Questions tagged [functional-programming]
Functional programming is a programming paradigm which primarily uses functions as means for building abstractions and expressing computations that comprise a computer program.
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Does the concept of "side-effect" predate functional programming?
When I was reviewing a book, I saw that there's a sentence claiming "side effect is a term coming from the domain of functional programming". I would think that the concept existed before ...
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How, if possible, can we efficiently compute with lazy data structures in 𝜆-calculus?
In Haskell, we can use the following code to define fibonacci numbers,
fibs = 1 : 1 : zipWith (+) fibs (tail fibs)
And its time complexity is linear.
I cannot find ...
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Is there one (or a few) canonical/ specific use cases for "functions returning functions" (beyond "decorators")?
Is there one (or a few) canonical/ specific use cases for "functions returning functions" (beyond "decorators")?
What can you do with "functions returning functions" ...
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Why do functional languages disallow reassignment of local variables?
Fair warning: I don't actually know a functional language so I'm doing all the pseudocode in Python
I'm trying to understand why functional languages disallow variable reassignment, e.g. ...
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Monad with a partial inverse, but not a comonad
I have encountered a structure that looks like a monad with a one-sided inverse and some additional properties. I am not sure which properties of this structure are essential and which are accidental, ...
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Is it possible to allow passing arguments as references without breaking referential transparency in functional languages?
Referential transparency is a relatively new concept to me, but I understood that it means that a function will always give the same answer given the same arguments.
Would passing arguments by ...
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Which overhead is smaller - function call or passing variables between processes?
the question is related to networking frameworks; callback-based approach requires you to call a callback function every time you receive a new data packet; this is not a good approach for high-load ...
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1answer
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Is this way to combine two functions into a new function called a function product?
I have been looking for a maths operation that allows me to combine functions in a specific way. For example if we have functions f and g both with single mappings from o to e and v to c respectively, ...
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Difference between function, method, routine, procedure, subprogram, subroutine, block, task
I don't know if I should have posted this on StackOverflow or here but what's the difference between these terms? Are the definitions of these dependent on the programming languages or they're things ...
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Set theory pertaining to category theory and functional programming
I'm reading an unfinished Introduction to Category Theory/Products and Coproducts of Sets and have come across the following:
A power set of a set is the set of all its subsets. A script 'P' is used ...
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What are advantages of "streaming" syntax in functional languages with for-yielding like Scala?
In Scala we can print list
val nums = (1 to 10).toList
with both
...
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1answer
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Example on Referential transparency (wikipedia)
I have a rather foolish question on an example
explaining the idea behind Referential transparency
Here is given an example i not understand:
Consider a function that returns the input from some ...
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Is there a functional programming language with inherent change propagation?
Change propagation in programming environments is an add-on at the framework level such as React.
There was a lot of work on dataflow virtual machines in the wake of Backus's Turing Award Lecture on ...
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Is mutual inductive type definition essential in coq core language?
I'm studying Coq's core language and I found that mutual inductive type definition is in it.
https://coq.inria.fr/refman/language/core/inductive.html#theory-of-inductive-definitions
Before I read the ...
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Plain-language example of how a functional style makes parallel programming easier
I read a few "function >> imperative/OOP" articles because I heard there was a move in imperative OOP languages toward a functional style of coding, especially encouraging pure ...
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What is name of type " Function->Value->Bool = if (Bool) Function (Value) " in Category theory?
I am very new to functional programming so sorry if the question is stupid.
Having this function
...
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Is there a uniform way of giving for any mathematical formula a hypercomputer that computes it?
Some mathematical formulas directly suggest an algorithm for computing it (even if sometimes an inefficient one).
For example, if we recursively define $\sum_{i=1}^nx_i=x_n+\sum_{i=1}^{n-1}x_i$, then ...
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Regarding Backus' Commentary on von Neumann-style Programming
in John Backus' 1978 FP paper "Can Programming Be Liberated from the von Neumann Style" he says
To help assemble the overall result from single words [von Neumann ie.
conventional mutation-...
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1answer
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Meaning of Free (Arbitrary Abstract Algebra Term)
I'm currently learning abstract algebra and the word free appears (free monoid, free vector space) throughout different literatures. Is there a general (and simple) definition of the word (and ...
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1answer
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Curry–Howard correspondence and functional programming "reliability"
The first time I heard about functional programming, someone told me "it's more reliable to code in a functional style because your type system is like a proof of correctness".
I recently ...
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What is the name of this type of program optimization where two loops operating over common data are combined into a single loop?
On an imperative programming language, let us consider the following program:
...
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Should I use Dr. Racket for learning Scheme?
I've been fiddling with software development for a couple of years and in trying to get into the gist of things I came across SICP, which uses Scheme.
Basically what I want to do at this stage is to ...
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Can a lambda expression be beta-equal to beta-normal forms?
Given a Lambda Expression Term T can it be beta-equal to two different Lambda Terms T1 and T2, both T1 and T2 are in beta-normal form?
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Computation equivalence of functional and procedural programming
I'm really interested in the idea of functional programming, it seems like a very modular way of doings things. I've seen some suggestion that functional programming is just as powerful as procedural ...
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1answer
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Show that term cons works by showing all beta reductions
I'm new to functional programming.
So the terms cons appends an element to the front of the list. Where cons ≜ λx:λl:λc:λn: c x (l c n).
How should I go about proving that cons works correctly using ...
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Constraint based analysis: understanding the program $[[ \text{fn} \ x => [x]^1]^2 [ \text{fn} \ y => [y]^3]^4]^5$
I am currently studying the textbook Principles of Program Analysis by Flemming Nielson, Hanne R. Nielson, and Chris Hankin. Chapter 1.4 Constraint Based Analysis says the following:
1.4 Constraint ...
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The word "algebra" in category theory
I am currently learning category theory and a saying that I see a lot is that X is the algebra of something (e.g. Monoid is an algebra of something). Can someone explain to me what that means? Thanks!
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Is well-founded recursion enough for practical total functional programming?
Total functional programming is a paradigm of non-Turing-complete programming languages where any program that type checks is proven to halt.
Well-founded recursion is a recursive definition of a ...
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How to prove that the Church encoding, forall r. (F r -> r) -> r, gives an initial algebra of the functor F?
The well-known Church encoding of natural numbers can be generalized to use an arbitrary (covariant) functor F. The result is the type, call it ...
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1answer
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Loop optimization of non-tail recursion
When researching how to optimize recursion into loops, I came upon (on Wikipedia) a general rule about this: Whenever a function is in form:
...
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2answers
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What are the implications of Homotopy Type Theory?
I've recently come across the topic of homotopy type theory and I'm interested to learn more. I have a very limited background in type theory.
Can anyone tell me, in functional programming terms or ...
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Is there difference between a function in mathematics to a function in computer science?
I never learned a lot of mathematics (generally only arithmetic) and never learned computer science in a formal frame.
I emphasize that I don't mean to ask about a "function" in programming (...
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Normalization-by-evaluation for untyped lambda calculus which results in 𝛽𝜂-normal form
Usual NbE algorithms for untyped lambda calculus, which use (P)HOAS to embed terms to a host language constructs, results in a beta-normal form of a terms.
Is there algorithms to (efficiently) exploit ...
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Can we think of a non-symmetric product type in Haskell?
Meta note: I asked this question here a while ago. It got an answer:
type a /\!! b = (a, ((b -> Void) -> Void))
Unfortunately, I do not reckon it to be ...
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For every imperative function, is there a functional counterpart with identical performance or even instructions?
Currently, I haven't learned about a functional language that can achieve the same performance as C/C++. And I have learned that some languages that favor functional programming to imperative ...
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What is the category theory interpretation of higher order abstract syntax?
Suppose you have a simple sort of lambda calculus abstract syntax tree. The fine details don't really matter.
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Repeating functions in functional programming?
Functional programming is said to be superior in many ways to imperitive programming. But I am struggling to find a simple functional way of writing:
...
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N-dimensional generalization of map and reduce?
Is there any conceptual generalization of higher-order functions like map and reduce but for N-dimensional objects (e.g. arrays or tensors)?
For mapping, I guess it would be a point-wise ...
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Can lists be defined in a special way so that they contain things of different type?
In https://www.seas.harvard.edu/courses/cs152/2019sp/lectures/lec18-monads.pdf it is written that
A type $\tau$ list is the type of lists with elements of type $\tau$
Why must a list contain ...
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Creating a large tuple from smaller tuples via a monad or applicative
Suppose I have a term $a :\alpha$ of the Simply-Typed Lambda Calculus (in the following, $\alpha, \beta, \gamma$ stand for arbitrary types) and I want to lift it to a term
$\lambda x_{\beta}. \;(x, \, ...
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The meaning and relevance of the locution ''no terminating implementation'' in type theory
In the context of a discussion of Haskell https://stackoverflow.com/questions/62509788/the-intuition-behind-the-definition-of-the-co-reader-monad, I was told that
There is no terminating ...
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2answers
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Lambda Calculus Conversion
How can I take a Haskell data type or function (eg fold, list, String, zip) and convert or translate it to a lambda calculus abstraction?
Example:
If sum computes a sum of all elements in a list, and
:...
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A monad is just a monoid in the category of endofunctors, what's the enlightenment?
Pardon the word play. I'm a little confused about the implication of the claim and hence the question.
Background: I ventured into Category Theory to understand the theoretical underpinnings of ...
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What's the meaning of linguistics?
In the programming language theory world, there are two important terminologies, i.e syntax, and semantics.
I can understand these two terminologies:
syntax is about sentence's structure (e.g. a valid ...
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1answer
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Functional Programming and Category Theory
I'm a math Ph.D. having done research in Algebraic Geometry and Algebraic Topology in grad school for my thesis and I've studied a fair amount of category theory in the process (e.g. having worked ...
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Is there a known way to make an efficient, compact, and fully persistent stack or queue?
In the world of mutable/ephemeral data structures and imperative programming languages, one of the classic ways to implement a stack or queue is to use array doubling: use mutation to fill up or empty ...
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Organizing a "speedback"
Speedback is the merging of speed-dating with feedback: a 2 min. 1-on-1 talk with all members of a group of people.
I'm in a team and I want to plan the ideal speedback setup: all team members have ...
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Uncurrying and Polymorphism
How do we uncurry functions when they are polymorphic? For example, is it possible to uncurry the following types? If so what is the uncurried type?
$\forall X. X \rightarrow int \rightarrow X$ ?
$...
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1answer
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Pattern matching on function application
Suppose we have a function f :: a -> b and a function g :: b -> a such that f . g = id....
