# Standard ML

Published articles for Standard ML.

This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles.

## The Universal Properties of Map, Fold, and Filter

DevFeed: [The Universal Properties of Map, Fold, and Filter](<https://devfeed.tech/articles/the-universal-properties-of-map-fold-and-filter-40331.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2013/09/30/the-universal-properties-of-map-fold-and-filter/>)

Published: 2013-09-30T09:00:53Z

Content type: article

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Functional programming](<https://devfeed.tech/topics/functional-programming.md>), [Category Theory](<https://devfeed.tech/topics/category-theory.md>), [functions](<https://devfeed.tech/topics/functions.md>), [Programming](<https://devfeed.tech/topics/programming.md>)

Tags: [categories](<https://devfeed.tech/tags/categories.md>), [category-theory](<https://devfeed.tech/tags/category-theory.md>), [foldr](<https://devfeed.tech/tags/foldr.md>), [free-object](<https://devfeed.tech/tags/free-object.md>), [functional-programming](<https://devfeed.tech/tags/functional-programming.md>), [functions](<https://devfeed.tech/tags/functions.md>), [list](<https://devfeed.tech/tags/list.md>), [monoids](<https://devfeed.tech/tags/monoids.md>), [programming](<https://devfeed.tech/tags/programming.md>), [standard-ml](<https://devfeed.tech/tags/standard-ml.md>), [universal-properties](<https://devfeed.tech/tags/universal-properties.md>)

### AI overview

This article gives category-theoretic characterizations of the functional programming functions map, fold, and filter. It argues that fold has the strongest universal characterization among the three and introduces a generalization related to transformations of standard compound data types.

### Source excerpt

A lot of people who like functional programming often give the reason that the functional style is simply more elegant than the imperative style. When compelled or inspired to explain (as I did in my old post, How I Learned to Love Functional Programming), they often point to the three "higher-order" functions map, fold, and filter, as providing a unifying framework for writing and reasoning about programs. But how unifying are they, really?

## A Sample of Standard ML, the TreeSort Algorithm, and Monoids

DevFeed: [A Sample of Standard ML, the TreeSort Algorithm, and Monoids](<https://devfeed.tech/articles/a-sample-of-standard-ml-the-treesort-algorithm-and-monoids-40310.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2013/04/07/a-sample-of-standard-ml-and-the-treesort-algorithm/>)

Published: 2013-04-07T21:57:37Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Standard ML](<https://devfeed.tech/topics/standard-ml.md>), [Functional programming](<https://devfeed.tech/topics/functional-programming.md>), [Category Theory](<https://devfeed.tech/topics/category-theory.md>), [Programming](<https://devfeed.tech/topics/programming.md>), [Polymorphism](<https://devfeed.tech/topics/polymorphism.md>)

Tags: [algorithms](<https://devfeed.tech/tags/algorithms.md>), [category-theory](<https://devfeed.tech/tags/category-theory.md>), [functional-programming](<https://devfeed.tech/tags/functional-programming.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [ml](<https://devfeed.tech/tags/ml.md>), [monoids](<https://devfeed.tech/tags/monoids.md>), [programming](<https://devfeed.tech/tags/programming.md>), [sorting](<https://devfeed.tech/tags/sorting.md>), [standard-ml](<https://devfeed.tech/tags/standard-ml.md>), [trees](<https://devfeed.tech/tags/trees.md>), [universal-properties](<https://devfeed.tech/tags/universal-properties.md>)

### AI overview

A tutorial introducing Standard ML through functional programming, category theory, and the TreeSort algorithm. It explains why ML is used for manually implementing category-theoretic ideas and highlights parametric polymorphism and type inference.

### Source excerpt

In this post we will assume the reader has a passing familiarity with some of the basic concepts of functional programming (the map, fold, and filter functions). We introduce these topics in our Racket primer, but the average reader will understand the majority of this primer without expertise in functional programming. Follow-ups to this post can be found in the Computational Category Theory section of the Main Content page. Preface: ML for Category Theory A few of my readers have been asking for more posts about functional languages and algorithms written in functional languages.