Write in F# language $($F sharp$)->$ do not use Python, C$++,$ C#$,$ C$,$ Java, etc...$$

The following:$$

In F# $$write an expression evaluation function that take as arguments a list of variable bindings and a string that is composed of letters and operators from the set $[+-*/$$@$].$It will scan the string from left to right, interpreting the string as an expression in postfix notation $($except for the $ and @ special characters$).$

$*$ When it encounters a letter, it should retrieve the value associated with that letter and push it on an operand stack.$$

$*$ When it encounters an arithmetic operator, it should pop two operands off of the stack, do the computation indicated by the operation, and then push the result onto the stack.$$

$*$ When it encounters a $$,$ it should should be interpreted as a swap operation, which pops two operands off of the stack, and pushes them back on in reverse order.$$

$*$ When the function encounters @$,$ it should read the next character, which will be a letter, $$then pop the top value from the stack and set that value as the new binding for the letter.

$*$ Any spaces in the string should be skipped.

$*$ When the input string is exhausted, the function should return the top value on the stack.

$*$ You may assume that all input strings are syntactically legal according to this list of rules.

For example, given a set of variables described by $[("$a$",5)$;$("$b$",2)$;$("$c$",9)],$ here is how several possible input strings would be interpreted:

$"$ab$+"$ should return $7($push $5,$ push $2,$ add$)$

"cab$+-"$ should return $2($push $9,$ push $5,$ push $2,$ add, subtract$)$

"cab$+$$$-"$ should return $-2($push $9,$ push $5,$ push $2,$ add, swap the top two values $(9$ and $7),$ subtract$)$

$"$ab$+$cb$-*"$ should return $49($push $5,$ push $2,$ add, push $9,$ push$2,$ subtract, multiply$)$

$"$ab$+$cb$-*$ @d bd$+"$ should return $51$

$($push $5,$ push $2,$ add, push $9,$ push$2,$ subtract, multiply, bind $49$ to d$,$ push $2,$ push $49,$ add$)$

See the bottom of this assignment for some additional test strings.

Your function should be able to handle arbitrarily complex expressions, which implies that the stack should be represented by a list. $$In order to handle what seems to be a requirement to remember a "state", you can use the accumulator technique we have seen for writing tail$-$recursive functions. $$That means your evaluation function that looks like this

let eval vars expr $=...$

should contain an inner recursive function with this signature:

let rec innerEval vars stack expr $=...$

A new value for 'stack' will be used in a recursive call whenever the stack is pushed or popped. $$Similarly$,$ an @ operation will require a new value of 'vars' to be created to hold the new binding and the 'expr' string will get shorter by $1$ or $2$ characters for each recursive call.

You will need a helper function that takes a string and the list of tuples representing variable bindings as arguments. Each element of the list will be a tuple consisting of a string and an int. Find the first tuple for which the string matches the first argument and return the corresponding integer. $$Note that this approach will allow you to add a new binding by creating a new list with that binding on the front. $$Using the first binding found will then guarantee that the value from the most recent one is returned.

This assignment has the following additional parameters:$$

$1.$ Do not use "mutable" variables.$$

$2.$ Functions should have no side effects. This includes:

$*$ no input $($other than the function's arguments$)-$ e$.$g$.,$ no user input or file input

$*$ no use of external state $-$ e$.$g$.,$ global or static variables

$3.$ Document each function in $$your code with an appropriate comment.

$*$ Use other comments as well, as your feel necessary.

Note that calling your eval function with a single argument $($the binding list$)$ should result in it returning a closure that then expects just an expression string to evaluate. $$Make sure that your function does this correctly, since I plan to test it that way. $$In fact, I plan to use List.map to apply the closure to a list of expression strings, something like this:

let testEval $=$ eval $[("$a$",5)$;$("$b$",2)$;$("$c$",9)]$

let exprList $=[]$

let resultList $=$ List.map testEval exprList

Debugging hint:$$the number of recursive calls is bounded by the size of the expression string, so there will$$ be only a limited number of them.$$ Print out the three input lists at the beginning of the innerEval function.

$===================================================================$

Here are more test strings using the same variables $[("$a$",5)$;$("$b$",2)$;$("$c$",9)]$ to check out your solution:

$"$ab$-$ab$*$ab$+--"$ should return $0($push $5,$ push $2,$ subtract $[5-2->3],$ push $5,$ push $2,$

$$ multiply $[5*2->10],$ push $5,$ push $2,$ add $[5+2->7],$ subtract $[10-7->3],$ subtract $[3-3->0])$

$"$bbb @q bqbq$*****"$ should return $64($six $2\text{'}$s on the stack before the multiplies$)$

$"$ca$-$ @b bc$$-"$ should return $5$

$($ push $9,$ push $5,$ subtract, bind $4$ to b$,$ push $4,$ push $9,$ swap $4$ and $9,$ subtract$)$