvar_list)
in (c', atyps_of T) end
| combterm_from_term _ _ (Free (v, T)) =
(CombConst (`make_fixed_var v, T, []), atyps_of T)
| combterm_from_term _ _ (Var (v as (s, _), T)) =
(if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
let
val Ts = T |> strip_type |> swap |> op ::
val s' = new_skolem_const_name s (length Ts)
in CombConst (`make_fixed_const s', T, Ts) end
else
CombVar ((make_schematic_var v, s), T), atyps_of T)
| combterm_from_term _ bs (Bound j) =
nth bs j
|> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
| combterm_from_term _ _ (Abs _) = raise Fail "HOL clause: Abs"
fun predicate_of thy ((@{const Not} $ P), pos) = predicate_of thy (P, not pos)
| predicate_of thy (t, pos) =
(combterm_from_term thy [] (Envir.eta_contract t), pos)
fun literals_of_term1 args thy (@{const Trueprop} $ P) =
literals_of_term1 args thy P
| literals_of_term1 args thy (@{const HOL.disj} $ P $ Q) =
literals_of_term1 (literals_of_term1 args thy P) thy Q
| literals_of_term1 (lits, ts) thy P =
let val ((pred, ts'), pol) = predicate_of thy (P, true) in
(FOLLiteral (pol, pred) :: lits, union (op =) ts ts')
end
val literals_of_term = literals_of_term1 ([], [])
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 Type_Infer.paramify_vars
else
t
| t => t)
(***************************************************************)
(* Type Classes Present in the Axiom or Conjecture Clauses *)
(***************************************************************)
fun set_insert (x, s) = Symtab.update (x, ()) s
fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
(*Remove this trivial type class*)
fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset;
fun tfree_classes_of_terms ts =
let val sorts_list = map (map #2 o OldTerm.term_tfrees) ts
in Symtab.keys (delete_type (List.foldl add_classes Symtab.empty sorts_list)) end;
fun tvar_classes_of_terms ts =
let val sorts_list = map (map #2 o OldTerm.term_tvars) ts
in Symtab.keys (delete_type (List.foldl add_classes Symtab.empty sorts_list)) end;
(*fold type constructors*)
fun fold_type_consts f (Type (a, Ts)) x = fold (fold_type_consts f) Ts (f (a,x))
| fold_type_consts _ _ x = x;
(*Type constructors used to instantiate overloaded constants are the only ones needed.*)
fun add_type_consts_in_term thy =
let
fun aux (Const x) =
fold (fold_type_consts set_insert) (Sign.const_typargs thy x)
| aux (Abs (_, _, u)) = aux u
| aux (Const (@{const_name Meson.skolem}, _) $ _) = I
| aux (t $ u) = aux t #> aux u
| aux _ = I
in aux end
fun type_consts_of_terms thy ts =
Symtab.keys (fold (add_type_consts_in_term thy) ts Symtab.empty);
(* ------------------------------------------------------------------------- *)
(* HOL to FOL (Isabelle to Metis) *)
(* ------------------------------------------------------------------------- *)
datatype mode = FO | HO | FT (* first-order, higher-order, fully-typed *)
fun string_of_mode FO = "FO"
| string_of_mode HO = "HO"
| string_of_mode FT = "FT"
fun fn_isa_to_met_sublevel "equal" = "=" (* FIXME: "c_fequal" *)
| fn_isa_to_met_sublevel "c_False" = "c_fFalse"
| fn_isa_to_met_sublevel "c_True" = "c_fTrue"
| fn_isa_to_met_sublevel "c_Not" = "c_fNot"
| fn_isa_to_met_sublevel "c_conj" = "c_fconj"
| fn_isa_to_met_sublevel "c_disj" = "c_fdisj"
| fn_isa_to_met_sublevel "c_implies" = "c_fimplies"
| fn_isa_to_met_sublevel x = x
fun fn_isa_to_met_toplevel "equal" = "="
| fn_isa_to_met_toplevel x = x
fun metis_lit b c args = (b, (c, args));
fun metis_term_from_typ (Type (s, Ts)) =
Metis_Term.Fn (make_fixed_type_const s, map metis_term_from_typ Ts)
| metis_term_from_typ (TFree (s, _)) =
Metis_Term.Fn (make_fixed_type_var s, [])
| metis_term_from_typ (TVar (x, _)) =
Metis_Term.Var (make_schematic_type_var x)
(*These two functions insert type literals before the real literals. That is the
opposite order from TPTP linkup, but maybe OK.*)
fun hol_term_to_fol_FO tm =
case strip_combterm_comb tm of
(CombConst ((c, _), _, Ts), tms) =>
let val tyargs = map metis_term_from_typ Ts
val args = map hol_term_to_fol_FO tms
in Metis_Term.Fn (c, tyargs @ args) end
| (CombVar ((v, _), _), []) => Metis_Term.Var v
| _ => raise Fail "non-first-order combterm"
fun hol_term_to_fol_HO (CombConst ((a, _), _, Ts)) =
Metis_Term.Fn (fn_isa_to_met_sublevel a, map metis_term_from_typ Ts)
| hol_term_to_fol_HO (CombVar ((s, _), _)) = Metis_Term.Var s
| hol_term_to_fol_HO (CombApp (tm1, tm2)) =
Metis_Term.Fn (".", map hol_term_to_fol_HO [tm1, tm2]);
(*The fully-typed translation, to avoid type errors*)
fun tag_with_type tm T =
Metis_Term.Fn (type_tag_name, [tm, metis_term_from_typ T])
fun hol_term_to_fol_FT (CombVar ((s, _), ty)) =
tag_with_type (Metis_Term.Var s) ty
| hol_term_to_fol_FT (CombConst ((a, _), ty, _)) =
tag_with_type (Metis_Term.Fn (fn_isa_to_met_sublevel a, [])) ty
| hol_term_to_fol_FT (tm as CombApp (tm1,tm2)) =
tag_with_type (Metis_Term.Fn (".", map hol_term_to_fol_FT [tm1, tm2]))
(combtyp_of tm)
fun hol_literal_to_fol FO (FOLLiteral (pos, tm)) =
let
val (CombConst((p, _), _, Ts), tms) = strip_combterm_comb tm
val tylits = if p = "equal" then [] else map metis_term_from_typ Ts
val lits = map hol_term_to_fol_FO tms
in metis_lit pos (fn_isa_to_met_toplevel p) (tylits @ lits) end
| hol_literal_to_fol HO (FOLLiteral (pos, tm)) =
(case strip_combterm_comb tm of
(CombConst(("equal", _), _, _), tms) =>
metis_lit pos "=" (map hol_term_to_fol_HO tms)
| _ => metis_lit pos "{}" [hol_term_to_fol_HO tm]) (*hBOOL*)
| hol_literal_to_fol FT (FOLLiteral (pos, tm)) =
(case strip_combterm_comb tm of
(CombConst(("equal", _), _, _), tms) =>
metis_lit pos "=" (map hol_term_to_fol_FT tms)
| _ => metis_lit pos "{}" [hol_term_to_fol_FT tm]) (*hBOOL*);
fun literals_of_hol_term thy mode t =
let val (lits, types_sorts) = literals_of_term thy t in
(map (hol_literal_to_fol mode) lits, types_sorts)
end
(*Sign should be "true" for conjecture type constraints, "false" for type lits in clauses.*)
fun metis_of_type_literals pos (TyLitVar ((s, _), (s', _))) =
metis_lit pos s [Metis_Term.Var s']
| metis_of_type_literals pos (TyLitFree ((s, _), (s', _))) =
metis_lit pos s [Metis_Term.Fn (s',[])]
fun has_default_sort _ (TVar _) = false
| has_default_sort ctxt (TFree (x, s)) =
(s = the_default [] (Variable.def_sort ctxt (x, ~1)));
fun metis_of_tfree tf =
Metis_Thm.axiom (Metis_LiteralSet.singleton (metis_of_type_literals true tf));
fun hol_thm_to_fol is_conjecture ctxt type_lits mode j old_skolems th =
let
val thy = Proof_Context.theory_of ctxt
val (old_skolems, (mlits, types_sorts)) =
th |> prop_of |> Logic.strip_imp_concl
|> conceal_old_skolem_terms j old_skolems
||> (HOLogic.dest_Trueprop #> literals_of_hol_term thy mode)
in
if is_conjecture then
(Metis_Thm.axiom (Metis_LiteralSet.fromList mlits),
type_literals_for_types types_sorts, old_skolems)
else
let
val tylits = types_sorts |> filter_out (has_default_sort ctxt)
|> type_literals_for_types
val mtylits =
if type_lits then map (metis_of_type_literals false) tylits else []
in
(Metis_Thm.axiom (Metis_LiteralSet.fromList(mtylits @ mlits)), [],
old_skolems)
end
end;
val metis_helpers =
[("COMBI", (false, @{thms Meson.COMBI_def})),
("COMBK", (false, @{thms Meson.COMBK_def})),
("COMBB", (false, @{thms Meson.COMBB_def})),
("COMBC", (false, @{thms Meson.COMBC_def})),
("COMBS", (false, @{thms Meson.COMBS_def})),
("fequal",
(false, @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]})),
("fFalse", (true, [@{lemma "x = fTrue | x = fFalse"
by (unfold fFalse_def fTrue_def) fast}])),
("fFalse", (false, [@{lemma "~ fFalse" by (unfold fFalse_def) fast}])),
("fTrue", (true, [@{lemma "x = fTrue | x = fFalse"
by (unfold fFalse_def fTrue_def) fast}])),
("fTrue", (false, [@{lemma "fTrue" by (unfold fTrue_def) fast}])),
("fNot",
(false, @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]})),
("fconj",
(false, @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
by (unfold fconj_def) fast+})),
("fdisj",
(false, @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
by (unfold fdisj_def) fast+})),
("fimplies",
(false, @{lemma "P | fimplies P Q" "~ Q | fimplies P Q"
"~ fimplies P Q | ~ P | Q"
by (unfold fimplies_def) fast+})),
("If", (true, @{thms if_True if_False True_or_False})) (* FIXME *)]
(* ------------------------------------------------------------------------- *)
(* Logic maps manage the interface between HOL and first-order logic. *)
(* ------------------------------------------------------------------------- *)
type metis_problem =
{axioms: (Metis_Thm.thm * thm) list,
tfrees: type_literal list,
old_skolems: (string * term) list}
fun is_quasi_fol_clause thy =
Meson.is_fol_term thy o snd o conceal_old_skolem_terms ~1 [] o prop_of
(*Extract TFree constraints from context to include as conjecture clauses*)
fun init_tfrees ctxt =
let fun add ((a,i),s) Ts = if i = ~1 then TFree(a,s) :: Ts else Ts in
Vartab.fold add (#2 (Variable.constraints_of ctxt)) []
|> type_literals_for_types
end;
(*Insert non-logical axioms corresponding to all accumulated TFrees*)
fun add_tfrees {axioms, tfrees, old_skolems} : metis_problem =
{axioms = map (rpair TrueI o metis_of_tfree) (distinct (op =) tfrees) @
axioms,
tfrees = tfrees, old_skolems = old_skolems}
(*transform isabelle type / arity clause to metis clause *)
fun add_type_thm [] lmap = lmap
| add_type_thm ((ith, mth) :: cls) {axioms, tfrees, old_skolems} =
add_type_thm cls {axioms = (mth, ith) :: axioms, tfrees = tfrees,
old_skolems = old_skolems}
fun const_in_metis c (pred, tm_list) =
let
fun in_mterm (Metis_Term.Var _) = false
| in_mterm (Metis_Term.Fn (nm, tm_list)) =
c = nm orelse exists in_mterm tm_list
in c = pred orelse exists in_mterm tm_list end
(* ARITY CLAUSE *)
fun m_arity_cls (TConsLit ((c, _), (t, _), args)) =
metis_lit true c [Metis_Term.Fn(t, map (Metis_Term.Var o fst) args)]
| m_arity_cls (TVarLit ((c, _), (s, _))) =
metis_lit false c [Metis_Term.Var s]
(*TrueI is returned as the Isabelle counterpart because there isn't any.*)
fun arity_cls (ArityClause {conclLit, premLits, ...}) =
(TrueI,
Metis_Thm.axiom (Metis_LiteralSet.fromList (map m_arity_cls (conclLit :: premLits))));
(* CLASSREL CLAUSE *)
fun m_class_rel_cls (subclass, _) (superclass, _) =
[metis_lit false subclass [Metis_Term.Var "T"], metis_lit true superclass [Metis_Term.Var "T"]];
fun class_rel_cls (ClassRelClause {subclass, superclass, ...}) =
(TrueI, Metis_Thm.axiom (Metis_LiteralSet.fromList (m_class_rel_cls subclass superclass)));
fun type_ext thy tms =
let val subs = tfree_classes_of_terms tms
val supers = tvar_classes_of_terms tms
and tycons = type_consts_of_terms thy tms
val (supers', arity_clauses) = make_arity_clauses thy tycons supers
val class_rel_clauses = make_class_rel_clauses thy subs supers'
in map class_rel_cls class_rel_clauses @ map arity_cls arity_clauses
end;
(* Function to generate metis clauses, including comb and type clauses *)
fun prepare_metis_problem mode0 ctxt type_lits cls thss =
let val thy = Proof_Context.theory_of ctxt
(*The modes FO and FT are sticky. HO can be downgraded to FO.*)
fun set_mode FO = FO
| set_mode HO =
if forall (forall (is_quasi_fol_clause thy)) (cls :: thss) then FO
else HO
| set_mode FT = FT
val mode = set_mode mode0
(*transform isabelle clause to metis clause *)
fun add_thm is_conjecture (isa_ith, metis_ith)
{axioms, tfrees, old_skolems} : metis_problem =
let
val (mth, tfree_lits, old_skolems) =
hol_thm_to_fol is_conjecture ctxt type_lits mode (length axioms)
old_skolems metis_ith
in
{axioms = (mth, isa_ith) :: axioms,
tfrees = union (op =) tfree_lits tfrees, old_skolems = old_skolems}
end;
val lmap = {axioms = [], tfrees = init_tfrees ctxt, old_skolems = []}
|> fold (add_thm true o `Meson.make_meta_clause) cls
|> add_tfrees
|> fold (fold (add_thm false o `Meson.make_meta_clause)) thss
val clause_lists = map (Metis_Thm.clause o #1) (#axioms lmap)
fun is_used c =
exists (Metis_LiteralSet.exists (const_in_metis c o #2)) clause_lists
val lmap =
if mode = FO then
lmap
else
let
val fdefs = @{thms fFalse_def fTrue_def fNot_def fconj_def fdisj_def
fimplies_def fequal_def}
val prepare_helper =
zero_var_indexes
#> `(Meson.make_meta_clause
#> rewrite_rule (map safe_mk_meta_eq fdefs))
val helper_ths =
metis_helpers
|> filter (is_used o prefix const_prefix o fst)
|> maps (fn (_, (needs_full_types, thms)) =>
if needs_full_types andalso mode <> FT then []
else map prepare_helper thms)
in lmap |> fold (add_thm false) helper_ths end
in
(mode, add_type_thm (type_ext thy (maps (map prop_of) (cls :: thss))) lmap)
end
end;