Monad

lastmod 2025-08-05created 2016-07-1915 edits

Comment

A functor preserves the meaning of the existing context. Using the example above, if a functor wraps a String type into an Int type, the result is also an Int type. It cannot convert to a different type.

A monad, on the other hand, can convert to a different type. It can wrap a String type into an Int type, apply it to an operation (or function), and then output the result as a Double type.

In a sense, a monad can be said to play a role similar to a cast in C.

Monad Laws

• 12.3.4. Monad Laws · Functional Programming in OCaml
• Scala:Monad#Monad Laws - Monad Laws in Scala

Comparing the monad approaches of Haskell and OCaml

• Comparing the monad approaches of Haskell and OCaml | GeekNews
  • [Original] Hackers' Pub - Monads: Beyond Simple Analogies—Reflections on Functional Programming Paradigms

Monads in Haskell: elegant abstraction

• Monads are a powerful abstraction tool, not merely a concept similar to Promise
• Code reuse across various contexts (Maybe, [], IO, State) through the Monad type class
• Generic functions (e.g., sequence, mapM) usable with any monad
• do notation enables highly readable code
• Consistently expresses diverse computational contexts with a single pattern

OCaml's different approach: pragmatism

• Uses the module system and functors instead of type classes
• Lack of syntactic support (e.g., do notation) makes monadic code more verbose
• Direct side effects are allowed, so monads are not essential
• Prefers direct use of option and result types and module-level abstraction
• Enables code that is easy to understand locally

Differences in language design philosophy

• Haskell: purely functional, so monads are essential for managing effects
• OCaml: allows side effects, enabling more direct code
• Philosophical differences about abstraction, explicitness, and the role of the type system
• Haskell emphasizes consistency and abstraction; OCaml emphasizes clarity and practicality

Concluding view

• Haskell's consistent abstraction is especially appealing in complex systems
• OCaml's direct approach is useful where immediate understanding matters
• Type classes and syntactic support enable especially elegant code structuring in Haskell
• Both approaches have their own merits, and the right choice depends on the situation

See also

• Haskell
  • Control.Monad.IO.Class
• Scala
• Functional programming

Favorite site

• [Recommended] Functor, Monad & Arrow concepts, my own way
• What is a Monad
• Monad horror stories - Kinoru - November 14, 2015
• Monads explained for beginner-to-intermediate Scala users (1)
• [Recommended] Monad Programming with Scala Future ¹
• 1 Understanding monads - WikibooksHaskell
• Samsung Tech Blog - Learning the concept of monads with Rust

References