Following standard definitions of Church-encoded natural numbers and lists represented as right folds, I want to write a function that takes a list of numbers as its argument and returns sum of its...

The following code is meant to print Church encoding of booleans as Haskell's Bool: {-#LANGUAGE FlexibleInstances #-} instance Show (t -> t -> t) where show b = show $ b True False Which...

Here is the sequential question after How to store data of a functional chain of Monoidal List? and Extracting data from a function chain without arrays and here I would like to express my respect ...

I am stuck up at the following step. It will be great if someone can help me out: 2 = λfx.f(f x) 3 = λfx.f(f(f x)) ADD = λm n f x. m f (n f x) My steps are: (λm n f x. m f (n f x)) (λf x.f(f(f...

Using Church encoding, it is possible to represent any arbitrary algebraic datatype without using the built-in ADT system. For example, Nat can be represented (example in Idris) as: -- Original ty...

OK, so I'm trying to implement the basics of lambda calculus. Here it goes. My numbers: def zero[Z](s: Z => Z)(z: Z): Z = z def one[Z](s: Z => Z)(z: Z): Z = s(z) def two[Z](s: Z => Z)(z:...

This is a literate haskell post. Simply save it as "ChurchList.lhs" to run it. > {-# LANGUAGE Rank2Types #-} A Church encoded list is a way of representing a list via a function. It resembles...

I am working through Software Foundations and am currently doing the exercises on Church numerals. Here is the type signature of a natural number: Definition nat := forall X : Type, (X -> X) -&...

Mind this program: {-# LANGUAGE RankNTypes #-} import Prelude hiding (sum) type List h = forall t . (h -> t -> t) -> t -> t sum_ :: (Num a) => List a -> a sum_ = \ list -> ...

I've been using the Free datatype in Control.Monad.Free from the free package. Now I'm trying to convert it to use F in Control.Monad.Free.Church but can't figure out how to map the functions. For...

I am working through SICP, and the problem 2.6 has put me in something of a quandary. In dealing with Church numerals, the concept of encoding zero and 1 to be arbitrary functions that satisfy cert...

I have not seen any mention of binary numerals in lambda calculus. Church numerals are unary system. I had asked a question of how to do this in Haskell here: How to implement Binary numbers in Has...

I have seen the following data constructor for Church numerals data Nat = Zero | Succ Nat deriving Show But this is unary numbers. How do we implement a data constructor for Binary numbers in H...

The dlist package contains the DList data type, which has lots of instances, but not Foldable or Traversable. In my mind, these are two of the most "list-like" type classes. Is there a performance ...

Or to be specific, why do we use foldr to encode lists and iteration to encode numbers? Sorry for the longwinded introduction, but I don't really know how to name the things I want to ask about so...

I'm playing with some lambda calculus stuff in Haskell, specifically church numerals. I have the following defined: let zero = (\f z -> z) let one = (\f z -> f z) let two = (\f z -> f (f ...

I had to implement the haskell map function to work with church lists which are defined as following: type Churchlist t u = (t->u->u)->u->u In lambda calculus, lists are encoded as f...

I'm attempting to implement church numerals in Haskell, but I've hit a minor problem. Haskell complains of an infinite type with Occurs check: cannot construct the infinite type: t = (t -> t1) ->...

Church encoding (aka Visitor Pattern) is a way of representing data as functions: instead of data T = C1 F1 F2 | C2 F3 F4 you can define data T = T (forall r. (F1 -> F2 -> r) -> (F3 -&...

I've been trying to work out how to implement Church-encoded data types in Scala. It seems that it requires rank-n types since you would need a first-class const function of type forAll a. a -> ...