F# for Scientists

List of Figures

• 2.1 The fold_range function can be used to accumulate the result of applying a function f to a contiguous sequence of integers, in this case the sequence [1,9). 40

• 2.2 Developing an application written entirely in F# using Microsoft Visual Studio 2005. 53

• 2.3 Visual Studio provides graphical throwback of the type information inferred by the F# compiler: hovering the mouse over the definition of a variable r in the source code brings up a tooltip giving the inferred type of r. 54

• 2.4 A project's properties page allows the compiler to be controlled. 55

• 2.5 The Add-in Manager is used to provide the F# interactive mode. 57

• 2.6 Creating a new C# class library project called ClassLibraryl inside a new solution called Interop. 59

• 2.7 Creating a new F# project called Projectl also inside the Interop solution. 59

• 2.8 Setting the startup project ofthe Interop solution to the F# project Project1 rather than the C# project ClassLibraryl as a DLL cannot be used to start an application . 60

• 3.1 Complexities of the ipow_l and ipow_2 functions in terms of the number T(n) of multiplies performed. 67

• 3.2 Complexities of the ipow_2 function in terms of the number of multiplies performed, showing: exact complexity T(n) (dots) and lower- and upper-bounds algorithmic complexities log₂(n) — 1 ≤ T (n) ≤ 2(1 + log₂ n) for n > 1 (lines). 68

• 3.3 Measured performance of the ipow_l and ipow_2 functions which have asymptotic algorithmic complexities of

• 3.4 Arrays are the simplest data structure, allowing ...