APL Programming Language Cheatsheet

In the vast landscape of programming languages, APL (A Programming Language) stands out as a unique and powerful tool. Developed in the 1960s by Kenneth E. Iverson, APL has gained a reputation for its concise and expressive syntax, making it a favorite among mathematicians, data scientists, and those seeking elegant solutions to complex problems. In this cheatsheet, we’ll explore the key elements of APL, providing a quick reference for both beginners and experienced programmers.

1. Basics of APL

1.1. Arrays

At the core of APL is the concept of arrays, which are multi-dimensional collections of data. APL allows you to perform operations on entire arrays at once, making it highly efficient for mathematical and numerical tasks.

⍝ Define a vector
vector ← 1 2 3 4 5

⍝ Define a matrix
matrix ← 3 3 ⍴ ⍳9

1.2. Functions

Functions in APL are denoted by symbols and are applied to arrays. A single symbol often represents a powerful operation.

⍝ Sum of array elements
+/ vector

⍝ Transpose a matrix
⍉ matrix

1.3. Operators

APL has a variety of operators for different operations. Some common ones include:

  • + Addition
  • - Subtraction
  • × Multiplication
  • ÷ Division
  • Matrix Inversion
  • Reshape
  • Rank operator
⍝ Reshape matrix
3 2 ⍴ matrix

2. Special Symbols

2.1. Reduction

The / symbol is used for reduction, a powerful concept in APL that collapses an array along a specified dimension.

⍝ Cumulative sum
+\ vector

2.2. Inner Product

The ∘. symbol represents the inner product, a versatile operator for combining elements of two arrays.

⍝ Outer product (dyadic)
vector ∘.× vector

⍝ Inner product (monadic)
+/ vector × vector

2.3. Each

The ¨ symbol, known as “each,” applies a function to each element of an array.

⍝ Square each element
vector ר vector

3. Control Flow

3.1. Conditional

APL uses a simple and concise syntax for conditional statements.

⍝ If-else
result ← (condition) { true-branch } { false-branch }

3.2. Looping

Loops in APL can be achieved using recursion or the operator.

⍝ While loop
{condition} ⍣ {body}

⍝ For loop
⍝ (Use recursion or apply a function to each element)

4. I/O Operations

4.1. Input

Taking input in APL is straightforward using the symbol.

⍝ Input a number
number ← ⎕

4.2. Output

Displaying output is done using the ⎕← symbol.

⍝ Display result
⎕← result

5. Tips and Tricks

5.1. Dyalog APL

Dyalog APL is a popular implementation of APL that provides a modern environment with a rich set of features.

5.2. Unicode Symbols

APL leverages a unique set of Unicode symbols. Familiarize yourself with them for efficient coding.

5.3. Online Resources

Explore online communities and resources to deepen your understanding of APL, such as the APL Official Website.


APL’s concise syntax and array-centric approach make it a fascinating language for those who appreciate mathematical elegance in programming. This cheatsheet serves as a quick reference, but diving deeper into APL will unveil its true power and potential for solving complex problems with simplicity. As you explore further, you’ll discover why APL remains an enduring and influential language in the world of programming.


1. What is APL known for in the programming world?

APL is renowned for its concise syntax, array manipulation capabilities, and its unique set of Unicode symbols, making it a favorite for mathematical and numerical tasks.

2. How do I perform basic arithmetic operations in APL?

Use symbols such as + for addition, - for subtraction, × for multiplication, and ÷ for division to perform basic arithmetic operations on arrays.

3. What is the role of arrays in APL?

Arrays in APL are fundamental data structures, allowing efficient manipulation of multi-dimensional data. Operations can be applied to entire arrays, enhancing code simplicity and efficiency.

4. How does APL handle conditional statements?

APL employs a concise syntax for conditional statements, utilizing the {condition} {true-branch} {false-branch} structure for efficient and readable code.

5. Where can I find additional resources to learn more about APL?

Explore online communities like the APL Wiki and APL Orchard, and consider using Dyalog APL, a popular implementation offering a modern environment and rich feature set for APL developers.