batonius / idris-fizzbuzz

Formally-proven FizzBuzz in Idris

Formally-proven FizzBuzz in Idris.

The fizzBuzz function accepts a non-zero natural number n and produces a vector of records with a Nat and a String fields along with the following properties proven at the compile time:

1. The vector has length exactly n, expressed in the vector itself.
2. The Nat field of the head element of the vector equals n, expressed as n = (i (safeHead nIsNotZP v)).
3. The vector is strictly ordered by the greater-than relation over the Nat fields of the elements, expressed as TotalOrderVect (FizzBuzzValueNatProp GT) v.
4. For every pair in the vector, the string field corresponds to the Nat field according to the FizzBuzz rules, expressed as All FizzBuzzProp v.

In other words, properties 1-3 guarantee the function produces the sequence n, (n-1)..1, while property 4 guarantees each element in the sequence has a valid String component. The final type signature of the fizzBuzz function looks like

fizzBuzz : (n : Nat) ->
           (nIsNotZP : Not (n = Z)) ->
           (v : Vect n FizzBuzzValue **
                (All FizzBuzzProp v,
                 n = (i (safeHead nIsNotZP v)),
                 TotalOrderVect (FizzBuzzValueNatProp GT) v))

To get a string from it you need something like the fizzBuzzDriver function:

fizzBuzzDriver : (n : Nat) -> Maybe String
fizzBuzzDriver n = case decEq n Z of
                        Yes _ => Nothing
                        No nIsNotZP => Just $ concatMap (++"\n") $
                                              reverse $
                                              map s $
                                              fst $
                                              fizzBuzz n nIsNotZP