Questions tagged [functional-style]

Questions about Mathematica's functional programming style, including the use of pure functions (Function[], #, &) and functions such as Map, Apply, Nest, and Through.

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41
votes
4answers
3k views

Function in Table

I need a table with the elements made of pure functions and list elements. This is a simplified example: I need a list as: ...
48
votes
2answers
5k views

Scan vs. Map vs. Apply

I cannot understand the difference between Apply, Scan, and Map. I have tried to play with ...
107
votes
9answers
5k views

Functional style using lazy lists?

Let's say I want to answer the question "what are the first 400 palindromic prime numbers?" The first approach that comes to my mind from the set of languages that I know is to use some sort of lazy ...
20
votes
3answers
5k views

How do I convert an argument list to a sequence of arguments?

I think this is a basic question, but I am having difficulty finding the answer in the documentation. Thread is not what I am looking for, I think. Suppose that I ...
25
votes
2answers
2k views

Using a list of tuples in a pure function

I want to use a list of tuples within a function to make assignments. Say I want to make assignments of the form value[i,j] = val What I have is a list of ...
130
votes
9answers
11k views

General strategies to write big code in Mathematica?

I think after six months of exposure to Mathematica and the Wolfram Language I am fairly OK with writing short codes and snippets. However, what are some general strategies to use in order to write ...
23
votes
1answer
866 views

Shorter syntax for Fold and FoldList?

I find it tedious to write out the following: a = {1, 2, 3, 4}; Fold[f, First @ a, Rest @ a] f[f[f[1, 2], 3], 4] It ...
38
votes
12answers
3k views

Map a function across a list conditionally

It seems that this is a really basic question, and I feel that the answer should be obvious to me. However, I am not seeing. Can you please help me? Thanks. Suppose I have a list of data ...
11
votes
3answers
11k views

Using sets of arguments from a list

Please Consider : list={{5,2,6},{2,8,3}} I need to get the product of all the element within list : As of now I do this : ...
39
votes
8answers
3k views

Can this be written well, without loops?

Inspired by this question I would like to know if the following code can be written without explicit loops (For, While, etc.) in a clean, efficient and non-contrived way. I have been unable to do so. ...
35
votes
3answers
1k views

Prefix operator with low precedence

The question is simple, but I will elaborate on the background as well for those interested in the idea: How to define a new operator with specified precedence value? Background Mathematica was ...
7
votes
3answers
965 views

Replace For-loop with functional code

I am very new to Mathematica. I have code written using for loops. I want to rewrite it using Map/Thread but I am not sure how ...
33
votes
3answers
725 views

FoldWhile and FoldWhileList

Mathematica has had NestWhile and NestWhileList for some time. But, to date, it has not implemented a built-in ...
14
votes
3answers
359 views

Using Through to evaluate complex expressions

Suppose we're given the expression f*g+h, where f,g,h are all pure functions. How can we evaluate this expression on some ...
28
votes
3answers
4k views

Programming a numerical method in the functional style

I am new to Mathematica and I would like to learn a bit more about functional programming. At the moment I have assignments like programming different numerical methods (for integration: ...
34
votes
3answers
790 views

Is there a comprehensive list of functions with operator forms?

As of version 10, Mathematica sports operator forms for many functions like Map, SortBy, ...
10
votes
2answers
424 views

Cases[data,Colon[key,_]] vs. Cases[data,key:_] toward XPath, XQuery

Exploring methods to index and search tree-structured key:value pairs via named-entity index (key paths) as opposed to Position-based indexing. Using Rule as ...
33
votes
2answers
2k views

Going full functional (Haskell style)

I'm trying to define some notation so that Mathematica code would be more functional, similar to Haskell (just for fun): currying, lambdas, infix operator to function conversion, etc.. And I have some ...
30
votes
2answers
1k views

What is the difference between Composition (@*) and sequential applications (@)?

What is the difference between f@*g@*h@x and f@g@h@x Both evaluate to f[g[h[x]]] ...
18
votes
4answers
965 views

Is there a more elegant and efficient way to write brainf*** style loops in Mathematica?

I'm having some fun writing a brainf*** interpreter in Mathematica. See this wiki article for more info. It works nicely but I'd like to find an elegant, preferably functional, way to handle the ...
9
votes
4answers
3k views

Alternatives to While Loops?

I am using Mathematica to run a probabilistic simulation. Essentially, I have a list of members of a population (they only have one, numerical, attribute, so it's just implemented as a list of ...
11
votes
4answers
419 views

Handy / flexible directory tree operations

Is there any shorter / more handy / more flexible way to get directory tree as a nested Rules/Associations list? I tried to incorporate ...
6
votes
5answers
346 views

How to nest my own “times” function to get powers

I have a "times" function. I'd like to create a power function using it. It should look like this for an 6th power: ...
29
votes
3answers
596 views

Analogies to Help New Users

In many of the classes that I teach, I require students to learn the basics of Mathematica which we use throughout the semester to do computations and to submit homeworks (in notebook form). Some ...
26
votes
3answers
778 views

How and why to use monadic programming in Mathematica?

This is a methodological question with two parts: How to use monadic programming in Mathematica? Why use monadic programming in Mathematica? In my opinion the questions are inter-related -- we ...
18
votes
7answers
2k views

How to map and sum a list fast?

The following takes a lot of memory and is slow: AbsoluteTiming[Total[Map[#^2 &, Range[1, 100000000]]]] I suspect this is because it first calculates and ...
5
votes
2answers
325 views

Overlapping pure functions

Let say I need and option for Plot: RegionFunction -> (-6 < #2 < 6 &) But I also want those ...
20
votes
4answers
628 views

How to keep some of the results of the NestList

I'm using some iterative arithmetics to calculate wave propagation with the help of NestList. I have to use a small step size for iteration to guarantee the accuracy, which lead to too much data (e.g, ...
12
votes
4answers
566 views

Thread a function over a list and with a non-atomic 2nd parameter?

From the documentation, Thread's behavior on functions where the first parameter is a List and the second is an atomic expression, is this: ...
10
votes
5answers
521 views

Transform a list of functions to a composition

How do I apply a list of functions in a nested way? Example: functionList = {f1,f2,f3} RequiredCommand[functionList,Pi] such that the required command returns ...
9
votes
2answers
358 views

Evaluation in lambda function

If I have a function, that returns a function, for example: f[a_] := a^2 * # & then f[3] == 3^2 # & Is there a way ...
1
vote
1answer
422 views

Arbitrary depth patterns/rules

Temporary message: I am now really confused. I am not sure how using Power and Unevaluated together works in the examples below. While answering this question, I stumbled upon the following. We ...
15
votes
4answers
973 views

How to replace the first occurence in an expression instead of replacing all?

Is there a function that replaces the first occurence of the expression instead of replacing all? For example, if I have HoldForm[x + 2 + 4 + x] /. x -> 4, is ...
6
votes
2answers
551 views

Variant of the cutting-stock problem in Mathematica

I'm pretty new to Mathematica and am trying to learn to solve problems in a functional way. The problem I was solving was to list the ways in which I could sum elements from a list (with repetitions), ...
11
votes
2answers
480 views

Combining pure functions

Is there an easy way to combine pure functions into a single pure function? For example, say I have f = #1^2 &; g = #1 - 2 &; and I want to define a new ...
7
votes
2answers
703 views

Define product derivative

How do I define the $n$th product derivative of a function in Mathematica? The first product derivative $f^\ast$ of a function $f$ is $$ f^\ast(x)=\exp\left(\frac{f^\prime(x)}{f(x)}\right) $$ The $n$...
3
votes
1answer
649 views

NestList with a list inside?

I'm new to Mathematica, and was looking for more efficient ways to implement the Do loop below. a, ...
2
votes
1answer
280 views

General function taking general number of arguments

The following is an edit of this post, for which a working solution was provided by John McGee. I have a different function and am not sure how to adapt the solution for it: I want to construct a ...
33
votes
5answers
2k views

Does every Symbol in Mathematica induce a monad?

From my question about types in Mathematica, I assume that every Symbol in Mathematica is a type if it appears as a Head of some ...
27
votes
3answers
1k views

Monad-like structures in Mathematica

I have been trying to code monad-like structures in Mathematica. However, I am facing some issues and I was wondering if anyone can help. I will give some background in the hope it can be useful to ...
11
votes
5answers
726 views

How to find first list element that differs from average of N previous elements by more than a given amount?

Given a list of real numbers, I need to write a function that returns the value of the first element in the list that differs from the mean of the previous $N$ elements by greater than $P$ standard ...
18
votes
1answer
1k views

How best to simulate n-body systems in a functional way?

I want to simulate a N-body system in the most functional way possible. The system I'm modeling are metallic colloidal particles in a solution of peroxide water, as here http://arxiv.org/pdf/1502....
14
votes
3answers
924 views

How can I improve my code for drawing a tree?

This code draws a tree, but it's not in the functional style. ...
13
votes
2answers
581 views

Choose between `Apply` and `Map`

Even though this might be too general question(or not answerable), I want to get some advice here. I apologize in advance if it is not a relevant question. I frequently have to process large list of ...
3
votes
1answer
89 views

Best way to apply a list of functions to a list of values?

This question is closely related to questions 83720, 17460, and 11298. How would you write the operator F = Through[#1[#2]] & in the prettiest, fastest, or ...
7
votes
2answers
333 views

Why are we so sure about Map results?

I do abuse it often but when I have faced this feature first time I was really suprised: i = 0; (i++; # - i) & /@ Range[5] {0, 0, 0, 0, 0} What am I ...
5
votes
1answer
195 views

How can I get all pairs of values from an association with elements key->list

I have an association of the form ds=<|key1 -> list1, key2 -> list2,... ,keyn -> listn|> I would like a simple way to map a function to all pairs <...
5
votes
4answers
867 views

How to transform Do loop to more efficient codes?

I'm new to Mathematica. Here is my original program: How to rewrite the Do part? ...
9
votes
3answers
522 views

Map over list of functions

I would like to convert a list of $n$ complex equations to a list of $2n$ real ones. At the moment I am doing it like this: ...
6
votes
2answers
594 views

Update a function avoiding infinite recursion

I am quite new to Mathematica and not completely familiar with functional programming. I am currently working with a function (call it foo) and wish to change its behaviour, for example, by adding 1 ...