The notation comes from Doaitse Swierstra and Luc Duponcheel: they had already identified this interface for parser combinators, and we felt it was important to respect their choices where it was meaningful to do so. I'm trying to remember how Doaitse pronounces them, but drawing a blank.
I prefer them to be seen and not heard. In fact, I prefer them not to be seen either, hence idiom brackets. But especially when defining an instance, it's helpful to have names. Not that it's down to me to name them: the whole Idiom vs Applicative vs goodness-knows-what shenanigans was a fascinating study of power. For what it's worth, in my own parlance
<*> is 'applied (to)' (the interface is 'pure and applied', like mathematics)*> is 'ignored'<* is 'ignoring'<$> is 'mapped (over)'<$ is perhaps 'after', but I'm not terribly conscious of calling it anything
The key ideas: the effects always sequence (whatever that means) left-to-right; the $ or * tell you whether what's to their left is pure or idiomatic; the chevrons tell you the resulting dataflow, pointing only to the signal.
An alternative pronunciation scheme, a level away from the individual operators, might translate
f <$> a <*> b <* c <*> d
to 'IDIOM: f, a, b, NOISE c, d' or some such. But that's really reading the bracket version
(|f a b (-c-) d|)
out loud.
I find 'money' and 'splat' amusing, but we might do well to prioritize semantics over asciidents of syntax.
