It I Begin Life on My Own Account, and Don't Like It Refresher (or introduction) for functor and monad Where applicative �ts 5FIRST, A QUICK SURVEY FIRST, A QUICK SURVEY 6FIRST, A QUICK SURVEY FIRST HASKELL SIGNATURES HOW TO READ HASKELL SIGNATURES 11REVIEW: (?) MONADS REVIEW: (?) MONADS A monad is A monad is also also a parameterized type (a class template) of one (free) argument. a parameterized has only Functor and Monad. At �rst, Haskell has only Functor and Monad. Functor and Monad classes �rst appeared in Haskell in the Haskell Report 1.3, May 1996. Functor and Monad classes �rst appeared

. . . . . . 20 4 Monads 23 4.1 The option monad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.2 The list monad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.3 The state monad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.4 The IO monad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 5 Writing Tactics 31 5.1 A First Look at the Tactic Monad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.2 Names and Expressions .

Functor Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 6.3.6 The Monad Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 6.3.7 The Bounded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 7.3 Exception Handling in the I/O Monad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 8 Foreign Function Interface 91 8.1 . . . . . . . . . . . . . . . . 152 II The Haskell 2010 Libraries 153 13 Control.Monad 155 13.1 Functor and monad classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 13

What is a monad? “A monoid in the category of endofunctors” 5© 2018 Bloomberg Finance L.P. All rights reserved. © 2023 Bloomberg Finance L.P. All rights reserved. The curse of the monad “In addition addition 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 All rights reserved. © 2023 Bloomberg Finance L.P. All rights reserved. Monad: a definition In functional programming, a monad is a structure that combines program fragments (functions) and wraps their

and Tactic Combinators . . . . . . . . . . . . . . . . . . . . . . . 110 7.2 The Metaprogramming Monad . . . . . . . . . . . . . . . . . . . . . . . 113 7.3 Names, Expressions, Declarations, and Environments side efects, exceptions, nondetermin- ism, and other efects. The underlying abstraction is called monad. Monads generalize programs with side efects. 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 → Type that depends on some type parameter

-> Type) where pure : a -> f a (<*>) : f (a -> b) -> f a -> f b 4.4 Monads and do-notation The Monad class allows us to encapsulate binding and computation, and is the basis of do-notation introduced notation. It extends Applicative as defined above, and is defined as follows: class 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 is an instance of Monad, defined using primitive functions. We can also define an instance for Maybe, as follows: instance Monad Maybe where Nothing >>= k = Nothing (Just x)

-> Type) where pure : a -> f a (<*>) : f (a -> b) -> f a -> f b 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 following syntactic 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 x)

-> Type) where pure : a -> f a (<*>) : f (a -> b) -> f a -> f b 4.4 Monads and do-notation The Monad class allows us to encapsulate binding and computation, and is the basis of do-notation introduced notation. It extends Applicative as defined above, and is defined as follows: class 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 is an instance of Monad, defined using primitive functions. We can also define an instance for Maybe, as follows: instance Monad Maybe where Nothing >>= k = Nothing (Just x)

Programming in C++ CppCon 2024-09-19 78Monad C++ Definition A monad is a type that implements the operations .transform .and_then .join together with some way to build a monad from a value. Jonathan Müller Programming in C++ CppCon 2024-09-19 79Monad C++ Definition A monad is a type that implements the operations .transform .and_then .join together with some way to build a monad from a value. Monads enable

inference can be used to infer monads associated with specific types. Lean knows about the option monad: open list def foo (l1 l2 l3 : list N) : option (list N) := do v10 ← nth l1 0, v20 ← nth l2 0, on the last line and returns it wrapped with the some constructor. Lean also knows about the list monad: open list def foo : list string := do n ← range 10, a ← ["a", "b", "c", "d", "e", "f", "g", "h" results are concatenated into a single list. The standard library also defines a state monad, and a special tactic monad provides metaprogramming access to an internal tactic state, allowing users to write