Questions tagged [haskell]

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28
votes
2answers
2k views

What functions can System F not compute?

In this wikipedia article on Turing Completeness it states that: The untyped lambda calculus is Turing complete, but many typed lambda calculi, including System F, are not. The value of typed ...
25
votes
5answers
2k views

Are there any annotated formal verification systems for pure functional programming languages?

ACSL (Ansi C Specification Language), is a specification for C code, annotated with special comments, that allows C code to be formally verified. I have not looked into it, but I imagine that the ...
14
votes
1answer
2k views

Why do functional programming languages require garbage collection?

What's stopping ghc from translating Haskell into a concatenative programming language such as combinatory logic and then simply using stack allocation for everything? According to Wikipedia, the ...
14
votes
4answers
621 views

Is eta-equivalence for functions compatiable with Haskell's seq operation?

Lemma: Assuming eta-equivalence we have that (\x -> ⊥) = ⊥ :: A -> B. Proof: ⊥ = (\x -> ⊥ x) by eta-equivalence, and <...
12
votes
2answers
628 views

What are the relations between Alternative, MonadPlus(LeftCatch) and MonadPlus(LeftDistributive)?

Following up What’s an example of a Monad which is an Alternative but not a MonadPlus?: Assume $m$ is a monad. What are the relations betweem $m$ being an Alternative, a MonadPlusCatch and a ...
8
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2answers
770 views

Explaining monad transformers in categorical terms

Most resource regarding categorical notions in programming describe monads, but I've never seen a categorical description of monad transformers. How could monad transformers be described in the terms ...
8
votes
1answer
261 views

A bicartesian closed category of strict complete partial orders (Hask)

It seems to be well-known that programming languages can't have sums, products and nontermination together. Q1. Is this true? Below (or in the above link I gave) is a partial argument. However, ...
7
votes
1answer
804 views

Practical implementation of Hindley–Milner with typeclasses — matching vs most general unifier

I'm trying to get a deep understanding of a (great) paper "Typing Haskell in Haskell". I'm having difficulties understanding the implementation of two methods there — the ...
6
votes
0answers
239 views

Generalizing Haskell: could we replace Hask with Cat?

N.B. I asked the same question on Stack Overflow but it was suggested that it is too theoretical for this forum. It is great that Haskell allows us to walk around in the category $Hask$. But ...
5
votes
2answers
298 views

Isomorphism between algebraic data-types

I have two types of trees in Haskell, defined as the least solution of the following equations: $T_1(A) \cong 1 + A + T_1(A) \times T_1(A)$ $T_2(A) \cong 1 + A \times T_2(A) + T_2(A) \times T_2(A)$ ...
4
votes
2answers
249 views

Can programming help one understand constructive mathematics?

I have read about the principles of constructive mathematics, for example, the principle of excluded middle is not allowed, and now I want to do some exercises to increase my understanding of the ...
4
votes
1answer
120 views

What are values relative to Hask?

According to ncatlab's page on category theory and haskell, "we can identify a subset of Haskell called Hask that is often used to identify concepts used in basic category theory. One considers ...
4
votes
1answer
357 views

Aren't Monads F-Algebra's? And then if that could be said are Comonad's F-Coalgebra's?

So considering a Monad to be a Triple (T:C -> C, η, µ) with eta and mu as the Natural transformations with appropriate signatures, isn't this in essence an F-Algebra? My thinking is that being both (...
4
votes
0answers
190 views

Type-and-effect systems, stochasticism and effect squelching: how about quicksort?

There's a feature of Haskell's type system which bugs me: you can't implement a randomized sorting algorithm without the use of randomness spilling out into all of its callers. That seems undesirable....
3
votes
1answer
126 views

Areas of research and open problems in functional programming [closed]

What are the major areas of functional programming that require more research and development? For example, I know a lot of people are asking for dependent types in Haskell, and someone at my uni is ...
3
votes
0answers
371 views

Distributive law between monads in Haskell

A distributive law between monads must satisfy laws that are usually given in terms of the units $\eta$ and multiplications $\mu$ of the two monads. Among the four laws there are: $\mu^S T \circ S l \...
1
vote
1answer
149 views

Is the topsort from “Structuring Depth-First Search Algorithms” guaranteed to be (reverse) stable?

In "Structuring Depth-First Search Algorithms in Haskell", implemented in Data.Graph in the Haskell standard library, an algorithm for topologically sorting graphs is given: ...
1
vote
1answer
135 views

Are the `ArrowApply` and `Monad` typeclasses equivalent?

It is stated e.g. on Hackage, that the ArrowApply and the Monad typeclasses are equivalent. I have my doubts about this. It is ...
0
votes
2answers
938 views

How to implement a functional programming language efficiently?

Thanks to Petr and Andrej for their feedback. I'm rephrasing my question and give a bit of a context: Functional programming languages are mostly based on lambda calculus. Implementing a functional ...