The following identities ought to hold for every Applicative (for some value of =):
return Fn.id <*> t = t
return Fn.compose <*> tf <*> tg <*> tx = tf <*> (tg <*> tx)
return f <*> return x = return (f x)
tf <*> return x = return (fun f -> f x) <*> tf
Note: <*> is the infix notation for apply.
The map
argument to Applicative.Make
says how to implement the applicative's
map
function. `Define_using_apply
means to define map t ~f = return f <*> t
.
`Custom
overrides the default implementation, presumably with something more
efficient.
Some other functions returned by Applicative.Make
are defined in terms of map
,
so passing in a more efficient map
will improve their efficiency as well.