Using Plait$($a sub extension of racket$),$ write the grammar of a language that accepts valid phone numbers with the area codes $787$ or $939.$ A valid phone number has the formar xxx$-$xxx$-$xxxx$.$ The x$$s are digits $0-9.$

Define a type $$digits$$ that can be any digit from $0-9.$ Define another type three$-$digits that is a sequence of $3$ digits and another type, four$-$digits that is a sequence of $4$ digits. Additionally define the type area code that can be $787$ or $939.$

Lastly create a function that validates if the phone number inputed is valid. Note: This should not be a program but a language. There must be parsing involved defining the types

use this BNF as reference:

::$=$

Val$()$ Val$()$ Val$()$ Val$()$

::$="787""939"$

Val$()787$ or $939$

$$::$=$

Val$()$ Val$(1)$ Val$(2)$ Val$(3)$

$$::$=$

Val$()$ Val$(1)$ Val$(2)$ Val$(3)$ Val$(4)$

$$::$="0""1""2""3""4""5""6""7""8""9"$

Val$()0$ to $9,$ corresponding to the digit value