The semantics of Mathematica's Thread function, someone needs to finally put this to rest

Question

Wolfram Research has had the same documentation for this function for the last 8 years at least:

Thread[f[args]]

\"threads\" f over any lists t

Answer 1

Thread is a bit like a generalization zip from other functional languages.

For simple cases, where all the elements of args from your example are lists,

Thread[f[args]]

is equivalent to

f @@@ Transpose[{args}]

as shown in the first couple examples in the documentation. The major wrinkle is when you have args that are not lists, in which case they're effectively curried out; for example,

Thread[g[{a, b}, c, {d, e}, f]]

is equivalent to

g[#1, c, #2, f]& @@@ Transpose[{{a, b}, {d, e}}]

I usually find myself using Thread to construct lists of rules or lists of equations.