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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Proving injectivity for an algorithm computing a function between sets of different types of partitions [closed]
I am attempting to solve the following problem:
Let $A$ be the set of partitions of $n$ with elements $(a_1, \dots, a_s)$ such that $a_i > a_{i+1}+a_{i+2}$ for all $i < s,$ taking $a_{s+1} = ...
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140 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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1answer
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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....
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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
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
49 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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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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What does this semantic specification do about shuffling a single card of a Deck?
I have 2 constructor functions and 2 additional function:
declare: d,d' = deck; c, c' = card
Constructor 1)
CreateDeck();
...
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1answer
58 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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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
22 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 ...
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2answers
111 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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38 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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166 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 ...
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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
89 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
29 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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50 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 ...
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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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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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62 views
Is this proof of the map fusion law correct?
I am reading Functional Programming in Scala, where I have been asked to prove the map fusion law. Since Scala is what I am familiar with, I am using as my notation a kind of pseudo-Scala.
Here is ...
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1answer
319 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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1answer
292 views
How to write a coterminating, effectful program?
[Using Idris for code examples and terminology, but the question is not about Idris per se]
In a post titled A Neighborhood of Infinity, @sigfpe argues that "the kind of open-ended loop we see in ...
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42 views
Evaluation of function
Is this the right approach to the question or am I off-track?
Function:
let rec collect f = function
| [] -> []
| x::xs -> f x @ collect f xs;;
Question:
...
2
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1answer
43 views
Can most programs (except the IO part) be re-written as a sequence of matrix operations?
I got this idea recently. If we do not consider the data IO part of software, imagine the data is in the memory and we need to come out with some decision (which product to recommend to a user, how to ...
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39 views
What is the point-free version of f(x,y)?
What is the point-free version of
f(x, y)
? Is it just f or some kind of function composition, since when curried there is an implicit function which is made ...
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2answers
50 views
Using function composition to turn a function into point free one
In Tacit Programming page on wikipedia, it is stated that the point free version of
p x y z = f (g x y) z is
p = ((.) f) . g
...
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Integer-array indexing (e.g. numpy.take) as function composition: where can I find more resources?
For context, one of Numpy's features is that an an array of integers can be passed as an index to an array, and this selects values at all of the specified positions, in any order with possible ...
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What is the relation between the formal definition of strictness and its intuitive notion
I am currently reading Functional Programming in Scala and have encountered a statement in the book I cannot quite make sense of.
On page 67, we are told the formal definition of strictness:
"If the ...
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1answer
68 views
Like transitive reduction, but removing vertices rather than edges?
Suppose I have a directed graph $G = (V, E)$ (or, which is the same, a relation on the set $V$ as defined by the adjacency matrix) that may contain three vertices $x, y, z$, such that $xy, xz, yz \in ...
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Can we always transform a set of lines to a function?
If I have n lines in a programming language like Python (globally or inside a function):
...
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Are the definitions of constructs in terms of lambda terms issues in implementation/design or uses of functional languages?
In Lambda Calculus, natural numbers, boolean values, list processing functions, recursion, if function are defined in terms of lambda terms. For example, natural numbers are defined as Church numerals,...
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Representing partialled/curried functions in postfix notation?
I'm working on a small query language in JSON. A query consists of a JSON array of JSON elements, such as strings, numbers, booleans, etc. Strings starting with a ...
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1answer
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Is “lazy evaluation” part of the compilation process or a run-time feature?
I'm studing the Clean functional programming language, and like other functional PL it uses Lazy Evaluation.
The thing that I can't get is when a PL that using ...
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2answers
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Is Lambda Calculus purely syntactic?
I've been reading for a few weeks about the Lambda Calculus, but I have not yet seen anything that is materially distinct from existing mathematical functions, and I want to know whether it is just a ...
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How to collect free/bound variables in Lambda Calculus?
I am building a simple interpreter for untyped lambda calculus, currently trying to implement alpha-reduction.
According to this document on LC:
Alpha-reduction is used to modify expressions of ...
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1answer
52 views
Lazy streams and infinite series
I just started Unix System Programming with Standard ML and starting on page 22 Shipman begins to explain a pure functional way of avoiding the constant state changes of typing at a keyboard:
A ...
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What is the difference between self-rewriting program and program-with-updates-and-restart
I am reading about Goedel machine http://people.idsia.ch/~juergen/goedelmachine.html and especially the article about possible implementation (in the Scheme language) of this machine http://people....
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Why in the Map Reduce Implementation, why not stream the records to the reducer (via TCP) as they are being produced by the mappers?
In the Map-Reduce implementation, the reducers start when all mappers finish their jobs. Why don't we stream the records from mappers to reducers while they are being processed instead? I think there ...
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1answer
27 views
Functional data structure fast to add and unorded deletion
I am looking for a functional data structure that would work in this role.
Adding items to the struct happens often. Removing items from the struct happens as often as adding them but I have no way ...
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1answer
214 views
Is the IO monad technically incorrect?
On the haskell wiki there is the following example of conditional usage of the IO monad (see here).
...
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1answer
575 views
Why are both caller-save registers and callee save registers needed?
I am having a difficult time understanding callee and caller-save registers. I get that caller-save registers are those which are needed after function call and hence caller saves them in caller ...
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2answers
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Is purely functional programming in some situations less efficient than imperative programming?
I am used to implementing algorithms in imperative languages. Many of the algorithms I have implemented use hash maps, hash sets, mutable arrays, heaps, doubly linked lists, etc. I understand that ...
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lambda calculus with church numerals
today I found this term in our exercises: ((^fx.f(f(f x)) ^gy.g(g y )) ^z.z + 1) (0)
I am quit unaware how to solve this type of question.
I know this is the church numeral 3 , 2 , the identity ...
