stepik.hs

data Nat = Zero | Suc Nat

fromNat :: Nat -> Integer
fromNat Zero = 0
fromNat (Suc n) = fromNat n + 1

add :: Nat -> Nat -> Nat                                                                                                
add Zero Zero = Zero                                                                                                    
add Zero n = n                                                                                                          
add n Zero = n                                                                                                          
add a (Suc n) = Suc (add a n)                                                                                           
                                                                                                                        
mul :: Nat -> Nat -> Nat                                                                                                
mul Zero n = Zero                                                                                                       
mul n Zero = Zero                                                                                                       
mul a (Suc Zero) = a                                                                                                    
mul (Suc Zero) a = a                                                                                                    
mul a (Suc n) = add a (mul a n)                                                                                         
                                                                                                                        
fac :: Nat -> Nat                                                                                                       
fac Zero = Zero                                                                                                         
fac (Suc Zero) = Suc Zero                                                                                               
fac k = facTimes k (Suc Zero) where                                                                                     
  facTimes Zero acc = acc                                                                                               
  facTimes x@(Suc n) acc = facTimes n (mul acc x)