Introducing ASML

Introducing ASML Enumerations, Conditionals and Loops, Quantifiers Lecture 13 Software Engineering COMP201

y y y 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 Min2 (S as Set of Integer) as Integer require S ne {} returnany x | x in S where not (exists y in S where y>x )

I. Enumerations • Enumerations provide a way of creating symbolic constants enumident [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

Initialised enumeration • By default,enumerationsare assigned integer values starting with • 0 for the first enumerator, • 1 for the second, and so on. // Initialised enumeration enum Punctuation Comma = 5 Period = 3 Semi = 1 Main() step if Comma < Period then WriteLine(Period) else WriteLine(Comma) // Partially initialised // enumeration enum Punctuation Comma Period = 100 Semi Main() step if Semi < Period then WriteLine(Period) else WriteLine(Semi)

Meaning eq = = ne <> lt < < gt > > lte <= gte >=  in  notin  subset  superset  subseteq  superseteq  II. Conditionals and Loops • Each of these operators compares two values and returns one of two possible Boolean values: trueorfalse

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 ] The result is: 1 is odd. 3 is odd. 5 is odd. S = {1..6} Main() step forall x in S if (x mod 2 = 1) then WriteLine ( x + “ is odd. ”)

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 Remember that sets have no intrinsic order The result is: 6 is even. 1 is odd. 2 is even. 3 is odd. 5 is odd. 4 is even S = {1..6} Main() step forall x in S if (x mod 2 = 1) then WriteLine(x+“ is odd. ”) else WriteLine ( x + “ is even. ”)

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

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

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. ”)

Operators

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

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.

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.

` 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.

Introducing ASML