さらにF#でhistomorphism/futumorphism

前回および前々回の投稿に引き続いて。
正直問題ないのかよく分かりませんな。具体例を当てはめてやらないとダメですね。

// 前回および前々回の定義を前提としています。

type ProdF<'c,'a,'x> =
    | ProdF of 'a * F<'x>
    interface F<'c> with
        member x.fmap f p =
            let rec fmap0 (f:'b -> 'd) (p : F<'b>) =
                match p :?> ProdF<'b,'a,'y> with
                | ProdF(a, fx) -> ProdF(a, fmap0 f fx) :> F<'d>
            fmap0 f p

let forkF f g x =
    ProdF(x |> fork f g)

let hdCV (xs : Nu<ProdF<'c,'a,'x>>) =
    match (out xs) :?> ProdF<Nu<ProdF<'c,'a,'x>>,'a,'x> with
    | ProdF(c, _) -> c

let tlCV (xs : Nu<ProdF<'c,'a,'x>>) =
    match (out xs) :?> ProdF<Nu<ProdF<'c,'a,'x>>,'a,'x> with
    | ProdF(_, fx) -> fx

let rec histo phi x =
    let y = unIn x
    y
    |> y.fmap (ana (fun z -> (forkF (histo phi) unIn z) :> F<Mu<'c>>))
    |> phi

type SumF<'c,'a,'x> =
    | SumF of Sum<'a, F<'x>>
    interface F<'c> with
        member x.fmap f p =
            let rec fmap0 (f:'b -> 'd) (p : F<'b>) =
                match p :?> SumF<'b,'a,'b> with
                | SumF(InL(a)) -> SumF(InL(a)) :> F<'d>
                | SumF(InR(x)) -> SumF(InR(fmap0 f x)) :> F<'d>
            fmap0 f p

let joinF f g s =
    match s with
    | SumF s0 -> join f g s0

let lastF (x : 'a) : Mu<SumF<'c,'a,'x>> = In (SumF (InL x))

let consF (x : F<Mu<SumF<'c,'a,'x>>>) : Mu<SumF<'c,'a,'x>> = In (SumF (InR x))

let rec futu (phi : 'a -> F<Mu<SumF<'c,'a,'x>>>) (x : 'a) = 
    let y = phi x
    y
    |> y.fmap (cata (fun z -> (joinF (futu phi) Wrap) (z :?> SumF<Nu<'a>,'a,Nu<'a>>)))
    |> Wrap