## Applicative: The Forgotten Functional Pattern ## +23 ## BEN DEANE ## 20 23 October 01 - 06 ## APPLICATIVE THE FORGOTTEN FUNCTIONAL PATTERN  for functor and monad • Where applicative fits ## FIRST, A QUICK SURVEY ## FIRST, A QUICK SURVEY • I've heard of these functional patterns I've written code that uses them, and it was good • I completely understand a) functors b) monads c) applicative ## FIRST, A QUICK SURVEY • I've heard of these functional patterns, but that's

Records 18 4 Type Classes 21 4.1 Default Definitions 21 4.2 Extending Classes 22 4.3 Functors and Applicatives 23 4.4 Monads and do-notation 23 4.5 Idiom brackets 25 4.6 Named Instances Integer Having defined Functor, we can define Applicative which abstracts the notion of function application: infixl 2 <** class Functor f => Applicative (f : Type -> Type) where pure : a -> do-notation introduced in Section "do" notation. It extends Applicative as defined above, and is defined as follows: class Applicative m => Monad (m : Type -> Type) where (>>=) : m a ->

Expressions 19 4 Type Classes 21 4.1 Default Definitions 21 4.2 Extending Classes 22 4.3 Functors and Applicatives 23 4.4 Monads and do-notation 23 4.5 Idiom brackets 25 4.6 Named Instances Integer Having defined Functor, we can define Applicative which abstracts the notion of function application: infixl 2 <** class Functor f => Applicative (f : Type -> Type) where pure : a -> do-notation introduced in Section "do" notation. It extends Applicative as defined above, and is defined as follows: class Applicative m => Monad (m : Type -> Type) where (>>=) : m a ->

first pass, and elaborates the method types and any default definitions on the second pass. ### 4.3 Functors and Applicatives So far, we have seen single parameter interfaces, where the parameter is of type Having defined Functor, we can define Applicative which abstracts the notion of function application: infixl 2 <*> interface Functor f => Applicative (f : Type -> Type) where pure : a -> do-notation introduced in Section “do” notation (page 14). It extends Applicative as defined above, and is defined as follows: interface Applicative m => Monad (m : Type -> Type) where (>>=) : m a ->

first pass, and elaborates the method types and any default definitions on the second pass. ### 4.3 Functors and Applicatives So far, we have seen single parameter interfaces, where the parameter is of type Having defined Functor, we can define Applicative which abstracts the notion of function application: infixl 2 <*> interface Functor f => Applicative (f : Type -> Type) where pure : a -> introduced in Section "do" notation (page 14). It extends Applicative as defined above, and is defined as follows: interface Applicative m => Monad (m : Type -> Type) where (>>=) : m a ->

Bloomberg Engineering ## What is a Monad actually? Let's Start with Functors TechAtBloomberg.com Bloomberg ## What's a functor?  functors? — Are std::array, std::vector functors? — etc. • Boost.Hana achieves this via Functor / Monad (and a few other) concepts Appendix A.1: Optional Functor Laws Adopted to C++ from http://learnyouahaskell.com/functors-applicative-functors-and-monoids 01: int val = 1; 02: std::optional myOpt {val}; 03: 04: // LAW 1: Identity

sortAndShow : (Ord a, Show a) => List a -> String sortAndShow xs = show (sort xs) #### 1.4.3 Functors and Applicatives So far, we have seen single parameter interfaces, where the parameter is of type List Integer Having defined Functor, we can define Applicative which abstracts the notion of function application: interface Functor f => Applicative (f : Type -> Type) where pure : a -> f a (<*>) do-notation introduced in Section “do” notation (page 12). It extends Applicative as defined above, and is defined as follows: interface Applicative m => Monad (m : Type -> Type) where (>>=) : m a ->

first pass, and elaborates the method types and any default definitions on the second pass. 1.4.3 Functors and Applicatives So far, we have seen single parameter interfaces, where the parameter is of type Functor, we can define Applicative which abstracts the notion of function application: 24 CHAPTER 1. THE IDRIS TUTORIAL v1.2.0 infixl 2 <*> interface Functor f => Applicative (f : Type -> Type) where do-notation introduced in Section “do” notation (page 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)

first pass, and elaborates the method types and any default definitions on the second pass. ## Functors and Applicatives So far, we have seen single parameter interfaces, where the parameter is of type Having defined Functor, we can define Applicative which abstracts the notion of function application: infixl 2 <*> interface Functor f => Applicative (f : Type -> Type) where pure : a -> do-notation introduced in Section “do” notation (page 13). It extends Applicative as defined above, and is defined as follows: interface Applicative m => Monad (m : Type -> Type) where (>>=) : m a ->

first pass, and elaborates the method types and any default definitions on the second pass. ## Functors and Applicatives So far, we have seen single parameter interfaces, where the parameter is of type Having defined Functor, we can define Applicative which abstracts the notion of function application: infixl 2 <*> interface Functor f => Applicative (f : Type -> Type) where pure : a -> do-notation introduced in Section “do” notation (page 13). It extends Applicative as defined above, and is defined as follows: interface Applicative m => Monad (m : Type -> Type) where (>>=) : m a ->