Transcript Introducing ASML - University of Liverpool

1
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
y
x
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 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)
II. Conditionals
and Loops
• Each of these operators compares two
values and returns one of two possible
Boolean values: true or false
eq
ne
lt
gt
lte
gte
in
notin
subset
superset
subseteq
superseteq
Meaning
=
=
<>

<
<
>
>
<=

>=







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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
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. ”)
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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
At least one condition must be true for
a true result
or
Inverts the value of a true or false
expression
implies True unless the first condition is true
and the second condition is false
not
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
p
implies
iff
q
T
T
F
T
T
T
q
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
The forall … holds
Quantifiers
• 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.