Due to laziness, Haskell types are both inductive and coinductive, or, there is no formal distinguishment between data and codata. All recursive types can contain an infinite nesting of constructors. In languages such as Idris, Coq, Agda, etc. a definition like ones = 1 : ones is rejected by the termination checker. Laziness means that … Read more
Clojure STM has 3 big unique features: Implements MVCC snapshot avoiding transactions restarts on read invalidation. Ensures references on read-writes provides a kind of manual control over resource acquisition order. Has explicit commute which reduces retries on commutative writes.
cabal repl –ghc-option=’-package xyz’ This will load the package you are calling cabal repl from and the package xyz. To do that after the fact, i.e. when you’re already in the REPL and want to load an extra helper module from another package: GHCi> :set -package xyz GHCi> :m +XYZ.Module.You.Suddenly.Need
Why I shouldn’t do something simple and only defining functions without defining new data types and typeclasses (with their instances). Why indeed? You could just define: checkState :: (a -> Bool) -> (a -> b) -> (a -> b) -> a -> b checkState is_repairable repairs destroy a = if (is_repairable a) then repairs a … Read more
The canonical way to do recursion with pure lambda expressions is to use a fixpoint combinator, which is a function with the property fixpoint f x = f (fixpoint f) x If we assume that such a combinator exists, we can write the recursive function as factorial = fixpoint (\ff n -> if n == … Read more
The key to understanding applicative functors is to figure out what structure they preserve. Regular functors preserve the basic categorical structure: they map objects and morphisms between categories, and they preserve the laws of the category (associativity and identity). But a category may have more structure. For instance, it may allow the definition of mappings … Read more
Here’s the functor class: class Functor f where fmap :: (a -> b) -> f a -> f b Note that “f” by itself is a type constructor because it’s applied to a type variable in the fmap line. Here are some examples to make this clear: Type constructors: IO Maybe Either String Types: IO … Read more
Well how about that! It turns out if you just type 1/0 it returns Infinity! On ghci: Prelude> 1/0 Infinity Prelude> :t 1/0 1/0 :: (Fractional t) => t Prelude> let inf=1/0 Prelude> filter (>=inf) [1..] and then of course it runs forever, never finding a number bigger than infinity. (But see ephemient’s comments below … Read more
The following is a stunt, but it’s quite a safe stunt so do try it at home. It uses some of the entertaining new toys to bake order invariants into mergeSort. {-# LANGUAGE GADTs, PolyKinds, KindSignatures, MultiParamTypeClasses, FlexibleInstances, RankNTypes, FlexibleContexts #-} I’ll have natural numbers, just to keep things simple. data Nat = Z | … Read more
FWIW, have a look at https://github.com/leepike/SmartCheck, which claims to derive better shrinks than one can usually do manually.