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The logical combinators that I know all have definitions in the untyped lambda calculus. Is there a typed variant of logical combinators?
by pklausler 6mo ago
The logical combinators that I know all have definitions in the untyped lambda calculus. Is there a typed variant of logical combinators?
- mercatop 6mo ago[dead]
- momentoftop 6mo agoMost of them have simple types and are easy to define in ML or Haskell. I : a -> a I x = x K : a -> b -> a K x y = x W : (a -> a -> b) -> a -> b W f x = f x x C : (a -> b -> c) -> b -> a -> c C f x y = f y x B : (a -> b) -> (c -> a) -> c -> b B f g x = f (g x) Q : (a -> b) -> (b -> c) -> a -> c Q f g x = g (f x) There are, however, combinators that do self-application (crucially used in the definition of the Y combinator) and these do not have simple types.