Book of Monads

Description

In functional programming, at the heart of input/output, failure, state, logic, and much more, lies a powerful abstraction called monad. This book provides a journey from the very first concepts, to the myriad of monads available to programmers, down to the categorical foundations. Monads are key to unlocking many powerful patterns in functional programming. Alas, many developers struggle at first with the concept and the applications of monads. This books provides a full dive into the subject, including thorough explanations of adjacent concepts such as functors, monad transformers, final tagless, or extensible effects. Introduction Type Classes Higher-kinded Abstraction Haskell's Newtype Language Extensions in Haskell I What is a Monad? Discovering Monads State Contexts Magical Multiplying Boxes Both, Maybe? I Don't Think That's an Option Two for the Price of One Functors Better Notation Block Notation Pattern Matching and Fail Lifting Pure Functions Lift2, Lift3, ..., Ap Applicatives Applicative Style Definition Using Tuples Utilities for Monadic Code Lifted Combinators Traversables Interlude: Monad Laws Laws for Functions Monoids Monad Laws II More Monads Pure Reader-Writer-State Monads The State Monad The Reader Monad The Writer Monad All at Once: the RWS Monad Bi-, Contra-, and Profunctors Failure and Logic Failure with Fallback Logic Programming as a Monad Catching Errors Monads for Mutability Mutable References Interfacing with the Real World Resource Management and Continuations The Bracket Idiom Nicer Code with Continuations Early Release III Combining Monads Functor Composition Combining Monads by Hand Many Concepts Go Well Together But Monads Do Not A Solution: Monad Transformers Monadic Stacks Classes of Monads, MTL-style Parsing for Free! Generic Lifting and Unlifting MonadTrans and Lift Base Monads: MonadIO and MonadBase Lifting Functions with Callbacks More on Manipulating Stacks IV Rolling Your Own Monads Defining Custom Monads Introduction Final Style Initial Style Operational Style and Freer Monads Transforming and Inspecting Computations Composing Custom Monads Final Style Initial and Operational Style Extensible Effects Performance of Free Monads Left-nested Concatenation Left-nested Binds V Diving into Theory A Roadmap Just a Monoid! Quick Summary Categories, Functors, Natural Transformations Monoids in Monoidal Categories The Category of Endofunctors Adjunctions Adjoint Functors Monads from Adjunctions The Kleisli Category Free Monads Bibliography