[formulathree]

The language of math itself is functional. In fact "functional programming" is basically programming as if everything was math. Think about it, does math allow for variable mutation inside a mathematical expression? No.

Interfaces that mutate internal values do not exist in mathematics. So, in essence, yes. Mathematical interfaces only support functional operations.

Haskell would be the language.

[yowlingcat]

Is this really true? Have you written idiomatic Haskell before? Not trying to question your familiarity if so, but a large part of doing so is utilizing interfaces that do just that.

One of the most critical parts necessary to fully grok idiomatic Haskell is how it uses mathematical interfaces, specifically category theoretic interfaces to structure internal state mutations -- specifically Monads and other structures. This specific interface utilizes two properties, identity and associativity, to do this and create one-way, sequenced computations still couched in formal rigor and laws.

Contrasted to other languages, in order to do any useful I/O in Haskell, one needs to understand and use Monads. Of course, the utility of the Monad includes but is not limited to just this use case.