A natural-number fold iterates its first argument once per successor. For addition, iterate Succ starting at the other operand; for multiplication, iterate addition starting at zero; for exponentiation, iterate multiplication starting at one:
addF :: Natural -> Natural -> Natural
addF m n = foldNat Succ n m

mulF :: Natural -> Natural -> Natural
mulF m n = foldNat (addF n) Zero m

powerF :: Natural -> Natural -> Natural
powerF m n = foldNat (mulF m) (Succ Zero) n
The common identity is , with interpreted through convert. Substituting each step and seed reproduces the recursive arithmetic equations of part (b).

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