Functional Programming for Under-4s

My grandson has recently learned to count, so I made a set of cards we could ‘play numbers’ with.

We both played. I showed him that you could write ‘maths sentences’ with the ‘and’ and the ‘is’ cards. Next time I visited, he searched in my bag and found the box of numbers. He emptied them out onto the sofa and completely unprompted, ‘wrote’:

I was ‘quite surprised’. We wrote a few more equations using small integers until one added to 8, then he remembered he had a train track that could be made into a figure-of-8 , so ‘Arithmetic Time’ was over but we squeezed in a bit of introductory set theory while tidying the numbers away.

From here on, I’m going to talk about computer programming. I won’t be explaining any jargon I use, so if you want to leave now, I won’t be offended.

I don’t want to take my grandson too far with mathematics in case it conflicts with what he will be taught at school. If schools teach computer programming, it will probably be Python and I gave up on Python.

Instead, I’ve been learning functional programming in the Clojure dialect of Lisp. I’ve been thinking for a while that it woud be much easier to learn functional programming if you didn’t already know imperative programming. There’s a famous text, known as ‘SICP’ or ‘The Wizard Book’ that compares Lisps with magic. What if I took on a sourceror’s apprentice to give me an incentive to learn faster? I need to grab him “to the age of 5”, before the Pythonista get him.

When I think about conventional programming, I make diagrams, and I’ve used Unified Modelling Language (UML) for business analysis, to model ‘data processing’ systems. An interesting feature of LIsps is that process is represented as functions and functions are a special type of data. UML is designed for Object Orient Programming. I haven’t found a way to make it work for Functional Programming (FP.)

So, how can I introduce the ideas of FP to a child who can’t read yet?
There’s a mathematical convention to represent a function as a ‘black-box machine’ with a hopper at the top where you pour in the values and an outlet at the bottom where the answer value flows out. My first thought was to make an ‘add function’ machine but Clojure “treats functions as first-class citizens”, so I’m going to try passing “+” in as a function, along the dotted line labelled f(). Here’s my first prototype machine, passed 3 parameters: 2, 1 and the function +, to configure the black box as an adding machine.

In a Lisp, “2 + 1” is written “(+ 2 1)”.
The ‘parens’ are ‘the black box’.

Now, we’ve made our ‘black box’ an adder, we pass in the integers 2 and 1 and they are transformed by the function into the integer 3.

We can do the same thing in Clojure. Lisp parentheses provide ‘the black box’ and the first argument is the function to use. Other arguments are the numbers to add.

We’ll start the Clojure ‘Read Evaluate Print Loop’ (REPL) now. Clojure now runs well from the command line of a Raspberry Pi 4 or 400 running Raspberry Pi OS.

$ clj
Clojure 1.11.1

user=> (+ 2 1)
3
user=>

Clearly, we have a simple, working Functional Program but another thing about functions is that they can be ‘composed’ into a ‘pipeline’, so we can set up a production line of functional machines, with the second function taking the output of the first function as one of it’s inputs. Using the only function we have so far:

![[5compose–IMG_20221116_135501768-2.jpg]]

In Clojure, we could write that explicitly as a pipeline, to work just like the diagram

(-> (+ 1 2) (+ 1))
4

or use the more conventional Lisp format (start evaluation at the innermost parens)

(+ (+ 1 2) 1)
4

However, unlike the arithmetic “+” operator, the Clojure “+” function can
add up more than 2 numbers, so we didn’t really need to compose the two “+” functions. This single function call would have got the job done:

(+ 1 2 1)
4

SImilarly, we didn’t need to use 2 cardboard black-boxes. We could just pour all the values we wanted adding up into the hopper of the first.

Clojure can handle an infinite number of values, for as long as the computer can, but I don’t think I’ll tell my grandson about infinity until he’s at least 4.

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Shop cop

Words interest me. As I’ve been getting interested in green woodworking and the appropriate tools, I’ve become more aware of the US term “shop”. A few days ago, in a discussion of why America is lagging behind on lower level tech education, someone suggested schools needed to reintroduce ‘shop’, to get kids interested in designing and making things. I think young Brits would know this as ‘Design Technology, Resistive Materials’. I did ‘Woodwork’ and ‘Metalwork’.

America takes its cars ‘to the shop’ because their ‘garages’ are being used as ‘car parks’. Obviously, it means ‘workshop’.  A shop where you buy work, a service instead of a product, as you walk down main street. Not at all like a job-shop in Britain where we try to sell spare labour to employers, or shop for jobs, if you prefer.

I came across a meaning from the world of share trading. A stock may be ‘shopped’ – actively sold. I think we’re finally getting to the meaning. A shop is a place (real or virtual) where goods, services and labour are traded, in either direction. A market stall. I almost wrote “store” but stores are where you keep things before selling our when they haven’t sold.

I was slightly side-tracked by coppers, copping criminals and taking them to the cop shop, trading their liberty for their crimes. My government assures me that if I haven’t committed a crime I won’t cop it. I wish I believed them. That’s the cost of lying in a market that depends on trust and information. Their share price is down.

April Fools’ Day Model of Space-Change

It is 1 April. This is NOT a joke but it may not be real. It’s a science thought experiment.

There’s a tiny bit of physics in my distant past but I am not a real physicist. In the last few years I’ve noticed the models of information I’m investigating resemble the ‘multi-worlds interpretation’ of quantum mechanics, which I have only heard about via radio, TV and Wikipedia. Quantum Mechanics is always rubbing up against Relativity, another idea about which I have a frustratingly inadequate understanding. I decided to investigate these worlds of weirdness but I find my brain getting horribly scrambled when I try to visualise space-time. I can’t and I don’t think anyone can. Our visual system has evolved for seeing a 3D world and that world changes. Humanity had lived, before the early 20th Century in a non-relativistic world. Those who do ‘get modern physics’ seem to rely on a mathematical understanding of the concepts.

In my models of information, I’d been thinking about the lack of a time-dimension in most computation. We usually model change in the world as a series of states, where data about a new state replaces the previous states. This starts to cause difficulties when computers have parallel paths of computation, as current multi-core processing chips do. Software has begun to address the problems with ‘immutability’. In simple terms, instead of replacing a value, a new value is added to the end of  a sequence, so historic values are retained. We have gone back before the memory-constrained computer age to learn from the Victorian hand-written ledger.

I became aware of research work at Cambridge University to reconcile ‘QM and R’ which also modelled time as state-change but I’ve found it very difficult to think about ‘the state change dimension of space’ as a sequence of events without falling back on ideas of time, speed and rate of change. The ‘idea of time’ which may be a cultural concept is deeply woven into our current paradigm.

In trying to free my mind of time, I’ve been hanging out in ‘the difficult time questions’ corner of Quora. Someone gave me a breakthrough by describing a simple clock:
Imagine going into deep space where gravity and friction to movement can be assumed to be zero. Throw an object. The distance it has travelled is a clock.

An April Fool thought experiment of time:
Make the object a spacecraft containing a holographic camera. Time passed can now be measured as a distance. Let us assume we prepared by asking someone to invent a unit of distance and mark it repeatedly on a very long tape, alongside the path of our space-craft. We don’t know the size of that unit. Now retrieve the holographic camera and put the recording medium in a holographic projector and project it onto a screen.
Think of the ‘slide-show’ as you being equivalent to you travelling along a sequence of equally spaced ‘holographic plates’. Consider changing the distance between plates in some regions of the recording (analogous to compressing time) or having instantaneously (enough) reversed the spacecraft during recording. Evidence of events would be passed in the opposite order but time would still be one way. Time could appear to be reversed if the projector was modified to play the recording in reverse order but that’s model hacking not reality.

Stage 2 – imagine this model as a streamed live-view of the universe, with the universe interfering with distances, as Relativity tells us it does, and has been observed. The problem is that a lot of the science assumes time is constant and that’s difficult to disprove from inside the space-time paradigm. We can only observe a space/state-change view and we may have invented time. Have fun with it.

Suits you?

Last night I went to a ‘Product Tank Birmingham’ workshop on ‘Empathy Mapping’. As an exercise, we looked at ‘a product meeting group’ and tried to identify its customers. There was a brief discussion about ‘Product Owners’ (from agile software development) and ‘Product Managers’ who often have a more marketing-led approach. Someone then commented on what ‘Product people’ think. I found I didn’t agree. I reflected on the difference between Product Owners (in this context: me), who care about giving people the product they want and Product Managers, who seem to care more about people’s relationship with the product.

I realised there is a half-way house and I have not, to date, worked in it. My experience in agile software development has been about “custom” development of software products for small teams with a shared view of what they want. I’ve realised for a while that my experience is very different to those Product Owners who have to develop a more generic product to ‘optimise’ across a set of potential or actual customers who have differing needs. There is an extra role there which is far more like my understanding of Product Management. I think the key difference is the need to correctly judge the closeness of fit needed to achieve mass market appeal vs the bespoke tailoring trade that I’ve worked in.

Early in my career, I worked as a programmer on a software package for pharmaceutical companies. We coded to specifications provided by 2 people, a salesman and our technical manager, who both travelled the world visiting customers’ sites. Looking back, I think the salesman was much better at identifying the features that would be valued by most customers. Is marketing USEFUL?

Apple Mac Mini 4,1 running Ubuntu Linux

An old Mac Mini server was ‘going in the skip’ because it had been replaced as an office server. It was handed to me instead, due to my reputation as an IT dumpster diver.
https://everymac.com/systems/apple/mac_mini/specs/mac-mini-core-2-duo-2.66-mid-2010-server-specs.html (server model: 2.66 GHz Core 2 Duo (P8800))

I did MANY upgrades to get it to the latest release, 10.13 High Sierra. A couple of weeks later, Apple announced that they were stopping further updates. I understood at the time this was because this generation of hardware had a 32-bit EFI boot system, despite being a 64-bit processor and that it was only possible to boot Ubuntu by modifying the Ubuntu OSI image. This may have been true at the time. I’ve tried to get to know MacOS but it sometimes feels really sluggish on this hardware and now I’m not seeing the latest features, I decided to consider giving up the struggle.

Today, I tried to boot an Ubuntu 64-bit image from a ‘live’ USB memory stick I’d built on another Ubuntu system. I wanted to see how it would fail. To my surprise, it booted. I had to go into Settings to add a WiFi connections. The only problem I had was that tinny sound came from the Mac Mini’s internal speaker. When I plugged the headphone socket to the TV, rather than being routed by HDMI and the TV’s stereo sound inputs as Mac OS would do, I had no sound. A full install might fix that.

You get (this) Mac to boot from another device by pressing the <Alt> key at startup.
(This didn’t work on a white iMac with a Core 2 Duo processor when I tried months ago but that was probably an earlier version of Ubuntu.)

RUNOFF another copy?

I was telling a story about my first job a couple of days ago. I was an ‘applications programmer’ at Cambridgeshire College of Art and Technology. There was an Argentinian lecturer who knew our systems. He asked if his wife could use the computer centre facilities to write up her research thesis during the Summer holidays. We were casual users of a text processing ‘tagging language’ for documentation. It was called DSR, Digital [Equipment Co.] Standard Runoff, so my colleague John suggested she used that. The ‘typing department’ had some fancy new ‘word processors’ (I think they were Wang) but we didn’t have any authority over them and wouldn’t be able to help her with problems. We also had doubts about whether they had the capacity for a whole thesis.

So it was that John and, in his absence, I provided occasional help to a charming, intelligent Argentinian woman during the outbreak of the Falklands War in 1982, while the British press ramped up the hatred of British idiots against the entire Argentinian nation. She was the first Argentinian I’d ever met and it was the first time I had any indication that fascism could also infect the UK or was personally shamed by the state of our newspapers. I remember us scooping up some hate-filled tabloid front page and dumping it, seconds before our guest arrived.

In later jobs I learned of Unix roff, nroff and troff and came to assume that Runoff was DEC’s version of the Unix tools. Today I discovered that isn’t true. DEC’s Runoff came from the common ancestor of the Unix tools, Runoff on CTSS then Multics (1964.)
“types out text segments in manuscript form.”

https://en.wikipedia.org/wiki/TYPSET_and_RUNOFF

CTSS was also the original home of LISP, ALGOL and the text editor QED, the predecessor of ed, vi and vim.

Tooling for Clojure and ClojureScript

[:ChangeLog
(:v0.2
“recognise that ‘resolving dependencies’ and ‘build’ are different operations.”
“Add conversion tools between project.clj & deps.edn”)
(:v0.3
“Remove CLI tools described as a build tool comment.”)]

WARNING
I still have much to learn about ClojureScript tooling but I thought I’d share what (I think) I’ve learned, as I have found it difficult to locate advice for beginners that is still current. This is very incomplete. It may stay that way or I may update it into a living document. I don’t actually have much advice to give and it’s only about the paths that have interested me.

Clojure development requires:

• a text editor,

and optionally,

• a REPL, for a dynamic coding environment
• dependency and build tool(s).

The absolute minimum Clojure environment is a Java .jar file, containing the clojure.main/main entry point, which can be called with the name of your file.clj as a parameter, to read and run your code. I don’t think anyone does that, after they’ve run it once to check it flies.

Based on 2 books, ‘Clojure for the Brave & True’ and ‘Living Clojure’, my chosen tools are emacs for editing, with CIDER connecting a REPL, and Leiningen as dependency & build tool. ‘lein repl’ can also start a REPL.
Boot is available as an alternative to Leiningen but I got the impression it might be a bit too ‘exciting’ for a Clojure noob like me, so I haven’t used it yet.
CIDER provides a client-server link between an editor (I’m learning emacs) and a REPL.

If you use Leiningen, it comes with a free set of assumptions about development directory structure and the expectation that you will create a file, project.cli in the root directory of each ‘project’, containing a :dependencies vector. Then magic happens. If your change the dependencies of your project, the config fairies work out everything else that needs changing.

Next, I wanted to start using ClojureScript (CLJS.) I assumed that the same set of tools would extend. I was wrong to assume.
Unfortunately, CLJS tooling is less standardised and doesn’t seem to have reached such a stable state.

In ‘Living Clojure’, Carin Meier suggests using cljsbuild. It uses the lein-cljsbuild plugin and the command:

lein cljsbuild auto

to start a process which automatically re-compiles whenever a change is saved to the cljs source file. If the generated JavaScript is open in a browser, then the change will be shown in the browser window. This is enough to get you going. It is my current state.

I’ve read that there are other tools such as Figwheel, now transitioning to ‘Figwheel Main’ which hot-load the transcribed code into the browser as you change it.
There is a lein-figwheel as well as a lein-cljsbuild, which at least sounds like a drop-in replacement. I suspect it isn’t that simple.

There are several REPLs, though there seems to be some standardisation around nrepl.
It was part of the Clojure project but now has its own nrepl/nrepl repository on Github. It is used by Clojure, ‘lein repl’ and by CIDER.

There is something called Piggieback which adds CLJS support to NREPL. There is a CIDER Piggieback and an NREPL Piggieback. I have NO IDEA! (yet.)
shadow-cljs exists. Sorry, that’s all I have there too.

At this point in my confusion, a dependency issue killed my tool-chain.
I think one of the config fairies was off sick that day. The fix was a re-install of an emacs module. This forced me to explore possible reasons. I discovered the Clojure ‘Getting Started’ page had changed (or I’d never read it.)
https://clojure.org/guides/getting_started

There are also (now?) ‘Deps and the CLI Tools’ https://clojure.org/guides/deps_and_cli and https://clojure.org/reference/deps_and_cli

I think these are new and I believe they are intended to be the beginners’ entry point into Clojure development, before you dive into the more complex tools. There are CLI commands: ‘clojure’ and a wrapper that provides line-editing, ‘clj’
and a file called ‘deps.edn’ which specifies the dependencies, much as ‘projects.clj’ :depencies vector does for Leiningen but with a different syntax.

I’m less clear if these are also intended as new tools for experts, to be used by ‘higher order’ tools like Leiningen and Figwheel, or whether they will be adopted by those tools.

[ On the day I wrote this, I had a tip from didibus on clojureverse.org that there are plugins for Leiningen and Boot to use an existing deps.edn,

• https://github.com/RickMoynihan/lein-tools-deps
• https://github.com/seancorfield/boot-tools-deps and:
  https://corfield.org/blog/2018/04/18/all-the-paths/, about boot-tools-deps)

so perhaps this is the coming future standard for specifying & resolving dependencies, while lein and boot continue to provide additional build capabilities. deps.edn refers to Maven. I discovered elsewhere that Maven references existed but were hidden away inside Leiningen. It looks like I need to learn a little about Apache Maven. I didn’t come to Closure via Java but I can see the advantages to Java practitioners of using their standard build tool. I may need to drop down into Java one day, so I guess I may as well learn about Java-land now.

Also via: https://clojureverse.org/t/has-anyone-written-a-tool-to-spit-out-a-deps-edn-from-a-project-clj/2086, there is a https://github.com/hagmonk/depify, which ‘goes the other way’, trying it’s best to convert a project.clj to a deps.edn. Hopefully that would be a ‘one-off’? ]

I chose the Clojure language for its simplicity. The tooling journey has been longer than I expected, so I hope this information cuts some corners for you.

[ Please let me know if I’m wrong about any of this or if there are better, current documents that I should read. ]

A new target for Software Developers: Sensei.

I originally wrote this as an answer to a question on Quora but I’m increasingly concerned at the cost of higher education for young people from families that are not wealthy. I had parents who would have sacrificed anything for my education but I had clever friends who were not so fortunate. The system is bleeding talent into dead-end jobs. Below, I consider other models of training as I hope it might start a conversation in the technology community and the political infrastructure that trickles money down into it.

Through learning about ‘Agile’ software development, I became interested in related ‘Lean’ thinking. It borrows from Japanese cultural ideas and the way the martial arts are taught. I think the idea is that first you do, then you learn and finally you understand (as illustrated by the film ‘Karate Kid’.) That requires a ‘master’ or ‘Sensei’ to guide and react to what s/he sees about each individual’s current practice. It seems a good model for programming too. There may be times when doing is easier if you gain some understanding before you ‘do’ and advice and assistance with problem solving could be part of this. I’m not alone in thinking this way, as I see phrases like “kata” and “koans” appearing around software development.

I’ve also seen several analogies to woodworking craft which suggests that a master-apprentice relationship might be appropriate. There is even a ‘Software Craftsmanship’ movement. This could work as well in agile software development teams, as it did for weavers of mediaeval tapestries.

A female Scrum Master friend assures me that the word “master” is not gendered in either of these contexts. Of course, not all great individual crafts people make good teachers but teams with the best teachers would start to attract the best apprentices.

If any good programmers aren’t sure about spending their valuable developer’s time teaching, I recommend the “fable in novella form” Jonathan Livingston Seagull, written by Richard Bach, about a young seagull that wants to excel at flying.

Small software companies ‘have a lot on’ but how much would they need to be paid to take on an apprentice in their development teams, perhaps with weekly day-release to a local training organisation? I’d expect a sliding scale to employment as they became productive or were rejected back into the cold, hard world if they weren’t making the grade.

Model Software

Today, I had to stop myself writing “solving the problem” about developing software. Why do we say that? Why do software people call any bounded area of reality “the problem domain”?

My change of mind has been fermenting for a while, due to modelling business processes, learning about incremental, agile software development and more recently writing and learning functional programming. In the shower this morning, I finally concluded that I think software is primarily a modelling medium. We solve problems using the models we build.

Wanting to create another first-person shooter game or to model the fluids in a thermo-nuclear reactor are challenges, not problems. We build models of systems we have defined and the systems don’t even have to be real. I read a couple of days ago that a famous modern philosopher said our world is made of both reality and our ideas. Assuming the computer hardware is real, the software can model either reality or our imagination; our chosen narrative.

‘Digital’ gets everyone working with software models instead of reality. Once everyone lives inside the shared model, when does it become our reality?

Or when did it?

Idea-bending minds, mind-bending ideas

Long ago, I took 4/9ths of an undergraduate physics degree, along with 4/9ths computer science and 1/9th mathematics. Having had little or no contact with physics in the intervening years, I’ve started to do some light reading about relativity in the last couple of years. This week, I came across a tip on Quora * to a fellow traveller in space-time: “stop thinking of the speed of light as a number”. Erm… WHAT?! As every school child knows, the maximum  speed of light (or any other form of electromagnetic radiation) in a vacuum is about 600,000 Km/s. That sounds like a number to me. The problem with speed in Einstein’s relativistic model of reality though, is that distance and time get very weird. That makes them hard to think about, so the advice was to ignore what we think we know and look at things in a new way.
[* – I’ll add an acknowledgement to the author of  the comment on Quora, if I ever find it again. It took me a while to understand what I’d read. ]

I’m not sure I was entirely paying attention when I studied physics last time. I don’t remember anyone explaining the precise nature of the the scientific method, or indeed what physics actually is; that’s metaphysics. This time around I see science as the process of understanding how nature works, using evidence rather than guessing then arguing the case for your beliefs. That is philosophy, or a religion. Physics, in particular, is about observing reality and working out what the rules are. It is NOT about saying why things happen. As science was becoming formalised, it was known as ‘natural philosophy’ i.e. philosophy that refers to evidence from nature.

Einstein’s Theories of Relativity say that matter and energy are equivalent. His equation of mass-energy equivalence records the relationship between the alternative mass and energy forms of matter. It is a very well known equation, even with people who have no idea what it refers to.

The form of the equation we are most familiar with is

E = mc²

E is the concentrated energy contained in a mass, m. E is a much bigger number than m because we know that c is a big number AND it’s squared.

This equation can be re-arranged to a form I don’t remember seeing or taking note of before:

c = √(E/m)

This new way (at least to me) of looking at this century old theory says that c is related to the ratio between the Energy and mass of an object. This ratio stays the same, even as space-time expands or contracts, according to the General Theory of Relativity. The recent confirmation by the LIGO project of gravitation waves that also travel at c, were also predicted, so this gives extra weight to the theory

I’ve realised that physics often relates things to each other, without saying which is the ‘fundamental thing’. Does gravity bend space-time or is the curvature of space-time what causes gravity? The equations work either way.

John Archibald Wheeler said it a different way: “Space-time tells matter how to move; matter tells space-time how to curve” and matter can be converted to energy, energy to matter.