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Record 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 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 object-oriented 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 is 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 is convenient to switch to a more general notation for constructed class types. Listing 6-2 shows the Vector2D example using a constructed class type.

As a system is being built, the test sets can be run whenever the requirements are completed or at any time later in the process to validate continued compliance with the requirement (also known as regression testing) Partition Tests Partition tests focus on the input and output data characteristics of the system Tests are created that test the outer, edge, and mean value ranges of the input or output data being tested For example, suppose a system is designed to accept input of a positive integer value in the range of 1 to 10 You can form partitions (called equivalence partitions or domains) of this data by testing the values {0, 1, 5, 10, 11} Some may take this further and include a negative value such as 1.

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There is one additional way to make code generic: by marking a function as inline You can use this technique for code that uses F# operators such as float, int, +, -, *, /, and other arithmetic operations As discussed in the section Understanding Generic Overloaded Operators, each use of these operators is normally statically resolved For example, consider the following code: let convertToFloat x = float x In the F# type system, the type of the float function is 'T -> float (requires member op_Explicit) This means the type 'T must support an explicit conversion from 'T to float Thus you can use it with integers, singles, doubles, decimals, and so on, but you can t use it with any old type The 'T is constrained As mentioned earlier, F# operators like float are statically resolved This means each use of float is associated with one statically inferred type.

The same applies to other operators such as +, *, and so on These operators also generally default to working over integers For example, this shows float being used with three different statically resolved types: float 30 + float 1 + float 3L To make code like this generic, you can use inline For example, consider this: let inline convertToFloatAndAdd x y = float x + float y convertToFloatAndAdd can be used with an integer and a float, or a decimal and an integer, or two decimals You can use inline to write code and algorithms that are implicitly generic over arithmetic type while still maintaining type safety This gives you generic, type-safe code while ensuring static resolution of basic numeric operations, making it easy to reason about the efficiency of your code.

Listing 6-2. A Vector2D Type with Length Precomputation via a Constructed Class Type type Vector2D(dx: float, dy: float) = let len = sqrt(dx * dx + dy * dy) member v.DX = dx member v.DY = dy member v.Length = len member v.Scale(k) = Vector2D(k*dx, k*dy) member v.ShiftX(x) = Vector2D(dx=dx+x, dy=dy) member v.ShiftY(y) = Vector2D(dx=dx, dy=dy+y) member v.ShiftXY(x,y) = Vector2D(dx=dx+x, dy=dy+y) static member Zero = Vector2D(dx=0.0, dy=0.0) static member OneX = Vector2D(dx=1.0, dy=0.0) 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 is helpful to look at the inferred type signature for the Vector2D type definition of Listing 6-2: 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 take a look at what s going on here. The first line says we re defining a type Vector2D with a construction sequence, where constructions take two arguments, dx

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