|
public MkListSort ( |
||
| name | ||
| elemSort | Microsoft.Z3.Sort | |
| Résultat | ||
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" },
{ "MODEL", "true" } };
using (Context ctx = new Context(cfg))
{
ListSort L = ctx.MkListSort("List", ctx.IntSort);
FuncDecl cons = L.ConsDecl;
FuncDecl car = L.HeadDecl;
FuncDecl cdr = L.TailDecl;
Expr nil = L.Nil;
Expr l1 = cons[ctx.MkInt(10), cons[ctx.MkInt(20), nil]];
Console.WriteLine(l1);
Console.WriteLine(cdr[l1].Simplify());
Console.WriteLine(car[l1].Simplify());
Console.WriteLine(ctx.MkEq(l1, nil).Simplify());
}
}
/// <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);
}
