Terminology for methods that mutate or don't mutate state

Question

Are there well established terms for referring to methods that do or do not mutate the object state?

For example of a well established term describing a type of function: "idempotent".

Answer 1

Pure Function is a well-established term referring to an operation which depends solely on its input arguments. It neither accesses nor mutates any non-local state. The concept of a pure function in programming is derived from mathematical functions. The opposite of a pure function is an impure function, which may perform IO, produce a side effect, or have some dependency on non-local state.

Note that the definition of a pure function is more strict than what this question asks for, since a pure function prohibits not only mutation of object state but also access to object state. To find a definition which fits between pure and impure functions, we can consider the Difference between a method and a function. Often, these two terms are conflated into one amorphous abstraction; but for the purpose of this question we will use more precise meanings: a method is coupled to an object whereas a function is independent.

From that simple definition we naturally reach the concept of Pure Methods. A pure method is just a pure function with one difference: in addition to its input arguments, the method implicitly receives a reference to its enclosing object, as if it had one extra argument.

I can't say that the term pure method is well established in the same way as pure function; but if we take the definition of a pure function, alongside the definition of a method, then I think the definition of a pure method follows intuitively. So to answer the question, pure is the keyword commonly used to indicate the presence or absence of mutation.