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  1. let sum = \(l : List Natural) ->
  2. 	List/fold Natural l Natural (
  3.     	\(x : Natural) -> \(s : Natural) ->
  4.         x + s
  5.     ) 0
  6. let equals = \(a : Natural) -> \(b: Natural) ->
  7. 	let da = Natural/subtract b a
  8.     let db = Natural/subtract a b
  9.     in Natural/isZero (da + db)
  10. let filter = \(t : Type) -> \(p : t -> Bool) -> \(l : List t) ->
  11.     List/fold t l (List t) (
  12.     	\(x : t) -> \(xs : List t) ->
  13.        		xs # (if p x then [x] else [] : List t)
  14.    	) ([] : List t)
  15. let divides = \(b : Natural) -> \(a : Natural) ->
  16. 	True != Natural/isZero (Natural/fold a Natural (
  17.     	\(x : Natural) ->
  18.         	let d = Natural/subtract b x
  19.             let e = Natural/subtract x b
  20.             in if Natural/isZero (d + e) then x else d
  21.     ) a)
  22. let enumerate = \(n : Natural) ->
  23. 	let r = Natural/fold n {n : Natural, l : List Natural} (
  24.         \(x : {n : Natural, l : List Natural}) ->
  25.             {n = (x.n + 1), l = x.l # [x.n]}
  26.     ) ({n = 1, l = [] : List Natural})
  27.     in r.l
  28. let factor = \(n : Natural) -> filter Natural (\(x : Natural) -> divides x n) (enumerate n)
  29. let perfect = \(n : Natural) ->
  30. 	equals (sum (factor n)) (n * 2)
  31. in filter Natural perfect (enumerate 100)
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https://ideone.com/i0eDVG
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Text (text 6.10)
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1 year ago
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