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# 4.3. Let Expressions¶

## 4.3.1. Let Blocks¶

In Section 2.4, when we introduced helper functions, we considered the following split function.

var split = function (pivot,list) {
count++;
if (fp.isNull(list)) {
return [[],[]];
} else {
if (fp.isLT(fp.hd(list), pivot)) {
return fp.makeList(
fp.cons(fp.hd(list), fp.hd(split(pivot,fp.tl(list)))),        // Call split
fp.hd(fp.tl(split(pivot,fp.tl(list))))                        // Call again
);
} else {
return fp.makeList(
fp.hd(split(pivot,fp.tl(list))),                              // Call split
fp.cons(fp.hd(list), fp.hd(fp.tl(split(pivot,fp.tl(list)))))  // Call again
);
}
}
};


While this works correctly, it is inherently inefficient because it always makes two recursive calls to split that are guaranteed to produce the exact same result.

It would be much better to cache the result of a call to split and then use that cached result in place of the two calls. We could do this in SLang 1 if we had the ability to declare a symbol local to the scope where it was needed and "assign" that symbol the result of calling split. Then, instead of calling split twice, we could just twice use the result that had been cached by association with the symbol. It is with this in mind that we introduce a let block in SLang1. Consider the following three examples of let block usage. In each example, the assignments to symbols following let are used in the expression enclosed in the keywords in and end.

Example 1

let
x = 1
y = 2
in
+(x,y)
end


Example 2

let
x = 1
in
let
f = fn(y) => +(y,x)
in
let
x = 2
in
(f 3)
end
end
end


Example 3

let
x = 1
sqr = fn (x) => *(x,x)
in
let
f = fn(y) => +(y,x)
in
let
x = 2
in
+(x,(sqr (f x)))
end
end
end


Interestingly, the let block is just syntactic sugar for an existing construct in SLang1. That is, when the SLang1 interpreter encounters a let block it can just "translate" it into that existing construct right away as it builds the abstract syntax tree. To see what this existing structure is, figure out what the sets of question marks should be in each of the following statements.

Statement 1: When we evaluate let x = 1 y = 2 in <exp> end, we return the value of ??? in an environment in which ??? and ??? are bound to ??? and ???, respectively.

Statement 2: When we evaluate (fn (x,y) => <exp> 1 2), we return the value of ??? in an environment in which ??? and ??? are bound to ??? and ??? , respectively.

Test whether you've filled in the question marks correctly by doing the following practice problems.

## 4.3.2. Let Blocks As Syntactic Sugar¶

This randomized problem focuses on let expressions as syntactic sugar. Solve it correctly three times in a row to get credit for it.

## 4.3.3. Nested Lets¶

This randomized problem focuses on the evaluation of nested let expressions. Solve it correctly three times in a row to get credit for it.

When you provide your answer, remember to include the full denoted value, for example ["Num",0] and not just 0.

## 4.3.4. Nested Lets with Closures¶

This randomized problem focuses on the evaluation of nested let expressions with closures. Solve it correctly three times in a row to get credit for it.

Again, when you provide your answer, remember to include the full denoted value.