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.
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.
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)
.
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.