public MkImplies ( |
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t1 | ||
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public void Run() { Dictionary<string, string> cfg = new Dictionary<string, string>() { { "AUTO_CONFIG", "true" } }; using (Context ctx = new Context(cfg)) { BoolExpr p1 = ctx.MkBoolConst("p1"); BoolExpr p2 = ctx.MkBoolConst("p2"); BoolExpr p3 = ctx.MkBoolConst("p3"); IntExpr x = ctx.MkIntConst("x"); IntExpr y = ctx.MkIntConst("y"); Solver s = ctx.MkSolver(); s.Assert(ctx.MkImplies(p1, ctx.MkGt(x, ctx.MkInt(10))), ctx.MkImplies(p1, ctx.MkGt(y, x)), ctx.MkImplies(p2, ctx.MkLt(y, ctx.MkInt(5))), ctx.MkImplies(p3, ctx.MkGt(y, ctx.MkInt(0)))); Console.WriteLine(s); Console.WriteLine(s.Check(p1, p2, p3)); Console.WriteLine("Core: "); foreach (Expr e in s.UnsatCore) Console.WriteLine(e); Console.WriteLine(s.Check(p1, p3)); Console.WriteLine(s.Model); } }
public void Run() { using (Context ctx = new Context()) { var s = ctx.MkFixedpoint(); BoolSort B = ctx.BoolSort; Sort BV8 = ctx.MkBitVecSort(8); FuncDecl edge = ctx.MkFuncDecl("edge", new Sort[]{BV8, BV8}, B); FuncDecl path = ctx.MkFuncDecl("path", new Sort[]{BV8, BV8}, B); BitVecExpr x = (BitVecExpr)ctx.MkBound(0,BV8); BitVecExpr y = (BitVecExpr)ctx.MkBound(1,BV8); BitVecExpr z = (BitVecExpr)ctx.MkBound(2,BV8); s.RegisterRelation(edge); s.RegisterRelation(path); s.AddRule(ctx.MkImplies((BoolExpr)edge[x,y],(BoolExpr)path[x,y])); s.AddRule(ctx.MkImplies(ctx.MkAnd((BoolExpr)path[x,y],(BoolExpr)path[y,z]), (BoolExpr)path[x,z])); for (uint i = 0; i < 128; ++i) { s.AddFact(edge, i, i+1); } Console.WriteLine(s.Query((BoolExpr)path[ctx.MkBV(0,8),ctx.MkBV(129,8)])); Console.WriteLine(s.GetAnswer()); Console.WriteLine(s.Query((BoolExpr)path[ctx.MkBV(0,8),ctx.MkBV(128,8)])); Console.WriteLine(s.GetAnswer()); Console.WriteLine(s.Query((BoolExpr)path[x,ctx.MkBV(20,8)])); Console.WriteLine(s.GetAnswer()); Console.WriteLine(s.Query(ctx.MkAnd((BoolExpr)path[x,y], (BoolExpr)path[y,ctx.MkBV(20,8)]))); Console.WriteLine(s.GetAnswer()); } }
/// <summary> /// Generates a slightly randomized expression. /// </summary> static BoolExpr MkRandomExpr(Context ctx, System.Random rng) { int limit = 1073741823; Sort i = ctx.IntSort; Sort b = ctx.BoolSort; Symbol sr1 = ctx.MkSymbol(rng.Next(0, limit)); Symbol sr2 = ctx.MkSymbol(rng.Next(0, limit)); Symbol sr3 = ctx.MkSymbol(rng.Next(0, limit)); FuncDecl r1 = ctx.MkFuncDecl(sr1, i, b); FuncDecl r2 = ctx.MkFuncDecl(sr2, i, b); FuncDecl r3 = ctx.MkFuncDecl(sr3, i, b); Symbol s = ctx.MkSymbol(rng.Next(0, limit)); Expr x = ctx.MkConst(s, i); BoolExpr r1x = (BoolExpr)ctx.MkApp(r1, x); BoolExpr r2x = (BoolExpr)ctx.MkApp(r2, x); BoolExpr r3x = (BoolExpr)ctx.MkApp(r3, x); Expr[] vars = { x }; BoolExpr rl1 = ctx.MkForall(vars, ctx.MkImplies(r1x, r2x)); BoolExpr rl2 = ctx.MkForall(vars, ctx.MkImplies(r2x, r1x)); BoolExpr rl3 = (BoolExpr)ctx.MkApp(r1, ctx.MkInt(3)); BoolExpr q = (BoolExpr)ctx.MkApp(r3, ctx.MkInt(2)); BoolExpr a1 = ctx.MkNot(q); BoolExpr q1 = ctx.MkExists(vars, ctx.MkAnd(r3x, r2x)); BoolExpr q2 = ctx.MkExists(vars, ctx.MkAnd(r3x, r1x)); BoolExpr[] all = { a1, q1, q2 }; return ctx.MkAnd(all); }
public void Run() { using (Context ctx = new Context()) { ctx.UpdateParamValue("DL_ENGINE","1"); ctx.UpdateParamValue("DL_PDR_USE_FARKAS","true"); // ctx.UpdateParamValue("VERBOSE","2"); var s = ctx.MkFixedpoint(); BoolSort B = ctx.BoolSort; IntSort I = ctx.IntSort; FuncDecl mc = ctx.MkFuncDecl("mc", new Sort[]{I, I}, B); ArithExpr x = (ArithExpr)ctx.MkBound(0,I); ArithExpr y = (ArithExpr)ctx.MkBound(1,I); ArithExpr z = (ArithExpr)ctx.MkBound(2,I); s.RegisterRelation(mc); BoolExpr gt = ctx.MkGt(x, ctx.MkInt(100)); s.AddRule(ctx.MkImplies(gt,(BoolExpr)mc[x,ctx.MkSub(x,ctx.MkInt(10))])); s.AddRule(ctx.MkImplies(ctx.MkAnd(ctx.MkNot(gt), (BoolExpr) mc[ctx.MkAdd(x,ctx.MkInt(11)),y], (BoolExpr) mc[y,z]), (BoolExpr) mc[x,z])); Console.WriteLine(s.Query(ctx.MkAnd((BoolExpr)mc[x,y], ctx.MkGt(y,ctx.MkInt(100))))); Console.WriteLine(s.GetAnswer()); Console.WriteLine(s.Query(ctx.MkAnd((BoolExpr)mc[x,y], ctx.MkLt(y,ctx.MkInt(91))))); Console.WriteLine(s.GetAnswer()); } }
/// <summary> /// Prove <tt>store(a1, i1, v1) = store(a2, i2, v2) implies (i1 = i3 or i2 = i3 or select(a1, i3) = select(a2, i3))</tt>. /// </summary> /// <remarks>This example demonstrates how to use the array theory.</remarks> public static void ArrayExample2(Context ctx) { Console.WriteLine("ArrayExample2"); Sort int_type = ctx.IntSort; Sort array_type = ctx.MkArraySort(int_type, int_type); ArrayExpr a1 = (ArrayExpr)ctx.MkConst("a1", array_type); ArrayExpr a2 = ctx.MkArrayConst("a2", int_type, int_type); Expr i1 = ctx.MkConst("i1", int_type); Expr i2 = ctx.MkConst("i2", int_type); Expr i3 = ctx.MkConst("i3", int_type); Expr v1 = ctx.MkConst("v1", int_type); Expr v2 = ctx.MkConst("v2", int_type); Expr st1 = ctx.MkStore(a1, i1, v1); Expr st2 = ctx.MkStore(a2, i2, v2); Expr sel1 = ctx.MkSelect(a1, i3); Expr sel2 = ctx.MkSelect(a2, i3); /* create antecedent */ BoolExpr antecedent = ctx.MkEq(st1, st2); /* create consequent: i1 = i3 or i2 = i3 or select(a1, i3) = select(a2, i3) */ BoolExpr consequent = ctx.MkOr(new BoolExpr[] { ctx.MkEq(i1, i3), ctx.MkEq(i2, i3), ctx.MkEq(sel1, sel2) }); /* prove store(a1, i1, v1) = store(a2, i2, v2) implies (i1 = i3 or i2 = i3 or select(a1, i3) = select(a2, i3)) */ BoolExpr thm = ctx.MkImplies(antecedent, consequent); Console.WriteLine("prove: store(a1, i1, v1) = store(a2, i2, v2) implies (i1 = i3 or i2 = i3 or select(a1, i3) = select(a2, i3))"); Console.WriteLine("{0}", (thm)); Prove(ctx, thm); }
public void Run() { Dictionary<string, string> cfg = new Dictionary<string, string>() { { "AUTO_CONFIG", "true" } }; using (Context ctx = new Context(cfg)) { Sort A = ctx.MkUninterpretedSort("A"); Sort B = ctx.MkUninterpretedSort("B"); FuncDecl f = ctx.MkFuncDecl("f", A, B); Expr a1 = ctx.MkConst("a1", A); Expr a2 = ctx.MkConst("a2", A); Expr b = ctx.MkConst("b", B); Expr x = ctx.MkConst("x", A); Expr y = ctx.MkConst("y", A); Solver s = ctx.MkSolver(); s.Assert(ctx.MkNot(ctx.MkEq(a1, a2))); s.Assert(ctx.MkEq(f[a1], b)); s.Assert(ctx.MkEq(f[a2], b)); s.Assert(ctx.MkForall(new Expr[] { x, y }, ctx.MkImplies(ctx.MkEq(f[x], f[y]), ctx.MkEq(x, y)), 1, new Pattern[] { ctx.MkPattern(f[x], f[y]) })); Console.WriteLine(s); Console.WriteLine(s.Check()); } }
public BoolExpr DependsOn(Context ctx, BoolExpr pack, BoolExpr[] deps) { BoolExpr[] q = new BoolExpr[deps.Length]; for (uint i = 0; i < deps.Length; i++) q[i] = ctx.MkImplies(pack, deps[i]); return ctx.MkAnd(q); }
public void Run() { using (Context ctx = new Context()) { BoolExpr p = ctx.MkBoolConst("p"); BoolExpr q = ctx.MkBoolConst("q"); Console.WriteLine(ctx.MkAnd(p, q)); Console.WriteLine(ctx.MkOr(p, q)); Console.WriteLine(ctx.MkAnd(p, ctx.MkTrue())); Console.WriteLine(ctx.MkOr(p, ctx.MkFalse())); Console.WriteLine(ctx.MkNot(p)); Console.WriteLine(ctx.MkImplies(p, q)); Console.WriteLine(ctx.MkEq(p, q).Simplify()); Console.WriteLine(ctx.MkEq(p, q)); BoolExpr r = ctx.MkBoolConst("r"); Console.WriteLine(ctx.MkNot(ctx.MkEq(p, ctx.MkNot(ctx.MkEq(q, r))))); Console.WriteLine(ctx.MkNot(ctx.MkEq(ctx.MkNot(ctx.MkEq(p, q)), r))); Console.WriteLine(ctx.MkEq(p, ctx.MkTrue())); Console.WriteLine(ctx.MkEq(p, ctx.MkFalse())); Console.WriteLine(ctx.MkEq(p, ctx.MkTrue()).Simplify()); Console.WriteLine(ctx.MkEq(p, ctx.MkFalse()).Simplify()); Console.WriteLine(ctx.MkEq(p, p).Simplify()); Console.WriteLine(ctx.MkEq(p, q).Simplify()); Console.WriteLine(ctx.MkAnd(p, q, r)); Console.WriteLine(ctx.MkOr(p, q, r)); IntExpr x = ctx.MkIntConst("x"); Console.WriteLine(x is BoolExpr); Console.WriteLine(p is BoolExpr); Console.WriteLine(ctx.MkAnd(p, q) is BoolExpr); Console.WriteLine(p is BoolExpr); Console.WriteLine(ctx.MkAdd(x, ctx.MkInt(1)) is BoolExpr); Console.WriteLine(p.IsAnd); Console.WriteLine(ctx.MkOr(p, q).IsOr); Console.WriteLine(ctx.MkAnd(p, q).IsAnd); Console.WriteLine(x.IsNot); Console.WriteLine(p.IsNot); Console.WriteLine(ctx.MkNot(p)); Console.WriteLine(ctx.MkNot(p).IsDistinct); Console.WriteLine(ctx.MkEq(p, q).IsDistinct); Console.WriteLine(ctx.MkDistinct(p, q).IsDistinct); Console.WriteLine(ctx.MkDistinct(x, ctx.MkAdd(x, ctx.MkInt(1)), ctx.MkAdd(x, ctx.MkInt(2))).IsDistinct); Console.WriteLine(); Console.WriteLine(ctx.MkBool(true)); Console.WriteLine(ctx.MkBool(false)); Console.WriteLine(ctx.BoolSort); Context ctx1 = new Context(); Console.WriteLine(ctx1.MkBool(true)); Console.WriteLine(ctx1.BoolSort); Console.WriteLine(ctx1.MkBool(true).Sort == ctx1.BoolSort); Console.WriteLine(ctx1.MkBool(true).Sort == ctx.BoolSort); Console.WriteLine(ctx1.MkBool(true).Sort != ctx.BoolSort); } }
public void Run() { using (Context ctx = new Context()) { var s = ctx.MkFixedpoint(); BoolExpr a = ctx.MkBoolConst("a"); BoolExpr b = ctx.MkBoolConst("b"); BoolExpr c = ctx.MkBoolConst("c"); s.RegisterRelation(a.FuncDecl); s.RegisterRelation(b.FuncDecl); s.RegisterRelation(c.FuncDecl); s.AddRule(ctx.MkImplies(a, b)); s.AddRule(ctx.MkImplies(b, c)); Console.WriteLine(s.Query(c)); s.AddRule(a); Console.WriteLine(s.Query(c)); } }
public void Run() { Dictionary<string, string> cfg = new Dictionary<string, string>() { { "AUTO_CONFIG", "true" } }; using (Context ctx = new Context(cfg)) { Sort T = ctx.MkUninterpretedSort("Type"); FuncDecl subtype = ctx.MkFuncDecl("subtype", new Sort[] { T, T }, ctx.BoolSort); FuncDecl array_of = ctx.MkFuncDecl("array_of", T, T); Expr root = ctx.MkConst("root", T); Expr x = ctx.MkConst("x", T); Expr y = ctx.MkConst("y", T); Expr z = ctx.MkConst("z", T); BoolExpr[] axioms = new BoolExpr[] { ctx.MkForall(new Expr[] { x }, subtype[x, x]), ctx.MkForall(new Expr[] { x, y , z }, ctx.MkImplies(ctx.MkAnd((BoolExpr)subtype[x,y], (BoolExpr)subtype[y,z]), (BoolExpr)subtype[x,z])), ctx.MkForall(new Expr[] { x, y }, ctx.MkImplies(ctx.MkAnd((BoolExpr)subtype[x, y], (BoolExpr)subtype[y,x]), ctx.MkEq(x, y))), ctx.MkForall(new Expr[] { x, y, z }, ctx.MkImplies(ctx.MkAnd((BoolExpr)subtype[x,y],(BoolExpr)subtype[x,z]), ctx.MkOr((BoolExpr)subtype[y,z], (BoolExpr)subtype[z,y]))), ctx.MkForall(new Expr[] { x, y }, ctx.MkImplies((BoolExpr)subtype[x,y], (BoolExpr)subtype[array_of[x], array_of[y]])), ctx.MkForall(new Expr[] { x }, (BoolExpr) subtype[root, x]) }; Solver s = ctx.MkSolver(); s.Assert(axioms); Console.WriteLine(s); Console.WriteLine(s.Check()); Expr[] universe = s.Model.SortUniverse(T); foreach (var e in universe) Console.WriteLine(e); Console.WriteLine(s.Model); } }
public void Run() { using (Context ctx = new Context()) { var s = ctx.MkFixedpoint(); BoolSort B = ctx.BoolSort; Sort BV8 = ctx.MkBitVecSort(8); FuncDecl f = ctx.MkFuncDecl("f", BV8, B); FuncDecl g = ctx.MkFuncDecl("g", BV8, B); BitVecExpr b0 = (BitVecExpr)ctx.MkBound(0,BV8); s.RegisterRelation(f); s.RegisterRelation(g); s.AddRule((BoolExpr)f[b0]); BitVecExpr mask0 = ctx.MkBV(0xFE,8); BoolExpr even = ctx.MkEq(b0,ctx.MkBVAND(b0,mask0)); s.AddRule(ctx.MkImplies(ctx.MkAnd((BoolExpr)f[b0],even), (BoolExpr)g[b0])); Console.WriteLine(s.Query((BoolExpr)g[b0])); Console.WriteLine(s.GetAnswer()); } }
/// <summary> /// Create a forest of trees. /// </summary> /// <remarks> /// forest ::= nil | cons(tree, forest) /// tree ::= nil | cons(forest, forest) /// </remarks> public static void ForestExample(Context ctx) { Console.WriteLine("ForestExample"); Sort tree, forest; FuncDecl nil1_decl, is_nil1_decl, cons1_decl, is_cons1_decl, car1_decl, cdr1_decl; FuncDecl nil2_decl, is_nil2_decl, cons2_decl, is_cons2_decl, car2_decl, cdr2_decl; Expr nil1, nil2, t1, t2, t3, t4, f1, f2, f3, l1, l2, x, y, u, v; // // Declare the names of the accessors for cons. // Then declare the sorts of the accessors. // For this example, all sorts refer to the new types 'forest' and 'tree' // being declared, so we pass in null for both sorts1 and sorts2. // On the other hand, the sort_refs arrays contain the indices of the // two new sorts being declared. The first element in sort1_refs // points to 'tree', which has index 1, the second element in sort1_refs array // points to 'forest', which has index 0. // Symbol[] head_tail1 = new Symbol[] { ctx.MkSymbol("head"), ctx.MkSymbol("tail") }; Sort[] sorts1 = new Sort[] { null, null }; uint[] sort1_refs = new uint[] { 1, 0 }; // the first item points to a tree, the second to a forest Symbol[] head_tail2 = new Symbol[] { ctx.MkSymbol("car"), ctx.MkSymbol("cdr") }; Sort[] sorts2 = new Sort[] { null, null }; uint[] sort2_refs = new uint[] { 0, 0 }; // both items point to the forest datatype. Constructor nil1_con, cons1_con, nil2_con, cons2_con; Constructor[] constructors1 = new Constructor[2], constructors2 = new Constructor[2]; Symbol[] sort_names = { ctx.MkSymbol("forest"), ctx.MkSymbol("tree") }; /* build a forest */ nil1_con = ctx.MkConstructor(ctx.MkSymbol("nil"), ctx.MkSymbol("is_nil"), null, null, null); cons1_con = ctx.MkConstructor(ctx.MkSymbol("cons1"), ctx.MkSymbol("is_cons1"), head_tail1, sorts1, sort1_refs); constructors1[0] = nil1_con; constructors1[1] = cons1_con; /* build a tree */ nil2_con = ctx.MkConstructor(ctx.MkSymbol("nil2"), ctx.MkSymbol("is_nil2"), null, null, null); cons2_con = ctx.MkConstructor(ctx.MkSymbol("cons2"), ctx.MkSymbol("is_cons2"), head_tail2, sorts2, sort2_refs); constructors2[0] = nil2_con; constructors2[1] = cons2_con; Constructor[][] clists = new Constructor[][] { constructors1, constructors2 }; Sort[] sorts = ctx.MkDatatypeSorts(sort_names, clists); forest = sorts[0]; tree = sorts[1]; // // Now that the datatype has been created. // Query the constructors for the constructor // functions, testers, and field accessors. // nil1_decl = nil1_con.ConstructorDecl; is_nil1_decl = nil1_con.TesterDecl; cons1_decl = cons1_con.ConstructorDecl; is_cons1_decl = cons1_con.TesterDecl; FuncDecl[] cons1_accessors = cons1_con.AccessorDecls; car1_decl = cons1_accessors[0]; cdr1_decl = cons1_accessors[1]; nil2_decl = nil2_con.ConstructorDecl; is_nil2_decl = nil2_con.TesterDecl; cons2_decl = cons2_con.ConstructorDecl; is_cons2_decl = cons2_con.TesterDecl; FuncDecl[] cons2_accessors = cons2_con.AccessorDecls; car2_decl = cons2_accessors[0]; cdr2_decl = cons2_accessors[1]; nil1 = ctx.MkConst(nil1_decl); nil2 = ctx.MkConst(nil2_decl); f1 = ctx.MkApp(cons1_decl, nil2, nil1); t1 = ctx.MkApp(cons2_decl, nil1, nil1); t2 = ctx.MkApp(cons2_decl, f1, nil1); t3 = ctx.MkApp(cons2_decl, f1, f1); t4 = ctx.MkApp(cons2_decl, nil1, f1); f2 = ctx.MkApp(cons1_decl, t1, nil1); f3 = ctx.MkApp(cons1_decl, t1, f1); /* nil != cons(nil,nil) */ Prove(ctx, ctx.MkNot(ctx.MkEq(nil1, f1))); Prove(ctx, ctx.MkNot(ctx.MkEq(nil2, t1))); /* cons(x,u) = cons(x, v) => u = v */ u = ctx.MkConst("u", forest); v = ctx.MkConst("v", forest); x = ctx.MkConst("x", tree); y = ctx.MkConst("y", tree); l1 = ctx.MkApp(cons1_decl, x, u); l2 = ctx.MkApp(cons1_decl, y, v); Prove(ctx, ctx.MkImplies(ctx.MkEq(l1, l2), ctx.MkEq(u, v))); Prove(ctx, ctx.MkImplies(ctx.MkEq(l1, l2), ctx.MkEq(x, y))); /* is_nil(u) or is_cons(u) */ Prove(ctx, ctx.MkOr((BoolExpr)ctx.MkApp(is_nil1_decl, u), (BoolExpr)ctx.MkApp(is_cons1_decl, u))); /* occurs check u != cons(x,u) */ Prove(ctx, ctx.MkNot(ctx.MkEq(u, l1))); }
/// <summary> /// Create a binary tree datatype. /// </summary> public static void TreeExample(Context ctx) { Console.WriteLine("TreeExample"); Sort cell; FuncDecl nil_decl, is_nil_decl, cons_decl, is_cons_decl, car_decl, cdr_decl; Expr nil, l1, l2, x, y, u, v; BoolExpr fml, fml1; string[] head_tail = new string[] { "car", "cdr" }; Sort[] sorts = new Sort[] { null, null }; uint[] sort_refs = new uint[] { 0, 0 }; Constructor nil_con, cons_con; nil_con = ctx.MkConstructor("nil", "is_nil", null, null, null); cons_con = ctx.MkConstructor("cons", "is_cons", head_tail, sorts, sort_refs); Constructor[] constructors = new Constructor[] { nil_con, cons_con }; cell = ctx.MkDatatypeSort("cell", constructors); nil_decl = nil_con.ConstructorDecl; is_nil_decl = nil_con.TesterDecl; cons_decl = cons_con.ConstructorDecl; is_cons_decl = cons_con.TesterDecl; FuncDecl[] cons_accessors = cons_con.AccessorDecls; car_decl = cons_accessors[0]; cdr_decl = cons_accessors[1]; nil = ctx.MkConst(nil_decl); l1 = ctx.MkApp(cons_decl, nil, nil); l2 = ctx.MkApp(cons_decl, l1, nil); /* nil != cons(nil, nil) */ Prove(ctx, ctx.MkNot(ctx.MkEq(nil, l1))); /* cons(x,u) = cons(x, v) => u = v */ u = ctx.MkConst("u", cell); v = ctx.MkConst("v", cell); x = ctx.MkConst("x", cell); y = ctx.MkConst("y", cell); l1 = ctx.MkApp(cons_decl, x, u); l2 = ctx.MkApp(cons_decl, y, v); Prove(ctx, ctx.MkImplies(ctx.MkEq(l1, l2), ctx.MkEq(u, v))); Prove(ctx, ctx.MkImplies(ctx.MkEq(l1, l2), ctx.MkEq(x, y))); /* is_nil(u) or is_cons(u) */ Prove(ctx, ctx.MkOr((BoolExpr)ctx.MkApp(is_nil_decl, u), (BoolExpr)ctx.MkApp(is_cons_decl, u))); /* occurs check u != cons(x,u) */ Prove(ctx, ctx.MkNot(ctx.MkEq(u, l1))); /* destructors: is_cons(u) => u = cons(car(u),cdr(u)) */ fml1 = ctx.MkEq(u, ctx.MkApp(cons_decl, ctx.MkApp(car_decl, u), ctx.MkApp(cdr_decl, u))); fml = ctx.MkImplies((BoolExpr)ctx.MkApp(is_cons_decl, u), fml1); Console.WriteLine("Formula {0}", fml); Prove(ctx, fml); Disprove(ctx, fml1); }
/// <summary> /// Create a list datatype. /// </summary> public static void ListExample(Context ctx) { Console.WriteLine("ListExample"); Sort int_ty; ListSort int_list; Expr nil, l1, l2, x, y, u, v; BoolExpr fml, fml1; int_ty = ctx.MkIntSort(); int_list = ctx.MkListSort(ctx.MkSymbol("int_list"), int_ty); nil = ctx.MkConst(int_list.NilDecl); l1 = ctx.MkApp(int_list.ConsDecl, ctx.MkInt(1), nil); l2 = ctx.MkApp(int_list.ConsDecl, ctx.MkInt(2), nil); /* nil != cons(1, nil) */ Prove(ctx, ctx.MkNot(ctx.MkEq(nil, l1))); /* cons(2,nil) != cons(1, nil) */ Prove(ctx, ctx.MkNot(ctx.MkEq(l1, l2))); /* cons(x,nil) = cons(y, nil) => x = y */ x = ctx.MkConst("x", int_ty); y = ctx.MkConst("y", int_ty); l1 = ctx.MkApp(int_list.ConsDecl, x, nil); l2 = ctx.MkApp(int_list.ConsDecl, y, nil); Prove(ctx, ctx.MkImplies(ctx.MkEq(l1, l2), ctx.MkEq(x, y))); /* cons(x,u) = cons(x, v) => u = v */ u = ctx.MkConst("u", int_list); v = ctx.MkConst("v", int_list); l1 = ctx.MkApp(int_list.ConsDecl, x, u); l2 = ctx.MkApp(int_list.ConsDecl, y, v); Prove(ctx, ctx.MkImplies(ctx.MkEq(l1, l2), ctx.MkEq(u, v))); Prove(ctx, ctx.MkImplies(ctx.MkEq(l1, l2), ctx.MkEq(x, y))); /* is_nil(u) or is_cons(u) */ Prove(ctx, ctx.MkOr((BoolExpr)ctx.MkApp(int_list.IsNilDecl, u), (BoolExpr)ctx.MkApp(int_list.IsConsDecl, u))); /* occurs check u != cons(x,u) */ Prove(ctx, ctx.MkNot(ctx.MkEq(u, l1))); /* destructors: is_cons(u) => u = cons(head(u),tail(u)) */ fml1 = ctx.MkEq(u, ctx.MkApp(int_list.ConsDecl, ctx.MkApp(int_list.HeadDecl, u), ctx.MkApp(int_list.TailDecl, u))); fml = ctx.MkImplies((BoolExpr)ctx.MkApp(int_list.IsConsDecl, u), fml1); Console.WriteLine("Formula {0}", fml); Prove(ctx, fml); Disprove(ctx, fml1); }
/// <summary> /// Prove <tt>x = y implies g(x) = g(y)</tt>, and /// disprove <tt>x = y implies g(g(x)) = g(y)</tt>. /// </summary> /// <remarks>This function demonstrates how to create uninterpreted /// types and functions.</remarks> public static void ProveExample1(Context ctx) { Console.WriteLine("ProveExample1"); /* create uninterpreted type. */ Sort U = ctx.MkUninterpretedSort(ctx.MkSymbol("U")); /* declare function g */ FuncDecl g = ctx.MkFuncDecl("g", U, U); /* create x and y */ Expr x = ctx.MkConst("x", U); Expr y = ctx.MkConst("y", U); /* create g(x), g(y) */ Expr gx = g[x]; Expr gy = g[y]; /* assert x = y */ BoolExpr eq = ctx.MkEq(x, y); /* prove g(x) = g(y) */ BoolExpr f = ctx.MkEq(gx, gy); Console.WriteLine("prove: x = y implies g(x) = g(y)"); Prove(ctx, ctx.MkImplies(eq, f)); /* create g(g(x)) */ Expr ggx = g[gx]; /* disprove g(g(x)) = g(y) */ f = ctx.MkEq(ggx, gy); Console.WriteLine("disprove: x = y implies g(g(x)) = g(y)"); Disprove(ctx, ctx.MkImplies(eq, f)); /* Print the model using the custom model printer */ Model m = Check(ctx, ctx.MkNot(f), Status.SATISFIABLE); Console.WriteLine(m); }