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Record and union types are symmetric: the values used to construct an object are the same as those stored in the object, which are a subset of those published by the object. This symmetry makes record and union types succinct and clear, and it helps give them other properties; for example, the F# compiler automatically derives generic equality, comparison, and hashing routines for these types. However, more advanced OO programming often needs to break these symmetries. For example, let s say you want to precompute and store the length of a vector in each vector value. It s clear you don t want everyone who creates a vector to have to perform this computation for you. Instead, you precompute the length as part of the construction sequence for the type. You can t do this using a record, except by using a helper function, so it s convenient to switch to a more general notation for class types. Listing 6-2 shows the Vector2D example using a class type.

3.00 1.00 0.00 1.00 1.00 1.00 1.00 0.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 1.00 2.00 56.00

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Listing 6-2. A Vector2D Type with Length Precomputation via a Class Type type Vector2D(dx: float, dy: float) = let len = sqrt(dx * dx + dy * dy) /// Get the X component of the vector member v.DX = dx /// Get the Y component of the vector member v.DY = dy /// Get the length of the vector member v.Length = len /// Return a vector scaled by the given factor member v.Scale(k) = Vector2D(k*dx, k*dy) /// Return a vector shifted by the given delta in the Y coordinate member v.ShiftX(x) = Vector2D(dx=dx+x, dy=dy) /// Return a vector shifted by the given delta in the Y coordinate member v.ShiftY(y) = Vector2D(dx=dx, dy=dy+y) /// Return a vector that is shifted by the given deltas in each coordinate member v.ShiftXY(x,y) = Vector2D(dx=dx+x, dy=dy+y) /// Get the zero vector static member Zero = Vector2D(dx=0.0, dy=0.0) /// Get a constant vector along the X axis of length one static member OneX = Vector2D(dx=1.0, dy=0.0) /// Get a constant vector along the Y axis of length one static member OneY = Vector2D(dx=0.0, dy=1.0) You can now use this type as follows: > let v = Vector2D(3.0, 4.0);; val v : Vector2D > v.Length;; val it : float = 5.0 > v.Scale(2.0).Length;; val it : float = 10.0 Once again, it s helpful to look at the inferred type signature for the Vector2D type definition of Listing 6-2:

This gives them a different role in practice, since they can be used to model both concrete languages and computational languages..

0.01 0.02 0.08 0.09 0.08 0.02 0.05 0.00 0.08 0.11 0.11 0.05 0.06 0.05 0.00 0.02 0.00 0.00 0.16 0.09 0.97 11.45

type Vector2D = new : dx:float * dy:float -> Vector2D member DX : float member DY : float member Length : float member Scale : k:float -> Vector2D member ShiftX : x:float -> Vector2D member ShiftY : y:float -> Vector2D member ShiftXY : x:float * y:float -> Vector2D static member Zero : Vector2D static member ConstX : dx:float -> Vector2D static member ConstY : dy:float -> Vector2D The signature of the type is almost the same as that for Listing 6-1 The primary difference is in the construction syntax Let s look at what s going on here The first line says you re defining a type Vector2D with a primary constructor This is sometimes called an implicit constructor The constructor takes two arguments, dx and dy The variables dx and dy are in scope throughout the (nonstatic) members of the type definition.

Any review of the libraries that are usable with F# and .NET is necessarily incomplete; there are just too many high-quality .NET libraries available, and more are appearing all the time. However, people often ask us which libraries we recommend. Table 10-17 shows some of the frameworks and libraries available at the time of writing that we think may be of interest to the readers of this book.

The second line is part of the computation performed each time an object of this type is constructed: let len = sqrt(dx * dx + dy * dy) Like the input values, the len value is in scope throughout the rest of the (nonstatic) members of the type The next three lines publish both the input values and the computed length as properties: member vDX = dx member vDY = dy member vLength = len The remaining lines implement the same methods and static properties as the original record type The Scale method creates its result by calling the constructor for the type using the expression Vector2D(k*dx, k*dy) In this expression, arguments are specified by position.

0.00 0.01 0.11 0.09 0.03 0.00 0.00 0.00 0.03 0.00 0.02 0.00 0.03 0.00 0.00 0.02 0.00 0.00 0.02 0.02 0.14 2.19

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