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Real World Haskell by Donald Bruce Stewart, Bryan O'Sullivan, John Goerzen

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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, in order to see what ghci will do with them. Basic arithmetic works similarly to languages such as C and Python—we write expressions in infix form, where an operator appears between its operands:

ghci> 2 + 2
ghci> 31337 * 101
ghci> 7.0 / 2.0

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
ghci> (+) 2 2

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

ghci> 313 ^ 15

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

The - used in the preceding code 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

    precedence parsing error
        cannot mix `(+)' [infixl 6] and prefix `-' [infixl 6] in the same infix 

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

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

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 whitespace (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

And here is one that seems similar to the previous problematic negative number example, but that 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)

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
ghci> False || True

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

ghci> True && 1

    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 it.

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 shortcut that we will revisit in a few pages

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 write correct code by making us perform some amount of debugging up front, before we ever run a program. If you come from a background of working with more permissive languages, this 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
ghci> 2 < 3
ghci> 4 >= 3.99

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

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

ghci> not True

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)
ghci> 1 + 4 * 4

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 ghci’s :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.) 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 preceding ghci output. 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

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.

Don’t worry about the error message

If the 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 such as 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

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 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.

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