Software Design and Development

Metalanguage Answers

Fill in the following table to check whether each example has the correct syntax

Example	Data type	Legal or illegal	Reason
A	letter	Legal	“A” is defined as a letter
7	integer	Legal	An integer may be defined as a single digit
77	integer	Legal	An integer may be defined as a digit followed by an integer, which may be… (and so on)
77	signed integer	Illegal	A signed integer must begin with “+” or “-”
-77	integer	Illegal	An integer must begin with a digit
-77	signed integer	Legal	Starts with “-” and followed by an integer
a1	address	Illegal	“a” is not defined as a letter
AB6	address	Illegal	An address is defined as a single letter, followed by an integer
C108	address	Legal	C108 is a letter followed by a legal integer
D	address	Illegal	An address must contain an integer
D-1	address	Illegal	An address must contain an integer but not a signed integer

As the designer of this new language, you want to add the ability to represent an address with more than one letter, followed by more than one digit. Write the BNF statement that would enable this to be done.

The definitions now read
<digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
<letter> ::= A | B | C | D | E | F
<integer> ::= <digit> | <digit> <integer>
<signed_integer> ::= + <integer> | -<integer>
<word> ::= <letter> | <letter> <word>
<address> ::= <word> <integer>
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Fill in the following table to check whether each example has the correct syntax

Example	Data type	Legal or illegal	Reason
a	letter	Legal	“a” is defined as a letter
t	letter	Illegal	“t” is NOT defined as a letter
b222	identifier	Legal	Matches the syntax of an identifier
-22	number	Legal	Matches the syntax of a number
-12.33	number	Legal	Matches the syntax of a number
21.		Illegal	A number must have a at least one digit after a “.”
a:="a2+3	expression	Legal	Matches the syntax of an expression
b1:="22+12-3	expression	Legal	Matches the syntax of an expression
b2:="14+2		Illegal	4 is not a digit, if 4 was defined as a digit this would be an legal expression

Outline whether the above ENBF is equivalent to the syntax defined in the EBNF example 2 above
No. In the example the sign (+ or -) is optional, it may or may not be present. In exercise 4, the sign must be there. To make the two versions do the same thing, you would need to add an optional brackets [ ]

digit = “0” | “1” | “2’ | “3” | “4” | “5” | “6” | “7“ | “8” | “9”
sign = “+”|”-“
integer = [sign] digit {digit}
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Construct EBNF to define an integer in base 2, allowing for a possible sign (+ or -). For example, 1 and 0 are digits, 10, 001, 101, +10, -1111 are all binary integers
digit = ‘0“ | “1“
sign = “+”/”-“
integer = [sign] digit {digit}

Note: there would be other correct ways to answer this question.
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Fill in the following table to check whether each selection example has the correct syntax

selection	Legal or Illegal	Reason
IF(p13>177, CALLA, CALLB)	Legal	No problem. 177 is a legal integer
IF(a0="p3," CALLA , CALLB)	Illegal	“="”" is not defined as a logical operator
If(p13<p12, CALLA CALLB)	Illegal	Statement must begin with “IF” and "," is missing between CALLA and CALLB

Convert the follow EBNF syntax to a syntax diagram:

digit = “1” |” 2” |” 3”
letter = “a” |” b” |”c”
operator = “+” |” –“
identifier = letter {letter | digit}
number = [“-“] digit {digit} [“.”digit { digit } ]
expression ="identifier" “:="”" (identifier | number) {operator (identifier| number)}