Providence Salumu Chapter 1. Getting Started

Chapter 1. Getting Started

Table of Contents

Your Haskell environment
Getting started with ghci, the interpreter
Basic interaction: using ghci as a calculator
Simple arithmetic
An arithmetic quirk: writing negative numbers
Boolean logic, operators, and value comparisons
Operator precedence and associativity
Undefined values, and introducing variables
Dealing with precedence and associativity rules
Command line editing in ghci
Lists
Operators on lists
Strings and characters
First steps with types
A simple program
Exercises

As you read the early chapters of this book, keep in mind that we will sometimes introduce ideas in restricted, simplified form. Haskell is a deep language, and presenting every aspect of a given subject all at once is likely to prove overwhelming. As we build a solid foundation in Haskell, we will expand upon these initial explanations.

Your Haskell environment

Haskell is a language with many implementations, of which two are in wide use. Hugs is an interpreter that is primarily used for teaching. For real applications, the Glasgow Haskell Compiler (GHC) is much more popular. Compared to Hugs, GHC is more suited to “real work”: it compiles to native code, supports parallel execution, and provides useful performance analysis and debugging tools. For these reasons, GHC is the Haskell implementation that we will be using throughout this book.

GHC has three main components.

  • ghc is an optimizing compiler that generates fast native code.

  • ghci is an interactive interpreter and debugger.

  • runghc is a program for running Haskell programs as scripts, without needing to compile them first.

[Note]How we refer to the components of GHC

When we discuss the GHC system as a whole, we will refer to it as GHC. If we are talking about a specific command, we will mention ghc, ghci, or runghc by name.

In this book, we assume that you're using at least version 6.8.2 of GHC, which was released in 2007. Many of our examples will work unmodified with older versions. However, we recommend using the newest version available for your platform. If you're using Windows or Mac OS X, you can get started easily and quickly using a prebuilt installer. To obtain a copy of GHC for these platforms, visit the GHC download page, and look for the list of binary packages and installers.

Many Linux distributors, and providers of BSD and other Unix variants, make custom binary packages of GHC available. Because these are built specifically for each environment, they are much easier to install and use than the generic binary packages that are available from the GHC download page. You can find a list of distributions that custom-build GHC at the GHC distribution packages page.

For more detailed information about how to install GHC on a variety of popular platforms, we've provided some instructions in Appendix A, Installing GHC and Haskell libraries.

Getting started with ghci, the interpreter

The interactive interpreter for GHC is a program named ghci. It lets us enter and evaluate Haskell expressions, explore modules, and debug our code. If you are familiar with Python or Ruby, ghci is somewhat similar to python and irb, the interactive Python and Ruby interpreters.

[Note]The ghci command has a narrow focus

We typically cannot copy some code out of a Haskell source file and paste it into ghci. This does not have a significant effect on debugging pieces of code, but it can initially be surprising if you are used to, say, the interactive Python interpreter.

On Unix-like systems, we run ghci as a command in a shell window. On Windows, it's available via the Start Menu. For example, if you installed using the GHC installer on Windows XP, you should go to “All Programs”, then “GHC”; you will then see ghci in the list. (See the section called “Windows” for a screenshot.)

When we run ghci, it displays a startup banner, followed by a Prelude> prompt. Here, we're showing version 6.8.3 on a Linux box.

$ ghci
GHCi, version 6.8.3: http://www.haskell.org/ghc/  :? for help
Loading package base ... linking ... done.
Prelude>

The word Prelude in the prompt indicates that Prelude, a standard library of useful functions, is loaded and ready to use. When we load other modules or source files, they will show up in the prompt, too.

[Tip]Getting help

If you enter :? at the ghci prompt, it will print a long help message.

The Prelude module is sometimes referred to as “the standard prelude”, because its contents are defined by the Haskell 98 standard. Usually, it's simply shortened to “the prelude”.

[Note]About the ghci prompt

The prompt displayed by ghci changes frequently depending on what modules we have loaded. It can often grow long enough to leave little visual room on a single line for our input.

For brevity and consistency, we have replaced ghci's default prompts throughout this book with the prompt string ghci>.

If you want to do this youself, use ghci's :set prompt directive, as follows.

Prelude> :set prompt "ghci> "
ghci>

The prelude is always implicitly available; we don't need to take any actions to use the types, values, or functions it defines. To use definitions from other modules, we must load them into ghci, using the :module command.

ghci> :module + Data.Ratio

We can now use the functionality of the Data.Ratio module, which lets us work with rational numbers (fractions).

Basic interaction: using ghci as a calculator

In addition to providing a convenient interface for testing code fragments, ghci can function as a readily accessible desktop calculator. We can easily express any calculator operation in ghci and, as an added bonus, we can add more complex operations as we become more familiar with Haskell. Even using the interpreter in this simple way can help us to become more comfortable with how Haskell works.

Simple arithmetic

We can immediately start entering expressions, to see what ghci will do with them. Basic arithmetic works similarly to languages like C and Python: we write expressions in infix form, where an operator appears between its operands.

ghci> 2 + 2
4
ghci> 31337 * 101
3165037
ghci> 7.0 / 2.0
3.5

The infix style of writing an expression is just a convenience: we can also write an expression in prefix form, where the operator precedes its arguments. To do this, we must enclose the operator in parentheses.

ghci> 2 + 2
4
ghci> (+) 2 2
4

As the expressions above imply, Haskell has a notion of integers and floating point numbers. Integers can be arbitrarily large. Here, (^) provides integer exponentiation.

ghci> 313 ^ 15
27112218957718876716220410905036741257

An arithmetic quirk: writing negative numbers

Haskell presents us with one peculiarity in how we must write numbers: it's often necessary to enclose a negative number in parentheses. This affects us as soon as we move beyond the simplest expressions.

We'll start by writing a negative number.

ghci> -3
-3

The - above is a unary operator. In other words, we didn't write the single number “-3”; we wrote the number “3”, and applied the operator - to it. The - operator is Haskell's only unary operator, and we cannot mix it with infix operators.

ghci> 2 + -3

<interactive>:1:0:
    precedence parsing error
        cannot mix `(+)' [infixl 6] and prefix `-' [infixl 6] in the same infix expression

If we want to use the unary minus near an infix operator, we must wrap the expression it applies to in parentheses.

ghci> 2 + (-3)
-1
ghci> 3 + (-(13 * 37))
-478

This avoids a parsing ambiguity. When we apply a function in Haskell, we write the name of the function, followed by its argument, for example f 3. If we did not need to wrap a negative number in parentheses, we would have two profoundly different ways to read f-3: it could be either “apply the function f to the number -3”, or “subtract the number 3 from the variable f”.

Most of the time, we can omit white space (“blank” characters such as space and tab) from expressions, and Haskell will parse them as we intended. But not always. Here is an expression that works:

ghci> 2*3
6

And here is one that seems similar to the problematic negative number example above, but results in a different error message.

ghci> 2*-3

<interactive>:1:1: Not in scope: `*-'

Here, the Haskell implementation is reading *- as a single operator. Haskell lets us define new operators (a subject that we will return to later), but we haven't defined *-. Once again, a few parentheses get us and ghci looking at the expression in the same way.

ghci> 2*(-3)
-6

Compared to other languages, this unusual treatment of negative numbers might seem annoying, but it represents a reasoned trade-off. Haskell lets us define new operators at any time. This is not some kind of esoteric language feature; we will see quite a few user-defined operators in the chapters ahead. The language designers chose to accept a slightly cumbersome syntax for negative numbers in exchange for this expressive power.

Boolean logic, operators, and value comparisons

The values of Boolean logic in Haskell are True and False. The capitalization of these names is important. The language uses C-influenced operators for working with Boolean values: (&&) is logical “and”, and (||) is logical “or”.

ghci> True && False
False
ghci> False || True
True

While some programming languages treat the number zero as synonymous with False, Haskell does not, nor does it consider a non-zero value to be True.

ghci> True && 1

<interactive>:1:8:
    No instance for (Num Bool)
      arising from the literal `1' at <interactive>:1:8
    Possible fix: add an instance declaration for (Num Bool)
    In the second argument of `(&&)', namely `1'
    In the expression: True && 1
    In the definition of `it': it = True && 1

Once again, we are faced with a substantial-looking error message. In brief, it tells us that the Boolean type, Bool, is not a member of the family of numeric types, Num. The error message is rather long because ghci is pointing out the location of the problem, and hinting at a possible change we could make that might fix the problem.

Here is a more detailed breakdown of the error message.

  • No instance for (Num Bool)” tells us that ghci is trying to treat the numeric value 1 as having a Bool type, but it cannot.

  • arising from the literal `1'” indicates that it was our use of the number 1 that caused the problem.

  • In the definition of `it'” refers to a ghci short cut that we will revisit in a few pages.

[Tip]Remain fearless in the face of error messages

We have an important point to make here, which we will repeat throughout the early sections of this book. If you run into problems or error messages that you do not yet understand, don't panic. Early on, all you have to do is figure out enough to make progress on a problem. As you acquire experience, you will find it easier to understand parts of error messages that initially seem obscure.

The numerous error messages have a purpose: they actually help us in writing correct code, by making us perform some amount of debugging “up front”, before we ever run a program. If you are coming from a background of working with more permissive languages, this way of working may come as something of a shock. Bear with us.

Most of Haskell's comparison operators are similar to those used in C and the many languages it has influenced.

ghci> 1 == 1
True
ghci> 2 < 3
True
ghci> 4 >= 3.99
True

One operator that differs from its C counterpart is “is not equal to”. In C, this is written as !=. In Haskell, we write (/=), which resembles the ≠ notation used in mathematics.

ghci> 2 /= 3
True

Also, where C-like languages often use ! for logical negation, Haskell uses the not function.

ghci> not True
False

Operator precedence and associativity

Like written algebra and other programming languages that use infix operators, Haskell has a notion of operator precedence. We can use parentheses to explicitly group parts of an expression, and precedence allows us to omit a few parentheses. For example, the multiplication operator has a higher precedence than the addition operator, so Haskell treats the following two expressions as equivalent.

ghci> 1 + (4 * 4)
17
ghci> 1 + 4 * 4
17

Haskell assigns numeric precedence values to operators, with 1 being the lowest precedence and 9 the highest. A higher-precedence operator is applied before a lower-precedence operator. We can use ghci to inspect the precedence levels of individual operators, using its :info command.

ghci> :info (+)
class (Eq a, Show a) => Num a where
  (+) :: a -> a -> a
  ...
  	-- Defined in GHC.Num
infixl 6 +
ghci> :info (*)
class (Eq a, Show a) => Num a where
  ...
  (*) :: a -> a -> a
  ...
  	-- Defined in GHC.Num
infixl 7 *

The information we seek is in the line “infixl 6 +”, which indicates that the (+) operator has a precedence of 6. (We will explain the other output in a later chapter.) The “infixl 7 *” tells us that the (*) operator has a precedence of 7. Since (*) has a higher precedence than (+), we can now see why 1 + 4 * 4 is evaluated as 1 + (4 * 4), and not (1 + 4) * 4.

Haskell also defines associativity of operators. This determines whether an expression containing multiple uses of an operator is evaluated from left to right, or right to left. The (+) and (*) operators are left associative, which is represented as infixl in the ghci output above. A right associative operator is displayed with infixr.

ghci> :info (^)
(^) :: (Num a, Integral b) => a -> b -> a 	-- Defined in GHC.Real
infixr 8 ^

The combination of precedence and associativity rules are usually referred to as fixity rules.

Undefined values, and introducing variables

Haskell's prelude, the standard library we mentioned earlier, defines at least one well-known mathematical constant for us.

ghci> pi
3.141592653589793

But its coverage of mathematical constants is not comprehensive, as we can quickly see. Let us look for Euler's number, e.

ghci> e

<interactive>:1:0: Not in scope: `e'

Oh well. We have to define it ourselves.

[Note]Don't worry about the error message

If the above “not in scope” error message seems a little daunting, do not worry. All it means is that there is no variable defined with the name e.

Using ghci's let construct, we can make a temporary definition of e ourselves.

ghci> let e = exp 1

This is an application of the exponential function, exp, and our first example of applying a function in Haskell. While languages like Python require parentheses around the arguments to a function, Haskell does not.

With e defined, we can now use it in arithmetic expressions. The (^) exponentiation operator that we introduced earlier can only raise a number to an integer power. To use a floating point number as the exponent, we use the (**) exponentiation operator.

ghci> (e ** pi) - pi
19.99909997918947
[Warning]This syntax is ghci-specific

The syntax for let that ghci accepts is not the same as we would use at the “top level” of a normal Haskell program. We will see the normal syntax in the section called “Introducing local variables”.

Dealing with precedence and associativity rules

It is sometimes better to leave at least some parentheses in place, even when Haskell allows us to omit them. Their presence can help future readers (including ourselves) to understand what we intended.

Even more importantly, complex expressions that rely completely on operator precedence are notorious sources of bugs. A compiler and a human can easily end up with different notions of what even a short, parenthesis-free expression is supposed to do.

There is no need to remember all of the precedence and associativity rules numbers: it is simpler to add parentheses if you are unsure.

Command line editing in ghci

On most systems, ghci has some amount of command line editing ability. In case you are not familiar with command line editing, it's a huge time saver. The basics are common to both Unix-like and Windows systems. Pressing the up arrow key on your keyboard recalls the last line of input you entered; pressing up repeatedly cycles through earlier lines of input. You can use the left and right arrow keys to move around inside a line of input. On Unix (but not Windows, unfortunately), the tab key completes partially entered identifiers.

[Tip]Where to look for more information

We've barely scratched the surface of command line editing here. Since you can work more effectively if you're more familiar with the capabilities of your command line editing system, you might find it useful to do some further reading.

On Unix-like systems, ghci uses the GNU readline library, which is powerful and customisable. On Windows, ghci's command line editing capabilities are provided by the doskey command.

Lists

A list is surrounded by square brackets; the elements are separated by commas.

ghci> [1, 2, 3]
[1,2,3]
[Note]Commas are separators, not terminators

Some languages permit the last element in a list to be followed by an optional trailing comma before a closing bracket, but Haskell doesn't allow this. If you leave in a trailing comma (e.g. [1,2,]), you'll get a parse error.

A list can be of any length. The empty list is written [].

ghci> []
[]
ghci> ["foo", "bar", "baz", "quux", "fnord", "xyzzy"]
["foo","bar","baz","quux","fnord","xyzzy"]

All elements of a list must be of the same type. Here, we violate this rule: our list starts with two Bool values, but ends with a string.

ghci> [True, False, "testing"]

<interactive>:1:14:
    Couldn't match expected type `Bool' against inferred type `[Char]'
      Expected type: Bool
      Inferred type: [Char]
    In the expression: "testing"
    In the expression: [True, False, "testing"]

Once again, ghci's error message is verbose, but it's simply telling us that there is no way to turn the string into a Boolean value, so the list expression isn't properly typed.

If we write a series of elements using enumeration notation, Haskell will fill in the contents of the list for us.

ghci> [1..10]
[1,2,3,4,5,6,7,8,9,10]

Here, the .. characters denote an enumeration. We can only use this notation for types whose elements we can enumerate. It makes no sense for text strings, for instance: there is not any sensible, general way to enumerate ["foo".."quux"].

By the way, notice that the above use of range notation gives us a closed interval; the list contains both endpoints.

When we write an enumeration, we can optionally specify the size of the step to use by providing the first two elements, followed by the value at which to stop generating the enumeration.

ghci> [1.0,1.25..2.0]
[1.0,1.25,1.5,1.75,2.0]
ghci> [1,4..15]
[1,4,7,10,13]
ghci> [10,9..1]
[10,9,8,7,6,5,4,3,2,1]

In the latter case above, the list is quite sensibly missing the end point of the enumeration, because it isn't an element of the series we defined.

We can omit the end point of an enumeration. If a type doesn't have a natural “upper bound”, this will produce values indefinitely. For example, if you type [1..] at the ghci prompt, you'll have to interrupt or kill ghci to stop it from printing an infinite succession of ever-larger numbers. If you are tempted to do this, type C to halt the enumeration. We will find later on that infinite lists are often useful in Haskell.

[Warning]Beware enumerating floating point numbers

Here's a non-intuitive bit of behaviour.

ghci> [1.0..1.8]
[1.0,2.0]

Behind the scenes, to avoid floating point roundoff problems, the Haskell implementation enumerates from 1.0 to 1.8+0.5.

Using enumeration notation over floating point numbers can pack more than a few surprises, so if you use it at all, be careful. Floating point behavior is quirky in all programming languages; there is nothing unique to Haskell here.

Operators on lists

There are two ubiquitous operators for working with lists. We concatenate two lists using the (++) operator.

ghci> [3,1,3] ++ [3,7]
[3,1,3,3,7]
ghci> [] ++ [False,True] ++ [True]
[False,True,True]

More basic is the (:) operator, which adds an element to the front of a list. This is pronounced “cons” (short for “construct”).

ghci> 1 : [2,3]
[1,2,3]
ghci> 1 : []
[1]

You might be tempted to try writing [1,2]:3 to add an element to the end of a list, but ghci will reject this with an error message, because the first argument of (:) must be an element, and the second must be a list.

Strings and characters

If you know a language like Perl or C, you'll find Haskell's notations for strings familiar.

A text string is surrounded by double quotes.

ghci> "This is a string."
"This is a string."

As in many languages, we can represent hard-to-see characters by “escaping” them. Haskell's escape characters and escaping rules follow the widely used conventions established by the C language. For example, '\n' denotes a newline character, and '\t' is a tab character. For complete details, see Appendix B, Characters, strings, and escaping rules.

ghci> putStrLn "Here's a newline -->\n<-- See?"
Here's a newline -->
<-- See?

The putStrLn function prints a string.

Haskell makes a distinction between single characters and text strings. A single character is enclosed in single quotes.

ghci> 'a'
'a'

In fact, a text string is simply a list of individual characters. Here's a painful way to write a short string, which ghci gives back to us in a more familiar form.

ghci> let a = ['l', 'o', 't', 's', ' ', 'o', 'f', ' ', 'w', 'o', 'r', 'k']
ghci> a
"lots of work"
ghci> a == "lots of work"
True

The empty string is written "", and is a synonym for [].

ghci> "" == []
True

Since a string is a list of characters, we can use the regular list operators to construct new strings.

ghci> 'a':"bc"
"abc"
ghci> "foo" ++ "bar"
"foobar"

First steps with types

While we've talked a little about types already, our interactions with ghci have so far been free of much type-related thinking. We haven't told ghci what types we've been using, and it's mostly been willing to accept our input.

Haskell requires type names to start with an uppercase letter, and variable names must start with a lowercase letter. Bear this in mind as you read on; it makes it much easier to follow the names.

The first thing we can do to start exploring the world of types is to get ghci to tell us more about what it's doing. ghci has a command, :set, that lets us change a few of its default behaviours. We can tell it to print more type information as follows.

ghci> :set +t
ghci> 'c'
'c'
it :: Char
ghci> "foo"
"foo"
it :: [Char]

What the +t does is tell ghci to print the type of an expression after the expression. That cryptic it in the output can be very useful: it's actually the name of a special variable, in which ghci stores the result of the last expression we evaluated. (This isn't a Haskell language feature; it's specific to ghci alone.) Let's break down the meaning of the last line of ghci output.

  • It's telling us about the special variable it.

  • We can read text of the form x :: y as meaning “the expression x has the type y”.

  • Here, the expression “it” has the type [Char]. (The name String is often used instead of [Char]. It is simply a synonym for [Char].)

[Tip]The joy of “it

That it variable is a handy ghci shortcut. It lets us use the result of the expression we just evaluated in a new expression.

ghci> "foo"
"foo"
it :: [Char]
ghci> it ++ "bar"
"foobar"
it :: [Char]

When evaluating an expression, ghci won't change the value of it if the evaluation fails. This lets you write potentially bogus expressions with something of a safety net.

ghci> it
"foobar"
it :: [Char]
ghci> it ++ 3

<interactive>:1:6:
    No instance for (Num [Char])
      arising from the literal `3' at <interactive>:1:6
    Possible fix: add an instance declaration for (Num [Char])
    In the second argument of `(++)', namely `3'
    In the expression: it ++ 3
    In the definition of `it': it = it ++ 3
ghci> it
"foobar"
it :: [Char]
ghci> it ++ "baz"
"foobarbaz"
it :: [Char]

When we couple it with liberal use of the arrow keys to recall and edit the last expression we typed, we gain a decent way to experiment interactively: the cost of mistakes is very low. Take advantage of the opportunity to make cheap, plentiful mistakes when you're exploring the language!

Here are a few more of Haskell's names for types, from expressions of the sort we've already seen.

ghci> 7 ^ 80
40536215597144386832065866109016673800875222251012083746192454448001
it :: Integer

Haskell's integer type is named Integer. The size of an Integer value is bounded only by your system's memory capacity.

Rational numbers don't look quite the same as integers. To construct a rational number, we use the (%) operator. The numerator is on the left, the denominator on the right.

ghci> :m +Data.Ratio
ghci> 11 % 29
11%29
it :: Ratio Integer

For convenience, ghci lets us abbreviate many commands, so we can write :m instead of :module to load a module.

Notice two words on the right hand side of the :: above. We can read this as a “Ratio of Integer”. We might guess that a Ratio must have values of type Integer as both numerator and denominator. Sure enough, if we try to construct a Ratio where the numerator and denominator are of different types, or of the same non-integral type, ghci complains.

ghci> 3.14 % 8

<interactive>:1:0:
    Ambiguous type variable `t' in the constraints:
      `Integral t' arising from a use of `%' at <interactive>:1:0-7
      `Fractional t'
        arising from the literal `3.14' at <interactive>:1:0-3
    Probable fix: add a type signature that fixes these type variable(s)
ghci> 1.2 % 3.4

<interactive>:1:0:
    Ambiguous type variable `t' in the constraints:
      `Integral t' arising from a use of `%' at <interactive>:1:0-8
      `Fractional t'
        arising from the literal `3.4' at <interactive>:1:6-8
    Probable fix: add a type signature that fixes these type variable(s)

Although it is initially useful to have :set +t giving us type information for every expression we enter, this is a facility we will quickly outgrow. After a while, we will often know what type we expect an expression to have. We can turn off the extra type information at any time, using the :unset command.

ghci> :unset +t
ghci> 2
2

Even with this facility turned off, we can still get that type information easily when we need it, using another ghci command.

ghci> :type 'a'
'a' :: Char
ghci> "foo"
"foo"
ghci> :type it
it :: [Char]

The :type command will print type information for any expression we give it (including it, as we see above). It won't actually evaluate the expression; it only checks its type and prints that.

Why are the types reported for these two expressions different?

ghci> 3 + 2
5
ghci> :type it
it :: Integer
ghci> :type 3 + 2
3 + 2 :: (Num t) => t

Haskell has several numeric types. For example, a literal number such as 1 could, depending on the context in which it appears, be an integer or a floating point value. When we force ghci to evaluate the expression 3 + 2, it has to choose a type so that it can print the value, and it defaults to Integer. In the second case, we ask ghci to print the type of the expression without actually evaluating it, so it does not have to be so specific. It answers, in effect, “its type is numeric”. We will see more of this style of type annotation in Chapter 6, Using Typeclasses.

A simple program

Let's take a small leap ahead, and write a small program that counts the number of lines in its input. Don't expect to understand this yet; it's just fun to get our hands dirty. In a text editor, enter the following code into a file, and save it as WC.hs.

-- file: ch01/WC.hs
-- lines beginning with "--" are comments.

main = interact wordCount
    where wordCount input = show (length (lines input)) ++ "\n"

Find or create a text file; let's call it quux.txt[1].

$ cat quux.txt
Teignmouth, England
Paris, France
Ulm, Germany
Auxerre, France
Brunswick, Germany
Beaumont-en-Auge, France
Ryazan, Russia

From a shell or command prompt, run the following command.

$ runghc WC < quux.txt
7

We have successfully written a simple program that interacts with the real world! In the chapters that follow, we will successively fill the gaps in our understanding until we can write programs of our own.

Exercises

1.

Enter the following expressions into ghci. What are their types?

  • 5 + 8

  • 3 * 5 + 8

  • 2 + 4

  • (+) 2 4

  • sqrt 16

  • succ 6

  • succ 7

  • pred 9

  • pred 8

  • sin (pi / 2)

  • truncate pi

  • round 3.5

  • round 3.4

  • floor 3.7

  • ceiling 3.3

2.

From ghci, type :? to print some help. Define a variable, such as let x = 1, then type :show bindings. What do you see?

3.

The words function counts the number of words in a string. Modify the WC.hs example to count the number of words in a file.

4.

Modify the WC.hs example again, to print the number of characters in a file.



[1] Incidentally, what do these cities have in common?

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Copyright 2007, 2008 Bryan O'Sullivan, Don Stewart, and John Goerzen. This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 License. Icons by Paul Davey aka Mattahan.

Providence Salumu