Can you create a simple 'EqualityComparer<T>' using a lambda expression

(There are two solutions here - see the end for the second one):

My MiscUtil library has a ProjectionEqualityComparer class (and two supporting classes to make use of type inference).

Here's an example of using it:

EqualityComparer<GalleryImage> comparer = 
    ProjectionEqualityComparer<GalleryImage>.Create(x => x.id);

Here's the code (comments removed)

// Helper class for construction
public static class ProjectionEqualityComparer
{
    public static ProjectionEqualityComparer<TSource, TKey>
        Create<TSource, TKey>(Func<TSource, TKey> projection)
    {
        return new ProjectionEqualityComparer<TSource, TKey>(projection);
    }

    public static ProjectionEqualityComparer<TSource, TKey>
        Create<TSource, TKey> (TSource ignored,
                               Func<TSource, TKey> projection)
    {
        return new ProjectionEqualityComparer<TSource, TKey>(projection);
    }
}

public static class ProjectionEqualityComparer<TSource>
{
    public static ProjectionEqualityComparer<TSource, TKey>
        Create<TKey>(Func<TSource, TKey> projection)
    {
        return new ProjectionEqualityComparer<TSource, TKey>(projection);
    }
}

public class ProjectionEqualityComparer<TSource, TKey>
    : IEqualityComparer<TSource>
{
    readonly Func<TSource, TKey> projection;
    readonly IEqualityComparer<TKey> comparer;

    public ProjectionEqualityComparer(Func<TSource, TKey> projection)
        : this(projection, null)
    {
    }

    public ProjectionEqualityComparer(
        Func<TSource, TKey> projection,
        IEqualityComparer<TKey> comparer)
    {
        projection.ThrowIfNull("projection");
        this.comparer = comparer ?? EqualityComparer<TKey>.Default;
        this.projection = projection;
    }

    public bool Equals(TSource x, TSource y)
    {
        if (x == null && y == null)
        {
            return true;
        }
        if (x == null || y == null)
        {
            return false;
        }
        return comparer.Equals(projection(x), projection(y));
    }

    public int GetHashCode(TSource obj)
    {
        if (obj == null)
        {
            throw new ArgumentNullException("obj");
        }
        return comparer.GetHashCode(projection(obj));
    }
}

Second solution

To do this just for Distinct, you can use the DistinctBy extension in MoreLINQ:

    public static IEnumerable<TSource> DistinctBy<TSource, TKey>
        (this IEnumerable<TSource> source,
         Func<TSource, TKey> keySelector)
    {
        return source.DistinctBy(keySelector, null);
    }

    public static IEnumerable<TSource> DistinctBy<TSource, TKey>
        (this IEnumerable<TSource> source,
         Func<TSource, TKey> keySelector,
         IEqualityComparer<TKey> comparer)
    {
        source.ThrowIfNull("source");
        keySelector.ThrowIfNull("keySelector");
        return DistinctByImpl(source, keySelector, comparer);
    }

    private static IEnumerable<TSource> DistinctByImpl<TSource, TKey>
        (IEnumerable<TSource> source,
         Func<TSource, TKey> keySelector,
         IEqualityComparer<TKey> comparer)
    {
        HashSet<TKey> knownKeys = new HashSet<TKey>(comparer);
        foreach (TSource element in source)
        {
            if (knownKeys.Add(keySelector(element)))
            {
                yield return element;
            }
        }
    }

In both cases, ThrowIfNull looks like this:

public static void ThrowIfNull<T>(this T data, string name) where T : class
{
    if (data == null)
    {
        throw new ArgumentNullException(name);
    }
}

Building on Charlie Flowers' answer, you can create your own extension method to do what you want which internally uses grouping:

    public static IEnumerable<T> Distinct<T, U>(
        this IEnumerable<T> seq, Func<T, U> getKey)
    {
        return
            from item in seq
            group item by getKey(item) into gp
            select gp.First();
    }

You could also create a generic class deriving from EqualityComparer, but it sounds like you'd like to avoid this:

    public class KeyEqualityComparer<T,U> : IEqualityComparer<T>
    {
        private Func<T,U> GetKey { get; set; }

        public KeyEqualityComparer(Func<T,U> getKey) {
            GetKey = getKey;
        }

        public bool Equals(T x, T y)
        {
            return GetKey(x).Equals(GetKey(y));
        }

        public int GetHashCode(T obj)
        {
            return GetKey(obj).GetHashCode();
        }
    }

You could group by the key value and then select the top item from each group. Would that work for you?