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(* Title: HOL/Tools/SMT/smt_builtin.ML
Author: Sascha Boehme, TU Muenchen
Tables of types and terms directly supported by SMT solvers.
*)
signature SMT_BUILTIN =
sig
(*for experiments*)
val filter_builtins: (typ -> bool) -> Proof.context -> Proof.context
(*built-in types*)
val add_builtin_typ: SMT_Util.class ->
typ * (typ -> (string * typ list) option) * (typ -> int -> string option) -> Context.generic ->
Context.generic
val add_builtin_typ_ext: typ * (Proof.context -> typ -> bool) -> Context.generic ->
Context.generic
val dest_builtin_typ: Proof.context -> typ -> (string * typ list) option
val is_builtin_typ_ext: Proof.context -> typ -> bool
(*built-in numbers*)
val dest_builtin_num: Proof.context -> term -> (string * typ) option
val is_builtin_num: Proof.context -> term -> bool
val is_builtin_num_ext: Proof.context -> term -> bool
(*built-in functions*)
type 'a bfun = Proof.context -> typ -> term list -> 'a
type bfunr = string * int * term list * (term list -> term)
val add_builtin_fun: SMT_Util.class -> (string * typ) * bfunr option bfun -> Context.generic ->
Context.generic
val add_builtin_fun': SMT_Util.class -> term * string -> Context.generic -> Context.generic
val add_builtin_fun_ext: (string * typ) * term list bfun -> Context.generic -> Context.generic
val add_builtin_fun_ext': string * typ -> Context.generic -> Context.generic
val add_builtin_fun_ext'': string -> Context.generic -> Context.generic
val dest_builtin_fun: Proof.context -> string * typ -> term list -> bfunr option
val dest_builtin_eq: Proof.context -> term -> term -> bfunr option
val dest_builtin_pred: Proof.context -> string * typ -> term list -> bfunr option
val dest_builtin_conn: Proof.context -> string * typ -> term list -> bfunr option
val dest_builtin: Proof.context -> string * typ -> term list -> bfunr option
val dest_builtin_ext: Proof.context -> string * typ -> term list -> term list option
val is_builtin_fun: Proof.context -> string * typ -> term list -> bool
val is_builtin_fun_ext: Proof.context -> string * typ -> term list -> bool
end;
structure SMT_Builtin: SMT_BUILTIN =
struct
(* built-in tables *)
datatype ('a, 'b) kind = Ext of 'a | Int of 'b
type ('a, 'b) ttab = ((typ * ('a, 'b) kind) Ord_List.T) SMT_Util.dict
fun typ_ord ((T, _), (U, _)) =
let
fun tord (TVar _, Type _) = GREATER
| tord (Type _, TVar _) = LESS
| tord (Type (n, Ts), Type (m, Us)) =
if n = m then list_ord tord (Ts, Us)
else Term_Ord.typ_ord (T, U)
| tord TU = Term_Ord.typ_ord TU
in tord (T, U) end
fun insert_ttab cs T f =
SMT_Util.dict_map_default (cs, [])
(Ord_List.insert typ_ord (perhaps (try Logic.varifyT_global) T, f))
fun merge_ttab ttabp = SMT_Util.dict_merge (Ord_List.merge typ_ord) ttabp
fun lookup_ttab ctxt ttab T =
let fun match (U, _) = Sign.typ_instance (Proof_Context.theory_of ctxt) (T, U)
in
get_first (find_first match) (SMT_Util.dict_lookup ttab (SMT_Config.solver_class_of ctxt))
end
type ('a, 'b) btab = ('a, 'b) ttab Symtab.table
fun insert_btab cs n T f =
Symtab.map_default (n, []) (insert_ttab cs T f)
fun merge_btab btabp = Symtab.join (K merge_ttab) btabp
fun lookup_btab ctxt btab (n, T) =
(case Symtab.lookup btab n of
NONE => NONE
| SOME ttab => lookup_ttab ctxt ttab T)
type 'a bfun = Proof.context -> typ -> term list -> 'a
type bfunr = string * int * term list * (term list -> term)
structure Builtins = Generic_Data
(
type T =
(Proof.context -> typ -> bool,
(typ -> (string * typ list) option) * (typ -> int -> string option)) ttab *
(term list bfun, bfunr option bfun) btab
val empty = ([], Symtab.empty)
val extend = I
fun merge ((t1, b1), (t2, b2)) = (merge_ttab (t1, t2), merge_btab (b1, b2))
)
fun filter_ttab keep_T = map (apsnd (filter (keep_T o fst)))
fun filter_builtins keep_T =
Context.proof_map (Builtins.map (fn (ttab, btab) =>
(filter_ttab keep_T ttab, Symtab.map (K (filter_ttab keep_T)) btab)))
(* built-in types *)
fun add_builtin_typ cs (T, f, g) =
Builtins.map (apfst (insert_ttab cs T (Int (f, g))))
fun add_builtin_typ_ext (T, f) = Builtins.map (apfst (insert_ttab SMT_Util.basicC T (Ext f)))
fun lookup_builtin_typ ctxt =
lookup_ttab ctxt (fst (Builtins.get (Context.Proof ctxt)))
fun dest_builtin_typ ctxt T =
(case lookup_builtin_typ ctxt T of
SOME (_, Int (f, _)) => f T
| _ => NONE)
fun is_builtin_typ_ext ctxt T =
(case lookup_builtin_typ ctxt T of
SOME (_, Int (f, _)) => is_some (f T)
| SOME (_, Ext f) => f ctxt T
| NONE => false)
(* built-in numbers *)
fun dest_builtin_num ctxt t =
(case try HOLogic.dest_number t of
NONE => NONE
| SOME (T, i) =>
if i < 0 then NONE else
(case lookup_builtin_typ ctxt T of
SOME (_, Int (_, g)) => g T i |> Option.map (rpair T)
| _ => NONE))
val is_builtin_num = is_some oo dest_builtin_num
fun is_builtin_num_ext ctxt t =
(case try HOLogic.dest_number t of
NONE => false
| SOME (T, _) => is_builtin_typ_ext ctxt T)
(* built-in functions *)
fun add_builtin_fun cs ((n, T), f) =
Builtins.map (apsnd (insert_btab cs n T (Int f)))
fun add_builtin_fun' cs (t, n) =
let
val c as (m, T) = Term.dest_Const t
fun app U ts = Term.list_comb (Const (m, U), ts)
fun bfun _ U ts = SOME (n, length (Term.binder_types T), ts, app U)
in add_builtin_fun cs (c, bfun) end
fun add_builtin_fun_ext ((n, T), f) =
Builtins.map (apsnd (insert_btab SMT_Util.basicC n T (Ext f)))
fun add_builtin_fun_ext' c = add_builtin_fun_ext (c, fn _ => fn _ => I)
fun add_builtin_fun_ext'' n context =
let val thy = Context.theory_of context
in add_builtin_fun_ext' (n, Sign.the_const_type thy n) context end
fun lookup_builtin_fun ctxt =
lookup_btab ctxt (snd (Builtins.get (Context.Proof ctxt)))
fun dest_builtin_fun ctxt (c as (_, T)) ts =
(case lookup_builtin_fun ctxt c of
SOME (_, Int f) => f ctxt T ts
| _ => NONE)
fun dest_builtin_eq ctxt t u =
let
val aT = Term.aT \<^sort>\<open>type\<close>
val c = (\<^const_name>\<open>HOL.eq\<close>, aT --> aT --> \<^typ>\<open>bool\<close>)
fun mk ts = Term.list_comb (HOLogic.eq_const (Term.fastype_of (hd ts)), ts)
in
dest_builtin_fun ctxt c []
|> Option.map (fn (n, i, _, _) => (n, i, [t, u], mk))
end
fun special_builtin_fun pred ctxt (c as (_, T)) ts =
if pred (Term.body_type T, Term.binder_types T) then
dest_builtin_fun ctxt c ts
else NONE
fun dest_builtin_pred ctxt = special_builtin_fun (equal \<^typ>\<open>bool\<close> o fst) ctxt
fun dest_builtin_conn ctxt =
special_builtin_fun (forall (equal \<^typ>\<open>bool\<close>) o (op ::)) ctxt
fun dest_builtin ctxt c ts =
let val t = Term.list_comb (Const c, ts)
in
(case dest_builtin_num ctxt t of
SOME (n, _) => SOME (n, 0, [], K t)
| NONE => dest_builtin_fun ctxt c ts)
end
fun dest_builtin_fun_ext ctxt (c as (_, T)) ts =
(case lookup_builtin_fun ctxt c of
SOME (_, Int f) => f ctxt T ts |> Option.map (fn (_, _, us, _) => us)
| SOME (_, Ext f) => SOME (f ctxt T ts)
| NONE => NONE)
fun dest_builtin_ext ctxt c ts =
if is_builtin_num_ext ctxt (Term.list_comb (Const c, ts)) then SOME []
else dest_builtin_fun_ext ctxt c ts
fun is_builtin_fun ctxt c ts = is_some (dest_builtin_fun ctxt c ts)
fun is_builtin_fun_ext ctxt c ts = is_some (dest_builtin_fun_ext ctxt c ts)
end;
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