SCALA

Continued Fraction Grammar. We will define continued fractions inductively by the grammar:

OneByNumber()

| NumPlusContFrac(, )

Here represents the Scala integer number type (positive/negative whole numbers).

Example 1:

The number g1 = 1/5 will be represented in our grammar by OneByNumber(5).

Example 2:

The number

g2= 12 + 13 + 14

will be represented in our grammar by

NumPlusContFrac(2,NumPlusContFrac(3,OneByNumber(4)))

(10 points) Write down an inductive definition of the grammar above in Scala. Use the same names for terminals/nonterminals as in the grammar. Map the nonterminal to the built-in type in Scala.

Your program should pass the following tests:

val g1 = NumPlusContFrac(2,NumPlusContFrac(3,NumPlusContFrac(4,OneByNumber(5))))

val g2 = OneByNumber(2)

val g3 = NumPlusContFrac(3, NumPlusContFrac(-1, OneByNumber(4)))

val g4 = NumPlusContFrac(1, OneByNumber(-2))