The first thing to realize about the continuation monad is that, fundamentally, it’s not really doing anything at all. It’s true! The basic idea of a continuation in general is that it represents the rest of a computation. Say we have an expression like this: foo (bar x y) z. Now, extract just the parenthesized … Read more
Continuations can be modelled as monads, using CPS, but they are not algebraic effects as they cannot be modelled using Lawvere theories. See Martin Hyland and John Power, 2007, The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads (pdf), ENTCS 172:437-458.
The s keeps objects inside the ST monad from leaking to the outside of the ST monad. — This is an error… but let’s pretend for a moment… let a = runST $ newSTRef (15 :: Int) b = runST $ writeSTRef a 20 c = runST $ readSTRef a in b `seq` c Okay, … Read more
You’ll get the point of Option better if you force yourself to never, ever, use get. That’s because get is the equivalent of “ok, send me back to null-land”. So, take that example of yours. How would you call display without using get? Here are some alternatives: getPerson2 foreach (_.display) for (person <- getPerson2) person.display … Read more
Edit: Just for fun, I’m going to do this right. Original answer preserved below The current adjunction code for category-extras now is in the adjunctions package: http://hackage.haskell.org/package/adjunctions I’m just going to work through the state monad explicitly and simply. This code uses Data.Functor.Compose from the transformers package, but is otherwise self-contained. An adjunction between f … Read more
Consider this monad which is isomorphic to the (Bool ->) monad: data Pair a = P a a instance Functor Pair where fmap f (P x y) = P (f x) (f y) instance Monad Pair where return x = P x x P a b >>= f = P x y where P x … Read more
Just FYI: The proposed JDK8 Optional class does satisfy the three Monad laws. Here’s a gist demonstrating that. All it takes be a Monad is to provide two functions which conform to three laws. The two functions: Place a value into monadic context Haskell’s Maybe: return / Just Scala’s Option: Some Functional Java’s Option: Option.some … Read more
A bunch of them are almost completely equivalent: mtl uses GHC extensions, but transformers is Haskell 98. monads-fd and monads-tf are add-ons to transformers, using functional dependencies and type families respectively, both providing the functionality in mtl that’s missing from transformers. mtl-tf is mtl reimplemented using type families. So essentially, mtl == transformers ++ monads-fd, … Read more
TL;DR go directly to the final example I’ll try and recap. Definitions The for comprehension is a syntax shortcut to combine flatMap and map in a way that’s easy to read and reason about. Let’s simplify things a bit and assume that every class that provides both aforementioned methods can be called a monad and … Read more
The State Monad : a model of mutable state The State monad is a purely functional environment for programs with state, with a simple API: get put Documentation in the mtl package. The State monad is commonly used when needing state in a single thread of control. It doesn’t actually use mutable state in its … Read more