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Preface

Have you ever been in a hurry and pounded in a nail using something other than a
hammer? Or perhaps settled an argument concerning distances with “the length of my
arm is about 20 inches, and that’s about two arm-lengths…?” You might not be willing to
fall for such obviously flawed short-cuts, but as your humble author I will admit that I
have.
There is elegance to using the right tool for the job. And, just like a hammer or a tape
measure, programming languages are tools like any other. Throughout this book you will
discover that while F# isn’t the best tool for every situation, it is the perfect tool for some
situations.
This book is about showing you how to use the F# programming language as a general-
purpose tool, with an emphasis on the specific domains where it can lead to dramatic
boots in productivity.
Along the way you will pick up a knack for functional programming; a semi-mysterious
collections of concepts that can help you rethink your programs regardless of the host
programming language.

Introducing F#
So what actually is F#? In a nutshell, F# is a multi-paradigm programming language built
on .NET, meaning that it supports several different styles of programming natively. I’ll
spare you the history of the language and instead just go over the big bullets:
• F# supports imperative programming. In F# you can modify the contents of memory,
read and write files, send data over the network, and so on.
• F# supports object-oriented programming. In F# you can abstract code into classes
and objects enabling you to simplify your code.
• F# supports functional programming, which is a style of programming which
emphasizes what a program should do, not explicitly how the program should work.
• F# is statically typed. Being statically typed means that type information is known at
compile time, leading to type-safe code. F# won’t allow you to put a square peg into
a round hole.
• F# is a .NET language. It runs on the Common Language Infrastructure (CLI) and so
it gets things like garbage collection (memory management) and powerful class

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libraries for free. F# also supports all .NET concepts natively, such as delegates,
enumerations, structures, P/Invoke, and so on.
Even without all the jargon, it is clear that F# is powerful language. But don’t worry;
we’ll cover it all step by step.

Who This Book Is For

This book isn’t intended to be an introductory text on programming and assumes
familiarity with basic concepts like looping, functions, and recursion. However, no
previous experience with functional programming or .NET is required.
If you come from a C# or VB.NET background then you should feel right at home. While
F# approaches programming from a different viewpoint, you can apply all of your
existing .NET know-how to programming in F#.
If you come from an OCaml or Haskell background then the syntax of F# should look
very familiar. F# has most of the features of those languages, and adds many more to
integrate well with .NET.

What You Need to Get Going

F# is “in the box” of Visual Studio 11. This includes the F# compiler and project system,
and contains all the features such as syntax highlighting and IntelliSense that you would
expect. Outside of Visual Studio and on non-Microsoft platforms, you can still write and
deploy F# applications using the open source Mono platform (http://www.mono-
project.com/).
If you are running F# on Windows, then the first chapter of this book will show you how
to get set up using Visual Studio. Otherwise, Appendix A will walk you through getting
F# set up on non-Microsoft platforms.
Also, it is important to note that all of the examples printed in this book (as well as many
more) may be found on GitHub. The best way to learn any new skill is to just start using
it, so I highly recommended that you take a moment to fork and explore the repository for
this book’s source code at: http://github.com/aChrisSmith/Programming-FS-Examples/.

How the Book Is Organized

This book is divided into three parts. Part I focuses on multi-paradigm programming in
F#. Early chapters will be devoted to programming in a specific F# paradigm, while later
ones will help flesh out your understanding of language capabilities. By the end of Part I
you will be fluent in the F# language and its idioms.
Part II will introduce a few lingering concepts but primarily focus on applying F# in
specialized areas. By the end of Part II you will know how to utilize F# as a scripting
language, for parallel programming, and for creating domain specific languages.
Part III should be considered optional for most F# developers, and focuses on advanced
language features that allow you to modify and extend the F# language.

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Part I, Multi-Paradigm Programming

Chapter 1, Introduction to F#, presents the F# language and the Visual Studio 11
integrated development environment (IDE). Even if you are familiar with Visual Studio I
recommend you read this chapter as F# has some unique characteristics when it comes to
building and running projects.
Chapter 2, Fundamentals, introduces the core types and concepts which will be the
foundation for all other chapters.
Chapter 3, Functional Programming, introduces functional programming and how to
write F# code using this style.
Chapter 4, Imperative Programming, describes how to mutate values and change
program state in an imperative manner.
Chapter 5, Object-oriented Programming, covers object-oriented programming from
creating simple types to inheritance and polymorphism.
Chapter 6, .NET Programming, goes over some style independent concepts exposed by
the .NET Framework and CLI.

Part II, Programming F#

Chapter 7, Applied Functional Programming, covers more advanced topics in functional
programming such as tail recursion and functional design patterns.
Chapter 8, Applied Object-Oriented Programming, describes how to develop and take
advantage of a rich type system. Special attention will be paid on how to leverage the
functional aspects of F# to make object-oriented code better.
Chapter 9, Asynchronous and Parallel Programming, takes a look at how to use F# to
take advantage of multiple cores on a processor and the facilities in the F# and .NET
libraries for parallel programming.
Chapter 10, Scripting, examines F# as a scripting language and how to make the most of
F# script files.
Chapter 11, Data Processing, focuses exclusively on using F# in “real world” scenarios
for doing distributed computations, interacting with web services, and working in
information-rich environments.

Part III, Extending the F# Language

Chapter 12, Reflection, provides a look at the .NET reflection library and how to use it to
create declarative programs.
Chapter 13, Computation Expressions¸ introduces an advanced F# language feature
which will enable you to eliminate redundant code and add new capabilities to the core
F# language.
Chapter 14, Quotations, introduces F# quotation expressions and how they can be used to
do metaprogramming as well as execute F# code on other computational platforms.

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Chapter 15, Type Providers, explains the F# compiler’s special machinery for integrating
typed data across multiple domains. (Don’t fret, that sentence will make sense when you
start the chapter.)
Appendixes
This book also features a couple of appendixes to flesh out any extra concepts you might
be interested in.
Appendix A, Overview of the .NET Libraries, does a quick sweep through the existing
technologies available on the .NET platform and how to use them from F#.
Appendix B, F# Interop, covers how to write F# to interoperate with existing libraries as
well as unmanaged code using P/Invoke and COM-interop.

Conventions Used in This Book

The following font conventions are used in this book:
Italic
Used for new concepts as they are defined.
Constant width
Used for code examples and F# keywords.
Constant width bold
Used for emphasis within program code.
Pay special attention to note styles within this text.

Notes like this are used to add more detail to the curious reader.

Warnings are indicated in this style are to help you avoid common
mistakes.

I’d Like to Hear from You

Although I’ve tested and verified the information in this book, you may find some
aspects of the F# language has changed since the writing (or perhaps even a bug in the
example!) Please let me know of any errors you find, as well as your suggestions for
future editions, at: http://oreilly.com/catalog/errata.csp?isbn=9780596153656.
In addition, you can use analog-mail by writing to:
O’Reilly Media, Inc.
1005 Gravenstein Highway North
Sebastopol, CA 95472
(800) 998-9938 (in the U.S. or Canada)
(707) 829-0515 (international/local)

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(707) 829-0104 (fax)

You can also send messages electronically. To be put on the mailing list or request a
catalog, send email to:
info@oreilly.com
To comment on the book, send email to:
bookquestions@oreilly.com
For information about this book and others, as well as additional technical articles and
discussion on F#, see the O’Reilly website:
http://www.oreilly.com
or the O’Reilly .NET DevCenter:
http://www.oreillynet.com/dotnet
or the Microsoft Developer Network portal for F#:
http://www.msdn.com/fsharp

Safari® Books Online

When you see a Safari® Books Online icon on the cover of your favorite technology
book it means the book is available online through the O’Reilly Network Safari
Bookshelf.
Safari offers a solution that’s better than e-books. It’s a virtual library that lets you easily
search thousands of top tech books, cut and paste code samples, download chapters, and
find quick answers when you need the most accurate, current information. Try it for free
at http://my.safaribooksonline.com.

Acknowledgments
In addition to the F# team at Microsoft for putting out a fantastic product, I’d like to
thank the following people for helping make the second edition of this book awesome:
Matt Douglass-Riely X

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Preface
Preface to the Second Edition

Hello! I’m writing this about three-years to the day that the first edition of Programming
F# came out. (And about one year before the second edition will be generally available.)
And it has been quite an experience.
Three years ago F# was just about to get its first official release in Visual Studio 2010.
Everyone on the team knew that developers would love our language, but we weren’t
sure where it would go. How it would be preceived.
But F# has not only been loved, it’s also achieved several important milestones. The first
one, was that this last year at the International Conference on Functional Programming
F# received the title as “the language for discriminating hackers”. While the
programming competition and “award” are just for fun, it demonstates that the language
isn’t just a toy.
Outside of the F# language front, the applications are growing. Job boards for F#
programmers are getting almost to much attention from head-hunters and recrutiers
aggressively looking to put F# developers in data mining, finance, and other technical
positions.
With that as the backdrop, there were a few key changes to the book for this second
edition aside from incorporating language advances for the F# 3.0 release.
First of all is the emphasis on more real-world examples. The first edition did a good job
of being a concise reference for the core language, but some readers left unsure of how to
actually apply F# to projects. This time around I’ve written dozens of large-scale
applications. To save space – again, to be concise – I’ve posted all the code on gitHub so
you can browse it freely and at your own pace at (github.com/achrissmith/programming-
fsharp/).
While with the explosive growth of mobile computing, F# in use as a server backend for
websites, and the unknown Windows 8 and the “Metro” UI style. It’s an exciting time to
be learning F# again!

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-Chris Smith
10/2011
Redmond, WA

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Part I
Multi-Paradigm Programming

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1
Introduction to F#

F# is a powerful language that spans multiple paradigms of development. This chapter

provides a brief introduction to the heart of F# – the F# compiler, tools, and its place in
Visual Studio 11.
In this chapter, you will create a couple of simple F# applications and then I’ll point out
key Visual Studio features for F# development. I won’t cover much of Visual Studio
here, so I encourage you to explore the IDE on your own.
If you are already familiar with Visual Studio, you should still skim through this chapter.
Creating and debugging F# projects works just like C# or VB.NET; however, F# has a
unique characteristic when it comes to multiple-file projects. In addition, F# has a feature
called F# Interactive which will dramatically increase your productivity. Not to be
missed!

Getting to Know F#
As with all programming books, it is customary to write a Hello, World application, and I
don’t want to deviate from tradition. Open up Notepad or your favorite text editor and
create a new file named HelloWorld.fs with the following text:
// HelloWorld.fs

printfn "Hello, World"

Success! You’ve just written your first F# program. To compile this application use the
F# compiler, fsc.exe, located in the Program Files (x86)\Microsoft
SDKs\F#\3.0\Framework\v4.0 folder. (Don’t worry, you won’t have to
remember that.)
The following snippet shows calling the F# compiler on the command line to build and
run your application.
C:\Programming F# Source\Ch01>fsc HelloWorld.fs
Microsoft (R) F# 3.0 Compiler build 4.0.30319.16909

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Copyright (c) Microsoft Corporation. All Rights Reserved.

C:\Programming F# Source\Ch01>HelloWorld.exe
Hello, World!

Visual Studio 11
Tools are the lifeblood of any programming language, and F# is no different. While you
can be successful writing F# code in your favorite text editor and invoking the compiler
from the command line, you’ll likely be more productive using tools. Like C# and
VB.NET, F# is a first-class citizen in Visual Studio with all the features that you might
expect, such as debugger support, IntelliSense, project templates, and so on.

Alternatively, you can try F# out in your browser at

http://www.tryfsharp.org/.

Let’s revisit our Hello, World application, but this time using Visual Studio.
To create your first F# project, open up the Visual Studio IDE and select File → New
Project from the menu bar to open the New Project dialog, as shown in Figure 1-1. Select
Visual F# in the left pane, select F# Application in the right pane, and then click OK.

Figure 1-1. Select F# Application to start your first F# project

After you click OK in the New Project dialog, you’ll see an empty code editor – a blank
canvas ready for you to create your F# masterpiece. Next, type the following code into
the F# editor:
printfn "Hello, World"
Now press Control + F5 to run your application. When your application starts, a console
window will appear and display the entirely unsurprising result shown in Figure 1-2.

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Figure 1-2. Hello World in F#

Your Second F# Program

It may be startling to see a program work without an explicit Main method. You will see
why this is admissible in the next chapter, but for now let’s create a more meaningful
Hello, World-type program to get a feel for basic F# syntax.
The code in Example 1-1 will create a program that accepts two command-line
parameters and prints them to the console. In addition, it displays the current time.
Example 1-1. Mega Hello World
// Mega Hello World
//
// Take two command line parameters and then print
// them along with the current time to the console.

open System

[<EntryPoint>]
let main (args : string[]) =

if args.Length <> 2 then

failwith "Error: Expected arguments <greeting> and <thing>"

let greeting, thing = args.[0], args.[1]

let timeOfDay = DateTime.Now.ToString("hh:mm tt")

printfn "%s, %s at %s" greeting thing timeOfDay

// Program exit code

0
Hopefully you are curious about what is going on. Let’s look at this program line-by-line
to see how it works.

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Values
Example 1-1 introduces three values named greeting, thing, and timeOfDay.
let greeting, thing = args.[0], args.[1]
let timeOfDay = DateTime.Now.ToString("hh:mm tt")

The key thing here is that the let keyword binds a name to a value. It is worth pointing
out that unlike most other programming languages, in F# values are immutable by
default, meaning they cannot be changed once initialized. We will cover why values are
immutable in Chapter 3, but for now it is sufficient to say it has to do with “functional
programming”.
F# is also case-sensitive, so any two values with names that only differ by case are
considered different.
let number = 1
let Number = 2
let NUMBER = 3

A value’s name can be any combination of letters, numbers, underscores _, and

apostrophes '. However, the name must begin with a letter or an underscore.

You can enclose the value’s name with a pair of tick-marks, in which
case the name can contain any character except for tabs and new lines.
This allows you to refer to values and functions exposed from other
.NET languages that may conflict with F# keywords.
let ``this.Isn’t %A% good value Name$!@#`` = 5

Whitespace Matters
Other languages like C# use semicolons and curly braces to indicate when statements and
blocks of code are complete. However, programmers typically indent their code to make
it more readable anyways, so these extra symbols often just add syntactic clutter.
In F#, whitespace – spaces and newlines – is significant. The F# compiler allows you to
use whitespace to delimit code blocks. For example, anything indented more than the if
keyword is considered to be in the body of the if statement. Because tab characters can
indicate an unknown number of space characters, they are prohibited in F# code.

You can configure the Visual Studio editor to automatically convert tab
characters into spaces by changing the relevant setting under Tools →
Options → Text Editor → F#.

Reviewing Example 1-1, notice that the body of the main method was indented by four
spaces, and the body of the if statement was indented by another four spaces.
let main (args : string[]) =

if args.Length <> 2 then

failwith "Error: Expected arguments <greeting> and <thing>"

let greeting, thing = args.[0], args.[1]

let timeOfDay = DateTime.Now.ToString("hh:mm tt")

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printfn "%s, %s at %s" greeting thing timeOfDay

// Program exit code

0

If the body of the if statement, the failwith "..." expression, was dedented four
spaces and therefore lined up with the if keyword, the F# compiler would produce a
warning. This is because the compiler wouldn’t be able to determine whether the
failwith was meant for the body of the if statement or the main function.
[<EntryPoint>]
let main (args : string[]) =

if args.Length <> 2 then

failwith "Error: Expected arguments <greeting> and <thing>"

Warning FS0058: Possible incorrect indentation: this token is offside of

context started at position (25:5). Try indenting this token further or
using standard formatting conventions.
The general rule is that anything belonging to a method or statement must be indented
further than the keyword that began the method or statement. So in Example 1-1
everything in the main method was indented past the first let and everything in the if
statement was indented past the if keyword. As you see and write more F# code you
will quickly find that omitting semicolons and curly braces makes the code easier to write
and much easier to read.

.NET Interop
Example 1-1 also demonstrates how F# can interoperate with existing .NET libraries.
open System

// ...

let timeOfDay = DateTime.Now.ToString("hh:mm tt")

This example shows the DateTime.Now property from the System namespace in the
mscorlib.dll assembly in use.
The .NET Framework contains a broad array of libraries for everything from graphics to
databases to web services. F# can take advantage of any .NET library natively by calling
directly into it. Conversely, any code written in F# can be consumed by other .NET
languages. This also means that F# applications can run on any platform that supports
.NET. So the F# programs you write can run on phones, tablets, PCs, and so on.

For more information on .NET libraries see Appendix A, Overview of

.NET Libraries. for a quick tour of what’s available. For more
information about F# inter-operating with other .NET languages refer
to Appendix B, F# Interop.

Comments
F# allows you to comment your code. To declare a single-line comment use two slashes
//; everything after them until the end of the line will be ignored by the compiler.

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// Program exit code

For larger comments you can use (* and *). Everything between the two tokens will be
ignored.
(*
Comment
spanning
multiple
lines
*)
For F# applications written in Visual Studio, there is a third type of comment – an XML
documentation comment. If a comment starting with three slashes, ///, is placed above
an identifier, Visual Studio will display the comment’s text when you hover the mouse
over the identifier.
Figure 1-3 shows applying an XML documentation comment and its associated tooltip.

Figure 1-3. XML documentation comments

F# Interactive
So far you have written some F# code and executed it, and the rest of the book will have
many more examples. While you could leave a wake of new projects to test out code,
Visual Studio comes with a tool called F# Interactive or FSI. The FSI window will not
only make it much easier to work through the examples in this book, but it will also help
you write applications.
F# Interactive is a tool known as a REPL, which stands for read, evaluate, print, loop. It
accepts F# code, compiles and executes it, then prints the results. This allows you to
quickly and easily experiment with F# without needing to create new projects or build a
full application to test the results of a code snippet.
Most Visual Studio configurations launch the F# Interactive window with the
Control+Alt+F keyboard combination. Once the FSI window is available, it accepts F#

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code until you terminate the input with ;; and a newline. The code entered is compiled
and executed as shown in Figure 1-4.
The FSI window prints any new values introduced as well as their types. Figure 1-4
shows val x : int = 42, declaring that a value x of type int was created with
value 42. If the FSI window evaluates an expression that was not assigned to a value, it
will instead assign it to the name it.

Figure 1-4. The F# Interactive window

As the F# compiler processes FSI input it will display the name, type, and value of
identifiers. For example, in Figure 1-4 the value x was introduced with type int and
value 42.

If you are running F# without Visual Studio, you can find the console
version of F# Interactive in the same directory you found fsc.exe
with the name fsi.exe.

Try running these other snippets in FSI. Remember that every code snippet is terminated
with a ;;.
> 2 + 2;;
val it : int = 4
> // Introduce two values
let x = 1
let y = 2.3;;

val x : int = 1

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val y : float = 2.3

> float x + y;;

val it : float = 3.3
> let cube x = x * x * x;;

val cube : int -> int

> cube 4;;

val it : int = 64
FSI can dramatically simplify testing and debugging your applications because you can
send F# code from your current project to the FSI window by highlighting it and pressing
Alt+Enter.
After selecting all the code in Example 1-1 within the code editor and pressing Alt+Enter
you will see the following in the FSI window:
>

val main : string [] -> int

This allows you to write code in the Visual Studio editor – which offers syntax
highlighting and IntelliSense – but test your code using the FSI window. You can check
the main ‘smethod's implementation by calling it from FSI.
> main [| "Hello"; "World" |];;
Hello, World at 10:52 AM
val it : int = 0

The majority of the examples in this book are taken directly from FSI
sessions. I encourage you to use FSI to follow along and experiment
with the F# language’s syntax.
You can find a copy of the source code for all examples in the book on
GitHub at https://github.com/aChrisSmith/Programming-FS-
Examples/.

Managing F# Source Files

When you are starting out with F# programming, most of the programs you write will
live only in FSI or perhaps in a single code file. Your F# projects however will quickly
grow and be broken up across multiple files and eventually multiple projects.
The F# language has some unique characteristics when it comes to managing projects
with multiple source files. In F# the order in which code files are compiled is significant.
You can only call into functions and classes defined earlier in the code file or in a
separate code file compiled before the file where the function or class is used. If you
rearrange the order of the source files your program may no longer build!

The reason for this significance in compilation order is type inference, a

topic covered in the next chapter.

F# source files are compiled from top to bottom in the order they are displayed in Visual
Studio’s Solution Explorer. Whenever you add a new code, file it is added at the bottom

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of the list, but if you want to rearrange the source files you can right click a code file and
select “Move Up” or “Move Down” as seen in Figure 1-5. The keyboard shortcut for
reordering project files is Alt+Up and Alt+Down.

Figure 1-5. Reordering files within an F# project

A feature sorely missing from Visual Studio is the ability to organize

an F# project’s source code files into subfolders. While not exposed by
the Visual Studio UI, you can edit the project file directly to achieve
this. Many of the in-depth examples of this book utilize this technique.

Now that you are armed with the logistical know-how for creating, compiling, and testing
F# applications, the rest of this book will focus exclusively on the syntax and semantics
of the F# programming language.

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In just a few chapters you’ll master the syntax of the F# language as well as be able to
apply it across several programming paradigms. Good luck and have fun!

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2
Fundamentals

In Chapter 1, you wrote your first F# program. I broke it down to give you a feel for what
you were doing, but much of the code is still a mystery. In this chapter, I’ll provide the
necessary foundation for you to understand that code fully, but more importantly, I’ll
present several more examples that you can use to grasp the basics of F# before you
move on to the more complex features.
The first section of this chapter covers primitive types, like int and string, which are
the building blocks for all F# programs. I’ll then cover functions so you can manipulate
data.
The fourth section details foundational types such as list, option, and unit.
Mastering these types will enable you to expand into the object-oriented and functional
styles of F# code covered in later chapters.
By the end of this chapter you will be able to write simple F# programs for processing
data. In future chapters you will learn how to add power and expressiveness to your code,
but for now let’s master the basics.

Primitive Types
A type is a concept or abstraction and is primarily about enforcing safety. Types represent
a proof of sorts if a conversion will work. Some types are straightforward – representing
an integer – while others are far more abstract – like a function. F# is statically typed,
meaning that type checking is done at compile-time. For example, if a function accepts an
integer as a parameter you will get a compiler error if you try to pass in a string.
Like C# and VB.NET, F# supports the full cast and crew of primitive .NET types. (Which
are standard across most programming languages.) They are built into the F# language
and separate from user-defined types which you define yourself.
To create a value, simply use a let binding via the let keyword. For example, the
following code defines a new value x in an FSI session. You can do much more with
let bindings, but we’ll save that for Chapter 3.

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> let x = 1;;

val x : int = 1

Numeric Primitives
Numeric primitives come in two varieties: integers and floating-point numbers. Integer
types vary by size, so that some types take up less memory and can represent a smaller
range of numbers. Integers can also be signed or unsigned based on whether or not they
can represent negative values.
Floating-point types vary in size too; in exchange for taking up more memory they
provide more precision for the values they hold.
To define new numeric values, use a let binding followed by an integer or floating-
point literal with an optional suffix. The suffix determines the type of integer or floating-
point number. For a full list of available primitive numeric types and their suffixes, see
Table 2-1.
> let answerToEverything = 42UL;;

val answerToEverything : uint64 = 42UL

> let pi = 3.1415926M;;

val pi : decimal = 3.1415926M

> let avogadro = 6.022e23;;

val avogadro : float = 6.022e23

Table 2-1. Numerical primitives in F#

Type Suffix .NET Type Range
byte uy System.Byte 0 to 255
sbyte y System.SByte –128 to 127
int16 s System.Int16 –32,768 to 32,767
uint16 us System.UInt16 0 to 65,535
int, int32 System.Int32 –231 to 231–1
uint32 u System.UInt32 0 to 232–1
int64 L System.Int64 –263 to 263–1
uint64 UL System.UInt64 0 to 264–1
float System.Double A double-precision floating
point based on the IEEE64
standard. Represents values
with approximately 15
significant digits.
float32 f System.Single A single-precision floating
point based on the IEEE32

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standard. Represents values

with approximately 7
significant digits.
decimal M System.Decimal A fixed-precision floating-
point type with precisely 28
digits of precision.
F# will also allow you to specify values in hexadesimal (base 16), octal (base 8), or
binary (base 2) using a prefix 0x, 0o, or 0b.
> let hex = 0xFCAF;;

val hex : int = 64687

> let oct = 0o7771L;;

val oct : int64 = 4089L

> let bin = 0b00101010y;;

val bin : sbyte = 42y

> (hex, oct, bin);;

val it : int * int64 * sbyte = (64687, 4089L, 42)
If you are familiar with the IEEE32 and IEEE64 standards, you can also specify floating-
point numbers using hex, octal, or binary. F# will convert the binary value to the floating-
point number it represents. When using a different base to represent floating-point
numbers, use the LF suffix for float types and lf for float32 types.
> 0x401E000000000000LF;;
val it : float = 7.5

> 0x00000000lf;;
val it : float32 = 0.0f

Arithmetic
You can use standard arithmetic operators on numeric primitives. Table 2-2 lists all
supported operators. Like most programming languages, integer division rounds down
discarding the remainder.

Table 2-2. Arithmetic operators

Operator Description Example Result
+ Addition 1 + 2 3
- Subtraction 1 – 2 -1
* Multiplication 2 * 3 6
/ Division 8L / 3L 2L

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** Power 1 2.0 ** 8.0 256.0

% Modulus 7 % 3 1

By default arithmetic operators do not check for overflow, so if you exceed the range
allowed by an integer value by addition it will overflow to be negative. (Similarly,
subtraction will result in a positive number if the number is too small to be stored in the
integer type.)
> 32767s + 1s;;
val it : int16 = -32768s

> -32768s + -1s;;

val it : int16 = 32767s

If integer overflow is a cause for concern, you should consider using a

larger type or using checked arithmetic, discussed in Chapter 7.

F# features all the standard mathematical functions you would expect, with a full listing
in Table 2-3.

Table 2-3. Common mathematical functions

Routine Description Example Result
abs Absolute value of a number abs -1.0 1.0
ceil Round up to the nearest integer ceil 9.1 10.0
exp Raise a value to a power of e. exp 1.0 2.718
floor Round down to the nearest integer floor 9.9 9.0
sign Sign of the value sign -5 -1
log Natural logarithm log 2.71828 1.0
log10 Logarithm in base 10 log10 1000.0 3.0
sqrt Square root sqrt 4.0 2.0
cos Cosine cos 0.0 1.0
sin Sine sin 0.0 0.0
tan Tangent tan 1.0 1.557
pown Compute the power of an integer pown 2L 10 1024L

Conversion Routines
One of the tenets of the F# language is that there are no implicit conversions. This means
that the compiler will not automatically convert primitive data types for you behind the
scenes, such as converting an int16 to an int64. This eliminates subtle bugs by
removing surprise conversions. Instead, to convert primitive values you must use an

1
Power, the ** operator, only works for float and float32 types. To raise the power of an
integer value you must either convert it to a floating-point number first or use the pown function.

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explicit conversion function listed in Table 2-4. All of the standard conversion functions
accept all other primitive types – including strings and chars.

Table 2-4. Numeric primitive conversion routines

Routine Description Example Result
sbyte Converts data to an sybte sbyte -5 -5y
byte Converts data to a byte byte "42" 42uy
int16 Converts data to an int16 int16 'a' 97s
uint16 Converts data to a unit16 uint16 5 5us
int32, int Converts data to an int int 2.5 2
uint32 Converts data to a uint32 uint32 0xFF 255
int64 Converts data to an int64 int64 -8 -8L
uint64 Converts data to a unit64 uint64 "0xFF" 255UL
float Converts data to a float float 3.1415M 3.1415
float32 Converts data to a float32 float32 8y 8.0f
decimal Converts data to a decimal decimal 1.23 1.23M

While these conversion routines accept strings, they parse strings using
the underling System.Convert family of methods, meaning that for
invalid inputs they throw System.FormatException exceptions.

BigInteger
If you are dealing with data larger than 264 F# has the bigint type for representing
arbitrarily large integers. (bigint type is simply an alias for the
System.Numerics.BigInteger type.)
bigint is integrated into the F# language; by using the I suffix for literals. Example 2-
1 defines data storage sizes as bigints.
Example 2-1. The BigInt type for representing large integers
> open System.Numerics

// Data storage units

let megabyte = 1024I * 1024I
let gigabyte = megabyte * 1024I
let terabyte = gigabyte * 1024I
let petabyte = terabyte * 1024I
let exabyte = petabyte * 1024I
let zettabyte = exabyte * 1024I;;

val megabyte : BigInteger = 1048576

val gigabyte : BigInteger = 1073741824
val terabyte : BigInteger = 1099511627776
val petabyte : BigInteger = 1125899906842624
val exabyte : BigInteger = 1152921504606846976

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val zettabyte : BigInteger = 1180591620717411303424

Although bigint is heavily optimized for performance, it is much

slower than using the primitive integer data types.

Bitwise Operations
Primitive integer types support bitwise operators for manipulating values at a binary
level. Bitwise operators are typically used when reading and writing binary data from
files. See Table 2-5.

Table 2-5. Bitwise operators

Operator Description Example Result
&&& Bitwise And 0b1111 &&& 0b0011 0b0011
||| Bitwise Or 0xFF00 ||| 0x00FF 0xFFFF
^^^ Bitwise Exclusive Or 0b0011 ^^^ 0b0101 0b0110
<<< Left Shift 0b0001 <<< 3 0b1000
>>> Right Shift 0b1000 >>> 3 0b0001

Characters
The .NET platform is based on Unicode, so most text is represented using 2-byte UTF-16
characters. To define a character value, you can put any Unicode character in single
quotes. Characters can also be specified using a Unicode hexadecimal character code.
The following snippet defines a list of vowel characters and prints the result of defining a
character using a hexadecimal value.
> let vowels = ['a'; 'e'; 'i'; 'o'; 'u'];;

val vowels : char list = ['a'; 'e'; 'i'; 'o'; 'u']

> printfn "Hex u0061 = '%c'" '\u0061';;

Hex u0061 = 'a'
val it : unit = ()
To represent special control characters you need to use an escape sequence, listed in
Table 2-6. An escape sequence is a backslash followed by a special character.

Table 2-6. Character escape sequences

Character Meaning
\' Single quote
\" Double quote

\\ Backslash
\b Backspace
\n Newline

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\r Carriage return
\t Horizontal tab
If you want to get the numeric representation of a .NET character’s Unicode value you
can pass it to any of the conversion routines listed in Table 2-3. Alternatively, you can get
the byte representation of a character literal by adding a B suffix.
> // Convert value of 'C' to an integer
int 'C';;
val it : int = 67
> // Convert value of 'C' to a byte
'C'B;;
val it : byte = 67uy

Strings
String literals are defined by enclosing a series of characters in double quotes, which can
span multiple lines. To access a character from within a string use the indexer syntax, .[
], and pass in a zero-based character index.
> let password = "abracadabra";;

val password : string = "abracadabra"

> let multiline = "This string

takes up
multiple lines";;

val multiline : string = "This string

takes up
multiple lines"

> multiline.[0];;
val it : char = 'T'
> multiline.[1];;
val it : char = 'h'
> multiline.[2];;
val it : char = 'i'
> multiline.[3];;
val it : char = 's'
If you want to specify a long string, you can break it up across multiple lines using a
single backslash \. If the last character on a line in a string literal is a backslash, the
string will continue on the next line after removing all leading whitespace characters.
> let longString = "abc-\
def-\
ghi";;

val longString : string = "abc-def-ghi"

You can use the escape sequence characters such as \t or \\ within a string if you want,
but this makes defining file paths and registry keys problematic. You can define a
verbatim string using the @ symbol, which takes the verbatim text between the quotation
marks and does not encode any escape sequence characters.

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> let normalString = "Normal.\n.\n.\t.\t.String";;

val normalString : string = "Normal.

.
. . .String

> let verbatimString = @"Verbatim.\n.\n.\t.\t.String";;

val verbatimString : string = "Verbatim.\n.\n.\t.\t.String"

Similar to adding the B suffix to a character to return its byte representation, adding B to
the end of a string will return the string’s characters in the form of a byte array. (Arrays
will be covered in Chapter 4.)
> let hello = "Hello"B;;

val hello : byte [] = [|72uy; 101uy; 108uy; 108uy; 111uy|]

Boolean Values
For dealing with values that can only be true or false, F# has the bool type
(System.Boolean) as well as standard Boolean operators listed in Table 2-7.

Table 2-7. Boolean operators

Operator Description Example Result
&& Boolean And true && false false
|| Boolean Or true || false true
not Boolean Not not false true

Example 2-2 builds truth tables for Boolean functions and prints them. It defines a
function called printTruthTable that takes a function named f as a parameter. That
function is called for each cell in the truth table and its result is printed. Later the
operators && and || are passed to the printTruthTable function.
Example 2-2. Printing truth tables
> // Print the truth table for the given function
let printTruthTable f =
printfn " |true | false |"
printfn " +-------+-------+"
printfn " true | %5b | %5b |" (f true true) (f true false)
printfn " false | %5b | %5b |" (f false true) (f false false)
printfn " +-------+-------+"
printfn ""
();;

val printTruthTable : (bool -> bool -> bool) -> unit

> printTruthTable (&&);;

|true | false |
+-------+-------+
true | true | false |
false | false | false |
+-------+-------+

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val it : unit = ()
> printTruthTable (||);;
|true | false |
+-------+-------+
true | true | true |
false | true | false |
+-------+-------+

val it : unit = ()

F# uses short circuit evaluation when evaluating Boolean expressions,

meaning that if the result can be determined after evaluating the first of
the two expressions then the second value won’t be evaluated. For
example:
true || f()
will evaluate to true, without executing function f. Likewise:
false && g()
will evaluate to false, without executing function g.

Comparison and Equality

You can compare numeric values using standard greater than, less than, and equality
operators listed in Table 2-8. All comparison and equality operators evaluate to a Boolean
value; the compare function returns -1, 0, or 1 depending on whether the first parameter
is less than, equal to, or greater than the second.

Table 2-8. Comparison operators

Operator Description Example Result
< Less than 1 < 2 true
<= Less than or equal 4.0 <= 4.0 true
> Greater than 1.4e3 > 1.0e2 true
>= Greater than or equal 0I >= 2I false
= Equal to "abc" = "abc" true
<> Not equal to 'a' <> 'b' true
compare Compare two values compare 31 31 0

Equality in .NET is a complex topic. There is value equality and

referential equality. For value types, comparison means that the values
are identical, such as 1 = 1. For reference types however, equality is
determined by overriding the System.Object method Equals. For
more information refer to section Object Equality in Chapter 5.

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Functions
Now that we have all of F#’s primitive types under our control, let’s define functions in
order to manipulate them.
You define functions the same way you define values, except everything after the name
of the function serves as the function’s parameters. The following defines a function
called square that takes an integer, x, and returns its square.
> let square x = x * x;;

val square : int -> int

> square 4;;

val it : int = 16

F# has no return keyword. So when you define a function, the last expression to be
evaluated in the function is what the function returns.
Let’s try another function to add 1 to the function’s input:
> let addOne x = x + 1;;

val addOne : int -> int

The output from FSI shows the function has type int -> int, which is read as “a
function taking an integer and returning an integer.” The signature gets a bit more
complicated when you add multiple parameters:
> let add x y = x + y;;

val add : int -> int -> int

Technically speaking, the type int -> int -> int is read as “a function taking an
integer which returns a function which takes an integer and returns an integer.” Don’t
worry about this “functions returning functions” jazz just yet. The only thing you need to
know for now is that in order to call a function, simply provide its parameters separated
by spaces.
> add 1 2;;

Val it : int = 3

Type Inference
Because F# is statically typed, calling the add method you just created with a floating-
point value will result in a compiler error.
> add 1.0 2.0;;

add 1.0 2.0;;

----^^^^

stdin(3,5): error FS0001: This expression was expected to have type

int
but here has type
float.

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You might be wondering then, why does the compiler think that this function only takes
integers? The + operator also works on floats too!
The reason is due to type inference. The F# compiler doesn’t require you to explicitly
state the types of all the parameters to a function. The compiler infers their types based
on usage.

Be careful not to confuse type inference with dynamic typing. Although

F# allows you to omit types when writing code, that doesn’t mean that
type checking is not enforced at compile time.

Because the + operator works for many different types such as byte, int, and
decimal, the compiler simply defaults to int if there is no additional information.
The following FSI session declares a function that will multiply two values. Just like
when + was used, the function is inferred to work on integers because no usage
information is provided.
> // No additional information to infer usage
let mult x y = x * y;;

val mult : int -> int -> int

Now if we have an FSI snippet that not only defines the mult function but also calls it
passing in floats, then the function’s signature will be inferred to be of type float ->
float -> float.
> // Type inference in action
let mult x y = x * y
let result = mult 4.0 5.5;;

val mult : float -> float -> float

val result : float = 22.0
However, you can provide a type annotation, or hint, to the F# compiler about what the
types are. To add a type annotation, simply replace a function parameter with the
following form:
(ident : type)
Where type is the type you wish to force the parameter to be. To constrain the first
parameter of our add function to be a float, simply redefine the function as:
> let add (x : float) y = x + y;;

val add : float -> float -> float

Notice that because you added the type annotation for value x, the type of the function
changed to float -> float -> float. This is because the only overload for +
which takes a float as its first parameter is float -> float -> float, so the
F# compiler now infers the type of y to be float as well.
Type inference dramatically reduces code clutter by having the compiler figure out what
types to use. However, the occasional type annotation is required and can sometimes
improve code readability.

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Generic Functions
You can write functions that work for any type of a parameter, for example an identity
function that simply returns its input.
> let ident x = x;;

val ident : 'a -> 'a

> ident "a string";;

val it : string = "a string"
> ident 1234L;;
val it : int64 = 1234L

Because the type inference system did not require a fixed type for value x in the ident
function, it was left generic. If a parameter is generic, it means that the parameter can be
of any type, such as an integer, string, or float.
The type of a generic parameter can have the name of any valid identifier prefixed with
an apostrophe, but are typically letters of the alphabet starting with ‘a’. The following
code redefines the ident function using a type annotation that forces x to be generic:
> let ident2 (x : 'a) = x;;

val ident2 : 'a -> 'a

Writing generic code is important for maximizing code reuse. We will continue to dive
into type inference and generic functions as the book progresses, so don’t sweat the
details just yet. Just note that whenever you see 'a, it can be an int, float, string,
a user-defined type, etc.

Scope
Each value declared in F# has a specific scope, which is the range of locations where the
value can be used. (More formally, this is called a declaration space.) By default, values
have module scope, meaning that they can be used anywhere after their declaration.
However, values defined within a function are scoped only to that function. So a function
can use any value defined previously on the “outside” of the function, but the outside’
cannot refer to values defined inside of a function.
In the following example a value named moduleValue is defined with module scope
and used inside of a function, while another value named functionValue is defined
within a function and raises an error when used outside of its scope.
> // Scope
let moduleValue = 10
let functionA x =
x + moduleValue;;

val moduleValue : int = 10

val functionA : int -> int

> // Error case

let functionB x =
let functionValue = 20
x + functionValue

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// 'functionValue' not in scope

functionValue;;

functionValue;;
^^^^^^^^^^^^^
error FS0039: The value or constructor 'functionValue' is not defined.
The scoping of values may not seem like that important of a detail, but one reason you
should be aware of it is because F# allows nested functions. You can declare new
function values within the body of a function. Nested functions have access to any value
declared in a higher scope, such as the parent function or module, as well as any new
values declared within the nested function.
The following code shows nested functions in action. Notice how function g is able to
use its parent function f ’s parameter fParam.
> // Nested functions
let moduleValue = 1

let f fParam =
let g gParam = fParam + gParam + moduleValue

let a = g 1
let b = g 2
a + b;;

val moduleValue : int = 1

val f : int -> int
It may seem like defining functions within functions can only lead to confusion, but the
ability to limit the scope of functions is very useful. It helps prevent pollution of the
surrounding module by allowing you to keep small, specific functions local to just where
they are needed. This will become more apparent once we start programming in the
functional style next chapter.
Once you do start using nested functions, it might become tedious to keep all the values
in scope straight. What if you want to declare a value named x, but that value is already
used in a higher scope? In F# having two values with the same name doesn’t lead to a
compiler error, rather it simply leads to shadowing. When this happens, both values exist
in memory, except there is no way to access the previously declared value. Instead, the
last one declared “wins.”
The following code defines a function which takes a parameter x, and then defines
several new values each named x as well.
> open System.Numerics
// Convert bytes to gigabytes
let bytesToGB x =
let x = x / 1024I // B to KB
let x = x / 1024I // KB to MB
let x = x / 1024I // MB to GB
x;;

val bytesToGB : BigInteger -> BigInteger

> let hardDriveSize = bytesToGB 268435456000I;;

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val hardDriveSize : BigInteger = 250

After each let binding in the previous example the value named x is shadowed and
replaced with a new one. This may look like the value of x is changing, but actually it is
just creating a new value of x and giving it the same name. The following shows an
example of how the code gets compiled.
let bytesToGB x =
let x_2 = x / 1024I // B to KB
let x_3 = x_2 / 1024I // KB to MB
let x_4 = x_3 / 1024I // MB to GB
x_4
This technique of intentionally shadowing values is useful for giving the illusion of
updating values without relying on mutation. If you want to actually update the value of
x you need to resort to mutability, which is covered in Chapter 4 Imperative
Programming.

Control Flow
Within a function, you can branch control flow using the if keyword. The condition
expression must be of type bool and if it evaluates to true then the given code is
executed, which in the following snippet prints a message to the console.
> // If statements
let printGreeting shouldGreet greeting =
if shouldGreet then
printfn "%s" greeting;;

val printGreeting : bool -> string -> unit

> printGreeting true "Hello!";;

Hello!
val it : unit = ()
> printGreeting false "Hello again!";;
val it : unit = ()

More complex code branching can be done using if expressions.

if expressions work just like you would expect: if the condition expression evaluates to
true then the first block of code executes, otherwise the second block of code executes.
However, something that makes F# much different from other languages is that if
expressions return a value.
For example, in the following example the value result is bound to the result of the if
expression. So if x % 2 = 0, then result’s value will be "Yes it is" otherwise
result's value will be "No it is not".
> // If expressions
let isEven x =
let result =
if x % 2 = 0 then
"Yes it is"
else
"No it is not"
result;;

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val isEven : int -> string

> isEven 5;;

val it : string = "No it is not"

You can nest if expressions to model more complicated branching, but this quickly
becomes difficult to maintain.
let isWeekend day =
if day = "Sunday" then
true
else
if day = "Saturday" then
true
else
false

F# has some syntactic sugar to help you combat deeply nested if expressions with the
elif keyword. With it you can chain together multiple if expressions without the need
for nesting.
let isWeekday day =
if day = "Monday" then true
elif day = "Tuesday" then true
elif day = "Wednesday" then true
elif day = "Thursday" then true
elif day = "Friday" then true
else false

Because the result of the if expression is a value, every clause of an if expression must
return the same type.
> // ERROR: Different types for if expression clauses
let x =
if 1 > 2 then
42
else
"a string";;

else "a string";;

------------------^^^^^^^^^^^

stdin(118,19): error FS0001: This expression was expected to have type

int
but here has type
string.
stopped due to error

But what if you only have a single if and no corresponding else? In that case, the
clause must return unit. unit is a special type in F# that means essentially no value.
(Alternatively you can think of unit as a manifestation of void from other
programming languages.) We’ll cover unit in more detail shortly.

Core Types
Previously we covered the primitive types available on the .NET platform, but those
alone are insufficient for creating meaningful F# programs. The F# library includes

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several core types that will allow you to organize, manipulate, and process data. Table 2-
9 lists a set of foundational types you will use throughout your F# applications.
In fact, these foundational types enable programming in the functional style, as we will
see in the next chapter.

Table 2-9. Core types in F#

Signature Name Description Example
unit Unit The unit value ()
int, float Concrete type A concrete type 42, 3.14
'a, 'b Generic type A generic (free) type
'a -> 'b Function type A function returning fun x -> x + 1
a value
'a * 'b Tuple type An ordered grouping ("eggs", "ham")
of values
'a list List type A list of values [ 1; 2; 3], [1 ..
3]
'a option Option type An optional value Some(3), None

Unit
The unit type is a value signifying nothing of consequence and is represented in code
via ().
> let x = ();;

val x : unit

> ();;
val it : unit = ()

if expressions without a matching else must return unit because if they did return a
value, what would happen if else-clause was executed instead? Also, in F# every
function must return a value, so if the function doesn’t conceptually return anything –
like printf – then it should return a unit value.
The ignore function can swallow a function’s return value if you want to return unit.
It is typically used when calling a function for its side effect and you want to ignore its
return value.
> let square x = x * x;;

val square : int -> int

> ignore (square 4);;

val it : unit = ()

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Tuple
A tuple – which can be pronounced as either “two-pull” or “tuh-pull” – is an ordered
collection of data and an easy way to group common pieces of data together. For
example, tuples can be used to track the intermediate results of a computation.

F# tuples use the underlying System.Tuple<_> type, though in

practice you will never use the Tuple<_> class directly.

To create an instance of a tuple, separate a group of values with commas, and optionally
place them within parentheses. A tuple type is described by a list of the tuple’s element’s
types, separated by asterisks. In the following example, dinner is an instance of a tuple
while string * string is the tuple’s type.
> let dinner = ("green eggs", "ham");;

val dinner : string * string = ("green eggs", "ham")

Tuples can contain any number of values of any type. In fact, you can even have a tuple
that contains other tuples!
The following code snippet defines two tuples. The first, named zeros, defines a tuple
of various manifestations of zero. The second, nested, defines a nested tuple. The tuple
has three elements, the second and third of which are themselves tuples.
> let zeros = (0, 0L, 0I, 0.0);;

val zeros : int * int64 * BigInteger * float = (0, 0L, 0I, 0.0)

> let nested = (1, (2.0, 3M), (4L, "5", '6'));;

val nested : int * (float * decimal) * (int64 * string * char) = ...

To extract values from two-element tuples you can use the fst and snd functions. fst
returns the first element of the tuple and snd returns the second.
> let nameTuple = ("John", "Smith");;

val nameTuple : string * string = ("John", "Smith")

> fst nameTuple;;

val it : string = "John"
> snd nameTuple;;
val it : string = "Smith"

Alternately, you can extract values from tuples by simply using a let binding. If you
have let followed by multiple identifiers separated by commas, then those names
capture the tuple’s values.
The following example creates a tuple value named snacks. Later the tuple’s values are
extracted into new identifiers named x, y, and z.
> let snacks = ("Soda", "Cookies", "Candy");;

val snacks : string * string * string = ("Soda", "Cookies", "Candy")

> let x, y, z = snacks;;

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val z : string = "Candy"

val y : string = "Cookies"
val x : string = "Soda"

> y, z;;
val it : string * string = ("Cookies", "Candy")
You will get a compile error if you try to extract too many or too few values from a tuple.
> let x, y = snacks;;

let x, y = snacks;;
-----------^^^^^^

stdin(8,12): error FS0001: Type mismatch. Expecting a

string * string
but given a
string * string * string.
The tuples have differing lengths of 2 and 3.
It is possible to pass tuples as parameters to functions, like any value. Likewise, a
function can return a tuple. In the following example the function tupledAdd takes two
parameters, x and y, in tupled form. Notice the difference in type signature between the
add and the tupledAdd functions.
> let add x y = x + y;;

val add : int -> int -> int

> let tupledAdd(x, y) = x + y;;

val tupledAdd : int * int -> int

> add 3 7;;

val it : int = 10

> tupledAdd(3, 7);;

val it : int = 10
Functions taking a single tuple as a parameter have a much different meaning when it
comes to the functional style of programming;, see Partial Function Application in
Chapter 3.

Lists
Whereas tuples group values into a single entity, lists allow you link data together to form
a chain. Doing so allows you to process list elements in bulk using aggregate operators,
discussed shortly.
The simplest way to define a list is as a semicolon-delimited collection of values enclosed
in brackets, though later you will learn to declare lists using the more powerful list
comprehension syntax. The empty list, which contains no items, is represented by [].
> // Declaring lists
let vowels = ['a'; 'e'; 'i'; 'o'; 'u']
let emptyList = [];;

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val vowels : char list = ['a'; 'e'; 'i'; 'o'; 'u']

val emptyList : 'a list = []

In our example the empty list had type 'a list because the empty list could be of any
type. With more information based on usage, the type inference system would be able to
pin it down to a more specific type.
Unlike list types in other languages, F# lists are quite restrictive in how you access and
manipulate them. In fact, for a list there are only two operations you can perform. (To see
how this limitation can be used to your advantage, refer to Chapter 7, Applied Functional
Programming.)
The first primitive list operation is cons, represented by the :: or cons operator. This
joins an element to the front or head of a list. The following example attaches the value
'y' to the head of the vowels list.
> // Using the cons operator
let sometimes = 'y' :: vowels;;

val sometimes : char list = ['y'; 'a'; 'e'; 'i'; 'o'; 'u']

The second primitive list operation, known as append, uses the @ operator. Append joins
two lists together. The following example joins the list odds and the list evens
together, resulting in a new list.
> // Using the append operator
let odds = [1; 3; 5; 7; 9]
let evens = [2; 4; 6; 8; 10]

val odds : int list = [1; 3; 5; 7; 9]

val evens : int list = [2; 4; 6; 8; 10]

> odds @ evens;;

val it : int list = [1; 3; 5; 7; 9; 2; 4; 6; 8; 10]

List ranges
Declaring list elements as a semicolon-delimited list quickly becomes tedious, especially
for large lists. To declare a list of ordered numeric values you can use the list range
syntax.
The first expression specifies the lower bound of the range and the second specifies the
upper bound. The result then is a list of values from the lower bound to the upper bound,
each incremented by one.
> let x = [1 .. 10];;

val x : int list = [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]

If an optional step value is provided, then the result is a list of values in the range
between two numbers separated by the stepping value. Note that the stepping value can
be negative.
> // List ranges
let tens = [0 .. 10 .. 50]
let countDown = [5L .. -1L .. 0L];;

val tens : int list = [0; 10; 20; 30; 40; 50]
val countDown : int64 list = [5L; 4L; 3L; 2L; 1L; 0L]

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List comprehensions
The most expressive method for creating lists is to use list comprehensions, a rich syntax
that allows you to generate lists inline with F# code. At the simplest level a list
comprehension is some code surrounded by rectangular brackets [ ]. The body of the
list comprehension will be executed until it terminates, and the list will be made up of
elements returned via the yield keyword. (Note that the list is fully generated in
memory when created. If you find yourself creating lists with thousands of elements,
consider using a seq<_>, discussed in the next chapter, instead.)
> // Simple list comprehensions
let numbersNear x =
[
yield x - 1
yield x
yield x + 1
];;

val numbersNear : int -> int list

> numbersNear 3;;

val it : int list = [2; 3; 4]
Most any F# code can exist inside of list comprehensions, including things like function
declarations and for loops. The following code snippet shows a list comprehension that
defines a function negate and returns the numbers 1 through 10, negating the even
ones.
> // More complex list comprehensions
let x =
[ let negate x = -x
for i in 1 .. 10 do
if i % 2 = 0 then
yield negate i
else
yield i ];;

val x : int list = [1; -2; 3; -4; 5; -6; 7; -8; 9; -10]

When using for loops within list comprehensions, you can simplify the code by using -
> instead of do yield. The following two code snippets are identical.
// Generate the first ten multiples of a number
let multiplesOf x = [ for i in 1 .. 10 do yield x * i ]

// Simplified list comprehension

let multiplesOf2 x = [ for i in 1 .. 10 -> x * i ]
Using list comprehension syntax will enable you to quickly and concisely generate lists
of data, which can then be processed in your code. Example 2-3 shows how you can use
list comprehensions to generate all prime numbers smaller than a given integer.
The example works by looping through all numbers between 1 and the given max value.
Then, it uses a list comprehension to generate all the factors of that number. It checks if
the generated list of factors has only two elements, then it yields the value because it is
prime. There certainly are more efficient ways to compute primes, but this demonstrates
just how expressive list comprehensions can be.

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Example 2-3. Using list comprehensions to compute primes

> // List comprehension for prime numbers
let primesUnder max =
[
for n in 1 .. max do
let factorsOfN =
[
for i in 1 .. n do
if n % i = 0 then
yield i
]

// n is prime if its only factors are 1 and n

if List.length factorsOfN = 2 then
yield n
];;

val primesUnder : int -> int list

> primesUnder 50;;

val it : int list = [2; 3; 5; 7; 11; 13; 17; 19; 23; 29; 31; 37; 41; 43; 47]

List module functions

The F# Library’s List module contains many methods to help you process lists. These
built-in methods listed in Table 2-10 are the primary way you will interact with lists in
F#.

Table 2-10. Common List module functions

Function and type Description
List.length Returns the length of a list.
'a list -> int
List.head Returns the first element in
'a list -> 'a a list.
List.tail Returns the given list
'a list -> 'a list without the first element.
List.exists Returns whether or not an
('a -> bool) -> 'a list -> bool element in the list satisfies
the search function.
List.rev Reverses the elements in a
'a list -> 'a list list.
List.tryfind Returns Some(x)where x
('a -> bool) -> 'a list -> 'a option is the first element for
which the given function
returns true. Otherwise
returns None. (Some and
None will be covered
shortly.)
List.zip Given two lists with the
'a list -> 'b list -> ('a * 'b) list same length, returns a

21
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f'Ag«κλήοντο Cass. Aug. t A le φυγὴν Gr. Pini Pun Man δΑσόλλυσ
cum a acorrectore inter versus scripto Cass. prodi Aug. es superscr.
ἀποχνύασι Mosqu. i Τεύγλουσαν Zr. C. Reg. k 'Αλικαρνασόν Reg.
Mosqu. " Καὶ μετὰ τοῦτο Cl. 42. Astyochus igitur, ut se habe-
adversus hostium naves tendunt, exibat, ad Symam celeriter
tendebat, stimantes, has esse naves illas, quas adventus sui famam
prevertere cw- ex Cauno venientes observabant. Et piens, si forte
classem Aostilem in impressione im eas statim facta, tres alto
naneisci posset. Sed imber cc- illarum depresserunt, aliasque
laceique nubilum perturbationem ejus rarunt; et in hoc prelio
vietoriam navibus attulit, et effecit, ut in tene- obtinuerunt, donec
plereque Zacebris vagarentur. Et simul ac dies gémeniorum naves
preter opinioilluxit, cum ejus classis esset disper- nem in ipsorum
conspectum sa, et sinistrum quidem cornu jam venerunt, a qwibus
etiam undique in Atheniensium conspectum veni- conclusi fuerunt.
Tune vero in faret, alterum vero circum insulam gam se conjecerunt,
et sex naves adhue vagaretur, confestim Charmi- amiserunt; at cum
eseteris in insunus et Athenienses cum navibus, lam Teuglussam
confugerunt; hinc que pauciores erant, quam viginti, vero, in
Halicarnassum, Postea vero,
Bell. Pelop. » an. 20. Olymp. U. C. Varr. 343. 174
ΘΟΥΚΥΔΙΔΟΥ͂ ποννήσιοι, ἐς Κνίδον κατεραντες, καὶ ξυμμιγεισῶν τῶν
ἐξ τῆς Καύνου $ di καὶ εἴκοσι νεῶν αὐτοῖς, ξυμπάσαις πλεύσαντες,
καὶ τροπαῖον ἐν τῇ Σύμη στήσαντες, πάλιν ἐς τὴν Κνίδον "er amener!
μγ΄. Oi δὲ ᾿Αϑηναῖοι, ἱ ταῖς ἐκ τῆς Σάμου ναυσὶ πάσαις, ὡς fir Sovro.
τὰ τῆς vU pA ues πλεύσαντες ἐς - Σύμην, καὶ ἐπὶ μὲν φὸ ἐν τῇ
Κνώδῳ ναυτικὸν oU, ἢ ὁρμήσαντες, οὐδ᾽ : ἐκεῖνοι €T ἐκείνους,
χεδόνρας ὃὲ τὰ ἐν τῇ Σύμη σπεύη τῶν γεῶν, καὶ ! Δορύριοις τοῖς ἐν
τῇ ἠπείρῳ προσξαλόντες, ἀπέπλευσαν ἧς τὴν Σάμον. ὥπασαι Ἢ δ᾽
ἤδη οὖσαι ἐν τῇ Κνίδῳ αἱ τῶν Πελοποννησίων γῆες " ἐπεσκευάζοντό
T6, εἴ τι ἔδει» καὶ πρὸς τὸν Τισσαφέρνην (σαρεγένετο yàg) λόγους
ἐποιοῦντο οἱ ἕνδεκα ἄνδρες TÀy Λακεδαιμονίων “ περί T& τῶν ἤδη
πεπραγμέYay, & τι μὴ ἤρεσκεν αὐτοῖς, καὶ περὶ TOU P μέλλοντος
τολόμῶν, ὅτῳ τρόπῳ ἄριστα καὶ 3 ξυμφορώτατα, ἄμφοτέροις
"πολεμήσεται. μάλιστα δὲ ὁ 5 Λίχας ἐσκόπει τὰ ποιούμιενο, καὶ τὼς
σπονδὰς * οὐδετέρας, " οὔτε τὰς ! Ταῖς deest Gr. ἘΚ Ὁρμίσαντες C.
Ald. Flor. Bas. Reg. Cass. Gr. Dan. Aug. | Λωρύμοις Zr. C. Ald. Flor.
Bas. atque ita apud Strabonem et débita Huds. Sic etiam Reg. Cass.
Gr. Dan. Cam. Aug. m Ai ἤδη Ar. C. Ainon habet Gr. 5 ᾿Επεσχεύαξόν
v: Mosqu. Ἑ Περὶ δὲ Afr. C. Aid. Flor. Bas. Reg. Gr. Aug. In . Cass.
erasa scriptura ἃ μύρα ἐν erat spatium vacuum inter περὶ et σῶν. P
Μέλλονφος, πολέμῳ ὅσῳ cobro Zlid. Flor. Bas. Steph. 1. Μέλλονσος
πολέμῳ, ὅτῳ v. Gr. Ἰτολέμῳ etiam Cam. et ex emendatione πολέμον.
Antea ἤρεσεν Mosqu. 4 Ξυμφιρώτατα Reg. T Ππεπολεμήσεται Marg.
Aid. Flor. Bas. ττολεμήσεσαι Cam. cum ceteris Mss. σολεμκηϑήσεται
Mosqu. * Λεΐχας C. Reg. t οὐδ᾽ ἑσέρας Gr. ἃ Ole: v. Θηρ. ἔφη, οὔτε
τὰς Χαλκιδίως Mosqu. Οὐδὲ τὰς Χαλκχιδέως, οὐδὲ τὰς Op. Cl.
Θηριμίνους Cass, Aug. Peloponnesii quidem, cum ad Cnidum
appulissent, et septem ac viginti naves ex Cauno profectas sibi
adjunxissent, eum universa classe Symam petierunt, ibique tropmo
Statuto, in Cnidi stationem redierunt. 43. Athenienses vero cum
omnibus navibus, que ad Samum-stabant, postquam navale prolium
commissum intellexerunt, in Symam iverunt. Cum autem nec ipsi
classem, quz ad Cnidum stabat, invasissent, nec illi, qui illic erant, in
ipsos impressionem fecissent, sed navium armamenta, quz erant in
Syma, sumsissent, et pondre quz sunt in continente, oppugnassent,
Samum redierunt. Cum autem omnes Pelo-. ponnesiorum naves in
Cnido jam essent, reficiebantur, si quid oportebat. Etundecim illi
Lacedzmoniorum viri cum Tissapherne (aderat enim) agebant cum
de rebus jam transactis, si qua illarum ipsis non placeret, tum etiam
de futuro bello, qua ratione optime et maxime ex utrorumque
utilitate gerendum esset. Precipue vero Lachas considerabat ea,
quae fiebant, et neutrum
ZYITPAOHSZ H. μδ΄. 115 Θηραμένους, ἔφη, καλῶς "
ξυγκεῖσγαι, ἀλλὰ δεινὸν Bell. εἶναι» εἰ * χώρας, ὅσης βασιλεὺς καὶ οἱ
πρόγονοι ἦρξαν an. 20. ὅτερον» ταύτης καὶ νῦν ἀξιώτει κρατεῖν,
(ἐνῆν γὰρ πὰ καὶ, νήσους ἑπάσας πάλιν δουλεύειν, καὶ Θεσσαλίαν, ud
καὶ Λοκροὺς, καὶ τὰ μέχρι Βοιωτῶν") καὶ ἀντ᾽ ἐλευ- 343. “)ερίας ἂν
Μηδικὴν ἀργὴν τοῖς Ἕλλησι τοὺς Λακεδα:ιμμονίους περιϑϑεῖναι.
ἑτέρας οὖν ἐκέλευε βελτίους σπένδεσῖγαι, ἢ ταύταις γε οὐ
χρήσεσίγαι" οὐδὲ τῆς τροφῆς, ἐπὶ τούτοις, δεῖσϑϑαι οὐδέν.
ὠγανακτῶν δὲ ὁ μὲν Τισσαφέρνης, ὠπεχώρησεν π᾿ αὐτῶν δ ὀργῆς»
καὶ ἄπρακτος. μδ΄. Y Oi δ᾽ ἐς τὴν Ῥόδον, ἐπικηρυκευοριένων ἀπὸ
τῶν δυνατωτάτων ἀνδρῶν, τὴν γνώμην εἶχον πλεῖν, ἐλπίζοντες
νῆσόν τε οὐκ ἀδύνατον καὶ Σναυξατῶν TATSu καὶ πεζῷ
προσάξεσϑγαι, καὶ ἅμα ἡγούμενοι αὐτοὶ ἀπὸ τῆς ὑπαρχούσης
ξυμμαχίας δυνατοὶ ἔσεσίγαι, Τισσαφέρνην μὴ αἰτοῦντες χρήματα,
τρίφειν τὰς ναῦς. πλεύσαντες οὖν εὐθὺς ἐν τῷ αὐτῷ χειμῶνι ἐκ τῆς
Κνίδου, καὶ προσξαλόντες " Καμείρῳ τῆς Ῥοδίας ἃ Συγκεῖσϑαι Cass.
Aug. Ἐυγκιῖσϑα, Gr. * Χώρας ὅσης ἧς βασιλεὺς Ar, C. Χώρας ἧς
βασιλεὺς Cl. Sic etiam Cass, et in marg. manu recenti γρ. ὅσης. απ.
consentit cum fr. et C. ἧς Aug. y Οἱ 3i is, et paullo post ἐντεῦθεν δὲ
ἐς Σάμον Gr. * Ναυτῶν Ar. Mosqu. qui et mox Νανατῶν Reg. Gr. sed
in Reg. deinde emendatum erat ναυξατῶν. * Καμίσρῳ Reg. Cass. Gr.
καρωρῷ Aug. fedus, aut a Chalcideo, aut a Theramene, bene factum
esse dicebat. Indignum enim profecto esse, si, euieunque provincie
Rex ejusque majores prius imperassent, huic nunc etiam Aer
imperare vellet. Oportuisset enim Aoc »odo et omnes insulas, et
'Thessaliam, et Locros, et regiones, que usque ad Beeotorum fines
pertinebant, in servitutem rursus redigi, et Lacedzmonios pro
libertate imperium Medorum Grecis cervicibus imponere. Alia igitur
Jedera meliora fieri jubebat, aut istis se non usurum, nec ob has
pactiones ullo stipendio opus esse. Tissaphernes autem indignatus,
ab ipsis iratus, et infecto negotio abscessit. 44. Illi vero in Rhodum, a
primoribus viris per praeconem arcessiti, navigare in animo
habebant: sperantes fore, ut insulam et navalibus et pedestribus
copiis instructam sibi adjungerent, simul etiam existimantes, se
prssentis societatis beneficio posse navales copias alere, nullam
uniam a 'Tissapherne petentes. tinus igitur per eandem hyemem ex
Cnido profecti, et ad Camirum *ore Rhodie primum appulsi cum
quatüor et nonaginta navibus, rmnul. * Ὅτ Rhodis primam urbem,
etc. Hups,
Bell. Pelop. an. 20. Olymp. * 92. 1. U. c. Varr 343. Jan. 6.
176 OOYKYAIAOY : ^ πρώτῃ ναυσὶ τέσσαρσι καὶ. " ἐννενήκοντοι»
ἐξεφόξησαν μὸν τοὺς πολλοὺς, οὐκ εἰδότας τὰ πρασσόμενοι, “καὶ
equo, ἄλλως τε, καὶ ἀτειχίστου οὔσης “τῆς “όλεως" εἶτα,
᾿ξυγκαλέσαντες οἱ Λακεδαιμόνιοι τούτους σε καὶ τοὺς ἐκ ὃ τῶν δυοῖν
πόλεοιν, Δίνδου τε καὶ ἢ ᾿Ιηλυσοῦ, Ῥοδίους, ὦ ἔπεισαν ἀποστῆναι ἢ
᾿Αϑηναίων. k χαὶ προσεχώρησε Ῥύδος ᾿ Πελοποννησίοις. τὰ οἱ δὲ
᾿Αϑηναῖοι κατὰ τὸν καιρὸν τοῦτον σαῖς ἐκ τῆς Σάμου γαυσὶν,
αἰσιϑόμμενοι» 8 ἔπλευσαν μὲν, βουλόμενοι Qum, καὶ ἐφάνησαν
πελάγιοι " ὑστερίσαντες ὁ δὲ οὐ πολλῷ; σὸ μὲν παραχρῆμα
ὠπέπλευσαν ἐς Χαλκῆν, ἐντεῦσεν δ᾽ ἐς Σάμον" ὕστερον δὲ & ἐκ τῆς
Χάλκης καὶ ἐκ τῆς Ka καὶ ἐκ τῆς Σώμου τοὺς ἐπίπλους Ὁ ποιούμενοι,
ἐπὶ τὴν Ῥόδον ἐπολέμουν. οἱ δὲ χρήματα d μὲν " ἐξέλεξαν μὲ die καὶ
τριάκοντα τάλαντα οἱ Πελοποννήσιοι παρὰ » Ῥοδίων, τὰ δ᾽ ἄλλα
ἡσύχαζον ἡμέρας ydo κοντὰ. ὠνελκύσωντες τὰς ναῦς. 007 » Πρὸς
ταῖς γαυσὶ Ald. Flor. Πρὸς τὴνταναυσὶ C. ΥἹρὸς τὴν ναυσὶ dr. — Iloà
σὴν γῆν ναυσὶ Bas. Πρὸς τὴν ναυσὶ Cass. Gr. et in marg. manu
recenti πρώτῃ Cass. Ἱρὸς τὴν ἄκραν ναυσὶ Dan. Πρὸς σὴν γῆν ναυσὶ
Cam. πρὸς τὴν ug. * ᾽Ενενήχκοντα Cass. Gr. Aug. 4 Ko)deest Gr. ^ *
Τῆς omittunt “114. Flor. f Συγκαλίσαντες Gr. 8 Toiv Zr. C. ΟἹ. Aug.
Reg. & 4lüs ᾿Ιάλυσσος,᾿ Ιάλυσος, et ᾿Ιαλυσὸς dicitur. "Vide Meursii
Rhodum l. 1. c. 9. 10. Huds. ᾿ϊηλυγοῦ Dan. ᾿Ιηλύσον dug. sed m,
Tec. corr, Ἰηλυσοῦ. εὐ Τῶν ᾿Αϑηναίων Gr. * Heec est illa defectio, de
qua loquitur Diodorus, *etsi Rhodiis non diserte nominatis, lib. XIII. .
Vide Meursii Rhodum 1. I. c. 22, p. 73. Huds, | πελλοαοννησίοις Gr.
et sic sarpe alibi. m» or» ᾿Αϑηναῖο Zr. π᾿ Ὑσχερήσαντες Zr. C. Cl. Gr.
Reg. Cass. Mosqu. 9 Δ᾽ οὐ πολλῷ Gr. » Sie distinguit ZE. Port.
πτοιούμνοι ἐπὶ πὴν Ῥόδον, ἐπολέμουν. Verum imi τῆς Ῥόδου legunt
Zr. C. Dana. 3 Mi» deest Gr. τ᾿ Ἐξιλέξανφες δύο x. v. 7. Gr. i pientes,
* et conspecti quidem tis quidem terrorem injecerunt, sunt dum
cursum in alto tenerent. Sed ignaris, qu&& agerentur, et ideo
profugerant, presertim quod urbs nullis muris esset munita. Sed
postea Lacedzmonii cum et istos, et duarum civitatum, Lindi et
Ielysi, cives Rhodios convocassent, ipsis persuaserunt, ut ab
Atheniensibus deficerent, Atque Rhodus se Peloponnesiis adjunxit.
À
Athenienses vero, eum Àoc intellexissent, sub idem tempus cum
classe e Samo solverunt, AKAodiorum defectionem antevertere
cueum serius aliquanto venissent, tunc quidem in Chalcen, hine vero
in Samum celeriter abierunt, Postea vero et ex Chalce et ex Co et ex
Samo incursiones in Rhodum facientes, bellum gerebant. Pelo nnesii
vero pecunias ad duo et triginta talenta à Rhodiis exegerunt, in
ceteris vero rebus, subductis navibus, ibi per octoginta dies
quieverunt. * Et, quum altum tenerent, in hostium conspectum
venerunt, sed jam tardiusculi. "ton post. πιλάγιοιγ sed post πολλῷ,
posuisset. Hus. Meoque in Chalcen, etc. alla; quasi distinctionis
notam
EYITPAOHZ H. μέ. 171 vg. Ἔν δὲ τούτῳ». xci ἔτι,
πρότερον, πρὶν ἐς τὴν Βεὶ!. Ῥόδον αὐτοὺς ἀναστῆναι, ϑγάδε
ἐπράσσετο. ᾿Αλκι- eso Cu0ns, μετὼ τὸν Χαλκιδέως ϑάνατον, καὶ τὴν
M Μιλήτῳ I yas voig Πελοποννησίοις ὕποπτος ὧν, καὶ Vn Ls tz αὐτῶν
ἰφικομένης, ἐπιστολῆς πρὸς ᾿Αστύοχον ἐκ Λακεδαίμονος, " ὥστ᾽
ἀποκτεῖναι; (ἦν γὰρ τῷ "wh ὦ LLL καὶ ἄλλως ἄπιστος ἐφαίνετο")
πρῶτον. μὲν ὑποχωρεῖ, δείσας» παρὼ 'T ισσαφέρνην, ἔπειτα
ἐκόώκου πρὸς αὐτὸν, "ὅσον y ἐδύνατο μάλιστα, τῶν Πελοποννήσίων
và πρώγματα. καὶ διδώσκαλος πάντων γιγνόμε. γος, τήν τε
ρισι)οφορὰν ξυνέτεμιεν, ἀντὶ δραχμῆς ᾿Αττικῆς ὥστε σειώξολον (σαὶ
τοῦτο μὴ ξυνεχῶς.) δίdoc you* λέγειν κελεύων τὸν Τισσαφέρνην
πρὸς αὐτοὺς, ὡς ᾿Αϑηναῖοιν ἐκ πλείονος χρόνου. ἐπιστήρνονες ὄντες
τοῦ γαυτικοῦ, ᾿τριώξολον. τοῖς ἑαυτῶν διδόασι» οὐ τοσοῦτὸν πενίᾳ»
TOY ἴα αὐτῶν μὴ οἱ ναῦται» ἐκ περιουσίας ὑξρίζοντες, οἱ p» τὼ
σώματα χείρω λέχωσι, δαπαγῶντες ἐς τοιαῦταγ ἀφ᾽ ὧν ἡ ἀσθένεια;
ξυμβαίνειν * d est : σὰ ἑξῆς, σὰ eio] σοῦ ' AX su Code «αὐτῶν Gr. 4l.
Flor. Bas. Cam. et ex emendatione ie" αὐτόν. b οἱ t "Ἐπ ἐν e “Ἐ. Port.
Huds. " *OQ»er: ἀποκτεῖναι Adr. C. Aug. Reg. Cass. Gr. τ Ὅσα Cam.
— Y ᾿Ἐδόνατο τὰ τῶν΄ Πελοποννησίων πράγματα Marg. Cam.
Mosqu. τ: De üs militaribus vide Petiti Leges Atticas, p. 554. Huds. «,
ἧ τι o qt i κο ctore Gr. mox i; σὰ σοιαῦτα Mosqu. est: οἱ δὲ τὰς ναῦς
χείρας ἔ Pudor t^ cna veia eres ἀπολιπόντες, καὶ τὸν λόμεενον μ , ᾿»
ax ξ vp bere cim edite ὁ 5, σϑὸν Ar. 45. μὰν vero, quinetiam aiuhà à
* ante, quam ipsi Peloponnesii cestra Rhodum versus ssent, heec,
quee sequuntur, gesta sunt. Alcibiades loponnesi e tem epistola de
eo interficiendo ad Astyochum ab ipsis Lacedzemone missa fuisset,
(erat enim Aeidi inimicus, et alioqui infidus videbatur ; metuens,
primum quidem ad Tissaphernem secessit: deinde vero apud sum,
quam maxime poterat, Peloeig διδόντες. 22. Port, wo Yers ἔχωσι, τὰς
ναῦς} ἀπολιπόντι; ἐ; εἰς, i. e. διὰ πὰ δίαλνανῶι Steph. "Es ὁμηρείαν
σοῦ bonc eo μισϑοῦ C. idetur hsec esse DA Eg ὁμηρείαν τοῦ
προσοφειλομεένεν gi ponmesiorum rebus nocebat. Et 7'issaphernem
omnia docens, sti dium imminait, ita ut pro ires cam Attica termi
oboli, nee ii assidue, solverentur : Tissaphernem hortaus, ut illis
diceret, Athenienses, qui longiore temporis spatio rei navalig peritiam
haberent, ternos duntarat obolos suis cíassiariis numerare, non tam
propter paupertatem, quam ne 3) sui nautz, propter affluentiam
sf$pendii insolentius viventes, partim quidem corpora imbecilliora
habe. rent, stipendium impendentes in ea, * Ante, quam Rhodum ad
deficiendum induxissent. Falla. VOL. 111. N 
. δὲ, τος ναῦς í ὀφειλόμενον paro». καὶ, τοὺς ἐδ ὅ f
στρατηγοὺς τῶν πόλεων, £0i000,6£V, CUTE δόντα χεῆἢ paras αὐτὸν
πεῖσαί» ὥστε 5 ξυγχωρῆσαι. ταῦτα ἑαυτῷ» ; πλὴν σῶν Συρακουσίων
τούτων δὲ; Ἑρμοκράτης τέ 178 OOYKYAIAOY d “ ἀπολιπόντες, w
ὁμηρείαν TO προσ* τριηράρχους. καὶ τοὺς ἠναντιοῦτο μόνος ὑπὲρ
τοῦ ξύμπαντος ξυμμωαχικοῦ, τάς T£ πόλεις ϑδοομόνας χρημάτων h
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ὠναίἌΝ k $e» πλουσιώτατοι ὄντες τῶν Ἑλλήνων, € £Tiπουρίᾳ δὲ ὁ
ὅμως σωζόμενοι, ἀξιοῦσι, καὶ τοῖς σώμασι καὶ σοῖς χρήμασιν ἄλλους
ὑπὲρ i ἐκείνων ἐλευδερίαις πωδυνεύειν. τὰς δ᾽ ἄλλας πόλεις, ἔφη, "
ἀδικεῖν, αἱ πὲς ᾿ΑϑΝηναίους, " πρότερον ἀποστῆναι; P ἀνάλουν, εἰ μὴ
καὶ νῦν τοσαῦτα καὶ ἔτι πλείω ὑπὸρ σφῶν τ αὐτῶν ἐψελήσουσιν
ἐσφέρειν. φόν τε Τισσαφέρνην, ἐπέφαινε, »γῦν μὲν, τοῖς ἰδίοις
χρήμασι dag uio εἰκότως Φφειδόμενον" ἣν δέ ποτε τροφὴ καταξῇ 5
παρὰ βασιλέως, ἐντελῆ αὐτοῖς ὠποδώσειν τὸν μισϑὸν, καὶ τὰς πόλεις
TOÀ. εἰκότα ὠφελήσειν. E ᾿Απολείπωσιν Cl. ὑπολισπόντες in marg. 4
Ὁμηρίαν Cass. Aug. a corr. p. dev. ὁμηρίαν Mosqu. .— * Τριηράρχας
4r. C. Reg. — f Διδόντα Ar. C. Reg. 8 Συγχωρῆσαι Cass. Gr. Aug. h
Pro ἀπήλασεν legendum videtur ἀσήλλασσέν, aut ἀπήλαυνεν. Steph.
| Τοῦ deest Feg. Mosqu. ἐν omissum manu recenti inter versus
habet Reg. i Uie «ῆς ἐκείνων Zr. C. Rem: Mosqu. m ᾿Αδικεῖν ἐς
᾿Αϑην. Gr. ? El; et paullo post εἰσφέρειν Reg. — 9 [dest: σπρόφερον
ἢ ἀσοσεσῆνωι. AE. Port. P ᾿Αναλοῦν Ald. Flor. Jas. Gr. ἀνάλοῦν Aug.
e. acut. et circumfl. 4 Καὶ νῦν καὶ φοσαῦτα dr. C, Cass. Dan. Aug. καὶ
ante $c; X. d. Mosqu. τ Αὐτῶν deest Reg. 5'Aqà Marg. Cam. unde
corporum imbecillitas contin- simi, et auxiliarium copiarum benegit,
partim vero elassem iénbecilliovem redderent, eam ac reliquum
stipendium ipsis debitum deserentes, «c trieravchis suo loco
relinquentes ut obsidem. 1dem ipsum edocuit, ut trierarehos et
civitatum duces, pecunia ipsis data, ad hanc rem sibi €oncedendam
induceret, exceptis Syracusanis. Horum enim dux Hermocrates, solus
omnium, socialis classis nomine Avie rei adversabatur. Civitates
quoque, quce pecuniam postulabant, ipse T'issaphernis nomine
repulsam passas amandabat, dicens, Chios quidem impudentes esse,
qui, euim essent omnium Grecorum ditisficio servarentur, postularent
tamen, ut alii et corporibus et pecuniis pro prvun libertate pericula
subirent, lias vero civitates injuste facere dicebat, si, qui pro
Athenieusibus, antequam ab illis defecissent, sumtus facere
consuevissent, nunc etiam pro se ipsis tantundem aüt etiam plus
conferre nollent. Dicebat etiam, Tissaphernem, nune quidem, quod
suis pecuniis bellum gereret, jure suis pecuniis parcere. si quando
stipendium a Rege mitteretur, se stipendium integrum ipsis
redditurum, et civitates, ut par esset, sublevaturum.,
YITPAOHZ H. pz. 179 νει. ὃὲ καὶ “τῷ Τισσαφέρνει, μὴ ἄγαν
ἐπείγεσθαι τὸν πόλεμον. EC μηδὲ βουληϑῆναι, «ομίσαντα 7 ναῦς
Φοινίσσας, " ὥσπερ, παρεσκευάζετο μελλήσει πλείοσι pae Soy
πορίζοντα, τοῖς αὐτοῖς τῆς τε γῆς καὶ τῆς ϑαλάσσης τὸ κράτος.
δοῦναι, ἔχειν δ. 345 M ἔρους ἐᾷν δίχα τὴν ἀρχὴν, καὶ βασιλεῖ ἐξεῖναι
ξῆὲ "τοὺς αὐτοὺς λυπηροὺς τοὺς ἑτέρους ἐπάγειν. “γέ»ορμένης δ᾽ ἂν
ἡ καϑ' ὃ ἕν τῆς ἐς γῆν καὶ ϑάλασσαν ἀρχῆς» ἀπορεῖν ἂν αὐτὸν, οἷς
τοὺς κρατοῦντας ἐξυγκαῦαἱρήσει, ἣν μὴ αὐτὸς βούληται μεγάλῃ
δαπάνῃ καὶ ἀναστάς ποτε διαγωνίσασιγαι. εὐτελέστερα δὲ τὰ δεινὰ
βεαχεῖ μορίῳ τῆς δαπάνης, "αὶ ἅμα μετὰ τῆς ἑαυτοῦ ἀσφαλείας
αὐτοὺς περὶ ebrei τοὺς Ἕλληνας ᾿κατατρίψαι. ἐπιτηδειοτέρους τε:
"ἔφη, τοὺς ᾿ΑΝηναΐους εἶναι κοινωγοὺς αὐτῷ τῆς ἀρχῆς" ἧσσον , PLE
τῶν χατὰ γῆν ἐφίεσνγαι» τὸν λόγον. T$ .* ξυμφορω“ τῷ tion abet
Dan. mox διαλόσα, Mosqu, (ec.acut)etgé Bas. — *^ gac- dr. C.
"Arzig παρισκενάξετο, μελλήσει, πλείοσι ete. id. Μελλήσει, τλ. B.
πορίζοντα τοῖς αὐτοῖς, τῆς τι εἴο. Flor. Bas. Aug. Μελλήσει, ups vag
etc. Steph. 1. Μελλήσειν, «λ. etc. Marg. Μελλήσει, ἃ De uu ua V cuu
trm ter i nau α est, pro, fs Sas. F. Port... *As TO ἬΝ ἀελλήσω
Mosqu. Y Scil. σοὺς X Tow; avri» Avr. Cass. Dan. Aug. er. Mosqu.
Auz. * E erid Marg. Cam. P Ἔφη A6... Men. adicibiades Timapheriü
praterea suadebat, ne nimium properaret bellum finire, neve vel
acci. tis Phoenicum navibus, quas niret terre marisque imperium,
ipsum Aegem destitutum iri sociis, pner cnr! Men rS me; tenta ore
tear net παρεσκευάξ, εἴ μελλήσει, εἴ «“λείοσε μισθὸν λήσῳ, itidem
cum ἢ eodem loco.A correctore à recenti adscripto, patitiiieiqe, καὶ
σοὺς ᾿Αϑηναίους. ΖΕ. Port. Υ Καϑ' ἕν desunt C. Καϑὲν Cass.
quibuseum γον, qui re. rum potirentur: nisi vellet ipsemet aliquando
copiis adductis cam ingenti et impensa et periculo inire certamen. [||
autem pericula, quze parvo sumtu subeuntur, leviora esse dicebat,
simul etiam fore, ut Hersine ullo suo periculo, Grzeos inter se
attereret. 'Adetiam, Athenienses imperii socios illi commodiores fore.
Imperium enim terrestre minus, quam Lacedcmonios, affectare, *et
belli gerendi rationem, Regi maxime convenientem, verbis factisque
se- '* Et rationem simul atque. operam bellandi utiliorem Regi
habere. Palla. factisque commodissime s Et verbis. cius, imul cum
ipso gesturos bellum. 4caNO Bell. an. 20. 92. 1. πον
180 OOYKYTAIAOT T0TOV καὶ τὸ ἔργον ἔχοντας πολεμεῖν"
τοὺς μὲν γὰρ . δυγκαταδουλοῦν ὁ ὧν σφίσι TÉ αὐτοῖς τὸ τῆς
ϑαλάσσης “μέρος, καὶ δεἐκείνῳ, ὃ ὅσοι ἐν τῇ βασιλέως Ἕλληνες οἷ|
κοῦσι" τοὺς δὲν τοὐναντίον; * Ouvrage ἥκειν. καὶ οὐκ εἰκὸς εἰναι»
Λακεδαιμονίους, ἀπὸ μὲν σφῶν σῶν “Ἑλλήνων ἐλευδεροῦν νῦν τοὺς
"EAAag6; 8 ἀπὸ 0 ἐκείνων τῶν βαρβάρων, ὃ zv μή. ποτε αὐτοὺς μὴ
ἐξέAor μὴ ἐλευδερῶσαι. τρίξειν οὖν ἐκέλευε πρῶτον ἀμΦοτέρους,
καὶ ὠποτερυόμοενον ὡς μέγιστα ὠπὸ τῶν ᾿ΑΝηναίων, ἔ ἔπειτ᾽ ἤδη
φοὺς Πελοποννησίους ὠπαλλάξαι ἐκ τῆς χώρας. καὶ διενοεῖτο τὸ
πλέον οὕτως ὁ Τισσαφέρνης» ὅσα γε ἀπὸ τῶν ποιουμένων ἣν
εἰκάσαι. τῷ γὰρ AX Gin ἰ διὰ ταῦτα, ὡς εὖ περὶ φούτων παραινοῦντι,
προσϑεὶς 1 ἑαυτὸν * ég πίστιν, TL» Té τροφὴν κακῶς ἐπόριζε, τοῖς
Lehosemirino καὶ opns οὐκ οἴου" ἀλλὰ καὶ» τὰς Φομίσσας ' γαὺς»
φάσκων, "ἢ ἥξειν, nx ἐκ dy τοῦ] περιόντος ἀγωνιεἴσιγαι», ἔφϑειρε τὰ
πράγματα" καὶ τὴν ὠκρυὴν τοῦ ναυτικοῦ αὐτῶν ἀφείἃ ᾿Εκείνων Zr.
C. Aid. Flor. Bas. Reg. Dan. | * ᾿Ελευϑερώσαντας Cass. Aug. Mosqu.
f Miv deest Reg. qox νῦν d ..Mosqu. 8 "Aq? δὲ ix. Gr. * Forsan
seribendum : ἤν sort αὐσοὺς (scil. σοὺς ᾿Αϑηναίουρ) ἐξέλωσι, 81
nihil mntetur: idem plane erit sensus ; quamvis inusitatior sit
loquendi formula, duabus particulis negativis pro una affirmativa
positis. Z&. Port. i Auzταῦτα Ald. Flor. Bas. Steph. |. Cass. ib.
᾿Αλκιβιάδι Mosqu. El Reg. Cass. Gr. Aug. Mosqu. ! ναῦς non agnoscit
Zr. Ναῦς Φοινίσσας Gr. «Ὀοινίσας Mosqu. ? Ἥχειν Marg. Dan. Ὁ Καὶ
deest Dan. * Τοῦ omittunt Cl. Gr. Cass. Cam. in Aug. add. a m. rec.
qui. Mam hos quidem ejus auxiliis mum Peloponnesios ex sud
regione munitos in suam ipsorum ditionem maris partem redacturos,
illumque adjutures in omnibus Grecis subigendis, qui Regis
provincias incolerent, lllos vero, contra, Graecos in libertatem
vindicaturos venire. Nee verisimile esse, Lacedamonios, Grzecos ab
ipsis quidem Grecis nunc liberare, ab illis vero Barbaris eosdem non
esse liberaturos, *si aliquando ipsos 4fhenienses everterint.
Suadebat igitur 2/Zj, ut utrosque prius attereret, et ubi quam
maximas 7es ab . Atheniensibus resecuisset, tunc de* Si quos antea
ab illis non liberassent. ala. T Et in caeteris apertius egit, quam. ut
occultaret, se non libenter iHis sociis gerere bellum. Falla. dimitteret.
Atque Tissaphernes hanc epinionem magna ex parte co rát,
quantum ex iis, que ab ipsó fiebant, conjicere licebat. Alecibiadi enim
ob hze, ut de his bene monenti, fidem habens, stipendium
Peloponnesiis paree dabat, neque navale prelium committere sinebát
: sed etiam dicendo, naves Phdenicum venturas, et ex abundanti
certaturas, res illorum evertit, Et ipsorum classi, qua longe
validissima fuerat, vires abstulit, δὲ cwtera faciebat apertius, quam
ut se occultare posEt alia non occulte egit, ut facile minime promto
animo rem gerere animadverteretur. aeacius,
ΞΥΤΡΡΑΦΗ͂Σ H. pP. 181 Afro, γενορυένην καὶ πάνυ ἰσχυρὰν,
τά τε ἄλλα καταy», ἢ ὥστε λανϑάνειν, OU προνύμως. Bell. Pe " an.
40. ec. Ὃ 2s ᾿Αλκιξιάδης ταῦτα ἅμα μὲν τῷ Τισ- rs σαφέξνει καὶ τῷ
βασιλεῖ, P ὧν παρ᾽ ἐκείνοις, ἄριστα εἶναι γορυίζων, παρήνει, ὥμω δὲ
τὴν ἑαυτοῦ xd syodoy ἐς τὴν “πατρίδα ἐπιϑεραπεύων, εἰδὼς, εἰ μὴ
διαφϑερεῖ αὐτὴν, ὅτι ἔσται ποτὲ αὐτῷ πείσαντι πατελϑεῖν. πεῖς σαι δ᾽
ἂν ἐνόμιζε s μάλιστα ἐκ τοῦ τοιούτου, εἰ Τίσσαφέρνης φαίνοιτο αὐτῷ
3 ἐσιτήδειος ὦν. ὅπερ καὶ ἐγέγετο. ἐπειδὴ γὰρ ἤσϑοντο αὐτὸν
ἰσχύοντα παρ αὐτῷ οἱ ἐν τῇ Σάμῳ ᾿Αϑηναίων στρατιῶται, τὰ μὲν καὶ
᾿Αλκιξιάδου "προσπέμψαντος λόγους ἐς τοὺς δυνατωτάτους αὐτῶν
ἄνδρας, d ὥστε purs * περὶ αὐτοῦ ἐς τοὺς βελτίστους τῶν gam, ὅτι
ἐπ᾿ ὁλι ίᾳ βούλεται, καὶ οὐ πονηρίαι, οὐδὲ δημοκρατίᾳ, τῇ “ξαυτὸν
ἐκξαλούσῃ, κατελ-ὼν, καὶ παρασχὼν Τισσαφέρνην φίλον αὐτοῖς,
ξυμπολιτεύειν, τὸ δὲ πλέον, καὶ ἀπὸ σφῶν αὐτῶν οἱ ἐν τῇ Σάμῳ
τριήραρχοί τε σῶν ᾿Αϑηγαίων, καὶ δυνατώτατοι, ὥρμηντο ἐς σὸ "
χκαταλ. ὕσαι τὴν δημοκρατίαν. P £i» Tz) ἐκείνοις ἄριστα due Veto»
Aid. Fir. Bas. Huds. Nempe in Bas. quod etiam in 4/d. et Flor. esse
puto, est ὧν, non Z». "Ων in Cass. recens factum erat, priore spiritu
et arcentu eraso. ὧν σιαρεκείνοις Aug. ὧν Mosqu. cui et d. τῷ ante
βασιλεῖ. 3 ᾿Επιτήδιος Mosqu. * Προσίμιψαντος Marg. Cam. * Ti pro
φερὶ Mosqu, MSS. * Καταλύσα, Mosqu. runt, partim quidem, quod et
ipse * 'Eavras ἰκξαλλούσῃ C. ἑαυτῶν εἴ ^ tum ix eam. i a poaae
Verte Peloponnesiis 41. Aleitiades 1 "teh hee Tissapherni, Regique,
dum apud illos esset, suadebat, simul quidem, quod de optima factu
duceret, simul etiam, quod suum jn patriam reditum curaret, quia
sciebat, si eam non everteret, fore aliquando, ut αὐ Atheniensibus
oratione sua adductis reditraret. Existimabat autem, se hac ratione
potissimum hoc ab illis impetraturum, si. rnem ipsi familiarem esse
constaret. Quod etiam accidit. Nam postquam milites Athenienses,
qui apud Samum erant, eum apud ipsum Tissaphernem grati&
pollere senseAlcibiades ad potentissimos illorum viros literas ante
misisset cum mandatis, ut apud optimos quosque viros mentio——
redire, ea conditione, ut respublica a paucis regeretur, non autem ab
improbissimis quibusque, nec a populari statu, a quo fuisset ejectus,
et Tissapbernis amicitia illis conciliata, una cum illis rempublicam
À
administrare: partim vero, idÀ-. magis, sua sponte trierarehi ium, qui
in Samo erant, et potentissimi quique animis erant propensis ad
evertendum statum x3 - d " Varr. 313.
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