Synonyms by Constraints

For whenever you need to translate an expanded type signature into the correct Lens/Prism/Traversal/&c. synonym.

Given a general type signature like p a (f b) -> p s (f t) the following constraints on p, f, a, b, s, and t determine the kind of lens you have.

Synonym	Constraints
Equality s t a b
Iso s t a b	Profunctor p
	Functor f
Prism s t a b	Choice p
	Applicative f
Review s t a b	Profunctor p
	Bifunctor p
	Settable f
Lens s t a b	(->) ~ p
	Functor f
Traversal s t a b	(->) ~ p
	Applicative f
Setter s t a b	(->) ~ p
	Settable f
Action m s a	(->) ~ p
	b ~ a
	t ~ s
	Effective m r f
MonadicFold m s a	(->) ~ p
	b ~ a
	t ~ s
	Effective m r f
	Applicative f
Getter s a	(->) ~ p
	b ~ a
	t ~ s
	Contravariant f
	Functor f
Fold s a	(->) ~ p
	b ~ a
	t ~ s
	Contravariant f
	Applicative f