|
public MkDatatypeSorts ( |
||
| names | names of datatype sorts | |
| c | Microsoft.Z3.Constructor | list of constructors, one list per sort. |
| return | Microsoft.Z3.DatatypeSort[] | |
public void Run()
{
Dictionary<string, string> cfg = new Dictionary<string, string>() {
{ "AUTO_CONFIG", "true" },
{ "MODEL", "true" } };
using (Context ctx = new Context(cfg))
{
Constructor c_leaf = ctx.MkConstructor("leaf", "is_leaf", new string[] { "val" }, new Sort[] { ctx.IntSort });
Constructor c_node = ctx.MkConstructor("node", "is_node", new string[] { "left", "right" }, new Sort[] { null, null }, new uint[] { 1, 1 });
Constructor[] constr_1 = new Constructor[] { c_leaf, c_node };
Constructor c_nil = ctx.MkConstructor("nil", "is_nil");
Constructor c_cons = ctx.MkConstructor("cons", "is_cons", new string[] { "car", "cdr" }, new Sort[] { null, null }, new uint[] { 0, 1 });
Constructor[] constr_2 = new Constructor[] { c_nil, c_cons };
DatatypeSort[] ts = ctx.MkDatatypeSorts(new string[] { "Tree", "TreeList" },
new Constructor[][] { constr_1, constr_2 });
DatatypeSort Tree = ts[0];
DatatypeSort TreeList = ts[1];
FuncDecl leaf = Tree.Constructors[0];
FuncDecl node = Tree.Constructors[1];
FuncDecl val = Tree.Accessors[0][0];
FuncDecl nil = TreeList.Constructors[0];
FuncDecl cons = TreeList.Constructors[1];
Expr t1 = leaf[ctx.MkInt(10)];
Expr tl1 = cons[t1, nil.Apply()];
Expr t2 = node[tl1, nil.Apply()];
Console.WriteLine(t2);
Console.WriteLine(val.Apply(t1).Simplify());
t1 = ctx.MkConst("t1", TreeList);
t2 = ctx.MkConst("t2", TreeList);
Expr t3 = ctx.MkConst("t3", TreeList);
Solver s = ctx.MkSolver();
s.Assert(ctx.MkDistinct(t1, t2, t3));
Console.WriteLine(s.Check());
Console.WriteLine(s.Model);
}
}
/// <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)));
}
