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import Data.Monoid

-- This code doesn't work... 
-- How can you make a multi-parameter data type be Foldable?

-- foldMap over `a` so it can be converted to a Monoid
data BinaryTree3 a v
  = Node3 a (BinaryTree3 a v) (BinaryTree3 a v)
  | Leaf3 a v
  deriving (Show)

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Optics By Example Cheat Sheets

The following are appendices from Optics By Example, a comprehensive guide to optics from beginner to advanced! If you like the content below, there's plenty more where that came from; pick up the book!

• Operators
• Composition Guide
• Substitution Guide
• Optical Constarints and Types

Operator Cheat Sheet

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Our web applications are getting increasingly more complicated. They are becoming more distributed and increasingly powered by combinations of complex, constantly changing and large datasets. All while users are increasingly more connected and want the latest information instantly without any slow page loads or stale information.

To address this, developers have turned to layers of caching and single page applications so that there are layers of aggregated and preloaded state as close to the user as possible, to be immediately available when it is requested. This comes at a high cost: it is very difficult to invalidate or update those caches when the upstream information changes. This is especially problematic when the stale caches can accidentally cause real bugs rather than show stale data to users.

The big issue here is that we're not just caching expensive-to-compute static data. We are caching data that changes over time. There are a number of architectual patterns that can be applied, but to date, n

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• mount indicators
• install air filter
• install rear rack
• install braided fuel line
• install headlight protector
• mount spotlights
• install windscreen
• change oil filters
• install foam air filter
• adjust rear shock

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Response to https://peerj.com/preprints/826v1/

1.

The method is dubious with respect to the conclusion.

The researchers do not analyse the code using any formal
or even established reliable methods. Instead, the metric that is used is "look
to see if some *detected* bug, which was fixed *post-release*.

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Parametricity, or Theorems for Free

Say more by saying less. Learn how parametric types, when used in conjunction with an adequately strong type system, help the programmer comprehend code by invalidating candidate programs. Parametricity helps the programmer by enabling deduction of theories about what a program cannot do, sometimes to the point of leaving no ambiguity.

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import System.Environment
import System.IO
import Control.Monad (when)

matchGlob :: String -> String -> Bool
matchGlob = undefined

main :: IO ()
main = do
  args <- getArgs

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module Every where

import Control.Lens
import Control.Monad.Fix

-- |
--
-- >>> everyN 2 []
-- []
--

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hardCoreFunction a b c =
  let z = a + b
      k = b + c
  in 
      error "todo" z + k        -- this obviously type-checks

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object blah { 
  case class OptionT[F[_], A](x: F[Option[A]])
  
  trait Functor[F[_]]
  object Functor {
    implicit val OptionFunctor: Functor[Option] =
      sys.error("todo")
  }
  object OptionT {
    implicit def OptionTFunctor[F[_]: Functor]: Functor[({ type l[a] = OptionT[F, a] })#l] =