Kata

The goal of this little kata to implement

• addition
• multiplication
• power

functions for Church numerals that are represented as

newtype Number = Nr (forall a. (a -> a) -> a -> a)

zero :: Number
zero = Nr (\ _ z -> z)

succ :: Number -> Number
succ (Nr a) = Nr (\ s z -> s (a s z))

one :: Number
one = succ zero

newtype Church = Church (forall a. (a -> a) -> a -> a)

zero :: Church
zero = Church (\_ x -> x)

succ :: Church -> Church
succ (Church n) = Church (\f x -> f (n f x))

one :: Church
one = succ zero

zero = f => x => x

succ = n => f => x => f (n (f) (x))

one = succ( zero )

// These definitions are actually in Preloaded

zero = \ f x . x

succ = \ n . f x . f (n f x)

one = succ zero

succ = lambda n: lambda f: lambda x: f(n(f)(x))
zero = lambda f: lambda x: x
one = succ(zero)

# These definitions are actually in Preloaded

hints

• you can finish it by just replacing the undefined placeholders in Haskell / typed holes in PureScript - no need to change the arguments - they might provide some hints.
• the solutions can be very short - you don't have to write much if you think about it
• you don't really need lambda-functions
• But if you feel like it replace them with your own ideas.