Functions are the basic building blocks in functional computer programming. In strongly typed functional programming, every function has a well-defined input type and output type. In this chapter, we'll discuss how to build simple F# programs using strongly typed functions.

Of all the strongly typed functional languages, I chose F# for this book because it's fairly popular, open source, and cross-platform. Other similar languages include Haskell, OCaml, and Scala, and even more mainstream languages like C# and TypeScript support strongly typed functional programming to varying degrees. You should be able to work through the exercises in this book with any of these languages (or others, if you're ambitious). However, all the examples are written in F#, so you'll at least need to be able to read it.

The first step, if you haven't already done so, is to install F# on your computer and make sure you can run code. Appendix the appendix has instructions to help you get set up. These first few chapters are designed to introduce you to functional programming and to get you up to speed with the F# language so you can read it and use it confidently throughout the rest of the book. We also provide a more in-depth reference online at ???????. Now let's get started with the most important concept: the function.

Function Application

• 1.1What do you get when you evaluate sqrt 1.0 + 3.0 in F# interactive? Why is the…
• 1.2Write an enthusiasticGreet function in F# that does the same thing as greet but…
• 1.3The built-in not function takes Boolean values like true or false as inputs.…
• 1.4Write an anonymous version of the greet function and apply it to the string
• 1.5Translate the following mathematical function into an F# function: …. Apply the…

Mathematical vs. Programmatic Functions

• 1.6The following is a function that takes integer inputs. What does it do?

Recursive Functions

• 1.7The factorial of a positive integer …, written …, is the product of the…
• 1.8Write a recursive function laugh that takes a positive integer … and returns a…

The Type of a Function

• 1.9Write some interesting F# functions that have the following types: int -> bool
• 1.10F# has a built-in function called String.length. Given its name and its type,

Generic Functions

• 1.11Write your own implementation of the ignore function.
• 1.12Define a function stringOfInt with type int -> string by giving the string…
• 1.13For what input values x does float(int(x)) return the same value as x? What…
• 1.14Implement the generic id function from scratch.

Composing Functions

• 1.15Letting … and …, give an example value of … such that … and … can return…
• 1.16Let f be a function of type int -> int that squares its input. What will be the…
• 1.17Define a function is3 that returns true if an input integer is 3, and false…
• 1.18Using the is3 function from , confirm that is3 >> String.length is not a valid…
• 1.19Using the laugh function from , what does the composition laugh >> String.length

Higher-Order Functions

• 1.20What are the types of the partially applied functions ((*) 3.14), ((-) 4), and
• 1.21Write a generic function c x y that always returns the value of x, no matter…
• 1.22Implement your own version of the pown function. (Hint: Write it recursively,…
• 1.23Write a function apply f x that returns the result of applying the function
• 1.24Write a function reverseCompose f g x that behaves like the opposite direction…
• 1.25Write a generic function twice f x that takes a function f and a value x and…
• 1.26Write a generic function repeat (n:int) (f:'T -> 'T) that composes a function

Function Equality

• 1.27Test that the following functions bool -> bool -> bool are equal: (Hint: Test…
• 1.28Write a function that takes two functions bool -> bool and returns true if…
• 1.29How many distinct functions of type bool -> bool are there? That is, how many…
• 1.30Write a function that takes two functions bool -> bool -> bool and returns true
• 1.31We know from basic algebra that …, for any integer …. Does it follow that the…

Currying

• 1.32Write an uncurried version of the pown function, having type int * int -> int
• 1.33Write a generic function uncurry that takes a function of type 'T -> ('U -> 'V)

Additional Practice

• 1.34Given any two F# functions f and g, which pairs among the following are equal?
• 1.35F# has built-in functions fst and snd that take a tuple of two values and…
• 1.36What is the type of the function id<string -> int>? What does it do?…
• 1.37Write a function that takes two functions of type (bool -> bool) -> bool and…
• 1.38Consider the following function int -> bool -> bool: Ideally, how does
• 1.39Implement a function int -> bool -> bool that is equal to repeatNot but that…
• 1.40Test that the sumTo function fails for sufficiently large inputs, by exceeding…
• 1.41Consider the following functions, using the repeat function that you wrote in
• 1.42The following function int -> int returns 1 for most inputs: Is it equal to the…