First of all, your function has the wrong type; I am pretty sure it should be (without the context) a -> (a -> b) -> b. GHC 7.10 is somewhat more helpful in pointing that out, because with your original code, it complains about a missing constraint Internal (a -> b) ~ (Internal a -> … Read more
Do you know about “vanishing” and “exploding” gradients in backpropagation? I’m not too familiar with Haskell so I can’t easily see what exactly your backprop is doing, but it does look like you are using a logistic curve as your activation function. If you look at the plot of this function you’ll see that the … Read more
Algebras I think the place to start would be to understand the idea of an algebra. This is just a generalization of algebraic structures like groups, rings, monoids and so on. Most of the time, these things are introduced in terms of sets, but since we’re among friends, I’ll talk about Haskell types instead. (I … Read more
What I recommend. Read code by people from different grad schools in the 1990s Oxford style Glasgow style or (this) Chalmers style (or this) York style Portland style or OGI style (or this) Utrecht style Yale style Special case: CMU/Elliott Read code by the old masters certain people (incomplete list) Marlow; Paterson; Peyton Jones; Gill; … Read more
Let’s start with a code example: foob :: forall a b. (b -> b) -> b -> (a -> b) -> Maybe a -> b foob postProcess onNothin onJust mval = postProcess val where val :: b val = maybe onNothin onJust mval This code doesn’t compile (syntax error) in plain Haskell 98. It requires … Read more
Short answers: The question’s key points, as I understand them, are the following: “is the auto-specialization transitive?” Should I only expect (+) to be specialized transitively with an explicit pragma? (apparently intended) Is this a bug of GHC? Is it inconsistent with the documentation? AFAIK, the answers are No, mostly yes but there are other … Read more
Why do we need monads? We want to program only using functions. (“functional programming (FP)” after all). Then, we have a first big problem. This is a program: f(x) = 2 * x g(x,y) = x / y How can we say what is to be executed first? How can we form an ordered sequence … Read more
Here’s an even simpler answer: A Monad is something that “computes” when monadic context is collapsed by join :: m (m a) -> m a (recalling that >>= can be defined as x >>= y = join (fmap y x)). This is how Monads carry context through a sequential chain of computations: because at each … Read more
The Haskell approach seems to be to just wrap imperative GUI toolkits (such as GTK+ or wxWidgets) and to use “do” blocks to simulate an imperative style That’s not really the “Haskell approach” — that’s just how you bind to imperative GUI toolkits most directly — via an imperative interface. Haskell just happens to have … Read more
What are some common uses for this language? Rapid application development. If you want to know “why Haskell?”, then you need to consider advantages of functional programming languages (taken from https://c2.com/cgi/wiki?AdvantagesOfFunctionalProgramming): Functional programs tend to be much more terse than their ImperativeLanguage counterparts. Often this leads to enhanced programmer productivity FP encourages quick prototyping. As … Read more