pure : a -> f a (<*>) : f (a -> b) -> f a -> f b ## Monads and do-notation The Monad interface allows us to encapsulate binding and computation, and is the basis of do-notation introduced It extends Applicative as defined above, and is defined as follows: interface Applicative m => Monad (m : Type -> Type) where (>>=) : m a -> (a -> m b) -> m b Inside a do block, the becomes let x = v in e IO has an implementation of Monad, defined using primitive functions. We can also define an implementation for Maybe, as follows: Monad Maybe where Nothing >>= k = Nothing (Just

Begin Life on My Own Account, and Don't Like It • Refresher (or introduction) for functor and monad • Where applicative fits ## FIRST, A QUICK SURVEY ## FIRST, A QUICK SURVEY • I've heard of these b) -> f a -> f b "class template" "value type" ## REVIEW: (?) MONADS A monad is also a parameterized type (a class template) of one (free) argument. Some examples of monads: only Functor and Monad. Functor and Monad classes first appeared in Haskell in the Haskell Report 1.3, May 1996. IO, [] and Maybe were both Functors and Monads at this time. Functor Monad ## HISTORY OF

1 The option monad 24 4.2 The list monad 25 4.3 The state monad 26 4.4 The IO monad 29 4.5 Related type classes 29 5 Writing Tactics 31 5.1 A First Look at the Tactic Monad 31 5.2 Names input and output. # MONADS In this chapter, we will describe a powerful abstraction known as a monad. A monad is a type constructor m : Type $ \rightarrow $ Type that comes equipped with two special operations “virtual $ \alpha $ ,” or, as some people describe it, “an $ \alpha $ inside a box.” For a given monad m, the function return has type $ \Pi\{\alpha:Type\} $ , $ \alpha\to m\alpha $ . The idea is that

3 The Read and Show Classes 77 6.3.4 The Enum Class 79 6.3.5 The Functor Class 80 6.3.6 The Monad Class 80 6.3.7 The Bounded Class 81 6.4 Numbers 81 ## CONTENTS 6.4.1 Numeric Literals ..... 82 I/O Functions ..... 87 7.2 Sequencing I/O Operations ..... 89 7.3 Exception Handling in the I/O Monad ..... 90 8 Foreign Function Interface ..... 91 8.1 Foreign Languages ..... 91 8.2 Contexts Haskell 2010 Libraries 153 13 Control.Monad 155 13.1 Functor and monad classes 155 13.2 Functions 157 13.2.1 Naming conventions 157 13.2.2 Basic Monad functions 157 13.2.3 Generalisations of

Bloomberg ## What is a monad? “A monoid in the category of endofunctors” ### TechAtBloomberg.com © 2023 Bloomberg Finance L.P. All rights reserved. ## Bloomberg ## The curse of the monad “In addition to to its being good and useful, it’s also cursed and the curse of the monad is that once you get the epiphany, once you understand - “oh that’s what it is” - you lose the ability to explain it to anybody else 2023 Bloomberg Finance L.P. All rights reserved. Bloomberg Engineering ## Monad: a definition In functional programming, a monad is a structure that combines program fragments (functions) and wraps their

106 7 Metaprogramming 109 7.1 Tactics and Tactic Combinators 110 7.2 The Metaprogramming Monad 113 7.3 Names, Expressions, Declarations, and Environments 116 7.4 First Example: A Conjunction-Destructuring side effects, exceptions, nondeterminism, and other effects. The underlying abstraction is called monad. Monads generalize programs with side effects. They are popular in Haskell to write imperative programs Operations and Three Laws The option type constructor is an example of a monad, called the option monad. In general, a monad is a unary type constructor m : Type $ \rightarrow $ Type that depends on

-> f a (<*>) : f (a -> b) -> f a -> f b #### 1.4.4 Monads and do-notation The Monad interface allows us to encapsulate binding and computation, and is the basis of do-notation introduced It extends Applicative as defined above, and is defined as follows: interface Applicative m => Monad (m : Type -> Type) where (>>=) : m a -> (a -> m b) -> m b Inside a do block, the becomes let x = v in e IO has an implementation of Monad, defined using primitive functions. We can also define an implementation for Maybe, as follows: Monad Maybe where Nothing >>= k = Nothing (Just

-> Type) where pure : a -> f a (<*>) : f (a -> b) -> f a -> f b 1.4.4 Monads and do-notation The Monad interface allows us to encapsulate binding and computation, and is the basis of do-notation introduced 13). It extends Applicative as defined above, and is defined as follows: interface Applicative m => Monad (m : Type -> Type) where (>>=) : m a -> (a -> m b) -> m b Inside a do block, the following syntactic becomes let x = v in e IO has an implementation of Monad, defined using primitive functions. We can also define an implemen- tation for Maybe, as follows: Monad Maybe where Nothing >>= k = Nothing (Just x) >>=

pure : a -> f a (<*>) : f (a -> b) -> f a -> f b ## Monads and do-notation The Monad interface allows us to encapsulate binding and computation, and is the basis of do-notation introduced It extends Applicative as defined above, and is defined as follows: interface Applicative m => Monad (m : Type -> Type) where (>>=) : m a -> (a -> m b) -> m b Inside a do block, the becomes let x = v in e IO has an implementation of Monad, defined using primitive functions. We can also define an implementation for Maybe, as follows: Monad Maybe where Nothing >>= k = Nothing (Just

pure : a -> f a (<*>) : f (a -> b) -> f a -> f b ## Monads and do-notation The Monad interface allows us to encapsulate binding and computation, and is the basis of do-notation introduced It extends Applicative as defined above, and is defined as follows: interface Applicative m => Monad (m : Type -> Type) where (>>=) : m a -> (a -> m b) -> m b Inside a do block, the becomes let x = v in e IO has an implementation of Monad, defined using primitive functions. We can also define an implementation for Maybe, as follows: Monad Maybe where Nothing >>= k = Nothing (Just