Thank You Ian Sharp

On July 16th, one of the most influential founders of what we today refer to as the “array language community” died peacefully, a few months after being diagnosed with lung cancer (link: Toronto Globe and Mail).

Ian Patrick Sharp

In 1964, Ian Patrick Sharp formed I.P.Sharp Associates (IPSA), together with six colleagues who were made redundant when Ferranti-Packard closed its computer division in Toronto, Canada. As Ian explains in a wonderful interview that was recorded in 1984 (link: Snake Island website), he was approached by people who wanted to recruit the whole team. Instead, he decided to form a company, since the team obviously had significant value.

The company was involved in the first APL implementation at IBM (APL\360). Subsequently, IBM allowed them to modify and enhance the system, and built a timesharing service that became known as SHARP APL. Roger Moore was a co-founder of IPSA and, in addition to being responsible for the supervisor that made SHARP APL a superior timesharing system, Roger was the chief architect of IPSANET, one of the worlds first packet switched networks.

In the late 1970s the combination of APL and IPSANET was revolutionary, and IPSA quickly attracted business from global corporate clients who used SHARP APL for e-mail, reporting and analytics, and a rapidly-growing collection of financial timeseries data – all completely new technologies at the time. In particular, the transmission of data over telephone lines changed the world. Ian had many absurd encounters with telecom monopolies who tried to protect old business models or profit from the new technology (link: archive.org).

A Stylised Map of the I.P.Sharp Associates APL Time-Sharing Network

Ian’s management style perfectly matched – and drove – the revolutionary technologies. As Ian explains so eloquently and humorously in the interview, IPSA recruited talented people without necessarily having specific tasks in mind. Ian set the tone and direction and then let people get on with it, moving around in the background to get a sense of how things were going and making adjustments without ever making a fuss. IPSA was a fantastic place to work and attracted a wonderfully diverse (in the most modern sense of the word) collection of smart people who developed revolutionary tools, helped a lot of customers, had a lot of fun, and made money.

Ultimately, IPSA was creative, problem-oriented and customer-driven to the extent that it failed to respond to fundamental changes in the market in time. At the end of the 1980s the timesharing revenues suddenly faded, and the company was acquired by Reuters for its timeseries databases and more or less disappeared overnight. However, IPSA had acted as a fantastic breeding ground for technology and talent for a quarter century, and there are hundreds of people who fondly and gratefully remember Ian for the way that he allowed them all to grow.

I don’t think it is a coincidence that so many of the active array language organisations have key players who were once IPSA employees (some of them appearing in more than one place thanks to relationships forged a very long time ago 😊).

  • Jsoftware: Roger Hui, Eric Iverson, Chris Burke, Ken Iverson
  • Kx: Arthur Whitney, Simon Garland, Stephen Taylor, Chris Burke
  • Dyalog: Gitte Christensen, Morten Kromberg, Roger Hui, Brian Becker, Dan Baronet
  • Snake Island Research: Robert Bernecky

As always, Roger has collected anecdotes about IPSA, Ian and other people who worked there, which you can find on jsoftware.com/papers/SharpQA.htm.

My Own IPSA Story

In 1978, my dad was moving out of an apartment in Oslo. At the same time, XEROX insisted that IPSA open an office in Oslo to support their international business, and several Canadians arrived there. I helped move some furniture and, sensing a keen interest and real excitement in programming, the IPSA Oslo team offered me a free account to play with APL timesharing, if I was interested. I effectively became a piece of furniture in the IPSA office after school, and had keys to the office so I could come and go as I pleased. After a year or so, they started throwing me bits of real work to do and paying me for my time. I think I was 17 at the time.

In addition to working as an APL consultant and tool builder, one of the things I did in my spare time was to write a tool for myself that would compare the entire contents of the e-mail directory with its state at the end of the previous week. Since IPSA was 100% managed by e-mail groups, this allowed me to know instantly when a new office was opened, a significant new project was started, and, of course, when new employees joined the company. By using this technique of harvesting e-mail addresses and sending unsolicited e-mail when an interesting project or person joined, I found my future partner both at home and the office – Gitte, the current CEO of Dyalog Ltd – only about 500km away in the IPSA Copenhagen branch.

I spent about a decade at IPSA and, after its sudden disappearance, Gitte and I have been trying to recreate the IPSA atmosphere in every team that we have been a member of. In a very real sense, I owe not only my career but almost everything of value about my life to Ian Sharp and the warm and welcoming company that he created.

Thank You, Ian!

A Blustery Spring

Dyalog version 17.1 will be released soon, with the HTMLRenderer working under Windows, macOS and GNU/Linux, the “Link” system providing infrastructure for connecting APL to source code management systems, pre-built Docker containers with Dyalog APL for Linux installed and many other enhancements that simplify the installation and maintenance of systems based on Dyalog APL.

We’ll be writing much more about version 17.1 soon, and next year’s 18.0 release in due course. The main purpose of this blog entry is to let you know about new members of the Dyalog team and, unfortunately, a couple of departures as well.

Departures


In February, John Scholes passed away. Together with Geoff Streeter, John was one of the original implementors of Dyalog APL in 1982-1983, a cornerstone of all aspects of the Dyalog language and business, and one of the pillars of the APL community. Many members of the community have paid tribute to our Genius, Gentleman and Mischievous Schoolboy at http://johnscholes.rip.

At the end of May 2019, Jay Foad is leaving Dyalog to return to his first love (as a software developer) and become a proper compiler geek again, after nearly a decade of helping move Dyalog APL forward and, for the last three years, helping to “herd the cats” as CTO. We will sorely miss Jay’s technical excellence but understand the desire to hit the sweet skill spot when the opportunity arises, and we wish him good fortune in that pursuit! You can read Jay’s farewell blog post here.

Jay’s management responsibilities will be shared between Richard Smith, our Development Manager and myself; I will be re-assuming the role of CTO until further notice.

New Faces in 2019

The good news is that we will welcome several new people to Dyalog in 2019 – new hands to write code in APL, to work on the APL interpreter, and to write documentation and training materials to help new and old users get their work done more effectively.

APL Consultants

In response to client requests and to help new clients get started writing their first APL systems, we are creating a consulting group in the USA. To date, we have recruited two members for this team: Nathan Rogers joined the team at the end of April and is based in Denver, Colorado, and Josh David starts work for Dyalog in early June (as soon as he graduates) and will be based in New Jersey. If you think you have heard of Josh before, that is probably because he was a winner of the Dyalog Problem-Solving Contest in 2016 (https://www.dyalog.com/news/112/420/2016-APL-Programming-Contest-Winners.htm) – and a runner up in 2015. Nathan found us thanks to Adam Brudzewsky’s work on Stack Exchange: https://chat.stackexchange.com/rooms/52405/the-apl-orchard. You can reach them both using e-addresses in the form firstname at dyalog.com.

When members of the consulting team are not working for clients, the intention is that they will be members of the APL Tools Group at Dyalog, working on new tools for APL application development and helping create test suites for Dyalog APL. They will also support Richard Park, who joined us late in 2018, to work on the creation of training materials and tutorials for new users.

Once we have a better idea of the demand for consulting in North America, we expect to grow the team. Please let us know if you could use hired APL hands – in any territory! If we don’t have the resources ourselves, we may be able to find someone else.

Programming Language Implementors

Nathan comes to us with experience from a broad set of tools and programming languages. In addition to writing tools in APL, he will be a part-time member of the core development team, working on the APL interpreter and its interfaces in C, C#, JavaScript, Python and other languages. However, he won’t spend enough time on this to make up for the loss of Jay, who (like most managers at Dyalog) spent a significant amount of his time writing code.

Therefore, as described at https://www.dyalog.com/careers.htm, we are recruiting at least one C / C++ programmer to help us grow the core team.

A Busy – and Exciting Time

2019 is looking like an extremely busy year, with significant growth at Dyalog. As usual, our plan is to bring all the new (and old) hands to the Dyalog user meeting, which will be held in Elsinore, Denmark this year – September 8th to 12th. Details of the programme will soon start to appear at https://www.dyalog.com/user-meetings/dyalog19.htm. If you would like to present an APL-related experience to the user community, make proposals for new features of Dyalog products or suggest topics that you would like Dyalog to speak about at the user meeting, then please let us know as soon as possible!

New York Dyalog Meetup

I am very pleased to announce the creation of the New York Dyalog APL Meetup group, details of which can be found online at https://www.meetup.com/New-York-Dyalog-APL-Meetup/. The meetup has been created and is organised by Paul Mansour, who is also sponsoring the venue for the inaugural meetup, scheduled for 6-9pm on Thursday February 7th, at Alley, 119 West 24th Street, New York. If you are interested in meeting APL users in the New York area, please join the Meetup group so that you will be notified of future events. Please sign up for events that you intend to attend so we know you are coming!

Meetup is a service used to organize online groups that host in-person events for people with similar interests, including programming languages. In addition to the New York group, there is also an APL Meetup group in Frankfurt which meets regularly. We welcome the creation of more local meetups! If you create one in your area, remember to inform us at Dyalog so that we can add a link from our event calendar, and arrange to stop by and speak when we are in your neighborhood!

The program for the meetup on February 7th is as follows:

6:00-6:30pm: Time for Networking

6:30-8:00: Morten Kromberg: New Ways of Working with APL

When you are busy solving problems, new technology can be an unwelcome distraction – but every now and again technologies appear which have the potential to make development, maintenance or distribution significantly easier. Morten will demonstrate some of the new ways of working with APL that have become available in the last few years, and also discuss likely features in the next couple of releases of Dyalog APL: 17.1 in Q2 of 2019 and 18.0 in 2020.

8:00-8:15 Short Break

8:15-9:00 Paul Mansour: Keeping it Simple – A Git Workflow for APLers.

Abstract: Git is great, but the newcomer can easily drown in a sea of commands and options. Git doesn’t tell you when or why to branch, when or why to merge or rebase, how to version your project or prepare a release. AcreFlow is a radically simplified Git workflow that answers these questions. It is implemented in Dyalog APL so you can branch, commit, and put out new versions directly from the APL session.

 

Beauty and the Beast

beauty-and-the-beastFinally, the last accessory I ordered for my Raspberry Pi Zero (that’s the little red thing behind my keyboard) has arrived – an Acer 43″ ET430K monitor. The Zero won’t quite drive this monitor at its maximum resolution of 3840×2160 pixels, but as you can see, you get enough real estate to do real graphics with “ASCII Art” (well, Unicode Art, anyway)!

Some readers will recognise the image as the famous Mandelbrot Set, named after the mathematician Benoit Mandelbrot, who studied fractals. According to Wikipedia a fractal is a mathematical set that exhibits a repeating pattern displayed at every scale – they are interesting because they produce patterns that are very similar to things we can see around us – both in living organisms and landscapes – they seem to be part of the fundamental fabric of the universe.

Fractals are are also interesting because they produce images of staggering beauty, as you can see on the pages linked to above and one of our rotating banner pages, where a one-line form of the APL expression which produced the image is embedded:

Website_banner_MbrotW

The colourful images of the Mandelbrot set are produced by looking at a selection of points in the complex plane. For each point c, start with a value of 0 for z, repeat the computation z = c + z², and colour the point according to the number of iterations required before the function becomes “unbounded in value”.

In APL, the function for each iteration can be expressed as {c+⍵*2}, where c is the point and ⍵ (the right argument of the function) is z (initially 0, and subsequently the result of the previous iteration):

      f←{c+⍵*2} ⍝ define the function
      c←1J1     ⍝ c is 1+i (above and to the right of the set)
      (f 0)(f f 0)(f f f 0)(f f f f 0) (f f f f f 0)
1J1 1J3 ¯7J7 1J¯97 ¯9407J¯193

If you are not familiar with complex numbers, those results may look a bit odd. While complex addition just requires adding the real and the imaginary parts independently, the result of multiplication of two complex numbers (a + bi) and (c + di) is defined as (ac-db) + (bc+ad)i. Geometrically, complex multiplication is a combined stretching and rotation operation.

Typing all those f’s gets a bit tedious, fortunately APL has a power operator , a second-order function that can be used to repeatedly apply a function. We can also compute the magnitude of the result number using |:

      (|(f⍣6)0)(|(f⍣7)0)
8.853E7 7.837E15

Let’s take a look at what happens if we choose a point inside the Mandelbrot set:

      c←0.1J0.1
      {|(f⍣⍵)0}¨ 1 2 3 4 5 6 7 8 9 10
0.1414 0.1562 0.1566 0.1552 0.1547 0.1546 0.1546 0.1546 0.1546 0.1546

Above, I used an anonymous function so I could pass the number of iterations in as a parameter, and use the each operator ¨ to generate all the results up to ten iterations. In this case, we can see that the magnitude of the result stabilises, which is why the point 0.1 + 0.1i is considered to be inside the Mandelbrot set.

Points which are just outside the set will require varying numbers of applications of f before the magnitude “explodes”, and if you colour points according to how many iterations are needed and pick interesting areas along the edge of the set, great beauty is revealed.

1200px-GalaxyOfGalaxies

The above image is in the public domain and was created by Jonathan J. Dickau using ChaosPro 3.3 software, which was created by Martin Pfingstl.

Our next task is to create array of points in the complex plane. A helper function unitstep generates values between zero and 1 with a desired number of steps, so I can vary the resolution and size of the image. Using it, I can create two ranges, multiply one of them by i (0J1 in APL) and use an addition table (∘.+) to generate the array:

      ⎕io←0 ⍝ use index origin zero
      unitstep←{(⍳⍵+1)÷⍵}
      unitstep 6
0 0.1667 0.3333 0.5 0.6667 0.8333 1
      c←¯3 × 0.7J0.5 - (0J1×unitstep 6)∘.+unitstep 6
      c
¯2.1J¯1.5 ¯1.6J¯1.5 ¯1.1J¯1.5 ¯0.6J¯1.5 ¯0.1J¯1.5 0.4J¯1.5 0.9J¯1.5
¯2.1J¯1   ¯1.6J¯1   ¯1.1J¯1   ¯0.6J¯1   ¯0.1J¯1   0.4J¯1   0.9J¯1  
¯2.1J¯0.5 ¯1.6J¯0.5 ¯1.1J¯0.5 ¯0.6J¯0.5 ¯0.1J¯0.5 0.4J¯0.5 0.9J¯0.5
¯2.1      ¯1.6      ¯1.1      ¯0.6      ¯0.1      0.4      0.9     
¯2.1J00.5 ¯1.6J00.5 ¯1.1J00.5 ¯0.6J00.5 ¯0.1J00.5 0.4J00.5 0.9J00.5
¯2.1J01   ¯1.6J01   ¯1.1J01   ¯0.6J01   ¯0.1J01   0.4J01   0.9J01  
¯2.1J01.5 ¯1.6J01.5 ¯1.1J01.5 ¯0.6J01.5 ¯0.1J01.5 0.4J01.5 0.9J01.5

The result is subtracted from 0.7J0.5 (0.7 + 0.5i) to get the origin of the complex plane slightly off centre in the middle, and multiplied the whole thing by 3 to get a set of values that brackets the Mandelbrot set.

Note that APL expressions are typically rank and shape invariant, so our function f can be applied to the entire array without changes. Since our goal is only to produce ASCII art, we don’t need to count iterations, we can just compare the magnitude of the result with 9 to decide whether the point has escaped:

      9<|f 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
      9<|(f⍣3) 0 ⍝ Apply f 3 times
1 1 1 0 0 0 1
1 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
1 0 0 0 0 0 0
1 1 1 0 0 0 1

We can see that points around the edge start escaping after 3 iterations. Using an anonymous function again, we can observe more and more points escape, until we recognise the (very low resolution) outline of the Mandelbrot set:


      ]box on
      {((⍕⍵)@(⊂0 0))' #'[9>|(f⍣⍵)0]}¨2↓⍳9
┌───────┬───────┬───────┬───────┬───────┬───────┬───────┐
│2######│3  ### │4      │5      │6      │7      │8      │
│#######│ ######│   ### │    #  │    #  │    #  │    #  │
│#######│#######│ ##### │  #### │  #### │   ### │   ### │
│#######│#######│###### │ ##### │ ##### │ ##### │ ####  │
│#######│#######│ ##### │  #### │  #### │   ### │   ### │
│#######│ ######│   ### │    #  │    #  │    #  │    #  │
│#######│   ### │       │       │       │       │       │
└───────┴───────┴───────┴───────┴───────┴───────┴───────┘

The last example allowed me to sneak in a preview of the new “at” operator coming in Dyalog v16.0. It is a functional merge operator that I am using to insert the formatted right argument (the number of iterations) into position (0 0) of each matrix.

If I use our remote IDE (RIDE) on my Windows machine and connect to the Pi, I can have an APL session on the Pi with 3840×2160 resolution. In this example, I experimented with grey scale “colouring” the result by rounding down and capping the result at 10, and using the character ⍟ (darkest) for 0, ○ for 1-5, × for 6-9, and blank for points that “escaped”, by indexing into an array of ten characters:

      '⍟○○○○○×××× '[10⌊⌊|(f⍣9)c]

Who needs OpenGL?! (click on the image to enlarge)

mandelbrot-ride4

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 the time:

      times←ReactionTimer.Play
      times
251 305 294 415 338 298 294 251 378
      ReactionTimer.AsciiChart times
425| 
400|    * 
375|         *
350+ 
325|     * 
300|  * 
275|   *  ** 
250+ *      * 

Retro is back in style – but of course I should point out that we can produce “proper” graphics using SharpPlot, a cross-platform graphics package that is included with Dyalog APL on all platforms. I’ve enhanced the ReactionTimer namespace with a function called SPHistogram. If you are using RIDE as the front end to APL on the Pi, this will render output from SharpPlot in a window:

    ReactionTimer.SPHistogram times

Reaction Time Histogram

The original ASCII chart simply plotted the observations in the order that they occurred. Above, the shaded areas show how many observations there were in each bucket (2 between 250ms and 275ms, 3 between 275ms and 300ms, and so on). At the same time, the individual observations can be seen along the X axis as vertical red lines. It is a little unfortunate that, presumably due to some artifact of the timing process, the values 251 and 294 occur twice – and these lines are drawn on top of each other.

The example highlights one of the things that makes SharpPlot a bit special: We have overlaid a histogram showing the frequency of reactions in each bucket, and used a “scatterplot” to where the Y value is always 0, to mark the individual observations along the X axis.

     ∇ SPHistogram times;heading;renderHtml;sp;svg;z 
[1]   heading←'Reaction Times' 
[2]   renderHtml←3500⌶ ⍝ Render HTML in Window 
[3] 
[4]   :If 0=⎕NC'#.SharpPlot' ⋄ #.⎕CY'sharpplot.dws' ⋄ :EndIf
[5] 
[6]   sp←⎕NEW #.SharpPlot(432 250) 
[7]   sp.Heading←heading 
[8] 
[9]   ⍝ Draw histogram 
[10]  sp.ClassInterval←25 
[11]  sp.SetXTickMarks 25 
[12]  sp.HistogramStyle←#.HistogramStyles.SurfaceShading 
[13]  sp.SetFillStyles #.FillStyle.Opacity30 
[14]  sp.DrawHistogram⊂times 
[15] 
[16]  ⍝ Add observations using ScatterPlot 
[17]  sp.SetMarkers #.Marker.UpTick 
[18]  sp.SetPenWidths 1 
[19]  sp.SetMarkerScales 3 
[20]  sp.DrawScatterPlot(times×0)(times) 
[21] 
[22]  ⍝ Render SVG and display in window 
[23]  svg←sp.RenderSvg #.SvgMode.FixedAspect 
[24]  z←heading renderHtml svg 
     ∇ 

Hopefully the code is more or less self-explanatory, but if you’d like to learn more about SharpPlot there is excellent documentation at http://sharpplot.com. The documentation is actually written for C# users, but there is an illustration of how to translate the documentation to APL (and VB) at http://www.sharpplot.com/Languages.htm.

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

BBC micro:bit displaying a happy face

BBC micro:bit displaying a happy face

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 answering e-mail, I should stay at home, turn up the radiators, make lots of tea (with honey!) and have some fun writing code on my Raspberry Pi! Can there be a better way to ensure a speedy recovery?

By the way, if you are already a user of Dyalog APL but you haven’t got a Pi yet, you should read The APLer’s Quick-start Guide to the Raspberry Pi, which Romilly Cocking completed a few days ago. This explains what your options are for buying hardware, and how to get going with a free copy of Dyalog APL. If you don’t read it now, your cold may be over before all the bits are delivered, so hurry up!

I wasn’t feeling THAT energetic this morning, so I decided to ease back into things by trying to replicate Romilly’s reaction timer, which is written in MicroPython. To begin with, I extended the microbit class that I developed for the Morse code display function with a few new methods to cover the API calls that allow me to check the state of the two buttons on each side of the micro:bit display (see the image above).

First, I added a method called is_true, which takes a MicroPython expression as an argument, evaluates it using the PyREPL function, and returns 0 or 1 depending on whether the expression returns False or True (and fails if it returns something else):

 ∇ r←is_true expr;t;z
 :Access Public
 r←1⊃t←'True' 'False'∊⊂z←PyREPL expr
 :If ~∨/t ⋄ ⎕←'True/False expected, got: ',z ⋄ ∘∘∘ ⋄ :EndIf
 ∇

This is a useful building block, which allows the simple construction of functions like was_pressed, which takes ‘a’ or ‘b’ as an argument and tells you whether the button in question has been pressed since you last asked:

∇ r←was_pressed button
 :Access Public
 r←is_true 'button_',button,'.was_pressed()' 
∇

Once this is done, writing the Play function in the ReactionTimer namespace is easy, you can find the rest of the code on GitHub. The APL version is different from the MicroPython version in that – once the user presses button B and stops the game – the reaction times (in milliseconds) are returned as an integer vector. So now we can have some fun with data!

In the spirit of the micro:bit, I thought I’d produce a low tech character based chart, trying to remember the skills that were start-of-the-art when I started using APL. The AsciiChart function in the ReactionTimer namespace takes a vector of timings as the right argument, and produces a chart:

      times←ReactionTimer.Play
      times
251 305 294 415 338 298 294 251 378
      ReactionTimer.AsciiChart times
425| 
400|    * 
375|         *
350+ 
325|     * 
300|  * 
275|   *  ** 
250+ *      * 

The code (which is also on GitHub) is listed below. Because this is a pure function, I used the modern dfns style of function definition rather than the old style procedural form that I’ve used for the object oriented code. The function works by allocating each value to a bucket of the size defined by the variable scale. The fun part is the use of the outer product with equals (∘.=) between the list of buckets on the left (rb) and the scaled values on the right (⌊⍵÷scale) – and then using this Boolean array to index into a two-element character vector to produce the chart. The rest is scaling calculations and finally decorating with “tik marks”:

 AsciiChart←{
     scale←25 ⍝ size of each row
     tiks←4 ⍝ tik spacing
     (max min)←(⌈/ , ⌊/) ⍵ ⍝ maximum and minimum
     base←⌊min÷scale ⍝ round down to nearest scale unit
     rb←base+0,⍳⌈(max-min)÷scale ⍝ row base values
     r←' *'[1+rb∘.=⌊⍵÷scale] ⍝ our chart
     r←((≢rb)⍴'+',(tiks-1)⍴'|'),' ',r ⍝ add tiks
     r←(⍕⍪rb×scale),r ⍝ add base values
     ⊖r ⍝ low values last (humans!)
 }

Although I might be feeling better tomorrow, I expect to be back soon. I have a couple of plastic bags full of resistors, LEDs, potentiometers and cameras (yes, plural) that I have not opened yet!