Tag: compilers

Peter Landin: Elegance from Logic

Celebrating LGBTQ+ Greats

Thousands of programming languages have been invented in the many decades since the first. But what makes a good language? A key idea behind language design is that they should make it easy to write complex algorithms in simple and elegant ways. It turns out that logic is key to that. Through his work on programming language design, Peter Landin as much as anyone, promoted both elegance and the linked importance of logic in programming. 

Pride flag with lambda x.x (identity) superimposed
Pride image by Image by Pete Linforth from Pixabay. Composite by PC

Peter was an eminent Computer Scientist who made major contributions to the theory of programming languages and especially their link to logic. However, he also made his mark in his stand against war, and support of the nascent LGBTQ+ community in the 1970s as a member of the Gay Liberation Front. He helped reinvigorate the annual Gay Pride marches as a result of turning his house into a gay commune where plans were made. It’s as a result of his activism as much as his computer science that an archive of his papers has been created in the Oxford Bodleian Library.

However, his impact on computer science was massive. He was part of a group of computing pioneers aiming to make programming computers easier, and in particular to move away from each manufacturer having a special programming language to program their machines. That approach meant that programs had to be rewritten to work on each different machine, which was a ridiculous waste of effort! Peter’s original contribution to programming languages was as part of the team who developed the programming language, ALGOL which most modern programming languages owe a debt to.

ALGOL included the idea of recursion, allowing a programmer to write procedures and functions that call themselves. This is a very mathematically elegant way to code repetition in an algorithm (the code of the function is executed each time it calls itself). You can get an idea of what recursion is about by standing between two mirrors. You see repeated versions of your reflection, each one smaller than the last. Recursion does that with problem solving. To solve a problem convert it to a similar but smaller version of the same problem (the first reflection). How do you solve that smaller problem? In the same way, as a smaller version of the same problem (the second reflection)… You keep solving those similar but smaller problems in the same way until eventually the problem is small enough to be trivial and so solved. For example, you can program a factorial method (multiplying all numbers from 1 to n together),in this way. You write that to compute factorial of a number, n, it just calls itself and computes the factorial of (n-1). It just multiply that result by n to get the answer. In addition you just need a trivial case eg that factorial of 1 is just 1.

factorial (1) = 1
factorial (n) = n * factorial (n-1)

Peter was an enthusiastic and inspirational teacher and taught ALGOL to others. This included teaching one of the other, then young but soon to be great, pioneers of Programming Theory, Tony Hoare. Learning about recursion led Hoare to work out a way, using recursion, to finally explain the idea that made his name in a simple and elegant way: the fast sorting algorithm he invented called Quicksort. The ideas included in ALGOL had started to prove their worth.

The idea of including recursion in a programming language was part of the foundation for the idea of functional programming languages. They are mathematically pure languages that use recursion as the way to repeat instructions. The mathematical purity makes them much easier to understand and so write correct programs in. Peter ran with the idea of programming in this way. He showed the power that could be derived from the fact that it was closely linked to a kind of logic called the Lambda Calculus, invented by Alonso Church. The Lambda Calculus is a logic built around  mathematical functions. One way to think about it is that it is a very simple and pure way to describe in logic what it means to be a mathematical function – as something that takes arguments and does computation on them to give results. This Church showed was a way to define all possible computation just as Turing’s Turing machine is. It provides a simple way to express anything that can be computed.

Peter showed that the Lambda Calculus could be used as a way to define programming languages: to define their “semantics” (and so make the meaning of any program precise).

Having such a precise definition or “semantics” meant that once a program was written it would be sure to behave the same way whatever actual computer it ran on. This was a massive step forward. To make a new programming language useful you had to write compilers for it: translators that convert a program written in the language to a low level one that runs on a specific machine. Programming languages were generally defined by the compiler up till then and it was the compiler that determined what a program did. If you were writing a compiler for a new machine you had to make sure it matched what the original compiler did in all situations … which is very hard to do.

So having a formal semantics, a mathematical description of what a compiler should do, really makes a difference. It means anyone developing a new compiler for a different machines can ensure the compiler matches that semantics. Ultimately, all compilers behave the same way and so one program running on two different manufacturer’s machines are guaranteed to behave the same way in all situations too.

Peter went on to invent the programming language ISWIM to illustrate some of his ideas about the way to design and define a programming language. ISWIM stands for “If you See What I Mean”. A key contribution of ISWIM was that the meaning of the language was precisely defined in logic following his theoretical work. The joke of the name meant it was logic that showed what he meant, very precisely! ISWIM allowed for recursive functions, but also allowed recursion in the definition of data structures. For example, a List is built from a List with a new node on the end. A Tree is built from two trees forming the left and right branches of a new node. They are defined in terms of themselves so are recursive.

Building on his ideas around functional programming, Peter also invented something he called the SECD machine (named after its components: a Stack, Environment, Control and Dump). It effectively implements the Lambda calculus itself as though it is a programming language.ISWIM provided a very simple but useful general-purpose low level language. It opened up a much easier way to write compilers for functional programming languages for different machines. Just one program needed to be written that compiled the language into SECD. Then you had a much simpler job of writing a compiler to convert from the low level SECD language to the low level assembly language of each actual computer.  Even better, once written, that low level SECD compiler could be used for different functional programming languages on a single machine. In SECD, Peter also solved a flaw in ALGOL that prevented functions being fully treated as data. Functions as Data is a powerful feature of the best modern programming languages. It was the SECD design that first provided a solution. It provided a mechanism that allowed languages to pass functions as arguments and return them as results just as you could do with any other kind of data without problem.

In the later part of his life Peter focussed much more on his work supporting the LGBTQ+ community having decided that Computer Science was not doing the good for humanity he once hoped. Instead, he thought it was just supporting companies making profit, ahead of the welfare of people. He decided that he could do more good as part of the LGBTQ+ community. Since his death there has been an acceleration in the massing of wealth by technology companies, whereas support for diversity has made a massive difference for good, so in that he was prescient. His contributions have certainly, though, provided a foundation for better software, that has changed the way we live in many ways for the better. Because of his work they are less likely to cause harm because of programming mistakes, for example, so in that at least he has done a great deal of good.

by Paul Curzon, Queen Mary University of London

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EPSRC supports this blog through research grant EP/W033615/1. 

Sorry to bug you: Grace Hopper

Close up head on of a flying butterfly or moth
Image by Josch13 from Pixabay

In the 2003 film The Matrix Reloaded, Neo, Morpheus, Trinity and crew continue their battle with the machines that have enslaved the human race in the virtual reality of the Matrix. To find the Oracle, who can explain what’s going on (which, given the twisty plot in the Matrix films, is always a good idea), Trinity needs to break into a power station and switch off some power nodes so the others can enter the secret floor. The computer terminal displays that she is disabling 27 power nodes, numbers 21 to 48. Unfortunately, that’s actually 28 nodes, not 27! A computer that can’t count and shows the wrong message!

Sadly, there are far too many programs with mistakes in them. These mistakes are known as bugs because back in 1945 Grace Hopper, one of the female pioneers of computer science, found an error caused by a moth trapped between the points at Relay 70, Panel F, of the Mark II Aiken Relay Calculator being tested at Harvard University. She removed the moth, and attached it to her test logbook, writing ‘First actual case of bug being found’, and so popularised the term ‘debugging’ for testing and fixing a computer program.

Grace Hopper is famous for more than just the word ‘bug’ though. She was one of the most influential of the early computer pioneers, responsible for perhaps the most significant idea in helping programmers to write large, bug-free programs.

As a Lieutenant in the US Navy reserves, having volunteered after Pearl Harbor, Grace was one of three of the first programmers of Harvard’s IBM Mark I computer. It was the first fully automatic programmed computer.

She didn’t just program those early computers though, she came up with innovations in the way computers were programmed. The programs for those early computers all had to be made up of so-called ‘machine instructions’. These are the simplest operations the computer can do: such as to add two numbers, move data from a place in memory to a register (a place where arithmetic can be done in a subsequent operation), jump to a different instruction in the program, and so on.

Programming in such basic instructions is a bit like giving someone directions to the station but having to tell them exactly where to put their foot for every step. Grace’s idea was that you could write programs in a language closer to human language where each instruction in this high-level language stood for lots of the machine instructions – equivalent to giving the major turns in those directions rather than every step.

The ultimate result was COBOL: the first widely used high-level programming language. At a stroke her ideas made programming much easier to do and much less error-prone. Big programs were now a possibility.

For this idea of high-level languages to work though you needed a way to convert a program written in a high-level language like COBOL into those machine instructions that a computer can actually do. It can’t fill in the gaps on its own! Grace had the answer – the ‘compiler’. It is just another computer program, but one that does a specialist task: the conversion. Grace wrote the first ever compiler, for a language called A-O, as well as the first COBOL compiler. The business computing revolution was up and running.

High-level languages like COBOL have allowed far larger programs to be written than is possible in machine-code, and so ultimately the expansion of computers into every part of our lives. Of course even high-level programs can still contain mistakes, so programmers still need to spend most of their time testing and debugging. As the Oracle would no doubt say, “Check for moths, Trinity, check for moths”.

– Peter W McOwan and Paul Curzon, Queen Mary University of London (from the archive)

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EPSRC supports this blog through research grant EP/W033615/1, and through EP/K040251/2 held by Professor Ursula Martin.