The use of i, j, k, and l as loop variables or integer counters has deep roots in both mathematics and early programming conventions. Here’s a bit of history and reasoning behind this tradition:
Mathematical Origin:
– The letters i, j, k, and l have long been used in mathematics as counters or indices in summations, matrices, and vector notation, particularly in linear algebra. For example, i and j are often used as row and column indices in matrices.|
– These variables are typically used as subscripts or iterators in formulas and equations. This usage has likely influenced their adoption in programming.
Fortran and Early Programming Languages:
– Fortran, one of the earliest high-level programming languages developed in the 1950s, influenced a lot of programming conventions, including loop variable naming. In Fortran, variables starting with I to N were integers by default, so i, j, and k became natural choices for counters, especially in loops.
– Because Fortran was widely adopted, these conventions spread to other programming languages, which influenced generations of programmers to use these variables as loop counters.
Compactness and Readability:
– Variables like i, j, and k are compact and readable. They’re short and easy to type, making them convenient for small loops or simple, local iterations.
– In nested loops, i, j, and k provide an easy-to-remember sequence, particularly for indexing multi-dimensional arrays.
Widespread Convention:
– By the time languages like C, Pascal, and later Java and Python emerged, the practice of using i, j, k, etc., for loop variables was already standard. These languages adopted many of the conventions from their predecessors, creating a legacy effect.
So, this usage was introduced in the earliest programming languages like Fortran and has since been carried forward, shaping conventions across almost all programming languages today.