Informally, a "pure program" an executable such that the
  stream of bytes entering it totally determines the stream of
  bytes leaving it.

  Many useful programs that I would like to write in Haskell
  don't fall into this category -- for example, network servers
  -- but a lot of their components do. Can these components can
  be Haskell functions without IO in their signatures?

  Though that seems reasonable, it is not, in general, true. For
  example,    System.Info.os    is generally treated as pure,
  though it is not. It's not clear to me how to disambiguate
  these "born again" values from really pure values.

--
_jsn
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