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object ttypes { | |
type ->[+A, +B] = (A, B) | |
type PairOf[+A] = A -> A | |
type SumOf[+A] = A \/ A | |
trait Interpret[T[_[_]]] { | |
type ^[Outer[_], Inner[_]] = Outer[T[Inner]] | |
trait Transform[F[_], G[_]] { | |
type FTF = F[T[F]] | |
type GTG = G[T[G]] | |
/** Bottom-up transforms. */ | |
type GAlgebraicM[W[_], M[_]] = F[W ^ G] => M[G ^ G] | |
type AlgebraicM[M[_]] = F ^ G => M[G ^ G] // GAlgebraicM[Id, M] | |
type GAlgebraic[W[_]] = F[W ^ G] => G ^ G // GAlgebraicM[W, Id] | |
type Algebraic = F ^ G => G ^ G // GAlgebraicM[Id, Id] | |
/** Top-down transforms. */ | |
type GCoalgebraicM[N[_], M[_]] = F ^ F => M[G[N ^ F]] | |
type CoalgebraicM[M[_]] = F ^ F => M[G ^ F ] // GCoalgebraicM[Id, M] | |
type GCoalgebraic[N[_]] = F ^ F => G[N ^ F] // GCoalgebraicM[N, Id] | |
type Coalgebraic = F ^ F => G ^ F // GCoalgebraicM[Id, Id] | |
} | |
} | |
} |
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