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APL Language

This category covers the APL language itself: how its primitives and operators work, how features like array notation and case conversion behave in practice, and the design questions behind new additions to the notation. Expect close readings of real expressions, worked examples, and the occasional deep dive into edge cases like empty arrays.

Case Conversion: Mapping and Folding

Dyalog v18.0 introduced ⎕C, which converts the case of characters in an array by mapping to lower case, mapping to upper case, or folding. This superseded an... Read

By

Richard Smth

Formal Proposal for APL Array Notation – Seeking Feedback

One of the defining features of the APL language is the ability to denote numeric vectors directly through juxtaposition — separating the elements by spaces,... Read

By

Morten Kromberg

Structural vs. Mathematical “Under”

The APL Farm has recently hosted discussions about the proposed under operator, asking “why Dyalog hasn’t implemented it a long time ago”. I... Read

By

Morten Kromberg

Code Golf: Generating Empty Arrays

By: Stefan Kruger Recently, I was looking for a Dyalog problem to pit my wits against, and I asked in the APL Orchard if Adám could make one up: @Adám Any... Read

By

guestBlogger

Towards Improvements to Stencil

Background The stencil operator ⌺ was introduced in Dyalog version 16.0 in 2017. Recently we received some feedback (OK, complaints) that (a) stencil does... Read

By

Roger Hui

Ascending and Descending

Lexicographic Ordering Lexicographic ordering is what the APL primitives ⍋ and ⍒ provide: ⎕io←0 ⍝ ⎕io delenda est ⎕rl←7*5 ⍝ to get... Read

By

Roger Hui

Dyalog ’18 Videos, Week 6

Happy New Year – and Welcome to the 6th week of Dyalog ’18 video releases! If you enjoy geometry, 2019 starts with a couple of real treats; one which... Read

By

Morten Kromberg

Progressive Index-Of

⎕io=0 is assumed throughout. A recent Forum post motivated investigations into the progressive index-of functions in the FinnAPL Idiom Library: pix ←... Read

By

Roger Hui

Is it Sorted?

Motivation I have been working on the Dyalog APL quicksort implementation. The following programming puzzle arose in the process of doing the QA for this work.... Read

By

Roger Hui

Dyadic Grade

⎕io=0 is assumed throughout. The essay talks only about ⍋ but the same ideas apply to ⍒. Background ⍋ has the distinction of being the first (in 1980)... Read

By

Roger Hui

Linear Interpolation

⎕io=0 assumed throughout; works in 1-origin with the obvious modifications. Introduction On Wednesday, a question arrived via Dyalog Support from an intern... Read

By

Roger Hui

Stencil Lives

⎕io←0 throughout. ⎕io delenda est. Stencil A stencil operator ⌺ is available with Dyalog version 16.0. In brief, stencil is a dyadic operator f⌺s... Read

By

Roger Hui

Stencil Maneuvers

Introduction The e-mail arrived in the early afternoon from Morten, in Finland attending the FinnAPL Forest Seminar. How do I speed this up and impress the... Read

By

Roger Hui

Calculation v Look-Up

(⎕io←0 and timings are done in Dyalog version 15.0.) Table Look-Up Some functions can be computed faster by table look-up than a more traditional and more... Read

By

Roger Hui

Beauty and the Beast

Finally, the last accessory I ordered for my Raspberry Pi Zero (that’s the little red thing behind my keyboard) has arrived – an Acer 43″... Read

By

Morten Kromberg

Charting Reaction Times on the Raspberry Pi

Earlier this week I collected some reaction timer data on my Pi using the BBC micro:bit as an input device. I only produced an “ASCII art” chart at... Read

By

Morten Kromberg

micro:bit Reaction Timer in APL on the Pi and BBC micro:bit

I have a bit of a cold today, so I decided that instead of hopping in an icy car and driving to the office in order to spend the day drinking coffee and... Read

By

Morten Kromberg

50847534

⎕io←0 throughout. I was re-reading A Mathematician’s Apology before recommending it to Suki Tekverk, our summer intern, and came across a statement... Read

By

Roger Hui

A Memo Operator

Abstract Some functions are simply stated and easily understood as multiply-recursive functions. For example, the Fibonacci numbers are {1≥⍵:⍵ ⋄ (∇... Read

By

Roger Hui

I-Beam Mnemonics

I-Beam (⌶) is an operator that takes as its operand a numeric code and derives a function which isn’t really considered to be part of the APL language... Read

By

Richard Smth

Shuffle Faster Please!

Andy reported that in the shuffle QA some functions take a long time: m9249   “4½ days so far” rankop  21.5 hours... Read

By

Roger Hui

Loops, Folds and Tuples

For-loops Given an initial state defined by a number of variables, a for-loop iterates through its argument array modifying the state.     A←... ⋄... Read

By

John Scholes

Quicksort in APL Revisited

A message in the Forum inquired on sorting strings in APL with a custom comparison function. First, sorting strings without a custom comparison function... Read

By

Roger Hui

Response to Feedback on Cut, Under and Merge

At Dyalog ’15 John Scholes and I presented proposals for future operators cut, under, and merge. Following the release of the video of this presentation,... Read

By

Roger Hui

The Reflex/Commute Operator

The monadic operator ⍨ is defined and modeled as follows: f⍨ ⍵ ←→ ⍵ f ⍵ ⍺ f⍨ ⍵ ←→ ⍵ f ⍺ {⍺←⍵ ⋄ ⍵ ⍺⍺ ⍺} Reflex Some... Read

By

Roger Hui

Parallel Programming with Futures/Isolates

Morten Kromberg went right to it with his well-prepared workshop on the prototype features that were introduced in version 14.0 of Dyalog APL. The features are... Read

By

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Permutations

I started composing a set of APL exercises in response to a query from a new APL enthusiast who attended Morten’s presentation at Functional Conf,... Read

By

Roger Hui

Type Comments

I’ve taken to commenting the closing brace of my inner dfns with a home-grown type notation pinched from the Functional Programming community: dref←{... Read

By

John Scholes

In Praise of Magic Functions: Part II

Part I of this post was concerned with the development speed and execution speed of magic functions and should be read before this post. Benefitting from... Read

By

Roger Hui

In Praise of Magic Functions: Part I

A magic function is an APL-coded (dfn) computation in the C source of the interpreter. For example, some cases of ∧.= are coded as... Read

By

Roger Hui

Response to Name Colouring for Dfns

This post contains comments to John Scholes’ post on name colouring; please continue to post any further comments with the original post. This is a very... Read

By

Morten Kromberg

Name Colouring for Dfns

APL is sometimes criticised because expressions that include names cannot, in general, be parsed without knowing whether the names represent functions or... Read

By

John Scholes

A Dialog on APL

A discussion between Nicolas Delcros and Roger Hui Nicolas, Prologue: From a language point of view, thanks to Ken Iverson, it is obvious that you want grade... Read

By

Roger Hui

Do Functions Know Their Own Names?

Going back a long way when John Scholes and I were writing version 0 of Dyalog there was a big discussion about whether functions knew their own names. This... Read

By

Geoff Streeter

Exploring Key

In ⍺ f⌸ ⍵, major cells of ⍺ specify keys for the corresponding major cells of ⍵, and f applies to each unique major cell of ⍺ and the major cells... Read

By

Roger Hui

Foo, Shmoo

“We do not realize what tremendous power the structure of an habitual language has. It is not an exaggeration to say that it enslaves us through the... Read

By

John Scholes

Changes of Heart

Karen Shaw started the ball rolling (hearts afluttering?) by asking Jay Foad to come up with a one-liner for St. Valentine’s Day; he then solicited... Read

By

Roger Hui

Zero-length Regular Expression Matches Considered Harmful

I was asked by a colleague why ⎕S reports two matches in the following example: ('d*'⎕S 0 1)'321' ┌───┬───┐ │0 3│3 0│... Read

By

Richard Smth

Solving the 2014 APL Problem Solving Competition – Cryptography Problem 3

This post is the continuation of the series where we examine some of the problems selected for the 2014 APL Problem Solving Competition. In this post... Read

By

Jay Foad

Solving the 2014 APL Problem Solving Competition – Cryptography Problem 2

This post is the continuation of the series where we examine some of the problems selected for the 2014 APL Problem Solving Competition. In this post... Read

By

Jay Foad

Solving the 2014 APL Problem Solving Competition – Cryptography Problem 1

This post is a continuation of the series where we examine some of the problems selected for the 2014 APL Problem Solving Competition. I’ll start by... Read

By

Jay Foad

The Diamond Kata

Acknowledgments Morten Kromberg is the other co-author of this text but the blogging software prevents his being listed as such. We are indebted to Jay Foad,... Read

By

Roger Hui

Cholesky Decomposition

Morten was visiting Dyalog clients and forwarded a request: Can we have the Cholesky decomposition? If A is a Hermitian, positive-definite matrix, its Cholesky... Read

By

Roger Hui

Three-and-a-bit

The most obvious expression for computing π in APL is ○1. But what if you can’t remember how ○ works, or your O key is broken, or you feel like... Read

By

Jay Foad

Quicksort in APL

Quicksort is a classic sorting algorithm invented by C.A.R. Hoare in 1961 [0, 1]. It has been known for some time that quicksort has a terse rendition in APL... Read

By

Roger Hui

Ken Iverson’s Favourite APL Expression?

What was Ken Iverson’s favourite APL expression? I don’t know that he had one and if he had I don’t know what it was, but if I have to guess …... Read

By

Roger Hui

Musings on Reduction

In one man’s humble opinion, reduction (⌿) is the Queen of Operators. Each (¨) comes a close second, but doesn’t get the cigar because each can... Read

By

John Scholes

Solving the 2014 APL Problem Solving Competition – it’s as easy as 1 1 2 3…

The winners of the 2014 APL Problem Solving Competition were recognized at the Dyalog ’14 user meeting and had a chance to share their... Read

By

Brian Becker

A Speed-Up Story

The first e-mail of the work week came from Nicolas Delcros. He wondered whether anything clever can be done with ∘.≡ on enclosed character strings. I... Read

By

Roger Hui

Selective Expression Tracing

Operator trace from dfns.dws is a simple and low-tech tool for displaying intermediate results of functions, during the evaluation of an expression. For... Read

By

John Scholes

Data-driven Conditionals

ACKNOWLEDGEMENT: My thanks to Andy Shiers for simplifying the examples Visitors to APL from other languages are sometimes a bit sniffy about our use of numbers... Read

By

John Scholes

Why Dyalog ’14 was a Shear Delight

Recent versions of Microsoft Windows support touch screens, which of course means that applications can respond to events originating from touches. Microsoft... Read

By

John Daintree

Isolated Mandelbrot Set Explorer

It amazes me that an equation so simple can produce images so beautiful and complex.  I was first introduced to the Mandelbrot set by the August 1985 issue... Read

By

Brian Becker

Dancing with the Bots

Last week the ‘bots were busy preparing for the J Language Conference in Toronto, where they made their first public appearance together. Upon returning... Read

By

Morten Kromberg

Creating Shortcuts (Microsoft Windows)

At Dyalog, a developer not only needs access to all of the readily available editions of the interpreter but also to earlier versions that are no longer... Read

By

John Daintree

Aligning Diff Output

‘Bots are off limits this week so here is a story from this year’s Iverson College – a fantastic week spent in the company of a wonderful mixture of... Read

By

Morten Kromberg

APL-Controlled Robot Performs Death-Defying Stunts Using PiCam

Regular readers will remember my whining about the poor precision of both infra-red and ultrasonic sensors. But today, the Raspberry Pi / Dyalog APL... Read

By

Morten Kromberg

PiServer at Thor8.dk

I’ve been wanting to run a Web Server from my home for many years. In fact, I have been paying for the domain Thor8.dk (my street address is Thorsvænget... Read

By

Morten Kromberg

APL at work in Africa

My dad is originally from the Cape, and I grew up in Botswana, so hopefully I can be forgiven for feeling that it is very cool to find Dyalog APL at the core... Read

By

Morten Kromberg

Elementary Cellular Light-Emitting Automaton

In response to an earlier post on driving an 8-bar LED using the Raspberry Pi, Roger Hui commented that 8 lights should be sufficient to display the output... Read

By

Morten Kromberg

Dyalog APL v14.0 Tech Preview

And now, as they say, for something completely different. Our robot is running Dyalog APL version 13.2 for the Raspberry Pi, which was released on our major... Read

By

Morten Kromberg

Dyalog APL now available for the Raspberry Pi!

Although the news had not yet appeared on the Dyalog webpage when this was written, the CTO blog has access to exclusive sources and is therefore able to... Read

By

Morten Kromberg

Fun with APL on the Raspberry Pi (without a Robot)

The official release of Dyalog APL for the Raspberry Pi now looks as if it going to happen on Friday! In preparation for this, we have been working on some... Read

By

Morten Kromberg

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