The following is a stunt, but it’s quite a safe stunt so do try it at home. It uses some of the entertaining new toys to bake order invariants into mergeSort. {-# LANGUAGE GADTs, PolyKinds, KindSignatures, MultiParamTypeClasses, FlexibleInstances, RankNTypes, FlexibleContexts #-} I’ll have natural numbers, just to keep things simple. data Nat = Z | … Read more
Absolutely, validation is the process of approving a given object state, while invariant enforcement happens before that state has even been reached. A corollary is that invariant enforcement is best performed by the thing that is being mutated (or created) itself, like a self-protection reflex, whereas validation is usually done by a third party. The … Read more
LINEAR-SEARCH(A, ν) 1 for i = 1 to A.length 2 if A[i] == ν 3 return i 4 return NIL Loop invariant: at the start of the ith iteration of the for loop (lines 1–4), ∀ k ∈ [1, i) A[k] ≠ ν. Initialization: i == 1 ⟹ [1, i) == Ø ⟹ ∀ k … Read more
You’ll have a lot of problems writing Java, especially multi-threaded code, if you can’t understand these simple ideas: Pre-conditions are the things that must be true before a method is called. The method tells clients “this is what I expect from you”. Post-conditions are the things that must be true after the method is complete. … Read more
Could someone provide me simple C# examples of convariance, contravariance, invariance and contra-invariance (if such thing exists). I have no idea what “contra-invariance” means. The rest are easy. Here’s an example of covariance: void FeedTheAnimals(IEnumerable<Animal> animals) { foreach(Animal animal in animals) animal.Feed(); } … List<Giraffe> giraffes = …; FeedTheAnimals(giraffes); The IEnumerable<T> interface is covariant. The … Read more
It doesn’t mean anything in particular in reference to Java. A class invariant is simply a property that holds for all instances of a class, always, no matter what other code does. For example, class X { final Y y = new Y(); } X has the class invariant that there is a y property … Read more
An invariant is more “conceptual” than a variable. In general, it’s a property of the program state that is always true. A function or method that ensures that the invariant holds is said to maintain the invariant. For instance, a binary search tree might have the invariant that for every node, the key of the … Read more