(I need help with problem 2. It's in Scalar/Scala, and I can't pass all the test cases. It would be greatly appreciated if you could show me how to do this problem and explain it.)

[ ]:

sealed trait Expr

type Tag = String 

type Identifier = String 

case class Const(d: Double) extends Expr

case class Ident(id:Identifier, tag: Tag) extends Expr

case class Plus(e1: Expr, e2: Expr) extends Expr

case class Mult(e1: Expr, e2: Expr) extends Expr 

case class Let(id: Identifier, tag: Tag, e1: Expr, e2: Expr) extends Expr

// Some helpful functions to write test cases -- you can ignore these.

def x(tag:String):Expr = Ident("x", tag)

def y(tag:String):Expr = Ident("y", tag)

def z(tag:String):Expr = Ident("z", tag)

def w(tag:String):Expr = Ident("w", tag)

[Fill in the ??? ]:

def getAllUseDefLinks(e: Expr, env: Map[Identifier, Tag]): Map[Tag, Tag] = 

 e match {

 case Const(_) => { Map.empty }

 case Ident(id, usetag) => {

 // YOUR CODE HERE

 ???

 }

 case Plus(e1, e2) => {

 // YOUR CODE HERE

 ???

 }

 case Mult(e1, e2) => {

 // YOUR CODE HERE

 ???

 }

 case Let(x, tag, e1, e2) => {

 // YOUR CODE HERE

 ???

 }

}

[ test cases ]:

/*

 let y@tag2 = x @use0 in 

 let x @tag1 = 10 in 

 x@use1 + x@use2

*/

val e = Let("y", "tag2", x("use0"), Let ("x", "tag1", Const(10), Plus(x("use1"), x("use2"))))

val map = getAllUseDefLinks(e, Map.empty)

assert (map("use0") == "UNDEFINED", s"Test1 failed: use0 must be associated with UNDEFINED. Your code returns ${map("use0")}")

assert (map("use1") == "tag1", s"Test1 failed: use0 must be associated with UNDEFINED. Your code returns ${map("use1")}")

assert (map("use2") == "tag1", s"Test1 failed: use0 must be associated with UNDEFINED. Your code returns ${map("use2")}")

passed(5)

[ test cases ]:

/* 

let x @tag3 = x @use0 + 10 in 

 let y@tag1 = 10 in 

 x@use1 * y @use2 */

val e = Let("x", "tag3", Plus(x("use0"), Const(10.0)), 

 Let ("y", "tag1", Const(10), Mult(x("use1"), y("use2"))))

val map = getAllUseDefLinks(e, Map.empty)

assert (map("use0") == "UNDEFINED", s"Test1 failed: use0 must be associated with UNDEFINED. Your code returns ${map("use0")}")

assert (map("use1") == "tag3", s"Test1 failed: use1 must be associated with UNDEFINED. Your code returns ${map("use1")}")

assert (map("use2") == "tag1", s"Test1 failed: use2 must be associated with tag1. Your code returns ${map("use2")}")

passed(5)

Problem 2: Tag Usages of Identifiers with Definitions In this problem, we will extend Lettuce by adding user-define generated (https//en.wikipedia.org/wiki/Use-define_chain). Example 1 In this example, we add "comment tagg" to each let binding (tagi, tag2, and tag3) and to each usage ( use1, use2, use3). The togs play no role in the program execution other than giving names to refer to the appropriate definitions and usages of identifiers. The purpose of this analysis is to produce a Map that maps usage tags to the let binding tags. This denotes that the usage tagged "use1" corresponds to the let-binding "tag3", "use2" usage corresponds to let binding "tog1" and "use3" usage corresponds to let binding "tag2". Abstract Syntax - First compute the use-def mappings for the RHS expression e1. - Nirst compute update the enwironment to note that identifier 18 is associated with tag. - Now, compute the mappings for in" exp - Conjoin the two maps for e1 and e2. Here are two nules for a identifiers. getAllseDefLinks(Ident(1d,usetag),env)={usetag"UNDENINED"}1d/domsin(env)(ident-undefined) Note that we reserve a special tag name UADEFINED (i.e, the string UNDEFINED") to denote identifiers that are not defined in the current scope - If the identifier Id does not belong to the domain of the environment, then retum a singleton mapping from the use-tag usetag associated with this use of id to the special tag unoEFINED: Part (A) : Complete the rule for Plus ( 5 points). Write down what should go in for ?1 and ?2 below. - If there are no antecedents just write "blank". - The empty map is represented as \{\} . - Concatenation of two maps is nap1 and map 2 is denoted map1 + map2: the scala operator for this is ++ though. YOUR ANSWER HERE Complete the rule for Const Write down what should go in for ?1 and 2 below. - If there are no antecedents just write "blank". - The empty map is represented as \{\} . - Concatenation of two maps is map1 and map2 is denoted nap1 + map2 . YOUR ANSWER HERE