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Introducing ASML

Enumerations,

Conditionals and Loops, Quantifiers

Lecture 13

Software Engineering COMP201

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Logical Operators, Quantifiers and Sets

Min1 (s as Set of Integer) as Integer

require s ne {}

return any x | x in s where forall y in s holds x lte y

Set s

x

y

y

y

Min2 (S as Set of Integer) as Integer

require S ne {} return any x | x in S where not (exists y in S where y>x )

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I. Enumerations

• Enumerations provide a way of creating symbolic constants

enum ident [enumElement-List]enum Color Red Green Blue

• This statement does two things– It declares an enumeration type called

Color– It establishes Red, Green and Blue as

symbolic constants called enumerators

• Let’s create a variable of that type:var range as Color

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Initialised enumeration

• By default, enumerations are assigned integer values starting with – 0 for the first enumerator,

– 1 for the second, and so on.

// Initialised enumerationenum Punctuation Comma = 5 Period = 3 Semi = 1Main() step if Comma < Period then WriteLine(Period) else WriteLine(Comma)

// Partially initialised // enumerationenum Punctuation Comma Period = 100 Semi Main() step if Semi < Period then WriteLine(Period) else WriteLine(Semi)

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II. Conditionals and Loops

• Each of these operators compares two values and returns one of two possible Boolean values: true or false

Meaningeq = =ne <>

lt < <gt > >lte <=

gte >=

in notin subset

superset subseteq superseteq

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The If Statement

• There are a variety of ways to use the results of comparison to modify the behaviour of a program

• The most basic of these is:

if expr [then] stmt-List

{ elseif expr [then] stmt-List }

[ else expr [then] stmt-List ]

S = {1..6}Main() step forall x in S if (x mod 2 = 1) then WriteLine ( x + “ is odd.

”)

The result is:1 is odd.3 is odd.5 is odd.

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If-then-else

• Be extending the if statement to an if-else statement, we can perform one action if the condition is true and another if it false

S = {1..6}Main() step forall x in S if (x mod 2 = 1) then WriteLine(x+“ is odd. ”) else WriteLine ( x + “ is even. ”)

The result is: 6 is even.1 is odd.

2 is even.3 is odd.5 is odd.4 is even

Remember that sets have no intrinsic

order

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If-then-elseif

• You can nest if-else statement to handle multiple possible conditions:

S = { “ham”, “turkey”, “bit”, “cheese”}Main() step x = any y | y in S if x = “ham” then WriteLine (“Ham sandwich”) elseif x = “turkey” then WriteLine (“Turkey sanwich”) elseif WriteLine (“Cheese sanwich”)

This program randomly selects one of the elements in set S, thus determining the

program’s output

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Logical Operators

• Using if statement with complex conditions can be rather clumsy

• To simplify the situation, use logical operations that allow you to combine a series of comparisons

Symbol Meaning

and Both conditions must be true for a true result

or At least one condition must be true for a true result

not Inverts the value of a true or false expression

implies True unless the first condition is true and the second condition is false

iff True when both conditions have the same value

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The and Operator

• Use the and operator when you have two conditions that must be true for a true result:

S = { 1 .. 12 }Main() x = any y | y in S step if (x<=6) and (x mod 2 = 1) then WriteLine (x + “is an odd number

between 1 and 6. ”)

step if (x>6) or (x mod 2 = 1) then WriteLine (x + “is greater than six or an

odd number. ”)

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Operators

p q not p p or q p and q p implies q

p

iff

q

T T F T T T T

T F F T F F F

F T T T F T F

F F T F F T T

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Quantifiers

• Quantifiers are used in quantifying expressions

• These expressions return true or false depending on whether a condition has been met – universally over some collection of

bindings ( forall … holds ) or– existentially by at least one example

( exists )

• They are called quantifiers because they specify how much of the collection (a set, sequence, or map) is included or executed by the condition

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The forall … holdsQuantifiers

• The forall expression holds quantifier requires that all members of the collection meet the specified condition

S = { 1, 2, 4, 6, 7, 8 }IsOdd( i as Integer) return (1 = i mod 2)Main() step

test1 = forall i in S holds IsOdd(i) if test1 then WriteLine ( “All odd numbers. ”) else WriteLine ( “Not all odd numbers. ”)

This prints the result:Not all odd numbers.

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The exist Quantifier

• The exist quantifier requires that at least one member of the collection meet the specified condition

S = { 1, 2, 4, 6, 7, 8, 9}IsOdd( i as Integer) return (1 = i mod 2)Main() step

test1 = exists i in S where IsOdd(i) if test1 then WriteLine ( “Some odd numbers. ”) else WriteLine ( “No odd numbers. ”)

This prints the result:Some odd numbers.

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`

S = { 2, 4, 6, 7, 9}IsOdd( i as Integer) return (1 = i mod 2)Main() step

test1 = exists unique i in S where IsOdd(i) if test1 then WriteLine ( “Some odd numbers. ”) else WriteLine ( “None or more than 1 odd

numbers. ”)

This prints the result:None or more than 1 odd numbers.