monads

In the following Agda code, I have a term language based on de Bruijn indices. I can define substitution over terms in the usual de Bruijn indices way, using renaming to allow the substitution to proceed under a binder. module Temp where data Type : Set where unit : Type _⇾_ : Type → Type → Type -- A context is a snoc-list of types. data Cxt : Set where ε : Cxt _∷_ : Cxt → Type → Cxt -- Context membership. data _∈_ (τ : Type) : Cxt → Set where here : ∀ {Γ} → τ ∈ Γ ∷ τ there : ∀ {Γ τ′} → τ ∈ Γ → τ ∈ Γ ∷ τ′ infix 3 _∈_ data Term (Γ : Cxt) : Type → Set where var : ∀ {τ} → τ ∈ Γ → Term Γ τ 〈〉 :

I'm using sized types, and have a substitution function for typed terms which termination-checks if I give a definition directly, but not if I factor it via (monadic) join and fmap. {-# OPTIONS --sized-types #-} module Subst where open import Size To show the problem, it's enough to have unit and sums. I have data types of Trie and Term , and I use tries with a codomain of Term inside Term , as part of the elimination form for sums. data Type : Set where 𝟏 : Type _+_ : Type → Type → Type postulate Cxt : Set → Set -- Every value in the trie is typed in a context obtained by extending Γ. data

I have a function that computes sum of squares for numeric types as shown below. import cats.syntax.functor._ import cats.syntax.applicative._ import cats.{Id, Monad} import scala.language.higherKinds object PowerOfMonads { /** * Ultimate sum of squares method * * @param x First value in context * @param y Second value in context * @tparam F Monadic context * @tparam T Type parameter in the Monad * @return Sum of squares of first and second values in the Monadic context */ def sumOfSquares[F[_]: Monad, A, T >: A](x: F[A], y: F[A])(implicit num: Numeric[T]) : F[T] = { def square(value:T): T =

I understand (I think) that there is a close relationship between Either and Except in Haskell, and that it is easy to convert from one to the other. But I'm a bit confused about best practices for handling errors in Haskell and under what circumstances and scenarios I would choose one over the other. For example, in the example provided in Control.Monad.Except , Either is used in the definition type LengthMonad = Either LengthError so that calculateLength "abc" is Right 3 If instead one were to define type LengthMonad = Except LengthError then calculateLength "abc" would be ExceptT (Identity

I'd like to use it in my code and would rather not duplicate it, but since it involves only massively generic words like "function" or "composition" I can't find it by searching. To be completely specific, I'm looking for instance Functor (x->) where fmap f p = f . p This is the basic reader (or environment) monad, usually referred to as ((->) e) . (This is (e ->) written as a partially applied function instead of as a section; the latter syntax is problematic to parse.) You can get it by importing Control.Monad.Reader or Control.Monad.Instances . 来源： https://stackoverflow.com/questions

Here's the code I'm trying to understand (it's from http://apocalisp.wordpress.com/2010/10/17/scalaz-tutorial-enumeration-based-io-with-iteratees/ ): object io { sealed trait IO[A] { def unsafePerformIO: A } object IO { def apply[A](a: => A): IO[A] = new IO[A] { def unsafePerformIO = a } } implicit val IOMonad = new Monad[IO] { def pure[A](a: => A): IO[A] = IO(a) def bind[A,B](a: IO[A], f: A => IO[B]): IO[B] = IO { implicitly[Monad[Function0]].bind(() => a.unsafePerformIO, (x:A) => () => f(x).unsafePerformIO)() } } } This code is used like this (I'm assuming an import io._ is implied) def