centralized handling of built-in types and constants;
also store types and constants which are rewritten during preprocessing;
interfaces are identified by classes (supporting inheritance, at least on the level of built-in symbols);
removed term_eq in favor of type replacements: term-level occurrences of type bool are replaced by type term_bool (only for the translation)
(* Title: HOL/Tools/SMT/z3_interface.ML
Author: Sascha Boehme, TU Muenchen
Interface to Z3 based on a relaxed version of SMT-LIB.
*)
signature Z3_INTERFACE =
sig
val smtlib_z3C: SMT_Config.class
val setup: theory -> theory
val interface: SMT_Solver.interface
datatype sym = Sym of string * sym list
type mk_builtins = {
mk_builtin_typ: sym -> typ option,
mk_builtin_num: theory -> int -> typ -> cterm option,
mk_builtin_fun: theory -> sym -> cterm list -> cterm option }
val add_mk_builtins: mk_builtins -> Context.generic -> Context.generic
val mk_builtin_typ: Proof.context -> sym -> typ option
val mk_builtin_num: Proof.context -> int -> typ -> cterm option
val mk_builtin_fun: Proof.context -> sym -> cterm list -> cterm option
val is_builtin_theory_term: Proof.context -> term -> bool
end
structure Z3_Interface: Z3_INTERFACE =
struct
structure U = SMT_Utils
structure B = SMT_Builtin
val smtlib_z3C = SMTLIB_Interface.smtlibC @ ["z3"]
(* interface *)
local
val {translate, extra_norm, ...} = SMTLIB_Interface.interface
val {prefixes, is_fol, header, serialize, ...} = translate
fun is_int_div_mod @{const div (int)} = true
| is_int_div_mod @{const mod (int)} = true
| is_int_div_mod _ = false
fun add_div_mod irules =
if exists (Term.exists_subterm is_int_div_mod o Thm.prop_of o snd) irules
then [(~1, @{thm div_by_z3div}), (~1, @{thm mod_by_z3mod})] @ irules
else irules
fun extra_norm' has_datatypes = extra_norm has_datatypes o add_div_mod
in
val setup =
B.add_builtin_fun' smtlib_z3C (@{const z3div}, "div") #>
B.add_builtin_fun' smtlib_z3C (@{const z3mod}, "mod")
val interface = {
class = smtlib_z3C,
extra_norm = extra_norm',
translate = {
prefixes = prefixes,
is_fol = is_fol,
header = header,
has_datatypes = true,
serialize = serialize}}
end
(* constructors *)
datatype sym = Sym of string * sym list
(** additional constructors **)
type mk_builtins = {
mk_builtin_typ: sym -> typ option,
mk_builtin_num: theory -> int -> typ -> cterm option,
mk_builtin_fun: theory -> sym -> cterm list -> cterm option }
fun chained _ [] = NONE
| chained f (b :: bs) = (case f b of SOME y => SOME y | NONE => chained f bs)
fun chained_mk_builtin_typ bs sym =
chained (fn {mk_builtin_typ=mk, ...} : mk_builtins => mk sym) bs
fun chained_mk_builtin_num ctxt bs i T =
let val thy = ProofContext.theory_of ctxt
in chained (fn {mk_builtin_num=mk, ...} : mk_builtins => mk thy i T) bs end
fun chained_mk_builtin_fun ctxt bs s cts =
let val thy = ProofContext.theory_of ctxt
in chained (fn {mk_builtin_fun=mk, ...} : mk_builtins => mk thy s cts) bs end
fun fst_int_ord ((i1, _), (i2, _)) = int_ord (i1, i2)
structure Mk_Builtins = Generic_Data
(
type T = (int * mk_builtins) list
val empty = []
val extend = I
fun merge (bs1, bs2) = Ord_List.union fst_int_ord bs2 bs1
)
fun add_mk_builtins mk =
Mk_Builtins.map (Ord_List.insert fst_int_ord (serial (), mk))
fun get_mk_builtins ctxt = map snd (Mk_Builtins.get (Context.Proof ctxt))
(** basic and additional constructors **)
fun mk_builtin_typ _ (Sym ("bool", _)) = SOME @{typ bool}
| mk_builtin_typ _ (Sym ("Int", _)) = SOME @{typ int}
| mk_builtin_typ _ (Sym ("int", _)) = SOME @{typ int} (*FIXME: delete*)
| mk_builtin_typ ctxt sym = chained_mk_builtin_typ (get_mk_builtins ctxt) sym
fun mk_builtin_num _ i @{typ int} = SOME (Numeral.mk_cnumber @{ctyp int} i)
| mk_builtin_num ctxt i T =
chained_mk_builtin_num ctxt (get_mk_builtins ctxt) i T
val mk_true = Thm.cterm_of @{theory} (@{const Not} $ @{const False})
val mk_false = Thm.cterm_of @{theory} @{const False}
val mk_not = Thm.capply (Thm.cterm_of @{theory} @{const Not})
val mk_implies = Thm.mk_binop (Thm.cterm_of @{theory} @{const HOL.implies})
val mk_iff = Thm.mk_binop (Thm.cterm_of @{theory} @{const HOL.eq (bool)})
val conj = Thm.cterm_of @{theory} @{const HOL.conj}
val disj = Thm.cterm_of @{theory} @{const HOL.disj}
fun mk_nary _ cu [] = cu
| mk_nary ct _ cts = uncurry (fold_rev (Thm.mk_binop ct)) (split_last cts)
val eq = U.mk_const_pat @{theory} @{const_name HOL.eq} U.destT1
fun mk_eq ct cu = Thm.mk_binop (U.instT' ct eq) ct cu
val if_term = U.mk_const_pat @{theory} @{const_name If} (U.destT1 o U.destT2)
fun mk_if cc ct cu = Thm.mk_binop (Thm.capply (U.instT' ct if_term) cc) ct cu
val nil_term = U.mk_const_pat @{theory} @{const_name Nil} U.destT1
val cons_term = U.mk_const_pat @{theory} @{const_name Cons} U.destT1
fun mk_list cT cts =
fold_rev (Thm.mk_binop (U.instT cT cons_term)) cts (U.instT cT nil_term)
val distinct = U.mk_const_pat @{theory} @{const_name distinct}
(U.destT1 o U.destT1)
fun mk_distinct [] = mk_true
| mk_distinct (cts as (ct :: _)) =
Thm.capply (U.instT' ct distinct) (mk_list (Thm.ctyp_of_term ct) cts)
val access = U.mk_const_pat @{theory} @{const_name fun_app}
(Thm.dest_ctyp o U.destT1)
fun mk_access array index =
let val cTs = Thm.dest_ctyp (Thm.ctyp_of_term array)
in Thm.mk_binop (U.instTs cTs access) array index end
val update = U.mk_const_pat @{theory} @{const_name fun_upd}
(Thm.dest_ctyp o U.destT1)
fun mk_update array index value =
let val cTs = Thm.dest_ctyp (Thm.ctyp_of_term array)
in Thm.capply (Thm.mk_binop (U.instTs cTs update) array index) value end
val mk_uminus = Thm.capply (Thm.cterm_of @{theory} @{const uminus (int)})
val mk_add = Thm.mk_binop (Thm.cterm_of @{theory} @{const plus (int)})
val mk_sub = Thm.mk_binop (Thm.cterm_of @{theory} @{const minus (int)})
val mk_mul = Thm.mk_binop (Thm.cterm_of @{theory} @{const times (int)})
val mk_div = Thm.mk_binop (Thm.cterm_of @{theory} @{const z3div})
val mk_mod = Thm.mk_binop (Thm.cterm_of @{theory} @{const z3mod})
val mk_lt = Thm.mk_binop (Thm.cterm_of @{theory} @{const less (int)})
val mk_le = Thm.mk_binop (Thm.cterm_of @{theory} @{const less_eq (int)})
fun mk_builtin_fun ctxt sym cts =
(case (sym, cts) of
(Sym ("true", _), []) => SOME mk_true
| (Sym ("false", _), []) => SOME mk_false
| (Sym ("not", _), [ct]) => SOME (mk_not ct)
| (Sym ("and", _), _) => SOME (mk_nary conj mk_true cts)
| (Sym ("or", _), _) => SOME (mk_nary disj mk_false cts)
| (Sym ("implies", _), [ct, cu]) => SOME (mk_implies ct cu)
| (Sym ("iff", _), [ct, cu]) => SOME (mk_iff ct cu)
| (Sym ("~", _), [ct, cu]) => SOME (mk_iff ct cu)
| (Sym ("xor", _), [ct, cu]) => SOME (mk_not (mk_iff ct cu))
| (Sym ("ite", _), [ct1, ct2, ct3]) => SOME (mk_if ct1 ct2 ct3)
| (Sym ("=", _), [ct, cu]) => SOME (mk_eq ct cu)
| (Sym ("distinct", _), _) => SOME (mk_distinct cts)
| (Sym ("select", _), [ca, ck]) => SOME (mk_access ca ck)
| (Sym ("store", _), [ca, ck, cv]) => SOME (mk_update ca ck cv)
| _ =>
(case (sym, try (#T o Thm.rep_cterm o hd) cts, cts) of
(Sym ("+", _), SOME @{typ int}, [ct, cu]) => SOME (mk_add ct cu)
| (Sym ("-", _), SOME @{typ int}, [ct]) => SOME (mk_uminus ct)
| (Sym ("-", _), SOME @{typ int}, [ct, cu]) => SOME (mk_sub ct cu)
| (Sym ("*", _), SOME @{typ int}, [ct, cu]) => SOME (mk_mul ct cu)
| (Sym ("div", _), SOME @{typ int}, [ct, cu]) => SOME (mk_div ct cu)
| (Sym ("mod", _), SOME @{typ int}, [ct, cu]) => SOME (mk_mod ct cu)
| (Sym ("<", _), SOME @{typ int}, [ct, cu]) => SOME (mk_lt ct cu)
| (Sym ("<=", _), SOME @{typ int}, [ct, cu]) => SOME (mk_le ct cu)
| (Sym (">", _), SOME @{typ int}, [ct, cu]) => SOME (mk_lt cu ct)
| (Sym (">=", _), SOME @{typ int}, [ct, cu]) => SOME (mk_le cu ct)
| _ => chained_mk_builtin_fun ctxt (get_mk_builtins ctxt) sym cts))
(* abstraction *)
fun is_builtin_theory_term ctxt t =
if B.is_builtin_num ctxt t then true
else
(case Term.strip_comb t of
(Const c, ts) => B.is_builtin_fun ctxt c ts
| _ => false)
end