edit_distance() does not compute the actual Damerau-Levenshtein distance when transpositions is set to True

[avena554]

I have recently noticed that edit_distance(s1, s2, transpositions=True) in nltk.metrics.distance does not compute the Damerau-Levenshtein distance between s1 and s2 -- i.e. the minimal number of operations among insertion, deletion, substitution and transpositions required to transform s1 into s2. As an example,

edit_distance("ca", "abc", transpositions=True) returns 3, where the distance is actually 2 (it can be achieved by first transposing c and a, then inserting b in the middle).

I am unsure whether this is intended behavior (apologies if it is). It seems that what the function computes in its present state, is what is referred to as 'Optimal String Alignment Distance' on Wikipedia (https://en.wikipedia.org/wiki/Damerau%E2%80%93Levenshtein_distance) -- which imho does not really have a natural and appealing interpretation. As a side note, despite its name, Optimal String Alignment is not a distance in the mathematical sense of the term (it does not satisfies the triangle inequality) which contradicts a comment in the heading of nltk.metrics.distance.

Best,
Antoine