Is there a canonical definition of “pure” function?
As noted in this paper Imperative Functional Programming, (1993) by Peyton-Jones and Wadler (among the group of researchers that created Haskell):


  We focus on purely-functional solutions, which rule out side effects,
  for two reasons. Firstly, the absence of side effects permits
  unrestricted use of equational reasoning and program transformation...


the focus is on absence of side-effects to enable program transformations (i.e compiler optimisations).

What are side-effects? This paper in turn points to Integrating functional and imperative programming (1986) by Gifford and Lucassen, which mentions four types of effect classes: Pure, Function, Observer and Procedure. So, the term "pure function" derives from this paper.


  
  a PURE is referentially transparent: it does not cause side-effects,
  its value is not affected by side-effects, and it returns the same
  value each time it is evaluated.
  


Note, however, that Peyton-Jones and Wadler mentioned shortcomings in this approach. Worth noticing, they say, is the programming language Clean that uses linear types to introduce side-effects in a safe manner (i.e. safe for the compiler). Basically, it threads the World as a variable in all I/O related functions, including the main entry point.

With that, it is possible to have a pure functional language interacting with the world and having side-effects (I/O, the OS, the Windowing system, etc), contradicting partially your wikipedia definition. One can in fact say that Haskell has Clean as one of its influencers; although it departs from linear types and uses another type-level construct (monads) to guarantee linearity, i.e. a single-reference at all times.