from (co)monad to (co)monoid

mon.fs

type IntG<'a> = IntG of int * 'a

let fmap f (IntG(i,v)) : IntG<_>= IntG(i,f v)

let mzeroInt32 = 0
let mappendInt32 a b = a + b
let destroyInt32 a = ()
let pairInt32 a = (a,a)
//monad
let ret x = IntG(mzeroInt32, x)
let join (IntG(i,IntG(i2,v))) = IntG(mappendInt32 i i2,v)
let bind v f = join (fmap f v)  
let (>>=) a b = bind a b
let fmapM ab ma = ma >>= (ret << ab)
//comonad
let extract (IntG(i,a)) = destroyInt32 i
                          a
let rec extend (f:(IntG<'a> -> 'b)) (c:IntG<'a>) =
    let (IntG(i,v)) = c
    let i,i1 = pairInt32 i
    IntG(i, f(IntG(i,v)))

let fmapC f = extend (f << extract)
let duplicate c = extend id c

type Int = IntG<unit>

//from monad to monoid 
let mzero () : Int = ret () 
let mappend a : Int = join a
//from comonad to comonoid
let destroy x : unit = extract x 
let pair (x: Int) = duplicate x

type DoubleInt = IntG<int>
let mzero2 () : DoubleInt = ret mzeroInt32 
let mappend2 a : DoubleInt = join a