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What is "lifting" in Scala?

Sometimes when I read articles in the Scala ecosystem I read the term "lifting" / "lifted". Unfortunately, it is not explained what that exactly means. I did some research, and it seems that lifting has something to do with functional values or something like that, but I was not able to find a text that explains what lifting actually is about in a beginner friendly way.

There is additional confusion through the Lift framework which has lifting in its name, but it doesn't help answer the question.

What is "lifting" in Scala?

What is referential transparency?

What does the term referential transparency mean? I've heard it described as "it means you can replace equals with equals" but this seems like an inadequate explanation.

What is a 'Closure'?

I asked a question about Currying and closures were mentioned. What is a closure? How does it relate to currying?

Best explanation for languages without null

Every so often when programmers are complaining about null errors/exceptions someone asks what we do without null.

I have some basic idea of the coolness of option types, but I don't have the knowledge or languages skill to best express it. What is a great explanation of the following written in a way approachable to the average programmer that we could point that person towards?

• The undesirability of having having references/pointers be nullable by default
• How option types work including strategies to ease checking null cases such as
  • pattern matching and
  • monadic comprehensions
• Alternative solution such as message eating nil
• (other aspects I missed)

How to use underscore.js as a template engine?

I'm trying to learn about new usages of javascript as a serverside language and as a functional language. Few days ago I heard about node.js and express framework. Then I saw about underscore.js as a set of utility functions. I saw this question on stackoverflow . It says we can use underscore.js as a template engine. anybody know good tutorials about how to use underscore.js for templating, especially for biginners who have less experience with advanced javascript. Thanks

What is 'Currying'?

I've seen references to curried functions in several articles and blogs but I can't find a good explanation (or at least one that makes sense!)

Why isn't Python very good for functional programming?

I have always thought that functional programming can be done in Python. Thus, I was surprised that Python didn't get much of a mention in this question, and when it was mentioned, it normally wasn't very positive. However, not many reasons were given for this (lack of pattern matching and algebraic data types were mentioned). So my question is: why isn't Python very good for functional programming? Are there more reasons than its lack of pattern matching and algebraic data types? Or are these concepts so important to functional programming that a language that doesn't support them can only be classed as a second rate functional programming language? (Keep in mind that my experience with functional programming is quite limited.)

Abusing the algebra of algebraic data types - why does this work?

The 'algebraic' expression for algebraic data types looks very suggestive to someone with a background in mathematics. Let me try to explain what I mean.

Having defined the basic types

• Product •
• Union +
• Singleton X
• Unit 1

and using the shorthand X² for X•X and 2X for X+X et cetera, we can then define algebraic expressions for e.g. linked lists

data List a = Nil | Cons a (List a) ↔ L = 1 + X • L

and binary trees:

data Tree a = Nil | Branch a (Tree a) (Tree a) ↔ T = 1 + X • T²

Now, my first instinct as a mathematician is to go nuts with these expressions, and try to solve for L and T. I could do this through repeated substitution, but it seems much easier to abuse the notation horrifically and pretend I can rearrange it at will. For example, for a linked list:

L = 1 + X • L

(1 - X) • L = 1

L = 1 / (1 - X) = 1 + X + X² + X³ + ...

where I've used the power series expansion of 1 / (1 - X) in a totally unjustified way to derive an interesting result, namely that an L type is either Nil, or it contains 1 element, or it contains 2 elements, or 3, etc.

It gets more interesting if we do it for binary trees:

T = 1 + X • T²

X • T² - T + 1 = 0

T = (1 - √(1 - 4 • X)) / (2 • X)

T = 1 + X + 2 • X² + 5 • X³ + 14 • X⁴ + ...

again, using the power series expansion (done with Wolfram Alpha). This expresses the non-obvious (to me) fact that there is only one binary tree with 1 element, 2 binary trees with two elements (the second element can be on the left or the right branch), 5 binary trees with three elements etc.

So my question is - what am I doing here? These operations seem unjustified (what exactly is the square root of an algebraic data type anyway?) but they lead to sensible results. does the quotient of two algebraic data types have any meaning in computer science, or is it just notational trickery?

And, perhaps more interestingly, is it possible to extend these ideas? Is there a theory of the algebra of types that allows, for example, arbitrary functions on types, or do types require a power series representation? If you can define a class of functions, then does composition of functions have any meaning?

What does "coalgebra" mean in the context of programming?

I have heard the term "coalgebras" several times in functional programming and PLT circles, especially when the discussion is about objects, comonads, lenses, and such. Googling this term gives pages that give mathematical description of these structures which is pretty much incomprehensible to me. Can anyone please explain what coalgebras mean in the context of programming, what is their significance, and how they relate to objects and comonads?

List filtering: list comprehension vs. lambda + filter

I happened to find myself having a basic filtering need: I have a list and I have to filter it by an attribute of the items.

My code looked like this:

my_list = [x for x in my_list if x.attribute == value]

But then i thought, wouldn't it be better to write it like this?

my_list = filter(lambda x: x.attribute == value, my_list)

It's more readable, and if needed for performance the lambda could be taken out to gain something.

Question is: are there any caveats in using the second way? Any performance difference? Am I missing the Pythonic Way™ entirely and should do it in yet another way (such as using itemgetter instead of the lambda)?

Is functional GUI programming possible?

I've recently caught the FP bug (trying to learn Haskell), and I've been really impressed with what I've seen so far (first-class functions, lazy evaluation, and all the other goodies). I'm no expert yet, but I've already begun to find it easier to reason "functionally" than imperatively for basic algorithms (and I'm having trouble going back where I have to).

The one area where current FP seems to fall flat, however, is GUI programming. 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. I haven't used F#, but my understanding is that it does something similar using OOP with .NET classes. Obviously, there's a good reason for this--current GUI programming is all about IO and side effects, so purely functional programming isn't possible with most current frameworks.

My question is, is it possible to have a functional approach to GUI programming? I'm having trouble imagining what this would look like in practice. Does anyone know of any frameworks, experimental or otherwise, that try this sort of thing (or even any frameworks that are designed from the ground up for a functional language)? Or is the solution to just use a hybrid approach, with OOP for the GUI parts and FP for the logic? (I'm just asking out of curiosity--I'd love to think that FP is "the future," but GUI programming seems like a pretty large hole to fill.)

Large-scale design in Haskell?

What is a good way to design/structure large functional programs, especially in Haskell?

I've been through a bunch of the tutorials (Write Yourself a Scheme being my favorite, with Real World Haskell a close second) - but most of the programs are relatively small, and single-purpose. Additionally, I don't consider some of them to be particularly elegant (for example, the vast lookup tables in WYAS).

I'm now wanting to write larger programs, with more moving parts - acquiring data from a variety of different sources, cleaning it, processing it in various ways, displaying it in user interfaces, persisting it, communicating over networks, etc. How could one best structure such code to be legible, maintainable, and adaptable to changing requirements?

There is quite a large literature addressing these questions for large object-oriented imperative programs. Ideas like MVC, design patterns, etc. are decent prescriptions for realizing broad goals like separation of concerns and reusability in an OO style. Additionally, newer imperative languages lend themselves to a 'design as you grow' style of refactoring to which, in my novice opinion, Haskell appears less well-suited.

Is there an equivalent literature for Haskell? How is the zoo of exotic control structures available in functional programming (monads, arrows, applicative, etc.) best employed for this purpose? What best practices could you recommend?

Thanks!

EDIT (this is a follow-up to Don Stewart's answer):

@dons mentioned: "Monads capture key architectural designs in types."

I guess my question is: how should one think about key architectural designs in a pure functional language?

Consider the example of several data streams, and several processing steps. I can write modular parsers for the data streams to a set of data structures, and I can implement each processing step as a pure function. The processing steps required for one piece of data will depend on its value and others'. Some of the steps should be followed by side-effects like GUI updates or database queries.

What's the 'Right' way to tie the data and the parsing steps in a nice way? One could write a big function which does the right thing for the various data types. Or one could use a monad to keep track of what's been processed so far and have each processing step get whatever it needs next from the monad state. Or one could write largely separate programs and send messages around (I don't much like this option).

The slides he linked have a Things we Need bullet: "Idioms for mapping design onto types/functions/classes/monads". What are the idioms? :)

What is Scala's yield?

I understand Ruby and Python's yield. What does Scala's yield do?

What is a y-combinator?

A y-combinator is a comp-sci concept from the "functional" side of things. Most programmers don't know much at all about them, if they've even heard about them.

What is a y-combinator? How do they work? What are they good for? Are they useful in procedural languages?

Monad in plain English? (For the OOP programmer with no FP background)

In terms that an OOP programmer would understand (without any functional programming background), what is a monad?

What problem does it solve and what are the most common places it's used?

EDIT:

To clarify the kind of understanding I was looking for, let's say you were converting an FP application that had monads into an OOP application. What would you do to port the responsibilities of the monads to the OOP app?