*-h{,SrSSKrSSK7 SSjrSSjrSrSrS rSS jrS r SS jr S r SSjr SSjr SrSrSrSrSrSrSSjrg)z" Usage: import common_z3 as CM_Z3 N)*c^SnSnUc U"U5nOU"X5nU(a [U5$U$)z order preserving >>> vset([[11,2],1, [10,['9',1]],2, 1, [11,2],[3,3],[10,99],1,[10,['9',1]]],idfun=repr) [[11, 2], 1, [10, ['9', 1]], 2, [3, 3], [10, 99]] c3@# 0nUHnX!;dM SX'Uv M g7fN)seqd_ss C/home/james-whalen/.local/lib/python3.13/site-packages/z3/z3util.py _uniq_normalvset.._uniq_normals% A{s  c3P# 0nUHnU"U5nXB;dMSX$'Uv M g7frr)r idfunr r h_s r _uniq_idfunvset.._uniq_idfun$s. AqB| s& &)list)r ras_listr rress r vsetrs8 }3#%49(S(cr[R"S5n[R"S5n[R"S5n[R"S5n[XX45 [[UR UR UR UR 45nU(aSR "U6$U$)Nrz {}.{}.{}.{})ctypesc_uintZ3_get_versionmapintvalueformat)as_strmajorminorbuildrevrss r get_z3_versionr'4s MM! E MM! E MM! E -- C5, S5;; U[[#))D EB ##R(( rc[5(a[U5(deSR[U5UR 5UR 55$)a Returns a 'stronger' hash value than the default hash() method. The result from hash() is not enough to distinguish between 2 z3 expressions in some cases. Note: the following doctests will fail with Python 2.x as the default formatting doesn't match that of 3.x. >>> x1 = Bool('x'); x2 = Bool('x'); x3 = Int('x') >>> print(x1.hash(), x2.hash(), x3.hash()) #BAD: all same hash values 783810685 783810685 783810685 >>> print(ehash(x1), ehash(x2), ehash(x3)) x_783810685_1 x_783810685_1 x_783810685_2 z{}_{}_{})z3_debugis_exprr strhash sort_kindvs r ehashr0As>zzqzzz   SVQVVXq{{} ==rcp[U5=(a% UR5R5[:H$)a EXAMPLES: >>> is_expr_var(Int('7')) True >>> is_expr_var(IntVal('7')) False >>> is_expr_var(Bool('y')) True >>> is_expr_var(Int('x') + 7 == Int('y')) False >>> LOnOff, (On,Off) = EnumSort("LOnOff",['On','Off']) >>> Block,Reset,SafetyInjection=Consts("Block Reset SafetyInjection",LOnOff) >>> is_expr_var(LOnOff) False >>> is_expr_var(On) False >>> is_expr_var(Block) True >>> is_expr_var(SafetyInjection) True is_constdeclkindZ3_OP_UNINTERPRETEDr.s r is_expr_varr7\s%0 A; A1668==?.AAArcp[U5=(a% UR5R5[:g$)a EXAMPLES: >>> is_expr_val(Int('7')) False >>> is_expr_val(IntVal('7')) True >>> is_expr_val(Bool('y')) False >>> is_expr_val(Int('x') + 7 == Int('y')) False >>> LOnOff, (On,Off) = EnumSort("LOnOff",['On','Off']) >>> Block,Reset,SafetyInjection=Consts("Block Reset SafetyInjection",LOnOff) >>> is_expr_val(LOnOff) False >>> is_expr_val(On) True >>> is_expr_val(Block) False >>> is_expr_val(SafetyInjection) False r2r.s r is_expr_valr9ws%. A; A1668==?.AAArcUc/n[5(a[U5(de[U5(a%[U5(aU$[ X/-[ 5$UR 5Hn[X!5nM [ U[ 5$)z >>> x,y = Ints('x y') >>> a,b = Bools('a b') >>> get_vars(Implies(And(x+y==0,x*2==10),Or(a,Implies(a,b==False)))) [x, y, a, b] )r)r*r3r9rr+childrenget_vars)fr&f_s r r<r<su z zzqzzz{{ q>>IS#& &**,B"!BB}rcdUR5[:Xa [U5nU$UR5[:Xa [ U5nU$UR5[ :Xa [ U5nU$UR5[:Xa [X5nU$[SXR54-5e)Nz%Cannot handle this sort (s: %sid: %d)) r5 Z3_INT_SORTInt Z3_REAL_SORTReal Z3_BOOL_SORTBoolZ3_DATATYPE_SORTConst TypeError)namevsortr/s r mk_varrKs zz|{" I H  % J H  % J H ) ) $  H?5**,BWWXXrcN^^[5(aT(a[T5(deUnT(aI[5(a.[[T55upEUU4SjnUSLd U"55e[ TU5nTS:aB[ S5 [ T5 [ S5 [ U5 [ S5 [ U5 [U5n[ USS9nUc [ S 5 g USLag [5(a[U[5(deU(aSUS 4$S/4$) a >>> r,m = prove(BoolVal(True),verbose=0); r,model_str(m,as_str=False) (True, None) #infinite counter example when proving contradiction >>> r,m = prove(BoolVal(False)); r,model_str(m,as_str=False) (False, []) >>> x,y,z=Bools('x y z') >>> r,m = prove(And(x,Not(x))); r,model_str(m,as_str=True) (False, '[]') >>> r,m = prove(True,assume=And(x,Not(x)),verbose=0) Traceback (most recent call last): ... AssertionError: Assumption is always False! >>> r,m = prove(Implies(x,x),assume=y,verbose=2); r,model_str(m,as_str=False) assume: y claim: Implies(x, x) to_prove: Implies(y, Implies(x, x)) (True, None) >>> r,m = prove(And(x,True),assume=y,verbose=0); r,model_str(m,as_str=False) (False, [(x, False), (y, True)]) >>> r,m = prove(And(x,y),assume=y,verbose=0) >>> print(r) False >>> print(model_str(m,as_str=True)) x = False y = True >>> a,b = Ints('a b') >>> r,m = prove(a**b == b**a,assume=None,verbose=0) E: cannot solve ! >>> r is None and m is None True c<>SnTS:aSRTU5nU$)NzAssumption is always False!z{} {})r )emsgassumeverboses r _fprove.._fs$4a<#??648D rFrNzassume: zclaim: z to_prove: rkzE: cannot solve !)NN)TNr) r)r*proveNotImpliesprint get_models isinstancer) claimrPrQto_prove is_proved_rRr=modelss `` r rVrVsZzzWV__,,H :: V-LI  % +rt +%68,!| j f  i e  l h H A Q F ~ !" 5 ::fd++ ++ &)# #"9 rc b[5(a[U5(deUS:de[5nURU5 /nSnUR 5[ :XaXA:aUS-nUR 5nU(dOoURU5 [[UVs/sHof"5XV:HPM sn55nURU5 UR 5[ :XaXA:aMUR 5[:XagUR 5[:XaUS:XagU$s snf)a Returns the first k models satisfying f. If f is not satisfiable, returns False. If f cannot be solved, returns None If f is satisfiable, returns the first k models Note that if f is a tautology, e.g.\ True, then the result is [] Based on http://stackoverflow.com/questions/11867611/z3py-checking-all-solutions-for-equation EXAMPLES: >>> x, y = Ints('x y') >>> len(get_models(And(0<=x,x <= 4),k=11)) 5 >>> get_models(And(0<=x**y,x <= 1),k=2) is None True >>> get_models(And(0<=x,x <= -1),k=2) False >>> len(get_models(x+y==7,5)) 5 >>> len(get_models(And(x<=5,x>=1),7)) 5 >>> get_models(And(x<=0,x>=5),7) False >>> x = Bool('x') >>> get_models(And(x,Not(x)),k=1) False >>> get_models(Implies(x,x),k=1) [] >>> get_models(BoolVal(True),k=1) [] rrNF) r)r*SolveraddchecksatmodelappendrWAndunknownunsat)r=rUr r`imr/blocks r rZrZsJzzqzzzAv vAEE!H F A '')s qu E GGI  aCa0aa012 e  '')s qu wwyG e Q 1s"D, c[USUS9S$)z >>> is_tautology(Implies(Bool('x'),Bool('x'))) True >>> is_tautology(Implies(Bool('x'),Bool('y'))) False >>> is_tautology(BoolVal(True)) True >>> is_tautology(BoolVal(False)) False Nr\rPrQr)rVr\rQs r is_tautologyrqUs uT7 ;A >>rc0[[U5SUS9S$)a >>> x,y=Bools('x y') >>> is_contradiction(BoolVal(False)) True >>> is_contradiction(BoolVal(True)) False >>> is_contradiction(x) False >>> is_contradiction(Implies(x,y)) False >>> is_contradiction(Implies(x,x)) False >>> is_contradiction(And(x,Not(x))) True Nror)rVrWrps r is_contradictionrsgs, s5z$ @ CCrc^[USS9n[U[5(a[U5S:H$g)a return True if f has exactly 1 model, False otherwise. EXAMPLES: >>> x, y = Ints('x y') >>> exact_one_model(And(0<=x**y,x <= 0)) False >>> exact_one_model(And(0<=x,x <= 0)) True >>> exact_one_model(And(0<=x,x <= 1)) False >>> exact_one_model(And(0<=x,x <= -1)) False rNrTrF)rZr[rlen)r=r`s r exact_one_modelrvs/(Q F&$6{arc:[5(a U[:XdU[:Xd U[:Xde[ U5S:Xa5[ US[ 5(d[ US[5(aUSn[5(a[SU55(deUVs/sHn[U5(dMUPM nnU(aP[ U5S:XaUS$U[:Xa [U5$U[:Xa [U5$[USUS5$gs snf)a >>> myAnd(*[Bool('x'),Bool('y')]) And(x, y) >>> myAnd(*[Bool('x'),None]) x >>> myAnd(*[Bool('x')]) x >>> myAnd(*[]) >>> myAnd(Bool('x'),Bool('y')) And(x, y) >>> myAnd(*[Bool('x'),Bool('y')]) And(x, y) >>> myAnd([Bool('x'),Bool('y')]) And(x, y) >>> myAnd((Bool('x'),Bool('y'))) And(x, y) >>> myAnd(*[Bool('x'),Bool('y'),True]) Traceback (most recent call last): ... AssertionError rrc3L# UHn[U[5(+v M g7fr)r[bool).0vals r myBinOp..s:z#t,,,s"$N) r)Z3_OP_OR Z3_OP_AND Z3_OP_IMPLIESrur[rtupleallr*OrrhrX)opLr{s r myBinOprs>zzX~yB-4GGG 1v{ 1Q4..*QqT52I2I aDzz::::::*WS\A* q6Q;Q4K >a5L ?q6MqtQqT"" +s D8Dc"[[/UQ76$r)rrrs r myAndrs 9 !q !!rc"[[/UQ76$r)rr~rs r myOrrs 8 a  rc$[[X/5$r)rr)abs r myImpliesrs =1& ))rcZ[[USUS5[USUS55$)Nrr)rhrX)r=s r Iffrs- wqtQqT"GAaD!A$$7 88rc h[5(a UbU/:Xd[U[5(deU(a^UVs/sHo"X4PM nn[USS9nU(a5SR UVVs/sHupBSR XB5PM snn5$U$U(a [ U5$U$s snfs snnf)z Returned a 'sorted' model (so that it's easier to see) The model is sorted by its key, e.g. if the model is y = 3 , x = 10, then the result is x = 10, y = 3 EXAMPLES: see doctest examples from function prove() c[U5$r)r+)rr_s r model_str..sQr)key z{} = {})r)r[ModelRefsortedjoinr r+)rlr!r/vsrUs r model_strrszzyAGz!X'>'>>>!" #A!$i # B/ 0 992F2!i..q42FG GIs1v&Q&$Gs B).B. )NT)Fr)Nr)r)T)__doc__rz3rr'r0r7r9r<rKrVrZrqrsrvrrrrrrrrr rsy )D >* B6B46  Vr>B?$D262j"!*9'r