FunctionalLoops
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To express choosing between two alternatives, Scala
has a conditional expression if-else.
To express choosing between two alternatives, Scala
has a conditional expression if-else.
It looks like a if-else in Java, but is used for expressions, not statements.
Example:
def abs(x: Int) = if (x >= 0) x else -x
x >= 0 is a predicate, of type Boolean.
Boolean expressions b can be composed of
true false // Constants !b // Negation b && b // Conjunction b || b // Disjunction
and of the usual comparison operations:
e <= e, e >= e, e < e, e > e, e == e, e != e
Here are reduction rules for Boolean expressions (e is an arbitrary expression):
!true --> false !false --> true true && e --> e false && e --> false true || e --> true false || e --> e
Note that && and || do not always need their right operand to be evaluated.
We say, these expressions use “short-circuit evaluation”.
We will define in this section a method
/** Calculates the square root of parameter x */ def sqrt(x: Double): Double = ...
The classical way to achieve this is by successive approximations using Newton's method.
To compute sqrt(x):
y (let's pick y = 1).y and x/y.Example:
Estimation Quotient Mean 1 2 / 1 = 2 1.5 1.5 2 / 1.5 = 1.333 1.4167 1.4167 2 / 1.4167 = 1.4118 1.4142 1.4142 ... ...
First, we define a method which computes one iteration step:
def sqrtIter(guess: Double, x: Double): Double = if (isGoodEnough(guess, x)) guess else sqrtIter(improve(guess, x), x)
Note that sqrtIter is recursive, its right-hand side calls itself.
Recursive methods need an explicit return type in Scala.
For non-recursive methods, the return type is optional.
Second, we define a method improve to improve an estimate and a test to check for termination:
def improve(guess: Double, x: Double) = (guess + x / guess) / 2 def isGoodEnough(guess: Double, x: Double) = abs(guess * guess - x) < 0.001
Third, we define the sqrt function:
def sqrt(x: Double) = sqrtIter(1.0, x)
You have seen simple elements of functional programing in Scala.
You have learned the difference between the call-by-name and call-by-value evaluation strategies.
You have learned a way to reason about program execution: reduce expressions using the substitution model.
Complete the following method definition that computes the factorial of a number:
The parameterless execute method has been deprecated and will be removed in a future version of ScalaTest. Please invoke execute with empty parens instead: execute().
The trap method is no longer needed for demos in the REPL, which now abreviates stack traces, and will be removed in a future version of ScalaTest