Can an analog of the S combinator be expressed in Haskell using only standard functions (without defining it by equation) and without using lambda (anonymous function)? I expect it to by of type (a...

Suppose there are some data types to express lambda and combinatorial terms: data Lam α = Var α -- v | Abs α (Lam α) -- λv . e1 | App (Lam α) (Lam α) -- e1 e2 deriving (Eq, Show) infixl 0 :@ d...

I am new to lambda calculus and struggling to prove the following. SKK and II are beta equivalent. where S = lambda xyz.xz(yz) K = lambda xy.x I = lambda x.x I tried to beta reduce SKK by open...

I'm starting to learn lambda calculus and I need to implement I, S, K combinators in Erlang. Of course, S, K, I stands for: S = λxyz.xz(yz) K = λxy.x I = λx.x I have no problem understanding I...