# 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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### 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: ...
6k views

### Scan vs. Map vs. Apply

I cannot understand the difference between Apply, Scan, and Map. I have tried to play with ...
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 ...
8k 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 ...
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 ...
13k 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 ...
910 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 ...
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 ...
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 : ...
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. ...
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 ...
1k 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 ...
403 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 ...
809 views

### FoldWhile and FoldWhileList

Mathematica has had NestWhile and NestWhileList for some time. But, to date, it has not implemented a built-in ...
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: ...
883 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, ...
2k 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]]] ...
465 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 ...
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 ...
1k 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 ...
996 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 ...
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 ...
335 views

### Overlapping pure functions

Let say I need and option for Plot: RegionFunction -> (-6 < #2 < 6 &) But I also want those ...
489 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 ...
1k 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 ...
364 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: ...
756 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 ...
2k 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....
3k 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 ...
780 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, ...
605 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: ...
581 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 ...
390 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 ...
456 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 ...
596 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), ...
1k views

### Converting expressions into functions

I have defined an expression, such as a = x I would like to convert this into a function, such as f[x_]:=x However, in my ...
641 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 ...
793 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 $n$...
685 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, ...
307 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 ...
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 ...
2k views

### What makes mathematica a "functional programming language"?

According to the website of mathematica itself, mathematica is a "functional progrmaming language". I am trying to understand what "functional programming" is. I don't think I have ever worked with "...
1k views

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 ...
751 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 ...
992 views

### How can I improve my code for drawing a tree?

This code draws a tree, but it's not in the functional style. ...
731 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 ...
146 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 ...
577 views

### How to organize expression by symbols (like Collect), but apply different functions to each coefficient

I want to mimic the functionality of Collect[expr, {vars}, func], but with the following modification: The function f that is ...