testing monoids with test.check

core_test.clj

(defn passes-monoid-props
  [f id a b c]
  (and (= (f (f a b) c) (f a (f b c)))  ;; associativity
       (= (f a id) a)   ;; identity element
       (= (f id a) a)))

(defspec plus-zero-are-monoid 100
  (prop/for-all [[a b c] (gen/vector gen/int 3)]
                (passes-monoid-props + 0 a b c)))

(defspec *-1-are-monoid 100
  (prop/for-all [[a b c] (gen/vector gen/int 3)]
                (passes-monoid-props * 1 a b c)))

(defspec concat-emptyvec-are-monoid 50
  (prop/for-all [[a b c] (gen/vector (gen/vector gen/any 5) 3)]
                (passes-monoid-props concat [] a b c)))

(defspec intersection-set-are-monoid 50
  (prop/for-all [[a b c] (gen/vector (gen/fmap set (gen/vector gen/any-printable 5))
                                     3)]
                (passes-monoid-props clojure.set/intersection a a b c)))

(defspec union-empty-set-are-monoid 50
  (prop/for-all [[a b c] (gen/vector (gen/fmap set (gen/vector gen/any-printable 5))
                                     3)]
                (passes-monoid-props clojure.set/union #{} a b c)))