Notation not recursive enough?

Question

My notation is not recursing enough. For example,

Notation[W[a_ | b_] ⟹ foo[a_, b_]/foo[b_]]
Notation[W[a__, b_ | c_] ⟹ W[a__ | c_]W[b_ | c_]]

Then

W[a, b, c, d | e]

will give

foo[d, e]W[a, b, c | e]/foo[e]

My question is why does the W[a, b, c | e] in the above not expand further until it gets to the foo level?

Answer 1

It doesn't recurse because you are using a definition of Notation (from the Notation` package) that is restricted to parsing:

This means that you will have to explicitly ShiftReturn for the notation to take effect. Notice the following:

You can achieve what you want using straightforward definitions instead:

Clear@WW
WW[a__, Verbatim[Alternatives][b_, c_]] := WW[Sequence @@ Most[{a}], Last@{a} | c] WW[b | c]
WW[Verbatim[Alternatives][a_, b_]] := foo[a, b]/foo[b]

which gives as expected:

WW[a, b, c, d | e]
(* (foo[a, e] foo[b, e] foo[c, e] foo[d, e])/foo[e]^4 *)