author | boehmes |
Mon, 20 Dec 2010 09:06:37 +0100 | |
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parent 41280 | a7de9d36f4f2 |
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permissions | -rw-r--r-- |
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(* Title: HOL/Tools/SMT/z3_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_INTERFACE = |
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sig |
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val smtlib_z3C: SMT_Utils.class |
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val setup: theory -> theory |
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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_Interface: Z3_INTERFACE = |
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struct |
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structure U = SMT_Utils |
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structure B = SMT_Builtin |
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val smtlib_z3C = SMTLIB_Interface.smtlibC @ ["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 {prefixes, header, is_fol, serialize, ...} = |
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SMTLIB_Interface.translate_config ctxt |
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in |
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{prefixes=prefixes, header=header, is_fol=is_fol, serialize=serialize, |
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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_by_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: SMT.z3div_def)} |
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val mod_by_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_by_z3div :: mod_by_z3mod :: extra_thms) |
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else (thms, extra_thms) |
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val setup_builtins = |
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B.add_builtin_fun' smtlib_z3C (@{const times (int)}, "*") #> |
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B.add_builtin_fun' smtlib_z3C (@{const z3div}, "div") #> |
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B.add_builtin_fun' smtlib_z3C (@{const z3mod}, "mod") |
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in |
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val setup = Context.theory_map ( |
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setup_builtins #> |
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SMT_Normalize.add_extra_norm (smtlib_z3C, add_div_mod) #> |
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SMT_Translate.add_config (smtlib_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 = ProofContext.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 = ProofContext.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 (bs1, bs2) = Ord_List.union fst_int_ord bs2 bs1 |
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123 |
) |
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124 |
|
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125 |
fun add_mk_builtins mk = |
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Mk_Builtins.map (Ord_List.insert fst_int_ord (serial (), mk)) |
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127 |
|
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128 |
fun get_mk_builtins ctxt = map snd (Mk_Builtins.get (Context.Proof ctxt)) |
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129 |
|
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130 |
|
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131 |
(** basic and additional constructors **) |
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132 |
|
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133 |
fun mk_builtin_typ _ (Sym ("bool", _)) = SOME @{typ bool} |
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| mk_builtin_typ _ (Sym ("Int", _)) = SOME @{typ int} |
135 |
| mk_builtin_typ _ (Sym ("int", _)) = SOME @{typ int} (*FIXME: delete*) |
|
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| mk_builtin_typ ctxt sym = chained_mk_builtin_typ (get_mk_builtins ctxt) sym |
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137 |
|
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138 |
fun mk_builtin_num _ i @{typ int} = SOME (Numeral.mk_cnumber @{ctyp int} i) |
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139 |
| mk_builtin_num ctxt i T = |
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140 |
chained_mk_builtin_num ctxt (get_mk_builtins ctxt) i T |
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141 |
|
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142 |
val mk_true = Thm.cterm_of @{theory} (@{const Not} $ @{const False}) |
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143 |
val mk_false = Thm.cterm_of @{theory} @{const False} |
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144 |
val mk_not = Thm.capply (Thm.cterm_of @{theory} @{const Not}) |
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145 |
val mk_implies = Thm.mk_binop (Thm.cterm_of @{theory} @{const HOL.implies}) |
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146 |
val mk_iff = Thm.mk_binop (Thm.cterm_of @{theory} @{const HOL.eq (bool)}) |
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147 |
val conj = Thm.cterm_of @{theory} @{const HOL.conj} |
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148 |
val disj = Thm.cterm_of @{theory} @{const HOL.disj} |
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149 |
|
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150 |
fun mk_nary _ cu [] = cu |
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151 |
| mk_nary ct _ cts = uncurry (fold_rev (Thm.mk_binop ct)) (split_last cts) |
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152 |
|
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153 |
val eq = U.mk_const_pat @{theory} @{const_name HOL.eq} U.destT1 |
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154 |
fun mk_eq ct cu = Thm.mk_binop (U.instT' ct eq) ct cu |
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155 |
|
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156 |
val if_term = U.mk_const_pat @{theory} @{const_name If} (U.destT1 o U.destT2) |
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157 |
fun mk_if cc ct cu = Thm.mk_binop (Thm.capply (U.instT' ct if_term) cc) ct cu |
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158 |
|
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159 |
val nil_term = U.mk_const_pat @{theory} @{const_name Nil} U.destT1 |
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160 |
val cons_term = U.mk_const_pat @{theory} @{const_name Cons} U.destT1 |
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161 |
fun mk_list cT cts = |
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162 |
fold_rev (Thm.mk_binop (U.instT cT cons_term)) cts (U.instT cT nil_term) |
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163 |
|
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164 |
val distinct = U.mk_const_pat @{theory} @{const_name distinct} |
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165 |
(U.destT1 o U.destT1) |
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166 |
fun mk_distinct [] = mk_true |
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167 |
| mk_distinct (cts as (ct :: _)) = |
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168 |
Thm.capply (U.instT' ct distinct) (mk_list (Thm.ctyp_of_term ct) cts) |
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|
169 |
|
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170 |
val access = U.mk_const_pat @{theory} @{const_name fun_app} U.destT1 |
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171 |
fun mk_access array = Thm.capply (U.instT' array access) array |
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|
172 |
|
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173 |
val update = U.mk_const_pat @{theory} @{const_name fun_upd} |
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174 |
(Thm.dest_ctyp o U.destT1) |
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175 |
fun mk_update array index value = |
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176 |
let val cTs = Thm.dest_ctyp (Thm.ctyp_of_term array) |
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177 |
in Thm.capply (Thm.mk_binop (U.instTs cTs update) array index) value end |
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178 |
|
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179 |
val mk_uminus = Thm.capply (Thm.cterm_of @{theory} @{const uminus (int)}) |
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180 |
val mk_add = Thm.mk_binop (Thm.cterm_of @{theory} @{const plus (int)}) |
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181 |
val mk_sub = Thm.mk_binop (Thm.cterm_of @{theory} @{const minus (int)}) |
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182 |
val mk_mul = Thm.mk_binop (Thm.cterm_of @{theory} @{const times (int)}) |
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183 |
val mk_div = Thm.mk_binop (Thm.cterm_of @{theory} @{const z3div}) |
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184 |
val mk_mod = Thm.mk_binop (Thm.cterm_of @{theory} @{const z3mod}) |
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185 |
val mk_lt = Thm.mk_binop (Thm.cterm_of @{theory} @{const less (int)}) |
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186 |
val mk_le = Thm.mk_binop (Thm.cterm_of @{theory} @{const less_eq (int)}) |
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|
187 |
|
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188 |
fun mk_builtin_fun ctxt sym cts = |
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189 |
(case (sym, cts) of |
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190 |
(Sym ("true", _), []) => SOME mk_true |
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191 |
| (Sym ("false", _), []) => SOME mk_false |
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192 |
| (Sym ("not", _), [ct]) => SOME (mk_not ct) |
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193 |
| (Sym ("and", _), _) => SOME (mk_nary conj mk_true cts) |
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194 |
| (Sym ("or", _), _) => SOME (mk_nary disj mk_false cts) |
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195 |
| (Sym ("implies", _), [ct, cu]) => SOME (mk_implies ct cu) |
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196 |
| (Sym ("iff", _), [ct, cu]) => SOME (mk_iff ct cu) |
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197 |
| (Sym ("~", _), [ct, cu]) => SOME (mk_iff ct cu) |
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198 |
| (Sym ("xor", _), [ct, cu]) => SOME (mk_not (mk_iff ct cu)) |
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199 |
| (Sym ("ite", _), [ct1, ct2, ct3]) => SOME (mk_if ct1 ct2 ct3) |
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200 |
| (Sym ("=", _), [ct, cu]) => SOME (mk_eq ct cu) |
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201 |
| (Sym ("distinct", _), _) => SOME (mk_distinct cts) |
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202 |
| (Sym ("select", _), [ca, ck]) => SOME (Thm.capply (mk_access ca) ck) |
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203 |
| (Sym ("store", _), [ca, ck, cv]) => SOME (mk_update ca ck cv) |
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204 |
| _ => |
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205 |
(case (sym, try (#T o Thm.rep_cterm o hd) cts, cts) of |
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206 |
(Sym ("+", _), SOME @{typ int}, [ct, cu]) => SOME (mk_add ct cu) |
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|
207 |
| (Sym ("-", _), SOME @{typ int}, [ct]) => SOME (mk_uminus ct) |
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208 |
| (Sym ("-", _), SOME @{typ int}, [ct, cu]) => SOME (mk_sub ct cu) |
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209 |
| (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) |
211 |
| (Sym ("mod", _), SOME @{typ int}, [ct, cu]) => SOME (mk_mod ct cu) |
|
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212 |
| (Sym ("<", _), SOME @{typ int}, [ct, cu]) => SOME (mk_lt ct cu) |
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213 |
| (Sym ("<=", _), SOME @{typ int}, [ct, cu]) => SOME (mk_le ct cu) |
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214 |
| (Sym (">", _), SOME @{typ int}, [ct, cu]) => SOME (mk_lt cu ct) |
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215 |
| (Sym (">=", _), SOME @{typ int}, [ct, cu]) => SOME (mk_le cu ct) |
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216 |
| _ => chained_mk_builtin_fun ctxt (get_mk_builtins ctxt) sym cts)) |
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217 |
|
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|
218 |
|
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219 |
|
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|
220 |
(* abstraction *) |
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221 |
|
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fun is_builtin_theory_term ctxt t = |
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if B.is_builtin_num ctxt t then true |
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else |
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centralized handling of built-in types and constants;
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parents:
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(case Term.strip_comb t of |
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226 |
(Const c, ts) => B.is_builtin_fun ctxt c ts |
d2b1fc1b8e19
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227 |
| _ => false) |
36899
bcd6fce5bf06
layered SMT setup, adapted SMT clients, added further tests, made Z3 proof abstraction configurable
boehmes
parents:
36898
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228 |
|
bcd6fce5bf06
layered SMT setup, adapted SMT clients, added further tests, made Z3 proof abstraction configurable
boehmes
parents:
36898
diff
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229 |
end |