// joining of 2 arrows
(>>>) :: arr a b -> arr b c -> arr a c

         (>>>)
a -- (f) --> b -- (g) --> c

// works on pairs
// f: a -> b
// g: a -> c

    +---------> a -> (f) -> b
    |                        \
a ->|         (&&&)           +--> (b, c)
    |                        /
    +---------> a -> (g) -> c

(&&&) :: arr a b -> arr a c -> arr a (b,c)


// works on pairs
// f: a -> b
// g: c -> d

         +----------> a -> (f) -> b ---+
         |                             |
(a, c) ->|          (***)              +--> (b, d)
         |                             |
         +----------> c -> (g) -> d ---+

(***) :: arr a b -> arr c d -> arr (a,c) (b,d)


// works on pairs
// f: a -> c
// g: b -> c

           +------> a -> (f) -> c
           |
(a or b) ->|       (|||)
           |
           +------> b -> (g) -> c

(|||) :: arr a c -> arr b c -> arr (Either a b) c


// works on pairs
// f: a -> b
// g: c -> d

           +------> a -> (f) -> b
           |                     \
(a or c) ->|       (+++)          + -- (b or d)
           |                     /
           +------> c -> (g) -> d

(+++) :: arr a b -> arr c d -> arr (Either a c) (Either b d)


// works on pairs
// f: a -> b
// c

         +----------> a -> (f) -> b ---+
         |                             |
(a, c) ->|          (first)            +--> (b, c)
         |                             |
         +----------> c ---------------+

first :: arr a b -> arr (a,c) (b,c)



// works on pairs
// c
// f: a -> b

         +----------> c ---------------+
         |                             |
(c, a) ->|          (second)           +--> (c, b)
         |                             |
         +----------> a -> (f) -> b ---+

second :: arr a b -> arr (c,a) (c,b)