monad -is:module

Properties to check that the Monad m satisfies the monad properties

The program we need to crack. Note that different users get different programs on the Advent-Of-Code site, so this is simply one example. You can simply cut-and-paste your version instead. (Don't forget the pragma NegativeLiterals to GHC so add x -1 parses correctly as add x (-1).)

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions. Instances of Monad should satisfy the following:

• Left identity return a >>= k = k a
• Right identity m >>= return = m
• Associativity m >>= (\x -> k x >>= h) = (m >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

• pure = return

• m1 <*> m2 = m1 >>= (\x1 -> m2
  >>= (\x2 -> return (x1 x2)))

The above laws imply:

• fmap f xs = xs >>= return .
  f

• (>>) = (*>)

and that pure and (<*>) satisfy the applicative functor laws. The instances of Monad for List, Maybe and IO defined in the Prelude satisfy these laws.

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions. Instances of Monad should satisfy the following:

• Left identity return a >>= k = k a
• Right identity m >>= return = m
• Associativity m >>= (\x -> k x >>= h) = (m >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

• pure = return

• m1 <*> m2 = m1 >>= (\x1 -> m2
  >>= (\x2 -> return (x1 x2)))

The above laws imply:

• fmap f xs = xs >>= return .
  f

• (>>) = (*>)

and that pure and (<*>) satisfy the applicative functor laws. The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions. Instances of Monad should satisfy the following:

• Left identity return a >>= k = k a
• Right identity m >>= return = m
• Associativity m >>= (\x -> k x >>= h) = (m >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

• pure = return

• m1 <*> m2 = m1 >>= (x1 -> m2
  >>= (x2 -> return (x1 x2)))

The above laws imply:

• fmap f xs = xs >>= return .
  f

• (>>) = (*>)

and that pure and (<*>) satisfy the applicative functor laws. The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions. Instances of Monad should satisfy the following laws:

• return a >>= k = k a

• m >>= return = m

• m >>= (\x -> k x >>= h) = (m
  >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

• pure = return

• (<*>) = ap

The above laws imply:

• fmap f xs = xs >>= return .
  f

• (>>) = (*>)

and that pure and (<*>) satisfy the applicative functor laws. The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions. Instances of Monad should satisfy the following laws:

• return a >>= k = k a

• m >>= return = m

• m >>= (\x -> k x >>= h) = (m
  >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

• pure = return

• (<*>) = ap

The above laws imply:

• fmap f xs = xs >>= return .
  f

• (>>) = (*>)

and that pure and (<*>) satisfy the applicative functor laws. The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

Runs the property monad for IO-computations.

prop_cat msg = monadicIO $ do
(exitCode, stdout, _) <- run (readProcessWithExitCode "cat" [] msg)

pre (ExitSuccess == exitCode)

assert (stdout == msg)

>>> quickCheck prop_cat
+++ OK, passed 100 tests.

Runs the property monad for ST-computations.

-- Your mutable sorting algorithm here
sortST :: Ord a => [a] -> ST s (MVector s a)
sortST = thaw . fromList . sort

prop_sortST xs = monadicST $ do
sorted  <- run (freeze =<< sortST xs)
assert (toList sorted == sort xs)

>>> quickCheck prop_sortST
+++ OK, passed 100 tests.

Lift control operations, like exception catching, through monad transformers This package defines the type class MonadBaseControl, a subset of MonadBase into which generic control operations such as catch can be lifted from IO or any other base monad. Instances are based on monad transformers in MonadTransControl, which includes all standard monad transformers in the transformers library except ContT. See the lifted-base package which uses monad-control to lift IO operations from the base library (like catch or bracket) into any monad that is an instance of MonadBase or MonadBaseControl. Note that this package is a rewrite of Anders Kaseorg's monad-peel library. The main difference is that this package provides CPS style operators and exploits the RankNTypes and TypeFamilies language extensions to simplify and speedup most definitions.

A class of monads which can log messages. See README and Haddocks at https://www.stackage.org/package/monad-logger