Interpreting types as abstract values [The Abstract of the lecture notes] We expound a view of type checking as evaluation with `abstract values'. Whereas dynamic semantics, evaluation, deals with (dynamic) values like 0, 1, etc., static semantics, type checking, deals with approximations like int. A type system is sound if it correctly approximates the dynamic behavior and predicts its outcome: if the static semantics predicts that a term has the type int, the dynamic evaluation of the term, if it terminates, will yield an integer. As object language, we use simply-typed and let-polymorphic lambda calculi with integers and integer operations as constants. We use Haskell as a metalanguage in which to write evaluators, type checkers, type reconstructors and inferencers for the object language.
One obvious solution is to do two passes -- one to lay everything out, then another to generate now that offsets are known.Here's where it gets clever. Rather than two passes, they instead write the code in such a way that the code-generator function's output is also passed as a parameter to the same function.
In denotational semantics and functional programming, the terms monad morphism, monad layering, monad constructor, and monad transformer have by now accumulated 20 years of twisted history. The exchange between Eric Kidd and sigfpe about the probability monad prompted me to investigate this history
Once you start thinking about structuring your code to use Option in languages which have built-in support for it, you’ll find yourself dreaming about such patterns in other, less fortunate languages. It’s really sort of bizarre how much this little device can open your mind to new possibilities. Take my code, and give it a try in your project. Better yet, implement something on your own which solves the problem more elegantly! The stodgy old Java “best practices” could use a little fresh air. P.S. Yes, I know that the original implementation of this was actually the Maybe monad in Haskell. I picked Option instead mainly because a) I like the name better, and b) it’s Scala, so it’s far more approachable than Haskell.
emir burak In Informatics, there are two (related) meanings of the word "monad": * A triple (T,eta,mu) following some laws in category theory * A way of structuring functional programs The first meaning can probably not be described easily in natural language. Michael Arbib and Ernest Manes' "Arrows, Structure, Functors - The Categorical Imperative". describe them as (generalized monoids) in Section 10.2 and through adjointness to the forgetful functor from algebras to sets. That last connection basically makes everything that we can write down or model using abstract syntax / universal algebra a monad. The second view is described in Wadler's papers. I mention category theory because we can describe things that are not computations as monads. It also reminds us why a monad is a collection of things taken together. With the List example in mind, a potentially more revealing account on monads (aka triples) can be found in the free book Barr, Wells
Just fire up your REPL and see for yourself how the malleable syntactic structures of the language grow in front of your eyes, alongside your program. Whether this is through Lisp macros or Ruby meta-programming or Scala control structures, the secret sauce is in the ability to implement more and more powerful abstractions within the language. But what makes one language shine more compared to another is the ability to combine abstractions leading to more powerful syntactic structures. Recently people have been talking about the Maybe monad and its myriads of implementation possibilities in Ruby. Because of its dynamic nature and powerful meta-programming facilities, Ruby allows you to write this .. @phone = Location.find(:first, ...elided... ).andand.phone Here andand is an abstraction of the Maybe monad that you can seamlessly compose with core Ruby syntax structures, effectively growing the Ruby language.
I know, I know, the world does not need yet another introduction to monads (or yet another article complaining that world does not need yet another introduction to monads). So you’ll be glad to know this isn’t one of those, in the sense that it’s not new
Our favorite iconoclast, Erik Meijer, presented a very interesting talk at a recent GOTO Chicago event, Functional Programming Night. He originally planned on doing his popular "Fundamentalist Fu
In Javascript understanding functional programming is becoming a necessity to quickly on-board and become productive thanks to React and Flux. But with Monad and Setoid groups, being able to grok FP…
If you go searching the internet for “monad” you’re going to get bombarded by impenetrable category theory math and a bunch of people “helpfully” explaining monads in terms of burritos and space…
This concepts are very used nowadays on functional programing, but because of the heavy mathematical background, sometimes it may be confusing to understand all the definitions. In this post I’ll try…
Google Tech Talk January 15, 2013 (more info below) Presented by Douglas Crockford ABSTRACT The wonders of monads are finally revealed without resorting to C...
Dealing with stateful computations can be a real pain when you are writing purely functional JavaScript code. It can result in things like undesired variable declarations, and if you are not using…
A pragmatic new design for high-level abstractions Monads (and, more generally, constructs known as “higher kinded types”) are a tool for high-level abstraction in programming languages1. Historically, there has been a lot of debate inside (and outside) the Rust community about whether monads would be a useful abstraction to have in the language. I’m not concerned with that here. You see, there’s a problem with talking about whether monads would be useful or not, and it’s this: there are a large number of design challenges to overcome to have any hope of implementing them at all — to the best of my knowledge, there currently exists no realistic (that is, practical) design for monads in Rust. In fact, there are so many obstacles that some people express doubt that it’s even possible. Strictly speaking, they’re a lot more than that, but we’re only interested in the programming angle here. ↩
This is part of a three part examining the underling mathematics and mechanics of Asynchronous programming with javascript When i wanted to make sense of the continuations , i started from the basics…
This guide will use JavaScript instead of a pure functional programming language (e.g. Haskell) to make things more approachable for developers accustomed to imperative languages. It will, however, assume you have basic knowledge of functional programming, including currying and lambdas.