lambda-calculus

I am trying to print church numerals in haskell using the definions: 0 := λfx.x 1 := λfx.f x Haskell code: c0 = \f x -> x c1 = \f x -> f x When I enter it in the haskell console I get an error which says test> c1 <interactive>:1:0: No instance for (Show ((t -> t1) -> t -> t1)) arising from a use of `print' at <interactive>:1:0-1 Possible fix: add an instance declaration for (Show ((t -> t1) -> t -> t1)) In a stmt of an interactive GHCi command: print it I am not able to exactly figure out what error says. Thank you! C. A. McCann The problem here is that, by default, it's not possible to print

I am trying to write a small compiler for a language that handles lambda calculus. Here is the ambiguous definition of the language that I've found: E → ^ v . E | E E | ( E ) | v The symbols ^, ., (, ) and v are tokens. ^ represents lambda and v represents a variable. An expression of the form ^v.E is a function definition where v is the formal parameter of the function and E is its body. If f and g are lambda expressions, then the lambda expression fg represents the application of the function f to the argument g. I'm trying to write an unambiguous grammar for this language, under the

Let those datatypes represent unary and binary natural numbers, respectively: data UNat = Succ UNat | Zero data BNat = One BNat | Zero BNat | End u0 = Zero u1 = Succ Zero u2 = Succ (Succ Zero) u3 = Succ (Succ (Succ Zero)) u4 = Succ (Succ (Succ (Succ Zero))) b0 = End // 0 b1 = One End // 1 b2 = One (Zero End) // 10 b3 = One (One End) // 11 b4 = One (Zero (Zero End)) // 100 (Alternatively, one could use `Zero End` as b1, `One End` as b2, `Zero (Zero End)` as b3...) My question is: is there any way to implement the function: toBNat :: UNat -> BNat That works in O(N) , doing only one pass through

I'm studying lambda calculus with the book "An Introduction to Functional Programming Through Lambda Calculus" by Greg Michaelson. I implement examples in Clojure using only a subset of the language. I only allow : symbols one-arg lambda functions function application var definition for convenience. So far I have those functions working : (def identity (fn [x] x)) (def self-application (fn [s] (s s))) (def select-first (fn [first] (fn [second] first))) (def select-second (fn [first] (fn [second] second))) (def make-pair (fn [first] (fn [second] (fn [func] ((func first) second))))) ;; def make