$1$B $(8$ points$)$: Define Closure for Function Calls with Zero or More Args.

We will now redefine closures for functions with zero or more args. When our function had one argument, our closures were defined as Closure$($id$,$ expr, env$).$ We would now like to define closures as Closure$([$id$1,...,$ idn$],$ expr, env$)$ where

$-$ id$1...,$ idn are the list of arguments for the function to be called.

$-$ expr is the body of the function and

$-$ env is the stored environment for static scoping.

$\backslash [$

$\backslash$begin$\{$aligned$\}$

$\backslash$text $\{$ Value $\}$ & $\backslash$Rightarrow $\backslash$text $\{$ num$($Double$)\}\backslash \backslash$

& $\backslash$Rightarrow $\backslash$text $\{$ closure$($String $\}\{\}^\{*\},\backslash$text $\{$ Expr, Environment$)\}\backslash \backslash$

& $\backslash$Rightarrow $\backslash$text $\{$ error $\}$

$\backslash$end$\{$aligned$\}$

$\backslash ]$

For Environment please use a scala immutable map from String to Value

$```$

sealed trait value

case class Num$($d: Double$)$ extends Value

case object Error extends Value

$//$ YOUR CODE HERE

case class Closure$($params: List$[$String$],$ expr: Expr, env: Map$[$String$,$ Value$])$ extends Value

$```$

defined trait Value

defined class Num

defined object Error

defined class Closure

$//$BEGIN TEST

val v$1=$ Closure$($List$("$x$","$y$","$z$"),$ Plus$($x$,$ y$),$ Map.empty$)$

val v$2=$ Closure$($Nil$,$ Const$(15),$ Map.empty$)$

val env$1$: Map$[$String$,$ value$]=$ Map$("$x$"->$ Num$(25\mathrm{.}0),"$y$"->$ v$2)$

val v$3=$ Closure$($List$("$x$"),$ Plus$($x$,$ Const$(25)),$ env$1)$

passed$(8)$

$//$END TEST

cmd$21.$sc:$2$: type mismatch;

found : ammonite.$\backslash$$sess.cmd$8.$wrapper.cmd$6.$Ident

required: string

val v$1=$ Closure$($List$("$x$","$y$","$z$"),$ Plus$($x$,$ y$),$ Map.empty$)$

cmd$21.$sc:$2$: type mismatch;

found : ammonite.$\backslash$$sess.cmd$7.$wrapper.cmd$6.$Ident

required: string

val v$1=$ Closure$($List$("$x$","$y$","$z$"),$ Plus$($x$,$ y$),$ Map.empty$)$

cmd$21.$sc:$5$: type mismatch;

found : ammonite.$\backslash$$sess.cmd$8.$wrapper.cmd$6.$Ident

required: string

val v$3=$ Closure$($List$("$x$"),$ Plus$($x$,$ Const$(25)),$ env$1)$

cmd$21.$sc:$5$: type mismatch;

found : cmd$21.$this.cmd$18.$ Const

required: string

val v$3=$ Closure$($List$("$x$"),$ Plus$($x$,$ Const$(25)),$ env$1)$

Compilation Failed