Archive
Happy 60th birthday: Algol 60
Report on the Algorithmic Language ALGOL 60 is the title of a 16-page paper appearing in the May 1960 issue of the Communication of the ACM. Probably one of the most influential programming languages, and a language that readers may never have heard of.
During the 1960s there were three well known, widely used, programming languages: Algol 60, Cobol, and Fortran.
When somebody created a new programming languages Algol 60 tended to be their role-model. A few of the authors of the Algol 60 report cited beauty as one of their aims, a romantic notion that captured some users imaginations. Also, the language was full of quirky, out-there, features; plenty of scope for pin-head discussions.
Cobol appears visually clunky, is used by business people and focuses on data formatting (a deadly dull, but very important issue).
Fortran spent 20 years catching up with features supported by Algol 60.
Cobol and Fortran are still with us because they never had any serious competition within their target markets.
Algol 60 had lots of competition and its successor language, Algol 68, was groundbreaking within its academic niche, i.e., not in a developer useful way.
Language family trees ought to have Algol 60 at, or close to their root. But the Algol 60 descendants have been so successful, that the creators of these family trees have rarely heard of it.
In the US the ‘military’ language was Jovial, and in the UK it was Coral 66, both derived from Algol 60 (Coral 66 was the first language I used in industry after graduating). I used to hear people saying that Jovial was derived from Fortran; another example of people citing the language the popular language know.
Algol compiler implementers documented their techniques (probably because they were often academics); ALGOL 60 Implementation is a real gem of a book, and still worth a read today (as an introduction to compiling).
Algol 60 was ahead of its time in supporting undefined behaviors 😉 Such as: “The effect, of a go to statement, outside a for statement, which refers to a label within the for statement, is undefined.”
One feature of Algol 60 rarely adopted by other languages is its parameter passing mechanism, call-by-name (now that lambda expressions are starting to appear in widely used languages, call-by-name has a kind-of comeback). Call-by-name essentially has the same effect as textual substitution. Given the following procedure (it’s not a function because it does not return a value):
procedure swap (a, b); integer a, b, temp; begin temp := a; a := b; b:= temp end; |
the effect of the call: swap(i, x[i]) is:
temp := i; i := x[i]; x[i] := temp |
which might come as a surprise to some.
Needless to say, programmers came up with ‘clever’ ways of exploiting this behavior; the most famous being Jensen’s device.
The follow example of go to usage appears in: International Standard 1538 Programming languages – ALGOL 60 (the first and only edition appeared in 1984, after most people had stopped using the language):
go to if Ab < c then L17 else g[if w < 0 then 2 else n] |
Orthogonality of language use won out over the goto FUD.
The Software Preservation Group is a great resource for Algol 60 books and papers.
Having all the source code in one file
An early, and supposedly influential, analysis of the Coronavirus outbreak was based on results from a model whose 15,000 line C implementation was contained in a single file. There has been lots of tut-tutting from the peanut gallery, about the code all being in one file rather than distributed over many files. The source on Github has been heavily reworked.
Why do programmers work with all the code in one file, rather than split across multiple files? What are the costs and benefits of having the 15K of source in one file, compared to distributing it across multiple files?
There are two kinds of people who work with code all in one file, novices and really capable developers. Richard Stallman is an example of a very capable developer who worked using files containing huge amounts of code, as anybody who looked at the early sources of gcc will be all to familiar.
The benefit of having all the code in one file is that it is easy to find stuff and make global changes. If the source is scattered over multiple files, then working on the code entails knowing which file to look in to find whatever; there is a learning curve (these days screens have lots of pixels, and editors support multiple windows with a different file in each window; I’m sure lots of readers work like this).
Many years ago, when 64K was a lot of memory, I sometimes had to do developer support: people would come to me complaining that the computer was preventing them writing a larger program. What had happened was they had hit the capacity limit of the editor. The source now had to be spread over multiple files to get over this ‘limitation’. In practice people experienced the benefits of using multiple files, e.g., editor loading files faster (because they were a lot smaller) and reduced program build time (because only the code that changed needed to be recompiled).
These days, 15K of source can be loaded or compiled in a blink of an eye (unless a really cheap laptop is being used). Computing power has significantly reduced these benefits that used to exist.
What costs might be associated with keeping all the source in one file?
Monolithic code makes sharing difficult. I don’t know anything about the development environment within which these researched worked. If there were lots of different programs using the same algorithms, or reading/writing the same file formats, then code reuse often provides a benefit that makes it worthwhile splitting off the common functionality. But then the researchers has to learn how to build a program from multiple source files, which a surprising number are unwilling to do (at least it has always been surprising to me).
Within a research group, sharing across researchers might be a possible (assuming they are making some use of the same algorithms and file formats). Involving multiple people in the ongoing evolution of software creates a need for some coordination. At the individual level it may be more cost-efficient for people to have their own private copies of the source, with savings only occurring at the group level. With software development having a low status in academia, I don’t see any of the senior researchers willingly take on a management role, for this code. Perhaps one of the people working on the code is much better than the others (it often happens), but are they going to volunteer themselves as chief dogs body for the code?
In the world of Open Source, where source code is available, cut-and-paste is rampant (along with wholesale copying of files). Working with a copy of somebody else’s source removes a dependency, and if their code works well enough, then go for it.
A cost often claimed by the peanut gallery is that having all the code in a single file is a signal of buggy code. Given that most of the programmers who do this are novices, rather than really capable developers, such code is likely to contain many mistakes. But splitting the code up into multiple files will not reduce the number of mistakes it contains, just distribute them among the files. Correlation is not causation.
For an individual developer, the main benefit of splitting code across multiple files is that it makes developers think about the structure of their code.
For multi-person projects there are the added potential benefits of reusing code, and reducing the time spent reading other people’s code (it’s no fun having to deal with 10K lines when only a few functions are of interest).
I’m not saying that the original code is good, bad, or indifferent. What I am saying is that the having all the source in one file may, or may not, be the most effective way of working. It’s complicated, and I have no problem going with the flow (and limiting the size of the source files I write), but let’s not criticise others for doing what works for them.
Enthusiasm on the Fortran standards committee
The Fortran language standards committee, SC22/WG5, has an unusual situation on its hands. Two people have put themselves forward to chair the committee, when the current chairman’s three year term ends. What is unusual is that it is often difficult to find anybody willing to do the job.
The two candidates are the outgoing chair (the person who invariably does the job, until they decide they have had enough, or can arm wrestle someone else to do it), and a scientist at Los Alamos; I don’t know either person.
SC22 (the ISO committee responsible for language standards), and INCITS (the US Standards body; the US is the Fortran committee secretariate) will work something out.
I had heard that the new guy was ruffling some feathers, and I thought good for him (committees could do with having their feathers ruffled every now and again). Then I read the running for convenor announcement; oh dear. Every committee has a way of working: the objectives listed in this announcement would go down really well with the C++ committee (which already does many of the points listed), but the Fortran committee don’t operate this way.
The language standards world appears to be very similar to the open source world, in that they are both driven by the people who do the work. One person can have a big impact in the open source world, simply by doing the work, but in the language standards world there is voting (people can vote in the open source world by using software or not). One person can write papers and propose lots of additions to a standard, but the agreement of committee members is needed before any wording is added to a draft standard, which eventually goes out for a round of voting by national bodies.
Over the years I have seen several people on a standards committee starting out very enthusiastic, writing proposals and expounding them at meetings; then after a year or two becoming despondent because nothing has happened. If committee members don’t like your proposal (or choose to spend their time on other proposals), they do nothing. A majority doing nothing is enough to stop something happening.
Once a language has become established, many of its users want the committee to move slowly. Compiler vendors don’t want to spend all their time keeping up with language updates (which rarely help sell more product), and commercial users don’t want the hassle of having to spend time working out how a new standard might impact them (having zero impact on existing is a common aim of language committees).
The young, the enthusiastic, and magazines looking to sell clicks are excited by change. An ISO language committee is generally not the place to find it.
Update
INCITS have nominated the current chair for the next three-year term.
Beta release of data analysis chapters: Evidence-based software engineering
When I started my evidence-based software engineering book, nobody had written a data analysis book for software developers, so I had to write one (in fact, a book on this topic has still to be written). When I say “I had to write one”, what I mean is that the 200 pages in the second half of my evidence-based software engineering book contains a concentrated form of such a book.
This 200 pages is now on beta release (it’s 186 pages, if the bibliography is excluded); chapters 8 to 15 of the draft pdf. Originally I was going to wait until all the material was ready, before making a beta release; the Coronavirus changed my plans.
Here is your chance to learn a new skill during the lockdown (yes, these are starting to end; my schedule has not changed, I’m just moving with the times).
All the code+data is available for you to try out any ideas you might have.
The software engineering material, the first half of the book, is also part of the current draft pdf, and the polished form should be available on beta release in about 6 weeks.
If you have a comment or find a problem, either email me or raise an issue on the book’s Github page.
Yes, a few figures and tables still bump into each other. I’m loath to do very fine-tuning because things will shuffle around a bit with minor changes to the words.
I’m thinking of running some online sessions around each chapter. Watch this space for information.
Predicting the future with data+logistic regression
Predicting the peak of data fitted by a logistic equation is attracting a lot of attention at the moment. Let’s see how well we can predict the final size of a software system, in lines of code, using logistic regression (code+data).
First up is the size of the GNU C library. This is not really a good test, since the peak (or rather a peak) has been reached.
We need a system that has not yet reached an easily recognizable peak. The Linux kernel has been under development for many years, and lots of LOC counts are available. The plot below shows a logistic equation fitted to the kernel data, assuming that the only available data was up to day: 2,900, 3,650, 4,200, and 5,000+. Can you tell which fitted line corresponds to which number of days?
The underlying ‘problem’ is that we are telling the fitting software to fit a particular equation; the software does what it has been told to do, and fits a logistic equation (in this case).
A cubic polynomial is also a great fit to the existing kernel data (red line to the left of the blue line), and this fitted equation can be extended into future (to the right of the blue line); dotted lines are 95% confidence bounds. Do any readers believe the future size of the Linux kernel predicted by this cubic model?
Predicting the future requires lots of data on the underlying processes that drive events. Modeling events is an iterative process. Build a model, check against reality, adjust model, rinse and repeat.
If the COVID-19 experience trains people to be suspicious of future predictions made by models, it will have done something positive.
Motzkin paths and source code silhouettes
Consider a language that just contains assignments and if-statements (no else arm). Nesting level could be used to visualize programs written in such a language; an if represented by an Up step, an assignment by a Level step, and the if-terminator (e.g., the } token) by a Down step. Silhouettes for the nine possible four line programs are shown in the figure below (image courtesy of Wikipedia). I use the term silhouette because the obvious terms (e.g., path and trace) have other common usage meanings.
How many silhouettes are possible, for a function containing 
statements? Motzkin numbers provide the answer; the number of silhouettes for functions containing from zero to 20 statements is: 1, 1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019. The recurrence relation for Motzkin numbers is (where is the total number of steps, i.e., statements):
Human written code contains recurring patterns; the probability of encountering an if-statement, when reading code, is around 17% (at least for the C source of some desktop applications). What does an upward probability of 17% do to the Motzkin recurrence relation? For many years I have been keeping my eyes open for possible answers (solving the number theory involved is well above my mathematics pay grade). A few days ago I discovered weighted Motzkin paths.
A weighted Motzkin path is one where the Up, Level and Down steps each have distinct weights. The recurrence relationship for weighted Motzkin paths is expressed in terms of number of colored steps, where: 
is the number of possible colors for the Level steps, and 
is the number of possible colors for Down steps; Up steps are assumed to have a single color:
setting: 
and 
(i.e., all kinds of step have one color) recovers the original relation.
The different colored Level steps might be interpreted as different kinds of non-nesting statement sequences, and the different colored Down steps might be interpreted as different ways of decreasing nesting by one (e.g., a goto statement).
The connection between weighted Motzkin paths and probability is that the colors can be treated as weights that add up to 1. Searching on “weighted Motzkin” returns the kind of information I had been looking for; it seems that researchers in other fields had already discovered weighted Motzkin paths, and produced some interesting results.
If an automatic source code generator outputs the start of an if statement (i.e., an Up step) with probability 
, an assignment (i.e., a Level step) with probability 
, and terminates the if (i.e., a Down step) with probability 
, what is the probability that the function will contain at least 
statements? The answer, courtesy of applying Motzkin paths in research into clone cell distributions, is:
![P_n=sum{i=0}{delim{[}{(n-2)/2}{]}}(matrix{2}{1}{{n-2} {2i}})C_{2i}a^{i}b^{n-2-2i}c^{i+1}](https://shape-of-code.com/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_951_57086dac25a2ff31c2230f0791800e35.png "P_n=sum{i=0}{delim{[}{(n-2)/2}{]}}(matrix{2}{1}{{n-2} {2i}})C_{2i}a^{i}b^{n-2-2i}c^{i+1}")
where: 
is the 
‘th Catalan number, and that [...] is a truncation; code for an implementation in R.
In human written code we know that 
, because the number of statements in a compound-statement roughly has an exponential distribution (at least in C).
There has been some work looking at the number of peaks in a Motzkin path, with one formula for the total number of peaks in all Motzkin paths of length n. A formula for the number of paths of length , having 
peaks, would be interesting.
Motzkin numbers have been extended to what is called higher-rank, where Up steps and Level steps can be greater than one. There are statements that can reduce nesting level by more than one, e.g., breaking out of loops, but no constructs increase nesting by more than one (that I can think of). Perhaps the rather complicated relationship can be adapted to greater Down steps.
Other kinds of statements can increase nesting level, e.g., for-statements and while-statements. I have not yet spotted any papers dealing with the case where an Up step eventually has a corresponding Down step at the appropriate nesting level (needed to handle different kinds of nest-creating constructs). Pointers welcome. A related problem is handling if-statements containing else arms, here there is an associated increase in nesting.
What characteristics does human written code have that results in it having particular kinds of silhouettes? I have been thinking about this for a while, but have no good answers.
If you spot any Motzkin related papers that you think could be applied to source code analysis, please let me know.
Update
A solution to the Number of statement sequences possible using N if-statements problem.
Comments on the COVID-19 model source code from Imperial
At the end of March a paper modelling the impact of various scenarios on the spread of COVID-19 infections, by the MRC Centre for Global Infectious Disease Analysis at Imperial College, appears to have influenced the policy of the powers that be. This group recently started publishing their modelling code on GitHub (good for them).
Most of my professional life has been spent analyzing other peoples’ code, for one reason or another (mostly Fortran, then Pascal, and then C). I had heard that the Imperial software was written in C, but the released code is written in R (as of six hours ago, there is the start of a Python version). Ok, I can work with R, but my comments will be general, since I don’t have lots of in depth experience reading R code.
The code comes from a research context, and is evolving, i.e., some amount of messiness is to be expected.
There is not a lot of code to talk about (248 lines setting things up, 111 lines for a Stan model, 371 lines of plotting code, and 85 lines of utility code). The analysis is performed by creating a model using the Stan statistical inference language (in which the high level structure of the problem is specified, compiled to a lower level form and then run; the Stan language is very similar to R). These days, lots of problems are coded using a relatively small number of lines that call fancy libraries to do the heavy lifting. It is becoming rare to have to write tens of thousands of lines of code to solve a problem.
I have two points to make about the code, all designed to reduce the likelihood of mistakes being made by the person working on the source. These points mainly apply to the Stan code, because that is where the important stuff happens, but are equally applicable to all code.
- Numeric literals are embedded in the code, values include:
2.4,1.0,0.5,0.03,1e-5, and1e-9. These values obviously mean something to the person who wrote the code, and they can probably be interpreted by experts in the spread of virus infections. But why are they scattered about the code, rather than appearing together (as a sequence of assignments to variables with meaningful names)? Having all the constants in one place makes it easier to spot when a mistake has been made, e.g., one value has been changed without a corresponding change in another value; it also makes it easier for people new to the code to figure out what is going on, - when commenting out code, make it very obvious, e.g., have
/**********************on its own line, and*****************************/on its own line. Using just/*and*/makes it easy to miss that code has been commented out.
Why have they started a Python implementation? Perhaps somebody on the team is more comfortable working with Python (when deadlines loom, it is always best to go with what you know).
Having both an R and Python version is good, in that coding mistakes are likely to show up as inconsistencies in the results produced. It’s always good to have the output of two independently written programs to compare (apart from the fact it may cost twice as much).
The README mentions performance issues. I imagine that most of the execution time is spent in the Stan code, so R vs. Python is not a performance issue.
Any reader with expertise tuning Stan models for performance might like to check out the code. I’m sure the Imperial folk would be happy to hear about worthwhile speed-ups.
Update
The R source code of the EuroMOMO model, which aims to “… explain number of deaths by a baseline, influenza activity and extreme ambient temperature.”
Influential programming languages: some of the considerations
Which programming languages have been the most influential?
Let’s define an influential language as one that has had an impact on lots of developers. What impact might a programming language have on developers?
To have an impact a language needs to be used by lots of people, or at least have a big impact on a language that is used by lots of people.
Figuring out the possible impacts a language might have had is very difficult, requiring knowledge of different application domains, software history, and implementation techniques. The following discussion of specific languages illustrate some of the issues.
Simula is an example of a language used by a handful of people, but a few of the people under its influence went on to create Smalltalk and C++. Some people reacted against the complexity of Algol 68, creating much simpler languages (e.g., Pascal), while others thought some of its feature were neat and reused them (e.g., Bourne shell).
Cobol has been very influential, at least within business computing (those who have not worked in business computing complain about constructs handling uses that it was not really designed to handle, rather than appreciating its strengths in doing what it was designed to do, e.g., reading/writing and converting a wide range of different numeric data formats). RPG may have been even more influential in this usage domain (all businesses have to specific requirements on formatting reports).
I suspect that most people could not point to the major influence C has had on almost every language since. No, not the use of { and }; if a single character is going to be used as a compound statement bracketing token, this pair are the only available choice. Almost every language now essentially uses C’s operator precedence (rather than Fortran‘s, which is slightly different; R follows Fortran).
Algol 60 has been very influential: until C came along it was the base template for many languages.
Fortran is still widely used in scientific and engineering software. Its impact on other languages may be unknown to those involved. The intricacies of floating-point arithmetic are difficult to get right, and WG5 (the ISO language committee, although the original work was done by the ANSI committee, J3). Fortran code is often computationally intensive, and many optimization techniques started out optimizing Fortran (see “Optimizing Compilers for Modern Architectures” by Allen and Kennedy).
BASIC showed how it was possible to create a usable interactive language system. The compactness of its many, and varied, implementations were successful because they did not take up much storage and were immediately usable.
Forth has been influential in the embedded systems domain, and also people fall in love with threaded code as an implementation technique (see “Threaded Interpretive Languages” by Loeliger).
During the mid-1990s the growth of the Internet enabled a few new languages to become widely used, e.g., PHP and Javascript. It’s difficult to say whether these were more influenced by what their creators ate the night before or earlier languages. PHP and Javascript are widely used, and they have influenced the creation of many languages designed to fix their myriad of issues.
Coronavirus: a silver lining for evidence-based software engineering?
People rarely measure things in software engineering, and when they do they rarely hang onto the measurements; this might also be true in many other work disciplines.
When I worked on optimizing compilers, I used to spend time comparing code size and performance. It surprised me that many others in the field did not, they seemed to think that if they implemented an optimization, things would get better and that was it. Customers would buy optimizers without knowing how long their programs took to do a task, they seemed to want things to go faster, and they had some money to spend buying stuff to make them feel that things had gotten faster. I quickly learned to stop asking too many questions, like “how fast does your code currently run”, or “how fast would you like it to run”. Sell them something to make them feel better, don’t spoil things by pointing out that their code might already be fast enough.
In one very embarrassing incident, the potential customer was interested in measuring performance, and my optimizer make their important program go slower! As best I could tell, the size of the existing code just fitted in memory, and optimizing for performance made it larger; the system started thrashing and went a lot slower.
What question did potential customers ask? They usually asked whether particular optimizations were implemented (because they had read about them someplace). Now some of these optimizations were likely to make very little difference to performance, but they were easy to understand and short enough to write articles about. And, yes. I always made sure to implement these ‘minor’ optimizations purely to keep customers happy (and increase the chances of making a sale).
Now I work on evidence-based software engineering, and developers rarely measure things, and when they do they rarely hang onto the measurements. So many people have said I could have their data, if they had it!
Will the Coronavirus change things? With everybody working from home, management won’t be able to walk up to developers and ask what they have been doing. Perhaps stuff will start getting recorded more often, and some of it might be kept.
A year from now it might be a lot easier to find information about what developers do. I will let you know next year.
Exercises in Programming Style: the python way
Exercises in Programming Style by Cristina Lopes is an interesting little book.
The books I have previously read on programming style pick a language, and then write various programs in that language using different styles, idioms, or just following quirky rules, e.g., no explicit loops, must use sets, etc. “Algorithms in Snobol 4” by James F. Gimpel is a fascinating read, but something of an acquired taste.
EPS does pick a language, Python, but the bulk of the book is really a series of example programs illustrating a language feature/concept that is central to a particular kind of language, e.g., continuation-passing style, publish-subscribe architecture, and reflection. All the programs implement the same problem: counting the number of occurrences of each word in a text file (Jane Austin’s Pride and Prejudice is used).
The 33 chapters are each about six or seven pages long, and contain a page or two or code. Everything is very succinct, and does a good job of illustrating one main idea.
While the first example does not ring true, things quickly pick up and there are lots of interesting insights to be had. The first example is based on limited storage (1,024 bytes), and just does not make efficient use of the available bits (e.g., upper case letters can be represented using 5-bits, leaving three unused bits or 37% of available storage; a developer limited to 1K would not waste such a large amount of storage).
Solving the same problem in each example removes the overhead of having to learn what is essentially housekeeping material. It also makes it easy to compare the solutions created using different ideas. The downside is that there is not always a good fit between the idea being illustrated and the problem being solved.
There is one major omission. Unstructured programming; back in the day it was just called programming, but then structured programming came along, and want went before was called unstructured. Structured programming allowed a conditional statement to apply to multiple statements, an obviously simple idea once somebody tells you.
When an if-statement can only be followed by a single statement, that statement has to be a goto; an if/else is implemented as (using Fortran, I wrote lots of code like this during my first few years of programming):
IF (I .EQ. J) GOTO 100 Z=1 GOTO 200 100 Z=2 200 |
Based on the EPS code in chapter 3, Monolithic, an unstructured Python example might look like (if Python supported goto):
for line in open(sys.argv[1]): start_char = None i = 0 for c in line: if start_char != None: goto L0100 if not c.isalnum(): goto L0300 # We found the start of a word start_char = i goto L0300 L0100: if c.isalnum(): goto L0300 # We found the end of a word. Process it found = False word = line[start_char:i].lower() # Ignore stop words if word in stop_words: goto L0280 pair_index = 0 # Let's see if it already exists for pair in word_freqs: if word != pair[0]: goto L0210 pair[1] += 1 found = True goto L0220 L0210: pair_index += 1 L0220: if found: goto L0230 word_freqs.append([word, 1]) goto L0300 L0230: if len(word_freqs) <= 1: goto L0300: # We may need to reorder for n in reversed(range(pair_index)): if word_freqs[pair_index][1] <= word_freqs[n][1]: goto L0240 # swap word_freqs[n], word_freqs[pair_index] = word_freqs[pair_index], word_freqs[n] pair_index = n L0240: goto L0300 L0280: # Let's reset start_char = None L0300: i += 1 |
If you do feel a yearning for the good ol days, a goto package is available, enabling developers to write code such as:
from goto import with_goto @with_goto def range(start, stop): i = start result = [] label .begin if i == stop: goto .end result.append(i) i += 1 goto .begin label .end return result |
Recent Comments