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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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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41 views
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 ...
2
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1answer
41 views
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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0answers
100 views
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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0answers
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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23 views
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 ...
3
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1answer
105 views
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 ...
2
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1answer
56 views
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:
...
4
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2answers
126 views
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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4answers
181 views
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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173 views
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
54 views
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
107 views
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, \, ...
3
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1answer
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
82 views
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
:...
2
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1answer
119 views
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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0answers
59 views
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 ...
3
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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 ...
2
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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 ...
2
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3answers
93 views
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?
$\forall X. X \rightarrow int \rightarrow X$ ?
$...
3
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1answer
24 views
Pattern matching on function application
Suppose we have a function f :: a -> b and a function g :: b -> a such that f . g = id....
4
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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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0answers
32 views
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 <...
2
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0answers
21 views
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. ...
0
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1answer
31 views
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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1answer
57 views
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
74 views
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 ...
0
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1answer
65 views
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
25 views
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 ...
3
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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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0answers
27 views
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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41 views
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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2answers
173 views
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 ...
9
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1answer
170 views
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
109 views
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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0answers
94 views
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 ...
2
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0answers
58 views
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:
...
5
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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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1answer
87 views
How does the function to curry and uncurrying another function work?
The following is the code to curry or uncurry a function in Haskell:
...
