The Haskell language is described in The Haskell Report via an informal presentation of its denotational semantics. Its types are all "lifted" from Sets to something like Scott Domains to account for partiality and non-termination, which are denoted by the value called "bottom" or _|_.
So, they are not strictly functions in the normal set-theoretic sense, but they are (mostly?) mathematically accurate continuous functions between Scott Domains. As the semantics are not formally defined, there is a limit to what you can say about them, but there is an interesting paper entitled "Fast and Loose Reasoning is Morally Correct" that shows that treating Haskell as if it worked in terms of total set-theoretic functions is a reasonable thing to do in some practical circumstances in the use of Haskell.
If you want really pure, total set-theoretic functions in a programming language, you will have to go to a total functional language such as Coq or Agda. You lose Turing-completeness when you stick to total functions, though, and most people only type-check their functions rather than actually running them (this is not as crazy as it sounds--these languages are primarily used to help formulate formal proofs, which are finished when they pass the type-checker).
In any case, the bit in the blog about FORTRAN and everything conflating procedures and algebraic functions strikes me as nonsense, at least without further explanation to clarify/justify it.
So, they are not strictly functions in the normal set-theoretic sense, but they are (mostly?) mathematically accurate continuous functions between Scott Domains. As the semantics are not formally defined, there is a limit to what you can say about them, but there is an interesting paper entitled "Fast and Loose Reasoning is Morally Correct" that shows that treating Haskell as if it worked in terms of total set-theoretic functions is a reasonable thing to do in some practical circumstances in the use of Haskell.
If you want really pure, total set-theoretic functions in a programming language, you will have to go to a total functional language such as Coq or Agda. You lose Turing-completeness when you stick to total functions, though, and most people only type-check their functions rather than actually running them (this is not as crazy as it sounds--these languages are primarily used to help formulate formal proofs, which are finished when they pass the type-checker).
In any case, the bit in the blog about FORTRAN and everything conflating procedures and algebraic functions strikes me as nonsense, at least without further explanation to clarify/justify it.