Alternatives in pure function construction

Question

When I declare a function f in the following form:

f[a|b] := 1

then I can use it like:

f[a] (* gives 1 *)

But when I try to use the form:

f=Function[a|b,1]

I get the following error, and I can't use it:

Function::flpar: Parameter specification a|b in Function[a|b,1] should be a symbol or a list of symbols.

Why does Alternatives[a,b] not "work" like a list {a,b} in this case?

Answer 1

Function does not do pattern matching. If you need pattern matching, you can do it manually:

Function[x,
  Switch[x,
    a|b, 1,
    _, 0 (* this is the default choice for input that don't match preceding patterns *)
  ]
]

Note that it is not possible to keep Function[...] unevaluated when there is no match.