Question

An accumulator is a procedure that is called repeatedly with a single numeric argument and accumulates its arguments into a sum. Each time it is called, it returns the currently accumulated sum. Write a procedure make-accumulator that generates accumulators, each maintaining an independent sum. The input to make-accumulator should specify the initial value of the sum; for example (define A (make-accumulator 5)) (A 10) 15 (A 10) 25

Short answer

Create a function that returns another function to maintain an accumulating sum.

Step-by-step solution

Understanding the Problem

We need to create a procedure that returns another procedure, which can be repeatedly called to accumulate a sum. This procedure should start with an initial value and then add any subsequent values given to it.

Define the make-accumulator Function

The make-accumulator function should accept an initial sum value as its argument and return a new function that maintains the running total.

Create the Accumulation Logic

Inside make-accumulator, define an inner function that updates and returns the accumulated sum whenever it is called with a new numeric argument.

Implement the make-accumulator in Code

Implement the logic in code to create the make-accumulator function. Here is a simple implementation in functional programming style, such as Scheme: ```scheme (define (make-accumulator initial-sum) (let ((current-sum initial-sum)) (lambda (x) (set! current-sum (+ current-sum x)) current-sum))) ``` This code maintains the accumulated sum using a closure and updates it every time the returned function is called.

Test the make-accumulator Function

Test the function make-accumulator by creating an accumulator that starts with an initial value and then calling it with arguments to verify if it correctly accumulates the sum. ```scheme (define A (make-accumulator 5)) ; A is initialized with 5 (A 10) ; Should return 15 (A 10) ; Should return 25 ``` In this test, the accumulator keeps adding the given input, and the results confirm that it works as expected.

Key concepts

Closures

In functional programming, closures are used to wrap up a function along with an environment in which it operates. Essentially, a closure is a function that retains access to its scope, even when the function is executed outside that scope. This allows the function to maintain its own state between calls.

In the context of the `make-accumulator` example, a closure is created when the inner procedure inside `make-accumulator` is defined. The environment comprises the variable `current-sum`, which retains the value across successive calls. When you call the returned procedure (e.g., `(A 10)`), it updates `current-sum` using your input.

• This allows the procedure to "remember" the accumulated sum.
• Every time the procedure is invoked, it can update and return this value.

Closures form the backbone of persistent state management in functional languages, providing a way to encapsulate variables without relying on mutable state found in other programming paradigms.

Procedures

In Scheme and other functional programming languages, procedures are fundamental units of code. They are blocks of commands designed to perform specific tasks, much like functions in other languages. Defining a procedure involves specifying a sequence of operations that can take inputs and return outputs.

For the `make-accumulator` exercise, the generated procedure serves as an accumulator. Once the outer `make-accumulator` function is called with an initial sum, it returns a new procedure. This returned procedure can then be repeatedly invoked with a number to add to the current sum.

• Procedures in Scheme are first-class citizens, which means they can be passed around as arguments or returned from other procedures.
• They can capture variables from the scope in which they were created, making them powerful for building complex functionality.

Procedures are a core part of the functional programming paradigm, promoting modular and reusable code structures.

Scheme Programming Language

Scheme is a minimalist and elegant dialect of the Lisp programming language family. Scheme supports a functional style of programming where functions are first-class citizens and can be treated like any other piece of data. This allows Scheme programs to be concise and expressive.

In Scheme, the usage of closures and procedures is prevalent. The example of `make-accumulator` highlights Scheme’s strengths in handling functions and closures. It uses `lambda` expressions to define anonymous functions, which can capture variables from their creation scope.

Scheme also employs special syntax for defining variables and procedures, such as:

• `define` for creating procedures and variables.
• `lambda` for creating anonymous function expressions.
• `let` for temporary variable bindings within a scope.

These components make Scheme a powerful and flexible language for tackling problems involving state and scope via functional abstractions, such as the task of creating accumulators that store and update state over time.