How do I compose Linq Expressions? ie Func<Exp<Func<X, Y>>, Exp<Func<Y, Z>>, Exp<Func<X, Z>>>

Question

I'm creating a Validator<T> class. I'm attempting to implement the Linq SelectMany extension methods for my validator to be able to compose expressions using a Linq query and validate the final result even when the underlying values change.

The following test code demonstrates my intent.

var a = 2;
var b = 3;

var va = Validator.Create(() => a, n => n >= 0 && n < 5);
var vb = Validator.Create(() => b, n => n >= 0 && n < 5);

var vc = from ia in va
         from ib in vb
         select ia + ib;

Debug.Assert(vc.Value == a + b); //2 + 3
Debug.Assert(vc.Value == 5);

Debug.Assert(vc.IsValid == true);

a = 7;

Debug.Assert(vc.Value == a + b); //7 + 3
Debug.Assert(vc.Value == 10);

Debug.Assert(va.IsValid == false);
Debug.Assert(vb.IsValid == true);
Debug.Assert(vc.IsValid == false);

I've seen the following question How do I compose existing Linq Expressions which shows me how to compose two Func<T, bool>'s together using an And expression, but I need to be able to compose functions together in a more, well, functional way.

I have, for example, the following two expressions:

public Expression<Func<T>> ValueExpression { get; private set; }
public Expression<Func<T, bool>> ValidationExpression { get; private set; }

I wish to create a new expression like this:

    public Expression<Func<bool>> IsValidExpression
    {
        get
        {
            // TODO: Compose expressions rather than compile & invoke.
        }
    }

More succinctly I'm trying to create these functions:

// Specific case
Func<Expression<Func<T>>, Expression<Func<T, bool>>, Expression<Func<bool>>>
// General case
Func<Expression<Func<X, Y>>, Expression<Func<Y, Z>>, Expression<Func<X, Z>>>

The general case function can be modified to accept different numbers of generic arguments as needed to compose any function.

I've searched Stack Overflow (of course) and the web, but haven't an example that solves this issue.

My code for the Validator<T> class is below.

public class Validator<T>
{
    public Validator(Expression<Func<T>> valueFunc,
        Expression<Func<T, bool>> validationFunc)
    {
        this.ValueExpression = valueFunc;
        this.ValidationExpression = validationFunc;
    }

    public Expression<Func<T>> ValueExpression { get; private set; }
    public Expression<Func<T, bool>> ValidationExpression { get; private set; }

    public T Value { get { return this.ValueExpression.Compile().Invoke(); } }

    public bool IsValid { get { return this.IsValidExpression.Compile().Invoke(); } }

    public Expression<Func<bool>> IsValidExpression
    {
        get
        {
            // TODO: Compose expressions.
        }
    }
}

My SelectMany extensions contain loads of yucky .Compile().Invoke() which I want to get rid of.

public static Validator<U> SelectMany<T, U>(this Validator<T> @this, Expression<Func<T, Validator<U>>> k)
{
    Expression<Func<T>> fvtv = @this.ValueExpression;
    Expression<Func<Validator<U>>> fvu = () => k.Compile().Invoke(fvtv.Compile().Invoke());
    Expression<Func<U>> fvuv = fvu.Compile().Invoke().ValueExpression;
    Expression<Func<U, bool>> fvtiv = u => @this.ValidationExpression.Compile().Invoke(fvtv.Compile().Invoke());
    return fvuv.ToValidator(fvtiv);
}

public static Validator<V> SelectMany<T, U, V>(this Validator<T> @this, Expression<Func<T, Validator<U>>> k, Expression<Func<T, U, V>> s)
{
    Expression<Func<Validator<U>>> fvu = () => @this.SelectMany(k);
    Expression<Func<T>> fvtv = @this.ValueExpression;
    Expression<Func<U>> fvuv = fvu.Compile().Invoke().ValueExpression;
    Expression<Func<T, bool>> fvtiv = @this.ValidationExpression;
    Expression<Func<U, bool>> fvuiv = u => fvu.Compile().Invoke().ValidationExpression.Compile().Invoke(u);
    Expression<Func<V>> fvv = () => s.Compile().Invoke(fvtv.Compile().Invoke(), fvuv.Compile().Invoke());
    Expression<Func<V, bool>> fvviv = v => fvtiv.Compile().Invoke(fvtv.Compile().Invoke()) && fvuiv.Compile().Invoke(fvuv.Compile().Invoke());
    return fvv.ToValidator(fvviv);
}

Thanks in advance!

Answer 1

The equivalent of Haskell's function composition operator

(.) :: (b->c) -> (a->b) -> (a->c)
f . g = \ x -> f (g x)

would in C# probably be something like

static Expression<Func<A, C>> Compose<A, B, C>(
    Expression<Func<B, C>> f,
    Expression<Func<A, B>> g)
{
    var x = Expression.Parameter(typeof(A));
    return Expression.Lambda<Func<A, C>>(
        Expression.Invoke(f, Expression.Invoke(g, x)), x);
}

Is this what you're looking for?

Example:

Compose<int, int, string>(y => y.ToString(), x => x + 1).Compile()(10); // "11"