For the function monad I find that (<*>) and (>>=)/(=<<) have two strikingly similar types. In particular, (=<<) makes the similarity more apparent: (<*>) :: (r -> ...

While learning Haskell, I came across a challenge to find two functions f and g, such that f g and f . g are equivalent (and total, so things like f = undefined or f = (.) f don't count). The given...

In a previous question SystemT Compiler and dealing with Infinite Types in Haskell I asked about how to parse a SystemT Lambda Calculus to SystemT Combinators. I decided to use plain algebraic data...

I'm following this blog post: http://semantic-domain.blogspot.com/2012/12/total-functional-programming-in-partial.html It shows a small OCaml compiler program for System T (a simple total function...

While searching for information on Raymond Smullyan's To Mock a Mockingbird, I stumbled upon Stephen Tetley's Haskell code for the basic combinators. I thought it was an interesting idea and decide...

I now understand the type signature of s (s k): s (s k) :: ((t1 -> t2) -> t1) -> (t1 -> t2) -> t1 And I can create examples that work without error in the Haskell WinGHCi tool: E...

Consider this combinator: S (S K) Apply it to the arguments X Y: S (S K) X Y It contracts to: X Y I converted S (S K) to the corresponding Lambda terms and got this result: (\x y -> x ...

I was fiddling with combinators in JavaScript and was being proud of (hopefully) getting S to work when I stumbled upon Wikipedia saying: "The Y combinator can be expressed in the SKI-calculus...

I'm trying out a very light-weight encoding of combinator calculus in scala. Initially, I'm simply implementing the S and K combinators, application and constant values. Later I hope to lift scala ...