Function Combinators with Ramda

Original Idea comes from Avaq/combinators.js.

Name	#	Haskell	Ramda	Crocks	Functional Signature	Functor m ⇒	Function f, g, h Evaluation
identity	I	id	identity	identity	a → a
constant	K	const	always	constant	a → b → a
eager application¹	A	($)	call		(() → b) → b
lazy application			thunkify, partial		(a → b) → a → (() → b)
thrush	T	(&)	applyTo	applyTo	a → (a → b) → b
tap			tap	tap	(a → b) → a → a
flip	C	flip	flip	flip	(a → b → c) → b → a → c		f(b, a)
compose	B	(.), fmap²	map², o	composeB	(b → c) → (a → b) → a → c	(b → c) → m b → m c	f(g(a))
substitution	S	ap²	ap²	substitution	(a → b → c) → (a → b) → a → c	m (b → c) → m b → m c	f(a, g(a))
chain			chain²		(a → b → c) → (b → a) → b → c	(a → m c) → m a → m c	f(g(b), b)
duplication	W	join²	unnest²		(a → a → b) → a → b	m (m b) → m b	f(a, a)
lift			converge, lift	converge	(b → c → d) → (a → b) → (a → c) → a → d	(b → c → d) → m b → m c → m d	f(g(a), h(a))
useWith			useWith	compose2	(c → d → e) → (a → c) → (b → d) → a → b → e		f(g(a), h(b))
psi	P	on	on	psi	(b → b → c) → (a → b) → a → a → c		f(g(a1), g(a2))
"compose inner"			map³		(a → d → c) → (b → d) → (a → b → c)	Functor n ⇒ m (d → c) → n d → m n c	f(a, g(b))
"lift partial"			map⁴		(d → b → c) → (a → d) → (a → b → c)	Functor n ⇒ (d → n c) → m d → m n c	f(g(a), b)
unit				unit	() → undefined

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¹) The A-combinator can be implemented as an alias of the I-combinator. Its implementation in Haskell exists because the infix nature gives it some utility. Its implementation in Ramda exists because it is overloaded with additional functionality.

²) Algebras like ap have different implementations for different types. They work like Function combinators only for Function inputs.

³) (mfd2c, nd) => map( fd2c => map(fd2c)(nd) )( mfd2c )

⁴) (fd2nc, md) => map(fd2nc, md)