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21 votes

Why do functional programming languages require garbage collection?

All of the following comments are premised on the choice of a standard implementation strategy using closures to represent function values and a call-by-value evaluation order: For the pure lambda ...
Neel Krishnaswami's user avatar
6 votes
Accepted

What are values relative to Hask?

At the level of precision used in the nlab page, values are global elements -- i.e., a value of type $A$ corresponds to a morphism $1 \to A$. If you want to be serious about this, there are some ...
Neel Krishnaswami's user avatar
3 votes
Accepted

Uncountability in intuitionistic logic

I tried to address the questions you raise in "Five stages of accepting constructive mathematics". And here are some textbooks: Constructive analysis by D. Bridges and E. Bishop is the &...
Andrej Bauer's user avatar
  • 29.2k
2 votes

Explaining monad transformers in categorical terms

How could monad transformers be described in the terms of category theory? There are two definitions: the "weak" and the "functorial" one. The "functorial" definition is ...
winitzki's user avatar
  • 542
2 votes

Uncountability in intuitionistic logic

I can't give you a (easily translatable) answer to the question regarding Haskell and the types, but the following might help you since you already mentioned ZFC: Take the axioms of ZFC and let's ...
Fabian's user avatar
  • 25
2 votes

Areas of research and open problems in functional programming

The computational implications of homotopy type theory & higher type theory. Homotopy type theory was invented and developed by a group of computer scientists and mathematicians as a new ...
xrq's user avatar
  • 1,185
1 vote
Accepted

Why can't opaque optics form a category?

optics do form a category where the objects are (Type, Type). However, the Optic type is ...
Szumi Xie's user avatar
1 vote

Explaining monad transformers in categorical terms

I would highly recommend the book book by Bartosz Milewski "Category Theory for Programmers" which goes into some detail about Monads from a Category Theoretic perpective. And it's also ...
Robert Long's user avatar
1 vote

Isomorphism between algebraic data-types

I don't think $T_1(A)$ and $T_2(A)$ are isomorphic in a meaningful way. That is, meaningful in the program where these data types are used. You can certainly convert one of them into another without ...
winitzki's user avatar
  • 542

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