The Forbidden Sandwich Inequalities: Unveiling the Reason Behind Programming Languages’ Restriction

In the world of programming, there are certain rules and restrictions that are put in place to ensure the smooth operation of code. One such restriction is the prohibition of “sandwich inequalities”. In mathematics, it is common to see “sandwich inequalities” showing that a quantity is greater than another but less than another, e.g. a < b < c means the same as a < b && b < c. However, most programming languages do not allow this. This article aims to unveil the reason behind this restriction in programming languages.

Understanding Sandwich Inequalities

Sandwich inequalities, also known as chained inequalities, are a common mathematical concept. They are used to express the relationship between three or more quantities. For example, the inequality a < b < c means that a is less than b and b is less than c. This is a simple and intuitive way to express these relationships in mathematics.

Why are Sandwich Inequalities Forbidden in Programming Languages?

The main reason why most programming languages do not support sandwich inequalities is due to the way they evaluate expressions. In programming, expressions are evaluated from left to right. So, in the case of a < b < c, the programming language would first evaluate a < b, and then try to compare the result (which is a boolean value of either true or false) with c. This would result in a type error, as you cannot compare a boolean value with a numerical value.

How do Programming Languages Handle Inequalities?

Instead of using sandwich inequalities, programming languages use logical operators to express the relationship between multiple quantities. For example, the sandwich inequality a < b < c would be expressed as a < b && b < c in most programming languages. This means that a is less than b AND b is less than c. This way, the programming language can evaluate each comparison separately and avoid any type errors.

Are there any Exceptions?

While most programming languages do not support sandwich inequalities, there are a few exceptions. For example, Python allows the use of sandwich inequalities as a shorthand for chaining comparisons. However, this is not a common feature and is not supported by most other programming languages.

Conclusion

While sandwich inequalities are a convenient way to express relationships between quantities in mathematics, they are not commonly supported in programming languages due to the way these languages evaluate expressions. Instead, programming languages use logical operators to express these relationships, which allows for more flexibility and avoids potential type errors. Understanding these differences is crucial for anyone looking to transition from a mathematical background to a programming one.