(import (algebraic-structures semigroup)
        (algebraic-structures monoid)
        (algebraic-structures group)
        (algebraic-structures monoid fold)
        (algebraic-structures list foldable))

(module (mod7 semigroup) = (algebraic-structures semigroup)
  (import scheme
          (chicken module)
          (chicken base))
  (export <>)

  (define (<> x y)
    (assert (integer? x))
    (assert (integer? y))
    (assert (not (zero? x)))
    (assert (not (zero? y)))
    (modulo (* x y) 7)))

(module (mod7 monoid) = (algebraic-structures monoid)
  (import scheme
          (chicken module)
          (chicken base))
  (reexport (mod7 semigroup))
  (export unit)

  (define unit 1))

(module (mod7 group) = (algebraic-structures group)
  (import scheme
          (chicken base)
          (chicken module)
          matchable)
  (reexport (mod7 monoid))
  (export inv)

  (define (inv n)
    (assert (integer? n))
    (assert (not (zero? n)))
    (match (modulo n 7)
      (1 1)
      (2 4)
      (3 5)
      (4 2)
      (5 3)
      (6 6))))

(module (mod7 fold) = ((algebraic-structures monoid fold) (mod7 monoid) (algebraic-structures list foldable)))

(import (prefix (mod7 group) mod7:)
        (prefix (mod7 fold) mod7:))