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Sometimes these changes include the discovery of new classes, the reorganization of the existing class, and even the formulation of the methods and properties of the class. In other words, writing the test before the code helps validate the design. That is really cool because once you complete the level of design you want for your iteration and begin writing the source code, you already have your tests completed! You can simply run your tests and demonstrate

Gets or sets the item at the given position in the matrix. Gets the number of (rows, columns) in the matrix. Gets the number of columns in the matrix. Gets the number of rows in the matrix. Gets a submatrix. See the slice syntax for arrays, also usable for matrices, in 4. Gets the transpose of the matrix.

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You can also use type annotations to discover why code is not as generic as you think it should be. For example, the following code has a mistake, and the F# type checker says the code is less generic than expected: let printSecondElements (inp : #seq<'a * int>) = inp |> Seq.iter (fun (x,y) -> printfn "y = %d" x) > ... enter the code above ... |> Seq.iter (fun (x,y) -> printfn "y = %d" x) --------------------------------------^^^^^^^^^ stdin(21,38): warning: FS0064: This construct causes code to be less generic than indicated by the type annotations. The type variable 'a has been constrained to the type 'int'. The mistake here is that we are printing the variable x instead of y, but it s not always so easy to spot what has caused this kind of problem. One way to track down this problem is to temporarily change the generic type parameter to some arbitrary, unrelated type, After all, if code is generic, then you should be able to use any type, and by changing the type variable to an unrelated type, you can track down where the inconsistency has first arisen. For example, let s change 'a to the type PingPong: type PingPong = Ping | Pong let printSecondElements (inp : #seq<PingPong * int>) = inp |> Seq.iter (fun (x,y) -> printfn "y = %d" x) You now get a different and in many ways more informative error message, localized to the first place that the value x marked with type PingPong is used in an unexpected way: > ... enter the code above ... |> Seq.iter (fun (x,y) -> printfn "y = %d" x) ------------------------------------------------^ stdin(27,47): error: FS0001: The type 'PingPong' is not compatible with any of the types byte,int16,int32,int64,sbyte,uint16,uint32,uint64,nativeint,unativeint, arising from the use of a printf-style format string

3. D. Rosenberg, M. Stephens, M. Collins-Cope. Agile Development with ICONIX Process (Berkeley, CA: Apress, 2005).

Gets or sets the item at the given position in the vector. Gets the number of rows in the vector. Gets a subvector. Gets the transpose of the vector.

F# sometimes requires a little help before a definition is automatically generalized. In particular, only function definitions and simple immutable data expressions are automatically generalized;

your code is working as designed. Of course, if you need to change the test and therefore the design, well, that s the beauty of agile development.

The F# matrix, vector, and row vector types support the use of operators such as +, -, and *. Table 10-12 shows some of the overloads supported. Table 10-12. Primary Operator Overloads Supported by the F# Matrix and Vector Types

this is called the value restriction For example, the following definition does not result in a generic type and gives an error: > let empties = Arraycreate 100 [];; ------^^^^^^ error: FS0030: Value restriction Type inference has inferred the signature val empties : '_a list [] but its definition is not a simple data constant Either define 'empties' as a simple data expression, make it a function, or add a type constraint to instantiate the type parameters The code attempts to create an array of empty lists Here the error message indicates that type inference has given empties the type '_a list [] The underscore (_) indicates that the type variable 'a is ungeneralized, that is, that this code is not fully generic.

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