zmactep

Alternative to the Church, Scott and Parigot encodings of data on the Lambda Calculus.

When it comes to encoding data on the pure λ-calculus (without complex extensions such as ADTs), there are 3 widely used approaches.

Church Encoding

The Church Encoding, which represents data structures as their folds. Using Caramel’s syntax, the natural number 3 is, for example. represented as:

0 c0 = (f x -> x)
1 c1 = (f x -> (f x))
2 c2 = (f x -> (f (f x)))

hediet

type StringBool = "true"|"false";


interface AnyNumber { prev?: any, isZero: StringBool };
interface PositiveNumber { prev: any, isZero: "false" };

type IsZero<TNumber extends AnyNumber> = TNumber["isZero"];
type Next<TNumber extends AnyNumber> = { prev: TNumber, isZero: "false" };
type Prev<TNumber extends PositiveNumber> = TNumber["prev"];

david-christiansen

module FizzBuzzC

%default total

-- Dependently typed FizzBuzz, constructively

-- A number is fizzy if it is evenly divisible by 3
data Fizzy : Nat -> Type where
  ZeroFizzy : Fizzy 0
  Fizz : Fizzy n -> Fizzy (3 + n)