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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1answer
29 views

What is the name of this type of program optimization?

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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55 views

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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1answer
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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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83 views

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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1answer
60 views

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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54 views

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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1answer
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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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3answers
127 views

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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1answer
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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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255 views

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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1answer
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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
121 views

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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56 views

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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1answer
152 views

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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Pattern matching on function application

Suppose we have a function f :: a -> b and a function g :: b -> a such that f . g = id....
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2answers
98 views

Why is the second operation of a Monad called bind?

I understand how monadic computation works, I am just wondering where does the name come from. I cannot relate the thing that the bind operator actually does (i.e. ...
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Compiling an impure language into a pure stack-based language

For a personal learning and fun project, I build an abstract virtual machine based on a stack. The instructions are simple and act on the top of the stack only. There are also stack operators such as <...
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Reducing Kleene's predecessor for Church numerals

I am trying to "reinvent" Kleene's predecessor myself. The following code snippet should be self-explanatory. The idea is to make a 2-tuple and count up from zero, i.e. ...
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1answer
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What kind of Grammar could this be

I am trying to sort Grammar into the Chomsky Hierarchy and I can do so for most of my examples but I am stumped by the following one: bX -> abY which Type of ...
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lambda calculus beta reductions: ((((lambda f (lambda x ((f x) f))) (lambda y (lambda g (g (* y y))))) 2) (lambda a a))

My question is in continuation to lambda calculus reduction: (((lambda f (lambda x (f x))) (lambda y (* y y))) 12) given the input: ...
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1answer
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Lambda Expression Reduction

I am unable to solve the following lambda expression using both normal order (Call-by-name) and applicative order (Call-by-value) reduction. I keep getting different answers for both. This is the ...
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1answer
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generic way to convert imperative if-then-else statements into functional style?

In this question, I asked about a reference for translating imperative code to functional code. I want to ask a more specific question here. How, in general, do we translate into functional style, a ...
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2answers
73 views

resource on translating imperative programs to functional programs

I'm not asking this question for the purpose of any particular project. Rather, I'm trying to understand how to translate non-trivial programs in imperative style to functional style. By functional ...
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1answer
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Converting a function with single parameter to a function with multiple parameters

I have been solving some algorithm questions recently and a pattern I have observed in some problems is as follows: Given a string or a list, do an aggregation operation on each of its elements. Here ...
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2answers
152 views

When is cumulative type universes useful?

AFAIK, a hierarchy of type universe(Type^0: Type^1: Type^2: ...) was introduced to avoid inconsistency caused by Type: Type. ...
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What is the maths name for a set which contains the Domain and Codomain of a function? [closed]

Im interested in this so that I can name a type parameter in a program I'm writing. There is function that that has three parameters. D, Domain C, Codomain X, where D is a subset of X and C is a ...
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Relationship between left identity and associativity

In an effort to better-grok monads I have reviewed many "Everything you need to know about Monads" tutorials out in the wild, but I feel like my understanding is still coming up a bit short. While ...
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Does the callback concept of programming have any basis in computer science?

Although I seriously code with computer languages in general since 2010 and as an amateur programmer with programming languages in particular since 2015 (primarily Bash and JavaScript imperative ...
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1answer
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Semantics for de Bruijn levels

There is an exceptionally simple way to embed simply typed lambda calculus with de Bruijn indices in a functional host language (discussed by Carette, Kiselyov & Shan, and by Kiselyov). The ...
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1answer
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Applying FP/Categorical terminology to non-FP languages

In my continuing effort to finally wrap my brain around advanced FP/categorical concepts, I've been reading dozens of articles and tutorials; what I have concluded is that: 1) Category Theory and ...
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2answers
45 views

If declarative programming is possible at the instruction/action level?

I am considering what the possibilities are with declarative programming. I have a firm understanding of how to use declarative programming in practice, but, short of having examples, I don't know if ...
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Predecessor function with recursive types

I am defining the type Nat of natural numbers a recursive sum type: $$ Nat = \mu X. Unit \oplus X$$ Now, I have defined zero ...
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Simulating extensible sums with dependent types?

ML-style languages have a concept of "extensible" or "open" sum types, where variants can be declared at any point, and there's not a fixed number of constructors for the type. They're usually used to ...
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49 views

Rules for consistency with mutual inductive families?

I'm trying to use a proof assistant to define a type and a relation that are mutually dependent on each other: ...
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1answer
345 views

Why does higher-order abstract syntax need an inverse to define catamorphisms?

In the introduction to the colorfully-named Boxes Go Bananas: Encoding Higher-Order Abstract Syntax with Parametric Polymorphism, Washburn and Weirich describe a problem in traditional formulations of ...
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How does the function to curry and uncurrying another function work?

The following is the code to curry or uncurry a function in Haskell: ...

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