Monoid

The lambda calculus is a foundational mathematical framework for studying functions. It forms the bedrock of functional programming, offering a powerful and elegant way to define and manipulate functions. Emacs Lisp, a dialect of Lisp heavily used within the Emacs editor, offers a flexible environment for exploring these concepts. In this article, we’ll embark on a journey to understand how the lambda calculus is expressed within Emacs Lisp, using illustrative examples to highlight the core concepts. ...

Overview Endo can be used as a form of composition by concating functions. In this concatination functions results are fed into the concatted function. The value is fed into Endo’s run function providing opportunities for lazy operations. I’m purposely being extremely explicit because I make to make sure that I understand each step of these functional implementations. ## Examples Example 1 // Endo monoid declaration // Endo :: (a -> a) -> Endo a const Endo = run => ({ run, // concat :: Endo a -> Endo a -> Endo a concat: other => Endo(x => run(other.run(x))) }) // Endo.empty :: () -> Endo a Endo.empty = () => Endo(x => x) // List monad for putting functions into a list. // List :: [a] -> List a const List = list => ({ list, // map :: (a -> b) -> List a -> List b map: fn => List(list.map(fn)), // fold :: ((b, a) -> b, b) -> List a -> List b fold: (fn, initialValue) => List(list.reduce(fn, initialValue)), // foldMap :: (a -> b) -> b -> List a -> b foldMap: (monoid, empty) => { return empty != null ? list.reduce((acc, x, i) => acc.concat(monoid(x, i)), empty) : list.map(monoid).reduce((acc, x) => acc.concat(x)) }, // extract :: () -> [a] extract: () => list, }) // Utility functions // compose :: (b -> c) -> (a -> b) -> a -> c const compose = f => g => x => f(g(x)) // curry :: ((a, b) -> c) -> a -> b -> c const curry = f => a => b => f(a, b) // toUpper :: String -> String const toUpper = str => str.toUpperCase() // exclaim :: String -> String const exclaim = str => `${str}!!` // to OrgHeader :: String -> String const toOrgHeader = str => `* ${str}` // toOrgTagList :: [String] -> String const toOrgTagList = xs => List(xs) .map((tag, index) => !index ? `:${tag}:` : `${tag}:` ) .fold((accumalator,tag, index) => accumalator.concat(tag) ,'') .extract() // Tag list for header const tags = ['javascript', 'completed', 'moved'] // addTagsToHeader :: [String] -> String -> String const addTagsToHeader = curry((tagList,str) => `${str} ${tagList}`) console.log(addTagsToHeader(toOrgTagList(tags))("A Header")) const result = List([addTagsToHeader(toOrgTagList(tags)),toOrgHeader, toUpper, exclaim]).foldMap(Endo, Endo.empty('')).run('hello') //> A Header :javascript:completed:moved: console.log(result) //> HELLO!! :javascript:completed:moved: