author | blanchet |
Thu, 13 Mar 2014 13:18:13 +0100 | |
changeset 56078 | 624faeda77b5 |
child 56090 | 34bd10a9a2ad |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/SMT2/z3_new_interface.ML |
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Author: Sascha Boehme, TU Muenchen |
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Interface to Z3 based on a relaxed version of SMT-LIB. |
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*) |
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signature Z3_NEW_INTERFACE = |
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sig |
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val smtlib2_z3C: SMT2_Utils.class |
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datatype sym = Sym of string * sym list |
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type mk_builtins = { |
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mk_builtin_typ: sym -> typ option, |
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mk_builtin_num: theory -> int -> typ -> cterm option, |
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mk_builtin_fun: theory -> sym -> cterm list -> cterm option } |
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val add_mk_builtins: mk_builtins -> Context.generic -> Context.generic |
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val mk_builtin_typ: Proof.context -> sym -> typ option |
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val mk_builtin_num: Proof.context -> int -> typ -> cterm option |
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val mk_builtin_fun: Proof.context -> sym -> cterm list -> cterm option |
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val is_builtin_theory_term: Proof.context -> term -> bool |
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end |
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structure Z3_New_Interface: Z3_NEW_INTERFACE = |
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struct |
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val smtlib2_z3C = SMTLIB2_Interface.smtlib2C @ ["z3"] |
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(* interface *) |
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local |
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fun translate_config ctxt = |
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let |
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val {serialize, ...} = SMTLIB2_Interface.translate_config ctxt |
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in |
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{header=K "", serialize=serialize, has_datatypes=true} |
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end |
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fun is_div_mod @{const div (int)} = true |
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| is_div_mod @{const mod (int)} = true |
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| is_div_mod _ = false |
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val div_as_z3div = @{lemma |
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"ALL k l. k div l = ( |
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if k = 0 | l = 0 then 0 |
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else if (0 < k & 0 < l) | (k < 0 & 0 < l) then z3div k l |
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else z3div (-k) (-l))" |
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by (simp add: SMT2.z3div_def)} |
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val mod_as_z3mod = @{lemma |
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"ALL k l. k mod l = ( |
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if l = 0 then k |
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else if k = 0 then 0 |
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else if (0 < k & 0 < l) | (k < 0 & 0 < l) then z3mod k l |
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else - z3mod (-k) (-l))" |
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by (simp add: z3mod_def)} |
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val have_int_div_mod = |
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exists (Term.exists_subterm is_div_mod o Thm.prop_of) |
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fun add_div_mod _ (thms, extra_thms) = |
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if have_int_div_mod thms orelse have_int_div_mod extra_thms then |
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(thms, div_as_z3div :: mod_as_z3mod :: extra_thms) |
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else (thms, extra_thms) |
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val setup_builtins = |
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SMT2_Builtin.add_builtin_fun' smtlib2_z3C (@{const times (int)}, "*") #> |
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SMT2_Builtin.add_builtin_fun' smtlib2_z3C (@{const z3div}, "div") #> |
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SMT2_Builtin.add_builtin_fun' smtlib2_z3C (@{const z3mod}, "mod") |
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in |
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val _ = Theory.setup (Context.theory_map ( |
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setup_builtins #> |
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SMT2_Normalize.add_extra_norm (smtlib2_z3C, add_div_mod) #> |
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SMT2_Translate.add_config (smtlib2_z3C, translate_config))) |
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end |
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(* constructors *) |
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datatype sym = Sym of string * sym list |
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(** additional constructors **) |
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type mk_builtins = { |
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mk_builtin_typ: sym -> typ option, |
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mk_builtin_num: theory -> int -> typ -> cterm option, |
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mk_builtin_fun: theory -> sym -> cterm list -> cterm option } |
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fun chained _ [] = NONE |
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| chained f (b :: bs) = (case f b of SOME y => SOME y | NONE => chained f bs) |
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fun chained_mk_builtin_typ bs sym = |
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chained (fn {mk_builtin_typ=mk, ...} : mk_builtins => mk sym) bs |
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fun chained_mk_builtin_num ctxt bs i T = |
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let val thy = Proof_Context.theory_of ctxt |
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in chained (fn {mk_builtin_num=mk, ...} : mk_builtins => mk thy i T) bs end |
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fun chained_mk_builtin_fun ctxt bs s cts = |
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let val thy = Proof_Context.theory_of ctxt |
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in chained (fn {mk_builtin_fun=mk, ...} : mk_builtins => mk thy s cts) bs end |
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fun fst_int_ord ((i1, _), (i2, _)) = int_ord (i1, i2) |
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structure Mk_Builtins = Generic_Data |
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( |
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type T = (int * mk_builtins) list |
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val empty = [] |
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val extend = I |
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fun merge data = Ord_List.merge fst_int_ord data |
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) |
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|
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fun add_mk_builtins mk = |
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Mk_Builtins.map (Ord_List.insert fst_int_ord (serial (), mk)) |
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|
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fun get_mk_builtins ctxt = map snd (Mk_Builtins.get (Context.Proof ctxt)) |
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123 |
|
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(** basic and additional constructors **) |
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|
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fun mk_builtin_typ _ (Sym ("Bool", _)) = SOME @{typ bool} |
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| mk_builtin_typ _ (Sym ("Int", _)) = SOME @{typ int} |
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| mk_builtin_typ _ (Sym ("bool", _)) = SOME @{typ bool} (*FIXME: legacy*) |
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| mk_builtin_typ _ (Sym ("int", _)) = SOME @{typ int} (*FIXME: legacy*) |
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| mk_builtin_typ ctxt sym = chained_mk_builtin_typ (get_mk_builtins ctxt) sym |
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132 |
|
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fun mk_builtin_num _ i @{typ int} = SOME (Numeral.mk_cnumber @{ctyp int} i) |
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| mk_builtin_num ctxt i T = |
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chained_mk_builtin_num ctxt (get_mk_builtins ctxt) i T |
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|
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val mk_true = Thm.cterm_of @{theory} (@{const Not} $ @{const False}) |
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val mk_false = Thm.cterm_of @{theory} @{const False} |
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val mk_not = Thm.apply (Thm.cterm_of @{theory} @{const Not}) |
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val mk_implies = Thm.mk_binop (Thm.cterm_of @{theory} @{const HOL.implies}) |
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val mk_iff = Thm.mk_binop (Thm.cterm_of @{theory} @{const HOL.eq (bool)}) |
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val conj = Thm.cterm_of @{theory} @{const HOL.conj} |
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val disj = Thm.cterm_of @{theory} @{const HOL.disj} |
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|
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fun mk_nary _ cu [] = cu |
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| mk_nary ct _ cts = uncurry (fold_rev (Thm.mk_binop ct)) (split_last cts) |
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|
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val eq = SMT2_Utils.mk_const_pat @{theory} @{const_name HOL.eq} SMT2_Utils.destT1 |
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fun mk_eq ct cu = Thm.mk_binop (SMT2_Utils.instT' ct eq) ct cu |
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val if_term = |
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SMT2_Utils.mk_const_pat @{theory} @{const_name If} |
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(SMT2_Utils.destT1 o SMT2_Utils.destT2) |
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fun mk_if cc ct cu = |
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Thm.mk_binop (Thm.apply (SMT2_Utils.instT' ct if_term) cc) ct cu |
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|
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val access = |
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SMT2_Utils.mk_const_pat @{theory} @{const_name fun_app} SMT2_Utils.destT1 |
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fun mk_access array = Thm.apply (SMT2_Utils.instT' array access) array |
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|
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val update = SMT2_Utils.mk_const_pat @{theory} @{const_name fun_upd} |
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(Thm.dest_ctyp o SMT2_Utils.destT1) |
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fun mk_update array index value = |
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let val cTs = Thm.dest_ctyp (Thm.ctyp_of_term array) |
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in |
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Thm.apply (Thm.mk_binop (SMT2_Utils.instTs cTs update) array index) value |
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end |
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|
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val mk_uminus = Thm.apply (Thm.cterm_of @{theory} @{const uminus (int)}) |
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val add = Thm.cterm_of @{theory} @{const plus (int)} |
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val int0 = Numeral.mk_cnumber @{ctyp int} 0 |
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val mk_sub = Thm.mk_binop (Thm.cterm_of @{theory} @{const minus (int)}) |
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val mk_mul = Thm.mk_binop (Thm.cterm_of @{theory} @{const times (int)}) |
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val mk_div = Thm.mk_binop (Thm.cterm_of @{theory} @{const z3div}) |
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val mk_mod = Thm.mk_binop (Thm.cterm_of @{theory} @{const z3mod}) |
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val mk_lt = Thm.mk_binop (Thm.cterm_of @{theory} @{const less (int)}) |
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val mk_le = Thm.mk_binop (Thm.cterm_of @{theory} @{const less_eq (int)}) |
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|
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fun mk_builtin_fun ctxt sym cts = |
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(case (sym, cts) of |
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(Sym ("true", _), []) => SOME mk_true |
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| (Sym ("false", _), []) => SOME mk_false |
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| (Sym ("not", _), [ct]) => SOME (mk_not ct) |
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| (Sym ("and", _), _) => SOME (mk_nary conj mk_true cts) |
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| (Sym ("or", _), _) => SOME (mk_nary disj mk_false cts) |
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| (Sym ("implies", _), [ct, cu]) => SOME (mk_implies ct cu) |
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| (Sym ("iff", _), [ct, cu]) => SOME (mk_iff ct cu) |
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| (Sym ("~", _), [ct, cu]) => SOME (mk_iff ct cu) |
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| (Sym ("xor", _), [ct, cu]) => SOME (mk_not (mk_iff ct cu)) |
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| (Sym ("if", _), [ct1, ct2, ct3]) => SOME (mk_if ct1 ct2 ct3) |
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| (Sym ("ite", _), [ct1, ct2, ct3]) => SOME (mk_if ct1 ct2 ct3) (* FIXME: remove *) |
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| (Sym ("=", _), [ct, cu]) => SOME (mk_eq ct cu) |
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| (Sym ("select", _), [ca, ck]) => SOME (Thm.apply (mk_access ca) ck) |
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| (Sym ("store", _), [ca, ck, cv]) => SOME (mk_update ca ck cv) |
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| _ => |
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(case (sym, try (#T o Thm.rep_cterm o hd) cts, cts) of |
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(Sym ("+", _), SOME @{typ int}, _) => SOME (mk_nary add int0 cts) |
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| (Sym ("-", _), SOME @{typ int}, [ct]) => SOME (mk_uminus ct) |
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| (Sym ("-", _), SOME @{typ int}, [ct, cu]) => SOME (mk_sub ct cu) |
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| (Sym ("*", _), SOME @{typ int}, [ct, cu]) => SOME (mk_mul ct cu) |
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| (Sym ("div", _), SOME @{typ int}, [ct, cu]) => SOME (mk_div ct cu) |
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| (Sym ("mod", _), SOME @{typ int}, [ct, cu]) => SOME (mk_mod ct cu) |
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| (Sym ("<", _), SOME @{typ int}, [ct, cu]) => SOME (mk_lt ct cu) |
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| (Sym ("<=", _), SOME @{typ int}, [ct, cu]) => SOME (mk_le ct cu) |
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| (Sym (">", _), SOME @{typ int}, [ct, cu]) => SOME (mk_lt cu ct) |
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| (Sym (">=", _), SOME @{typ int}, [ct, cu]) => SOME (mk_le cu ct) |
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| _ => chained_mk_builtin_fun ctxt (get_mk_builtins ctxt) sym cts)) |
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|
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|
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|
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(* abstraction *) |
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|
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fun is_builtin_theory_term ctxt t = |
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if SMT2_Builtin.is_builtin_num ctxt t then true |
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else |
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(case Term.strip_comb t of |
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(Const c, ts) => SMT2_Builtin.is_builtin_fun ctxt c ts |
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| _ => false) |
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|
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end |