Suppose I want to sort a bunch of strings into order first by length, and then, once they are sorted by length, sort each group that is the same length by some other comparison. We can easily build such a device with higher-order programming:

```static Comparison<string> FirstByLength(Comparison<string> thenBy)
{
return (string x, string y) =>
{
// Null strings are sorted before zero-length strings; remember, we need to provide a total ordering.
if (x == null && y == null)
return 0;
if (x == null)
return -1;
if (y == null)
return 1;
if (x.Length > y.Length)
return 1;
if (x.Length < y.Length)
return -1;
// They are the same length; sort on some other criterion.
return thenBy(x, y);
};
}
```

Super. This idea of composing new comparison functions out of old ones is pretty neat. We can even built a reversal device:

```static Comparison<string> Reverse(Comparison<string> comparison)
{
return (string x, string y) => -comparison(x, y);
}
```

Something is subtly wrong in at least one of these comparison functions. Where’s the defect?

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Let’s restate that contract again. The comparison function returns a negative integer if the first argument is smaller than the second, a positive integer if the first is greater than the second, and zero if they are equal. Any negative integer will do, and in particular, `Int32.MinValue `is a negative integer. Suppose we have a bizarre comparison function that returns `Int32.MinValue `instead of `-1`:

```Comparison<string> bizarre = whatever;
```

and we compose it:

```Comparison<string> reverseFirstByLength = Reverse(FirstByLength(bizarre));
```

Suppose two strings are equal in length and bizarre returns `Int32.MinValue `for those strings. `Reverse `should return a positive number, but` -Int32.MinValue `either throws an exception (in a checked context) or returns `Int32.MinValue `right back (in an unchecked context). Remember, there are more negative numbers that fit into an integer than positive numbers, by one.

The right implementation of `Reverse `is either to spell it out:

```static Comparison<string> Reverse(Comparison<string> comparison)
{
return (string x, string y) =>
{
int result = comparison(x, y);
if (result > 0) return -1;
if (result < 0) return 1;
return 0;
};
}
```

Or to simply swap left and right:

```static Comparison<string> Reverse(Comparison<string> comparison)
{
return (string x, string y) => comparison(y, x);
}
```

Next time on FAIC: Another way that comparisons go wrong.