ap
is consistent with bind
.
ap
is consistent with bind
.
As with semigroups, monadic effects only change when their order is changed, not when the order in which they're combined changes.
As with semigroups, monadic effects only change when their order is changed, not when the order in which they're combined changes.
A series of maps may be freely rewritten as a single map on a composed function.
A series of maps may be freely rewritten as a single map on a composed function.
Lifted functions can be fused.
Lifted functions can be fused.
empty[A]
is a polymorphic value over A
.
point
distributes over function applications.
point
distributes over function applications.
The identity function, lifted, is a no-op.
The identity function, lifted, is a no-op.
point(identity)
is a no-op.
point(identity)
is a no-op.
point
is a left and right identity, F-wise.
point
is a left and right identity, F-wise.
Lifted f
applied to pure a
is just f(a)
.
Lifted f
applied to pure a
is just f(a)
.
empty
short-circuits its right.
map
is like the one derived from point
and ap
.
map
is like the one derived from point
and ap
.
Lifted point
is a no-op.
Lifted point
is a no-op.