Pavel Lepin pbl64k

## encodings.md

      
        
          
            
              
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                pbl64k
                / encodings.md
            
            
              Created
              June 8, 2018 09:08
                — forked from zmactep/encodings.md
            
              
                Number encodings
              
          
        
      
        
  
      
    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 -&gt; (f (f x)))