Programmers are humans too:
On the design of notations

Steven Pemberton, CWI, Amsterdam

The Author

Contents

ME

ME

= Maine

Apparent Rule

Looking at GA= Georgia, and FL= Florida, it appears that there is no real rule.

Apparent Rule

Looking at GA= Georgia, and FL= Florida, it appears that there is no real rule.

What I could work out is:

Codes

NE: Nevada or Nebraska?

Codes

NE: Nevada or Nebraska?

It's Nebraska, but NB would have been a better choice

Codes

NE: Nevada or Nebraska?

It's Nebraska, but NB would have been a better choice

MI: Mississippi, Missouri, Michigan, or Minnisota?

Codes

NE: Nevada or Nebraska?

It's Nebraska, but NB would have been a better choice

MI: Mississippi, Missouri, Michigan, or Minnisota?

It's Michigan, but MG would have been a better choice

Codes

NE: Nevada or Nebraska?

It's Nebraska, but NB would have been a better choice

MI: Mississippi, Missouri, Michigan, or Minnisota?

It's Michigan, but MG would have been a better choice

MS: Mississippi, Missouri, or Minnisota?

Codes

NE: Nevada or Nebraska?

It's Nebraska, but NB would have been a better choice

MI: Mississippi, Missouri, Michigan, or Minnisota?

It's Michigan, but MG would have been a better choice

MS: Mississippi, Missouri, or Minnisota?

It's Mississippi, but MP would have been a better choice.

Active and Passive

But solving these problems with reading 2-letter codes would still not solve the problem of writing them: your passive and active abilities are different.

Doing it better

I couldn't believe it wasn't possible to do the 2-letter codes better.

So I wrote a program (in ABC as it happens; more on that later).

The best rule I came up with:

The point

My point here is that the 2-letter codes were introduced because of automation.

But that is no excuse for ignoring the needs of people.

People are strange...

The fact is, people are strange, yes even you, even me.

For instance, someone did research in whether tools affected how people wrote.

People are strange...

The fact is, people are strange, yes even you, even me.

For instance, someone did research in whether tools affected how people wrote.

People are strange...

The fact is, people are strange, yes even you, even me.

For instance, someone did research in whether tools affected how people wrote.

People are strange...

The fact is, people are strange, yes even you, even me.

For instance, someone did research in whether tools affected how people wrote.

People are strange...

Research into interfaces for playing chess:

People are strange...

Research into interfaces for playing chess:

Mouse was by far the fastest

People are strange...

Research into interfaces for playing chess:

Mouse was by far the fastest

But with direct manipulation, people won more often...

Example

Hold your hand up.

Count the number of triangles on the next screen, and check your result.

Drop your hand when you have counted.

 Triangles

A lot of different shapes randomly placed

Now do the same

but count the red shapes.

Red

A lot of shapes, randomly coloured, randomly placed

Usability

Usability is about designing things (software/programming languages/cookers) to allow people to do their work:

Efficient, Error-free, Enjoyable or
Fast, Faultless and Fun

Don't confuse usability with learnability: they are distinct and different.

HCI

The problem is that the people designing things are usually not the people who will be using those things, and they tend to design for themselves.

So... you have to use HCI techniques:

Notations

No one really talks seriously about the usability of notations.

The design of notations affects what you can do with them.

Dijkstra

The ease of manipulation with numbers is greatly dependent on the nomenclature we have chosen for them -- Dijkstra

Numbers

For instance, Roman numerals:

Homework

I was helping my children with their maths homework, and a question arose for me:

Why do they make things so difficult?

So I went back to first principles.

Warning

What follows was more than a year's work, using reams of paper. It is hard work making things simple. It resulted in a monograph that I wrote for my sons' birthdays. You can read it here: Numbers.

As a colleague who designs program interfaces complained: "When you succeed in making an interface as easy to use as a coffee machine, they treat you like a plumber"

Addition

We'll use base 1 numbers: // is 2, /// is 3

We define addition as sticking two numbers together:

//+///=/////

The complement of addition

We define subtraction as

(a+b) − b = a

This is a declarative definition. It tells you the what but not the how.

Because addition is commutative:

(a+b) = (b+a)

you can use subtraction to obtain both the left and right operands of addition:

(a+b) − a =

(b+a) − a = b

Mystery numbers

Subtraction creates a new sort of number we didn't start with, since we have expressions now like

3 − 5

the result of which we can't write with stripes.

Negative numbers upset mathematicians right up into the 19th century, being referred to as "fictitious" solutions.

Even banks didn't start using negative numbers until recently.

Zero

Whether subtraction also introduces zero, or whether it was there from the start is something mathematicians disagree on to this day.

At least historically though, it wasn't originally considered a number.

Zero is the identity for addition and subtraction since

(a+0) = a

We also have a monadic version of − as a shorthand:

−a = 0 − a

Multiplication

We go up a level, and define multiplication in terms of addition:

a × 3 = a + a + a

and it also has an identity value:

a×1 = a

(That was handwaving; the true definition of multiplication is:

(a + b) × c = a×c + b×c

It still defines multiplication in terms of addition.)

The complement of multiplication

We define division in exactly the same way as we did with subtraction:

(a×b) ÷ b = a

And since multiplication is also commutative, you can extract both a and b in the same way as we did with subtraction.

(I use ÷ instead of / because when user-testing with my target audience, they said "Please use the same symbols as on a calculator".)

More mystery numbers

Division adds the rationals to the mix, since we now have numbers such as

2÷3

(We may represent such numbers as ⅔, but we should recognise this as just an uncalculated expression, just as −5 is)

Monadic divide

Oddly, there is no monadic version of divide. But if we define it using the same pattern:

÷a = 1 ÷ a

something surprising happens: identities that we know from the lower level have exactly the same form as ones at this level. For instance:

Identities

−−a = a
÷÷a = a

Identities

a−−b = a + b
a÷÷b = a × b

Identities

−(a−b) = (b−a)
÷(a÷b)  = (b÷a)

(This shows that while subtraction and division aren't commutative, they are commutable.)

Up another level

Just as multiplication is defined as repeated addition, so is raising to the power defined as repeated multiplication:

a↑3 = a × a × a

One difference at this level: ↑ is not commutative:

2↑3 ≠ 3↑2

Which means it has two complements, one to give a and one to give b.

The complements of power

First for a, which uses our regular pattern:

(a↑b)↓b = a

This is of course what we know of as root, where x↓y traditionally, and weirdly, is notated

y√x

The other complement of power

Now we need b:

(a↑b)⇓a = b

This is logarithm, where x⇓y is equally weirdly notated traditionally as

logy x

So if ↑ is a higher version of multiplication, then ↓ and ⇓ are just higher versions of division.

The point

Apart from making the close relationship between root and log obvious, defining them in this way suddenly exposes that literally dozens of well known identities have a similar form to identities at the two lower levels!

Just to pluck a few out:

Identities 1

a×(−b) = −(a×b)

Identities 1

a×(−b) = −(a×b)
a↑(−b) =  ÷(a↑b)

Identities 1

a×(−b) = −(a×b)
a↑(−b) =  ÷(a↑b)

          (a−b = 1/ab)

Identities 2

a×(÷b) = a÷b

Identities 2

a×(÷b) = a÷b
a↑(÷b) = a↓b

Identities 2

a×(÷b) = a÷b
a↑(÷b) = a↓b

               (a1/b = b√a)

Identities 3

÷(a÷b) = b÷a

Identities 3

÷(a÷b) = b÷a
÷(a⇓b) = b⇓a

Identities 3

÷(a÷b) = b÷a
÷(a⇓b) = b⇓a

               (1/ logba = logab)

Why is this notation better?

⇒ Consistent

⇒ Easier to use (once you've learnt it)

⇒ Exposes otherwise hidden relationships, such as the close relationship between log and root.

⇒ Use the same methods for solving equations:

a+2 = 4
a = 4−2

a × 2 = 4
a = 4 ÷ 2

a↑2 = 4
a = 4↓2

2↑a = 4
a = 4⇓2

Programming languages

A most important, but also most elusive, aspect of any tool is the influence on the habits of those who train themselves in its use. If the tool is a programming language, this influence is -- whether we like it or not -- an influence on our thinking habits. -- Dijkstra

Programmers are possibly human too

Imagine, hypothetically, that programmers are humans...despite all evidence to the contrary:

Programmers are possibly human too

Imagine, hypothetically, that programmers are humans...despite all evidence to the contrary:

Programmers are possibly human too

Imagine, hypothetically, that programmers are humans...despite all evidence to the contrary:

Programmers are possibly human too

Imagine, hypothetically, that programmers are humans...despite all evidence to the contrary:

Programmers are possibly human too

Imagine, hypothetically, that programmers are humans...despite all evidence to the contrary:

Programmers are possibly human too

Imagine, hypothetically, that programmers are humans...despite all evidence to the contrary:

Also pretend, just for a moment, that their chief method of communicating with a computer was with programming languages.

Programmers are (possibly) human too

Imagine, hypothetically, that programmers are humans...despite all evidence to the contrary:

Also pretend, just for a moment, that their chief method of communicating with a computer was with programming languages.

What should you do?

ABC

We designed a programming language: ABC

We used the HCI principles:

ABC: results

ABC: results

ABC: results

ABC: results

ABC: results

ABC went on to form the basis of Python.

Declarative programming

1957: The first municipal computer (Norwich, UK)

The First Computer in Norwich

Just one of 21 cabinets making up the computer.

2015: The Raspberry Pi Zero

Raspberry Pi in Norwich

The first computer so cheap that they gave it away on the cover of a magazine

How do they compare?

The Elliot ran for about a decade, 24 hours a day.

How long do you think it would take the Raspberry Pi Zero to duplicate that amount of computing?

How do they compare?

The Elliot ran for about a decade, 24 hours a day.

How long do you think it would take the Raspberry Pi Zero to duplicate that amount of computing?

The Raspberry Pi Zero is about one million times faster...

Compare

The Raspberry Pi is not only one million times faster. It is also one millionth the price.

A factor of a million million.

A terabyte is a million million bytes: nowadays we talk in terms of very large numbers.

Want to guess how long a million million seconds is?

Compare

The Raspberry Pi is not only one million times faster. It is also one millionth the price.

A factor of a million million.

A terabyte is a million million bytes: nowadays we talk in terms of very large numbers.

Want to guess how long a million million seconds is?

30,000 years...

A really big number...

Moore's Law

In fact a million million times improvement is about what you would expect from Moore's Law over 58 years.

Except: the Raspberry Pi is two million times smaller as well, so it is much better than even that.

Pricing of new technology

When a new technology is introduced, it is often priced not on what it costs to produce, but based on what it costs to do the same with the technology it is replacing.

For example, when Edison first introduced electric light into homes, electricity was priced based on what it would cost to produce the same amount of light by traditional means, but now with additional benefits of instant light, and no flames.

Similarly, early computers were priced based on what it would cost to do the same amount of computation using people.

1957

In the 50's, computers were so expensive that nearly no one bought them, but leased them.

To rent time on a computer then would cost you of the order of $1000 per hour: several times the annual salary of a programmer!

When you leased a computer you would get programmers for free to go with it.

Compared to the cost of a computer, a programmer was almost free.

The design of programming languages

The first programming languages were designed in the 50s:

Cobol, Fortran, Algol, Lisp.

They were designed with that economic relationship of computer and programmer in mind.

It was much cheaper to let the programmer spend lots of time producing a program than to let the computer do some of the work for you.

Programming languages were designed so that you tell the computer exactly what to do, in its terms, not what you want to achieve in yours.

Back to now

It happened slowly, almost unnoticed, but nowadays we have the exact opposite position:

Compared to the cost of a programmer, a computer is almost free.

I call this Moore's Switch.

Moore's Switch

Moore's Switch illustrated
Relative costs of computers and programmers, 1957-now

But, we are still programming in programming languages that are direct descendants of the languages designed in the 1950's!

We are still telling the computers what to do.

Declarative programming

A new way of programming: declarative programming.

This describes what you want to achieve, but not how to achieve it..

Let me give some examples

The first declarative definition

Declarative approaches describe the solution space.

A classic example is when you learn in school that

The square root of a number n is the number r such that r × r = n

This doesn't tell you how to calculate the square root; but no problem, because we have machines to do that for us.

Procedural code

function f a: {
    x ← a
    x' ← (a + 1) ÷ 2
    epsilon ← 1.19209290e-07
    while abs(x − x') > epsilon × x: {
        x ← x'
        x' ← ((a ÷ x') + x') ÷ 2
    }
    return x'
}

This is why documentation is so essential in procedural programming.

What does 'Declarative programming' mean?

A Procedural Clock

A clock in C, 1000+ lines

1000 lines, almost all of it administrative. Only 2 or 3 lines have anything to do with telling the time.

And this was the smallest example I could find. The largest was more than 4000 lines.

A Declarative Clock

type clock = (h, m, s)
displayed as 
   circled(combined(hhand; mhand; shand; decor))
   shand = line(slength) rotated (s × 6)
   mhand = line(mlength) rotated (m × 6)
   hhand = line(hlength) rotated (h × 30 + m ÷ 2)
   decor = ...
   slength = ...
   ...
clock c
c.s = system:seconds mod 60
c.m = (system:seconds div 60) mod 60
c.h = (system:seconds div 3600) mod 24

A Running Declarative Clock

The Views System

XForms

XForms is a declarative system for defining applications. BBC Sport App

It is a W3C standard, and in worldwide use.

Example: 150 person years becomes 10!

A certain company makes one-off BIG machines (walk in): user interface is very demanding — traditionally needed:

5 years, 30 people.

With XForms this became:

1 year, 10 people.

Do the sums. Assume one person costs 100k a year. Then this has gone from a 15M cost to a 1M cost. They have saved 14 million! (And 4 years)

Example: Insurance Industry

Manager: I want you to come back to me in 2 days with estimates of how long it will take your teams to make the application.

Example: Insurance Industry

Manager: I want you to come back to me in 2 days with estimates of how long it will take your teams to make the application.

[Two days later]

Programmer: I'll need 30 days to work out how long it will take to program it.

Example: Insurance Industry

Manager: I want you to come back to me in 2 days with estimates of how long it will take your teams to make the application.

[Two days later]

Programmer: I'll need 30 days to work out how long it will take to program it.

XFormser: I've already programmed it!

Example: NHS

The British National Health Service started a project for a health records system.

Example: NHS

The British National Health Service started a project for a health records system.

One person then created a system using XForms.

State

XForms is all about state. (Which means it meshes well with REST - Representational State Transfer).

Initially the system is in a state of stasis.

When a value changes, by whatever means, the system updates related values to bring it back to stasis.

This is like spreadsheets, but much more general.

The result is: programming is much easier, since the system does all the administrative work for you.

Example

I've got a position in the world as x and y coordinates, and I want to display the map tile of that location at a certain zoom.

My data:

x, y, zoom

Openstreetmap has a REST interface for getting such a thing:

http://openstreetmap.org/<zoom>/<x>/<y>.png

Map interface

However, the Openstreetmap coordinate system changes at each level of zoom.

As you zoom out, there are in each axis half as many tiles, so there are ¼ as many tiles. And the interface indexes tiles, not locations.

So to get a tile:

  1. You have to know how big a tile is
  2. you have to calculate the correct index using this plus the zoom.

Declarative Example

The data: x, y, zoom

scale = 226 - zoom
tilex = floor(x/scale)
tiley = floor(y/scale)
url = concat("http://tile.openstreetmap.org/", zoom, "/", tilex, "/", tiley, ".png")

That is really all that is needed (modulo syntax, which looks like this:)

<bind ref="tilex" calculate="floor(../x div ../scale)"/>

That's the form. Now the content:

<input ref="zoom" label="zoom"/>
<input ref="x" label="x"/>
<input ref="y" label="y"/>
<output ref="url" mediatype="image/*"/>

and the tile will be updated each time any of the values change.

Live tile with zoom

Source

Map

Source

Map

Source

Conclusion

For historical reasons, present programming languages are at the wrong level of abstraction: they don't describe the problem, but only one particular solution.

Declarative programming allows programmers to be ten times more productive: what you now write in a week, would take a morning; what now takes a month would take a couple of days.

Once project managers realise they can save 90% on programming costs, they will switch to declarative programming.

I believe that eventually everyone will program declaratively: fewer errors, more time, more productivity.