monadplus

import Data.Kind (Type)

-- Let's proof that inequality relation forms a total order
-- i.e. reflexive, transitive, antisymmetric and total.
-- https://en.wikipedia.org/wiki/Inequality_(mathematics)#Formal_definitions_and_generalizations

type (<=) :: Nat -> Nat -> Type
data n <= m where
  ZLE :: Z <= m
  SLE :: m <= n -> S m <= S n

monadplus

import Control.Monad.Except
import Data.Generics.Product
import Data.Generics.Sum
import Data.Kind
import GHC.Generics

newtype Err1 = Err1 String
  deriving stock (Generic)

newtype Err2 = Err2 String

monadplus

readFile is problematic

System.IO.readFile/writeFile uses the default encoding of the system which may be problematic (see real world issue).

readFile is lazy by default:

• readFile "text" >>= writeFile "text" . map toUpper will fail (resource is busy) unless readFile is strict.
• Data.ByteString.Lazy.readFile closes the file after all bytes are read (which may never happen).
• System.IO.withFile closes it for you but it is dangerous e.g. withFile "input.txt" ReadMode hGetContents >>= write "output.txt" throws hGetContents: illegal operation (delayed read on closed handle)the file is closed before the data is actually read (the data is lazily read).

monadplus

{-# LANGUAGE DataKinds #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE TypeFamilies #-}
module Scratch where

import Data.Kind

data Protection = None | Password

monadplus

{-# LANGUAGE AllowAmbiguousTypes #-}
-- {-# LANGUAGE ApplicativeDo #-}
-- {-# LANGUAGE Arrows #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE BinaryLiterals #-}
-- {-# LANGUAGE BlockArguments #-}
-- {-# LANGUAGE CApiFFI #-}
-- {-# LANGUAGE ConstrainedClassMethods #-}
{-# LANGUAGE ConstraintKinds #-}
-- {-# LANGUAGE CPP #-}

monadplus

{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE DerivingVia #-}
{-# LANGUAGE DerivingStrategies #-}
{-# LANGUAGE DeriveFoldable #-}
{-# LANGUAGE DeriveFunctor #-}

import Data.Foldable

monadplus

Randomized Median Algorithm

Input: A set S of n elements over a totally ordered universe.

Output: The median element of S, denoted by m.

1. Pick a (multi-)set R of elements in S, chosen independently and uniformly at random with replacement.
2. Sort the set R.
3. Let d be the ()th smallest element in the sorted set R.
4. Let u be the ()th smallest element in the sorted set R.

monadplus

 _   _            _   _            _           _               _           _
| | | |          | | | |          (_)         | |             | |         | |
| | | |___  ___  | |_| |__   ___   _ _ __   __| | _____  __   | |    _   _| | _____
| | | / __|/ _ \ | __| '_ \ / _ \ | | '_ \ / _` |/ _ \ \/ /   | |   | | | | |/ / _ \
| |_| \__ \  __/ | |_| | | |  __/ | | | | | (_| |  __/>  < _  | |___| |_| |   <  __/
 \___/|___/\___|  \__|_| |_|\___| |_|_| |_|\__,_|\___/_/\_( ) \_____/\__,_|_|\_\___| https://use-the-index-luke.com/sql/
                                                          |/

Data is stored in heap with no order. Index are redundant data structures for fast lookup.

monadplus

                  _                            _
                 | |                          | |
  _ __   ___  ___| |_ __ _ _ __ ___  ___  __ _| |
 | '_ \ / _ \/ __| __/ _` | '__/ _ \/ __|/ _` | |
 | |_) | (_) \__ \ || (_| | | |  __/\__ \ (_| | |
 | .__/ \___/|___/\__\__, |_|  \___||___/\__, |_|
 | |                  __/ |                 | |
 |_|                 |___/                  |_|

monadplus

-- Common Table Expressions

-- : Problem

-- 1) For each film count the number of actors starring in it
SELECT f.id, count(*) as actors FROM films f LEFT JOIN films_actors fa ON f.id = fa.film_id GROUP BY f.id;

-- 2) For each film, #actors, its prequel and sequel count number of actors starring in them.
SELECT films.id, films.prequel_id, films.sequel_id,
films.actors AS actors,