let

Introduction

The name let is used because it reflects its mathematical origins of introducing temporary bindings, as in “Let ( x = 2 ) and ( y = 3 )”.

A let statement in Scheme is a binding construct used to define variables within a localized scope. It allows you to create temporary bindings for variables and then execute a block of code using those bindings. This is particularly useful for keeping code modular and avoiding global variable pollution.

There are three main forms of let in Scheme:

• let: Standard let for creating simple local bindings.
• let*: Sequential let, where bindings can depend on the results of previous bindings.
• Named let: A special form of let that creates recursive loops or named procedures.

In its simplest form, let creates local variable bindings and evaluates an expression with those bindings.

(let ((variable1 value1)
      (variable2 value2))
  expression)

• Bindings: A list of pairs where each pair assigns a value to a variable.
• Expression: The body of the let, which can use the locally defined variables.

Example

(let ((x 10)
      (y 20))
  (+ x y))

• This defines two local variables, x (10) and y (20).
• It then computes (+ x y) using these variables.

Result: 30

The let* Construct

The let* construct is similar to let, but bindings are evaluated sequentially. This means later bindings can depend on earlier ones.

(let* ((variable1 value1)
       (variable2 expression-using-variable1))
  expression)

Example

(let* ((x 10)
       (y (+ x 5)))
  (* x y))

• The first binding assigns 10 to x.
• The second binding calculates y as (+ x 5), using the value of x.
• The body computes (* x y).

Result: 150

Named let

A named let is a special form of let that provides a name for the let block itself, turning it into a recursive procedure. This is useful for creating loops or recursive computations.

(let name ((variable1 initial-value1)
           (variable2 initial-value2))
  body-expression)

• Name: The let block is given a name, effectively defining a function.
• Bindings: Initial values for variables, similar to a standard let.
• Body: The expression can call the named let recursively.

Example: Looping with Named let

(let loop ((n 5)
           (result 1))
  (if (= n 0)
      result
      (loop (- n 1) (* result n))))

• The loop function starts with n = 5 and result = 1.
• If n is 0, it returns the result.
• Otherwise, it calls itself recursively with n - 1 and result * n.

Result: 120 (Factorial of 5)

Summary Table

Examples

Using let for Local Computation

(let ((x 2)
      (y 3))
  (+ (* x x) (* y y)))

Result: 13 (Calculates x² + y²)

Using let* for Sequential Dependencies

(let* ((x 2)
       (y (* x x))
       (z (* y x)))
  z)

Result: 8 (Calculates x³)

Using Named let for Recursive Computation

(let factorial ((n 5)
                (result 1))
  (if (= n 0)
      result
      (factorial (- n 1) (* result n))))

Result: 120 (Factorial of 5)

By using let, let*, and named let, Scheme enables modular, recursive, and sequential programming with clear scoping rules.