What is the difference between statically typed and dynamically typed languages?

Question

I hear a lot that new programming languages are dynamically typed but what does it actually mean when we say a language is dynamically typed vs. statically typed?

Answer 1

The terminology "dynamically typed" is unfortunately misleading. All languages are statically typed, and types are properties of expressions (not of values as some think). However, some languages have only one type. These are called uni-typed languages. One example of such a language is the untyped lambda calculus.

In the untyped lambda calculus, all terms are lambda terms, and the only operation that can be performed on a term is applying it to another term. Hence all operations always result in either infinite recursion or a lambda term, but never signal an error.

However, were we to augment the untyped lambda calculus with primitive numbers and arithmetic operations, then we could perform nonsensical operations, such adding two lambda terms together: (λx.x) + (λy.y). One could argue that the only sane thing to do is to signal an error when this happens, but to be able to do this, each value has to be tagged with an indicator that indicates whether the term is a lambda term or a number. The addition operator will then check that indeed both arguments are tagged as numbers, and if they aren't, signal an error. Note that these tags are not types, because types are properties of programs, not of values produced by those programs.

A uni-typed language that does this is called dynamically typed.

Languages such as JavaScript, Python, and Ruby are all uni-typed. Again, the typeof operator in JavaScript and the type function in Python have misleading names; they return the tags associated with the operands, not their types. Similarly, dynamic_cast in C++ and instanceof in Java do not do type checks.