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# The Specter of Undefined Behavior

If you’ve ever spoken to a programmer, and really got them on a roll, they may have said the words “undefined behavior” to you. Since you speak English, you probably know what each of those words mean, and can imagine a reasonable meaning for them in that order. But then your programmer friends goes on about “null-pointer dereferencing” and “invariant violations” and you start thinking about cats or football or whatever because you are not a programmer.

I often find myself being asked what it is that I do. Since I’ve spent the last few years working on my Computer Science degree, and have spent much of that time involved in programming language research, I often find myself trying to explain this concept. Unfortunately, when put on the spot, I usually am only able to come up with the usual sort of explanation that programmers use among themselves: “If you invoke undefined behavior, anything can happen! Try to dereference a null pointer? Bam! Lions could emerge from your monitor and eat your family!” Strictly speaking, while I’m sure some compiler writer would implement this behavior if they could, it’s not a good explanation for a person who doesn’t already kind of understand the issues at play.

Today, I’d like to give an explanation of undefined behavior for a lay person. Using examples, I’ll give an intuitive understanding of what it is, and also why we tolerate it. Then I’ll talk about how we go about mitigating it.

## Division By Zero

Here is one that most of us know. Tell me, what is `8 / 0`? The answer of course is “division by zero is undefined.” In mathematics, there are two sorts of functions: total and partial. A total function is defined for all inputs. If you say `a + b`, this can be evaluated to some result no matter what you substitute for `a` and `b`. Addition is total. The same cannot be said for division. If you say `a / b`, this can be evaluated to some result no matter what you substitute for `a` and `b` unless you substitute `b` with `0`. Division is not total.

If you go to the Wikipedia article for division by zero you’ll find some rationale for why division by zero is undefined. The short version is that if it were defined, then it could be mathematically proven that one equals two. This would of course imply that cats and dogs live in peace together and that pigs fly, and we can’t have that!

However, there is a way we can define division to be total that doesn’t have this issue. Instead of defining division to return a number, we could define division to return a set of numbers. You can think of a set as a collection of things. We write this as a list in curly braces. `{this, is, a, set, of, words}` I have two cats named Gatito and Moogle. I can have a set of cats by writing `{Gatito, Moogle}`. Sets can be empty; we call the empty set the null set and can write it as `{}` or using this symbol `∅`. I’ll stick with empty braces because one of the things I hate about mathematics is everybody’s insistence on writing in Greek.

So here is our new total division function:

``````totalDivide(a, b)
if (b does not equal 0)
output {a / b}
otherwise
output {}
``````

If you use `totalDivide` to do your division, then you will never have to worry about the undefined behavior of division! So why didn’t Aristotle (or Archimedes or Yoda or whoever invented division) define division like this in the first place? Because it’s super annoying to deal with these sets. None of the other arithmetic functions are defined to take sets, so we’d have to constantly test that the division result did not produce the empty set, and extract the result from the set. In other words: while our division is now total, we still need to treat division by zero as a special case. Let us try to evaluate `2/2 + 2/2` and `totalDivide(2,2) + totalDivide(2,2)`:

``````1: 2/2 + 2/2
2: 1 + 1
3: 2
``````

Even showing all my work, that took only 3 lines.

``````1: let {1} = totalDivide(2,2)
2: let {1} = totalDivide(2,2)
3: 1 + 1
4: 2
``````

Since you can’t add two sets, I had to evaluate `totalDivide` out of line, and extract the values and add them separately. Even this required my human ability to look at the denominator and see that it wasn’t zero for both cases. In other words, making division total made it much more complicated to work with, and it didn’t actually buy us anything. It’s slower. It’s easier to mess up. It has no real value. As humans, it’s fairly easy for us to look at the denominator, see that it’s zero, and just say “undefined.”

## Cartons of Eggs

I’m sure many of you have a carton of eggs in your fridge. Go get me the 17th egg from your carton of eggs. Some of you will be able to do this, and some of you will not. Maybe you only have a 12 egg carton. Maybe you only have 4 eggs in your 18 egg carton, and the 17th egg is one of the ones that are missing. Maybe you’re vegan.

A basic sort of construct in programming is called an “array.” Basically, this is a collection of the same sort of things packed together in a region of memory on your computer. You can think of a carton of eggs as an array of eggs. The carton only contains one sort of thing: an egg. The eggs are all packed together right next to each other with nothing in between. There is some finite amount of eggs.

If I told you “for each egg in the carton, take it out and crack it, and dump it in a bowl starting with the first egg”, you would be able to do this. If I told you “take the 7th egg and throw it at your neighbor’s house” you would be able to do this. In the first example, you would notice when you cracked the last egg. In the second example you would make sure that there was a 7th egg, and if there wasn’t you probably picked some other egg because your neighbor is probably a jerk who deserves to have his house egged. You did this unconsciously because you are a human who can react to dynamic situations. The computer can’t do this.

If you have some array that looks like this (array locations are separated by | bars | and * stars * are outside the array) ` ***|1|2|3|*** ` and you told the computer “for each location in the array, add 1 to the number, starting at the first location” it would set the first location to be 2, the second location to be 3, the third location to be 4. Then it would interpret the bits in the location of memory directly to the right of the third location as a number, and it would add 1 to this “number” thereby destroying the data in that location. It would do this forever because this is what you told the machine to do. Suppose that part of memory was involved in controlling the brakes in your 2010 era Toyota vehicle. This is obviously incredibly bad, so how do we prevent this?

The answer is that the programmer (hopefully) knows how big the array is and actually says “starting at location one, for the next 3 locations, add one to the number in the location”. But suppose the programmer messes up, and accidentally says “for the next 4 locations” and costs a multinational company billions of dollars? We could prevent this. There are programming languages that give us ways to prevent these situations. “High level” programming languages such as Java have built-in ways to tell how long an array is. They are also designed to prevent the programmer from telling the machine to write past the end of the array. In Java, the program will successfully write |2|3|4| and then it will crash, rather than corrupting the data outside of the array. This crash will be noticed in testing, and Toyota will save face. We also have “low level” programming languages such as C, which don’t do this. Why do we use low level programming languages? Let’s step through what these languages actually have the machine do for “starting at location one, for the next 3 locations, add one to the number in the location”: First the C program:

NOTE: location[some value] is shorthand for “the location identified by some value.” egg_carton[3] is the third egg in the carton. Additionally, you should read these as sequential instructions “first do this, then do that” Finally, these examples are greatly simplified for the purposes of this article.

``````1: counter = 1
2: location[counter] = 1 + 1
3: if (counter equals 3) terminate
4: counter = 2
5: location[counter] = 2 + 1
6: if (counter equals 3) terminate
7: counter = 3
8: location[count] = 3 + 1
9: if (counter equals 3) terminate
``````

Very roughly speaking, this is what the computer does. The programmer will use a counter to keep track of their location in the array. After updating each location, they will test the counter to see if they should stop. If they keep going they will repeat this process until the stop condition is satisfied. The Java programmer would write mostly the same program, but the program that translates the Java code into machine code (called a compiler) will add some stuff:

``````1: counter = 1
2: if (counter greater than array length) crash
3: location[counter] = 1 + 1
4: if (counter equals 3) terminate
5: counter = 2
6: if (counter greater than array length) crash
7: location[counter] = 2 + 1
8: if (counter equals 3) terminate
9: counter = 3
10: if (counter greater than array length) crash
11: location[count] = 3 + 1
12: if (counter equals 3) terminate
``````

As you can see, 3 extra lines were added. If you know for a fact that the array you are working with has a length that is greater than or equal to three, then this code is redundant.

For such a small array, this might not be a huge deal, but suppose the array was a billion elements. Suddenly an extra billion instructions were added. Your phone’s processor likely runs at 1-3 gigahertz, which means that it has an internal clock that ticks 1-3 billion times per second. The smallest amount of time that an instruction can take is one clock cycle, which means that in the best case scenario, the java program takes one entire second longer to complete. The fact of the matter is that “if (counter greater than array length) crash” definitely takes longer than one clock cycle to complete. For a game on your phone, this extra second may be acceptable. For the onboard computer in your car, it is definitely not. Imagine if your brakes took an extra second to engage after you push the pedal? Congressmen would get involved!

In Java, reading off the end of an array is defined. The language defines that if you attempt to do this, the program will crash (it actually does something similar but not the same, but this is outside the scope of this article). In order to enforce this definition, it inserts these extra instructions into the program that implement the functionality. In C, reading off the end of an array is undefined. Since C doesn’t care what happens when you read off the end of an array, it doesn’t add any code to your program. C assume you know what you’re doing, and have taken the necessary steps to ensure your program is correct. The result is that the C program is much faster than the Java program.

There are many such undefined behaviors in programming. For instance, your computer’s division function is partial just like the mathematical version. Java will test that the denominator isn’t zero, and crash if it is. C happily tells the machine to evaluate `8 / 0`. Most processors will actually go into a failure state if you attempt to divide by zero, and most operating systems (such as Windows or Mac OSX) will crash your program to recover from the fault. However, there is no law that says this must happen. I could very well create a processor that sends lions to your house to punish you for trying to divide by zero. I could define `x / 0 = 17`. The C language committee would be perfectly fine with either solution; they just don’t care. This is why people often call languages such as C “unsafe.” This doesn’t mean that they are bad necessarily, just that their use requires caution. A chainsaw is unsafe, but it is a very powerful tool when used correctly. When used incorrectly, it will slice your face off.

## What To Do

So, if defining every behavior is slow, but leaving it undefined is dangerous, what should we do? Well, the fact of the matter is that in most cases, the added overhead of adding these extra instructions is acceptable. In these cases, “safe” languages such as Java are preferred because they ensure program correctness. Some people will still write these sorts of programs in unsafe languages such as C (for instance, my own DMP Photobooth is implemented in C), but strictly speaking there are better options. This is part of the explanation for the phenomenon that “computers get faster every year, but [insert program] is just as slow as ever!” Since the performance of [insert program] we deemed to be “good enough”, this extra processing power is instead being devoted to program correctness. If you’ve ever used older versions of Windows, then you know that your programs not constantly crashing is a Good Thing.

This is fine and good for those programs, but what about the ones that cannot afford this luxury? These other programs fall into a few general categories, two of which we’ll call “real-time” and “big data.” These are buzzwords that you’ve likely heard before, “big data” programs are the programs that actually process one billion element arrays. An example of this sort of software would be software that is run by a financial company. Financial companies have billions of transactions per day, and these transactions need to post as quickly as possible. (suppose you deposit a check, you want those funds to be available as quickly as possible) These companies need all the speed they can get, and all those extra instructions dedicated to totality are holding up the show.

Meanwhile “real-time” applications have operations that absolutely must complete in a set amount of time. Suppose I’m flying a jet, and I push the button to raise a wing flap. That button triggers an operation in the program running on the flight computer, and if that operation doesn’t complete immediately (where “immediately” is some fixed, non-zero-but-really-small amount of time) then that program is not correct. In these cases, the programmer needs to have very precise control over what instructions are produced, and they need to make every instruction count. In these cases, redundant totality checks are a luxury that is not in the budget.

Real-time and big data programs need to be fast, so they are often implemented in unsafe languages, but that does not mean that invoking undefined behavior is OK. If a financial company sets your account balance to be `check value / 0`, you are not going to have a good day. If your car reads the braking strength from a location off to the right of the braking strength array, you are going to die. So, what do these sorts of programs do?

One very common method, often used in safety-critical software such as a car’s onboard computer is to employ strict coding standards. MISRA C is a set of guidelines for programming in C to help ensure program correctness. Such guidelines instruct the developer on how to program to avoid unsafe behavior. Enforcement of the guidelines is ensured by peer-review, software testing, and Static program analysis.

Static program analysis (or just static analysis) is the process of running a program on a codebase to check it for defects. For MISRA C, there exists tooling to ensure compliance with its guidelines. Static analysis can also be more general. Over the last year or so, I’ve been assisting with a research project at UCSD called Liquid Haskell. Simply put, Liquid Haskell provides the programmer with ways to specify requirements about the inputs and outputs of a piece of code. Liquid Haskell could ensure the correct usage of division by specifying a “precondition” that “the denominator must not equal zero.” (I believe that this actually comes for free if you use Liquid Haskell as part of its basic built-in checks) After specifying the precondition, the tool will check your codebase, find all uses of division, and ensure that you ensured that zero will never be used as the denominator.

It does this by determining where the denominator value came from. If the denominator is some literal (i.e. the number `7`, and not some variable `a` that can take on multiple values), it will examine the literal and ensure it meets the precondition of division. If the number is an input to the current routine, it will ensure the routine has a precondition on that value that it not be zero. If the number is the output from some other routine, it verifies that the the routine that produced the value has, as a “postcondition”, that its result will never be zero. If the check passes for all usages of division, your use of division will be declared safe. If the check fails, it will tell you what usages were unsafe, and you will be able to fix it before your program goes live. The Haskell programming language is very safe to begin with, but a Haskell program verified by Liquid Haskell is practically Fort Knox!

## The Human Factor

Humans are imperfect, we make mistakes. However, we make up for it in our ability to respond to dynamic situations. A human would never fail to grab the 259th egg from a 12 egg carton and crack it into a bowl; the human wouldn’t even try. The human can see that there is only 12 eggs without having to be told to do so, and will respond accordingly. Machines do not make mistakes, they do exactly what you tell them to, exactly how you told them to do it. If you tell the machine to grab the 259th egg and crack it into a bowl, it will reach it’s hand down, grab whatever is in the space 258 egg lengths to the right of the first egg, and smash it on the edge of a mixing bowl. You can only hope that nothing valuable was in that spot.

Most people don’t necessarily have a strong intuition for what “undefined behavior” is, but mathematicians and programmers everywhere fight this battle every day.

# Pure Functional Memoization

There are many computation problems that resonate through the ages. Important Problems. Problems that merit a capital P.

The Halting Problem…

P versus NP…

The Fibonacci sequence…

The Fibonacci sequence is a super-important computation Problem that has vexed mathematicians for generations. It’s so simple!

``````fibs 0 = 0
fibs 1 = 1
fibs n = (fibs \$ n - 1) + (fibs \$ n - 2)``````

Done! Right? Let’s fire up ghci and find out.

``````*Fibs> fibs 10
55``````

… looking good…

``````*Fibs> fibs 40

``````

… still waiting…

``````
102334155
``````

… Well that sure took an unfortunate amount of time. Let’s try 1000!

``````*Fibs> fibs 1000
*** Exception: <<You died before this returned>>``````

To this day, science wonders what `fibs(1000)` is. Well today we solve this!

## Memoization

The traditional way to solve this is to use Memoization. In an imperative language, we’d create an array of size n, and prepopulate `arr[0] = 0` and `arr[1] = 1`. Next we’d loop over 2 to n, and for each we’d set `arr[i] = arr[i-1] + arr[i-2]`.

Unfortunately for us, this is Haskell. What to do… Suppose we had a map of the solutions for 0 to i, we could calculate the solution for i + 1 pretty easily right?

``````fibsImpl _ 0 = 0
fibsImpl _ 1 = 1
fibsImpl m i = (mo + mt)
where
mo = Map.findWithDefault undefined (i - 1) m
mt = Map.findWithDefault undefined (i - 2) m``````

We return 0 and 1 for i = 0 and i = 1 as usual. Next we lookup n – 1 and n – 2 from the map and return their sum. This is all pretty standard. But where does the map come from?

It turns out that this is one of those times that laziness is our friend. Consider this code:

``````fibs' n = let m = fmap (fibsImpl m)
(Map.fromList (zip [0..n]
[0..n])) in
Map.findWithDefault undefined n m``````

When I first saw this pattern (which I call the Wizard Pattern, because it was clearly invented by a wizard), I was completely baffled. We pass the thing we’re creating into the function that’s creating it? Unthinkable!

It turns out that this is just what we need. Because of laziness, the fmap returns immediately, and `m` points to an unevaluated thunk. So, for i = 0, and i = 1, fibsImpl will return 0 and 1 respectively, and the map will map 0 -> 0 and 1 -> 1. Next for i = 2, Haskell will attempt to lookup from the map. When it does this, it will be forced to evaluate the result of i = 0 and i = 1, and it will add 2 -> 1 to the map. This will continue all the way through i = n. Finally, this function looks up and returns the value of fibs n in linearish time. (As we all know, Map lookup isn’t constant time, but this is a lot better than the exponential time we had before)

So let’s try it out.

``````*Fibs> fibs' 1
1
*Fibs> fibs' 10
55
*Fibs> fibs' 40
102334155``````

… so far so good…

``````*Fibs> fibs' 100
354224848179261915075
*Fibs> fibs' 1000
43466557686937456435688527675040625802564660517371780402481729089536555417949051890403879840079255169295922593080322634775209689623239873322471161642996440906533187938298969649928516003704476137795166849228875
*Fibs> fibs' 10000
33644764876431783266621612005107543310302148460680063906564769974680081442166662368155595513633734025582065332680836159373734790483865268263040892463056431887354544369559827491606602099884183933864652731300088830269235673613135117579297437854413752130520504347701602264758318906527890855154366159582987279682987510631200575428783453215515103870818298969791613127856265033195487140214287532698187962046936097879900350962302291026368131493195275630227837628441540360584402572114334961180023091208287046088923962328835461505776583271252546093591128203925285393434620904245248929403901706233888991085841065183173360437470737908552631764325733993712871937587746897479926305837065742830161637408969178426378624212835258112820516370298089332099905707920064367426202389783111470054074998459250360633560933883831923386783056136435351892133279732908133732642652633989763922723407882928177953580570993691049175470808931841056146322338217465637321248226383092103297701648054726243842374862411453093812206564914032751086643394517512161526545361333111314042436854805106765843493523836959653428071768775328348234345557366719731392746273629108210679280784718035329131176778924659089938635459327894523777674406192240337638674004021330343297496902028328145933418826817683893072003634795623117103101291953169794607632737589253530772552375943788434504067715555779056450443016640119462580972216729758615026968443146952034614932291105970676243268515992834709891284706740862008587135016260312071903172086094081298321581077282076353186624611278245537208532365305775956430072517744315051539600905168603220349163222640885248852433158051534849622434848299380905070483482449327453732624567755879089187190803662058009594743150052402532709746995318770724376825907419939632265984147498193609285223945039707165443156421328157688908058783183404917434556270520223564846495196112460268313970975069382648706613264507665074611512677522748621598642530711298441182622661057163515069260029861704945425047491378115154139941550671256271197133252763631939606902895650288268608362241082050562430701794976171121233066073310059947366875
*Fibs> fibs' 100000
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55482452247416927774637522135201716231722137632445699154022395494158227418930589911746931773776518735850032318014432883916374243795854695691221774098948611515564046609565094538115520921863711518684562543275047870530006998423140180169421109105925493596116719457630962328831271268328501760321771680400249657674186927113215573270049935709942324416387089242427584407651215572676037924765341808984312676941110313165951429479377670698881249643421933287404390485538222160837088907598277390184204138197811025854537088586701450623578513960109987476052535450100439353062072439709976445146790993381448994644609780957731953604938734950026860564555693224229691815630293922487606470873431166384205442489628760213650246991893040112513103835085621908060270866604873585849001704200923929789193938125116798421788115209259130435572321635660895603514383883939018953166274355609970015699780289236362349895374653428746875``````

Neat. Even that last one only took a few seconds to return!

# Into The (Local) Cloud!

I, and I’m sure many of you use Github. If not, and you care to get started, I’ve written about this before. However, sometimes you don’t want to work in the open. If this is the case, then you likely aren’t going to be using Github. Sure, you can pay for private repos, or you can use alternatives like Bitbucket that provide free private repos. Personally, I prefer to keep my private things out of The Cloud (TM).

I have a headless computer hooked up to my home network running Debian that I use as a file server. I find it convenient to have my various projects that aren’t on Github in git repositories on my server. It provides a backup, and makes it easy to keep my desktop and laptop in sync. So, let’s talk about that.

## Making The Repository

This is a pretty straightforward process. Much like the usual ways of making a local repository, we’ll be using `git-init`, however, we need to create a bare repository, otherwise we’ll have issues pushing and pulling. To do this, enter the following in the directory on the server where you want the repository to live:

``git init --bare [repo_name]``

Where `[repo_name]` is the name of the repository. A folder with this name will be created in the current directory.

This repository is special; you cannot work directly in it, you must clone and use push/pull.

## Meanwhile, on Our Workstation

Back on the machine where we’ll be working, we first need to clone our newly created repository:

``git clone [username]@[server]:[path_to_repo]``

Here, `[username]` is your user on the server that has SSH access, `[server]` is the IP address or hostname of the server, and `[path_to_repo]` is the location of the repo on the server. When you do this, you’ll get a warning about cloning an empty repo which you can ignore. After all, of course it’s empty, you just made it!

…and guess what? That’s all there is to it! You can push and pull as normal at this point, and should be ready to go.

## But DMP Guy, I Already Have A Repo!

So, you already got a repo, and you want to move it to a central server? This isn’t much more difficult. First, get the repo itself to the server somehow. I recommend SFTP:

``````sftp [username]@[server]
sftp> put [compressed_repo]
sftp> bye``````

Where `[username]` is an account and `[server]` is the server and `[compressed_repo]` is your repo directory compressed in your favorite manner.

After this is done, ssh to the server, then find and uncompress the repo. Next we make a bare repo out of it:

``git clone --bare [orig_repo] [bare_version]``

Here, `[orig_repo]` is the original repo that you just extracted, and `[bare_version]` is the name you want to give the new bare version. After this is done, you can `rm -rf [orig_repo]`, and then clone and use `[bare_version]` as described above.

# Might It Be Case Sensitive?

So today I thought I’d mess around with the new SDL2 Bindings for Haskell.

I set up a cabal project and added my `build-depends`:

``build-depends: base >=4.8 && <4.9, sdl2 >= 2, openglraw``

OK! Let’s do this!

``````\$ cabal install
Resolving dependencies...
cabal: Could not resolve dependencies:
trying: gl-tut-0.1.0.0 (user goal)
next goal: openglraw (dependency of gl-tut-0.1.0.0)
Dependency tree exhaustively searched.

Note: when using a sandbox, all packages are required to have consistent
dependencies. Try reinstalling/unregistering the offending packages or
recreating the sandbox.``````

What is this nonsense? No possible build plan? I don’t believe it!

``````\$ cabal install sdl2-2.0.0 openglraw
Resolving dependencies...
Notice: installing into a sandbox located at

...``````

OK, that works…

Maybe it’s magically case sensitive?

``build-depends: base >=4.8 && <4.9, sdl2 >= 2.0, OpenGLRaw``

…work this time you POS! I COMMAND YOU!

``````\$ cabal install
Resolving dependencies...
Notice: installing into a sandbox located at

...``````

…and of course it works…

It turns out that cabal packages can be case sensitive. Sometimes.

# Getting Started With GLib in Emacs

Recently, I decided to start doing some C. In the past, I’ve used GLib in my C programs, and I’m a fan. I decided that I’d like to use GLib in my current endeavors. All that said, before I can use it, I have to be able to build it. Unfortunately, nothing in my life just works, so it took some configuring.

## The Makefile

In my last post, I talked about creating a Makefile, and walked through it. I forgot one huge thing though: pkg-config!

Previously in DMP Photobooth, I used pkg-config to manage my library compiler flags. To that end, let’s make some changes to the Makefile I wrote previously. First, let’s refer back to what I wrote before:

``````COMPILE_FLAGS = -c -g -Wall -Wextra -std=c11 \$(OPTIMIZE_LEVEL)
LINK_FLAGS = -g -Wall -Wextra -std=c11 \$(OPTIMIZE_LEVEL)

It’s pretty straightforward. I have a compile flag set for compiling a .o, and for compiling a program. I also have a LINKER_LIBS variable to pass to the compile command. This isn’t part of the COMPLIE/LINK_FLAGS because the sources and object code being compiled must appear first or GCC complains. Now, let’s take a look at the new snippet:

``````COMPILE_FLAGS = -c -g -Wall -Wextra -std=c11 \$(OPTIMIZE_LEVEL) \
\$(shell pkg-config --cflags \$(PKG_CONFIG_LIBS))
LINK_FLAGS = -g -Wall -Wextra -std=c11 \$(OPTIMIZE_LEVEL) \
\$(shell pkg-config --cflags \$(PKG_CONFIG_LIBS))

PKG_CONFIG_LIBS = glib-2.0 gl sdl2
MANUAL_LIBS = -ldl
LINKER_LIBS = \$(MANUAL_LIBS) \$(shell pkg-config --libs \$(PKG_CONFIG_LIBS))``````

Things are getting just a bit more complicated now. You’ll notice there are three LIBS related variables. PKG_CONFIG_LIBS is the list of libraries to be passed to the pkg-config command. MANUAL_LIBS, as the name implies, is a list of manually configured -l strings. For the life of me, I couldn’t figure out what to pass to pkg-config to get it to spit out `-ldl`, so I’m forced to do it this way.

Regardless, LINKER_LIBS now contains the MANUAL_LIBS, and the output of `\$(shell pkg-config --libs \$(PKG_CONFIG_LIBS))` which produces the necessary -l strings for all the PKG_CONFIG_LIBS.

On top of that, I’ve added the output of `\$(shell pkg-config --cflags \$(PKG_CONFIG_LIBS))` to the COMPILE_FLAGS and LINK_FLAGS. This will ensure that if any pkg-config library needs special compiler flags, that they get used.

Great, now that’s done. A quick `make`, and everything seems to be working. We’re in business! …right?

## Convincing Flycheck

If only it could be that easy. I created a new source and entered the following:

``#include <glib.h>``

Flycheck wasn’t convinced though; it put some red jaggies under this, and a quick mouse over of the error shows that flycheck doesn’t think that file exists. I began getting deja vu. After some googling, I determined that I can add arbitrary paths to `flycheck-clang-include-path` (I’m using the flycheck clang checker, if you’re using gcc this variable is going to be different. I’m guessing `flycheck-gcc-include-path`) to rectify the issue. To do this, enter:

``````M-x customize-variable [ENTER]
flycheck-clang-include-path [ENTER]``````

This will get you a customize window for this variable. I added the following:

``````/usr/include/glib-2.0
/usr/lib/x86_64-linux-gnu/glib-2.0/include``````

…and things seem to be working fine. That said, I imagine if I get more involved in the GLib stack, I’m going to have to add all of these guys:

Not a huge deal, but I’ll cross that bridge when I come to it.

# Fun With Makefiles

Lately, I’ve been toying with the idea of trying my hand at some graphics programming. After spending the better part of yesterday trying to figure out how to even get started, I think I have a way ahead.

Building hello triangle using OpenGL is a fairly involved task. First, you need to settle on a graphics library. There are two choices here: OpenGL and DirectX. Obviously, I’ll be selecting OpenGL in order to avoid Microsoft vendor lock-in.

Next, you need a library to display a window for you. Sure, you could do it yourself, but then you’d get bogged down in a quagmire of platform specific issues. If you’ve been reading the blog, you know I don’t care for this sort of platform dependent nonsense, so I’ve tenatively settled on SDL 2. SDL is a cross platform multimedia library that handles sound, input, window creation, and the like. I plan to use this, in conjunction with an OpenGL context to do my work.

After you have that in order, you need an OpenGL Function Loader. Apparently the folks at Khronos were inspired by DMP Photobooth’s module system, there isn’t some opengl.h file you can just include and get your functions: you get to call `dlopen` and use `dlsym` to get function pointers. This wouldn’t be a huge issue if there were just a few functions, but there are thousands of them. In light of this, I’ve elected to go with GL3W for the time being. GL3W is a simple python script that generates a .c file containig the function pointers, and a .h to include.

All of this leads us to the topic of today’s post. How do we build this mess of libraries and random .c files?

## We’ll Make it Work

The obvious answer here is that we need to use some sort of build system. Given my past experience with the abominations produced by NetBeans, I’ve elected to roll my own. Let’s take a look:

``.DEFAULT_GOAL := all``

First, we have the default goal. By default, the default goal is the first one in the file. However, I like to make things explicit. Here, we set the default goal to “all”, which builds the code for all targets.

Next, we define some variables:

``````CC = gcc
COMPILE_FLAGS = -c -g -Wall -Wextra -std=c11 \$(OPTIMIZE_LEVEL)
LINK_FLAGS = -g -Wall -Wextra -std=c11 \$(OPTIMIZE_LEVEL)
OPTIMIZE_LEVEL = -Og

RM = rm -f
UNIVERSAL = gl3w gl_includes.h``````

The first variable, `CC` is built-in, and defaults to gcc. Again, I’m redefining it here to be explicit. After that, I define `COMPILE_FLAGS` and `LINK_FLAGS`, which are the flags I want to pass when I’m compiling someing to be link at a future time, and when I’m compiling and linking respectively. I define `OPTIMIZE_LEVEL` separately, because I want to potentially change it, and I don’t want to have to worry about if the two are in sync.

`LINKER_LIBS` are the libraries I’m going to be using. `RM` is the rm command, with flags, to be used in the clean target. `UNIVERSAL` is a list of files and targets that all buid targets depend on.

``````all : chapter1 chapter2 chapter3 chapter4 chapter5 chapter6 chapter7 chapter8 \
chapter9 chapter10 chapter11 chapter12 chapter13 chapter14 chapter15 \
chapter16 chapter17

chapter1 : \$(UNIVERSAL) chapter1.c
@echo "Building chapter 1:"

...

chapter17 : \$(UNIVERSAL)
@echo "Building chapter 17:"``````

Here we have the meat of our makefile. The tutorial I’m following has 17 chapters, and I’ll be building code from each. We have an “all” target that builds each chapter, and we have a target for each chapter that builds an executable. Each chapter target depends on UNIVERSAL and its own files.

``````gl3w : gl3w.c GL/gl3w.h GL/glcorearb.h
\$(CC) \$(COMPILE_FLAGS) gl3w.c``````

Here we build the source files that GL3W produces. I’m compiling it into a .o file so that it can be linked into the code for the various chapters.

``````clean:
@echo "Deleting .o files..."
\$(RM) *.o
@echo "Deleting core..."
\$(RM) core
@echo "Deleting chapters..."
\$(RM) chapter1
\$(RM) chapter2
\$(RM) chapter3
\$(RM) chapter4
\$(RM) chapter5
\$(RM) chapter6
\$(RM) chapter7
\$(RM) chapter8
\$(RM) chapter9
\$(RM) chapter10
\$(RM) chapter11
\$(RM) chapter12
\$(RM) chapter13
\$(RM) chapter14
\$(RM) chapter15
\$(RM) chapter16
\$(RM) chapter17``````

Finally, I have my clean target. Here we delete all the cruft that builds up in the build process.

It’s a simple makefile, but I feel it’ll make this process easier. I can just do the exercises and hopefully spend less time fiddling with gcc.

Consider this function:

``````headInTail :: [a] -> [a]

Pretty straightforward, right? It takes a list, extracts the head and sticks it in the tail. Surely you’ve written something like this before. It should be fine, right?

``````*Main> headInTail [1,2,3]
[2,3,1]``````

…checks out. Let’s try a few more:

``````*Main> headInTail "hello"
"elloh"
["cat"]``````

…good. And the moment we’ve all been waiting for:

``````*Main> headInTail []
*** Exception: Prelude.tail: empty list``````

Oh yeah, `head` and `tail` don’t work for empty lists… Normally, we have some choices on how to proceed here. We could wrap the function in a `Maybe`:

``````maybeHeadInTail :: [a] -> Maybe [a]

…which introduces an annoying `Maybe` to deal with just to stick our heads in our tails. Or, we could just do something with the empty list:

``````headInTail :: [a] -> [a]

…but what if returning the empty list isn’t the correct thing to do?

Another choice is to document this behavior (as `head` and `tail` do), and just never call `headInTail []`. But how can we guarantee that we never attempt to call this function on an empty list? Shouldn’t this be the type system’s problem?

Unfortunately, not all is roses and puppies. Sometimes the type system cannot help us. Sometimes somebody thought it’d be a good idea to use Haskell’s Evil exception system. Whatever the case, there are tools to help us.

Liquid Haskell is a static code analysis tool that is used to catch just these sorts of problems. Liquid Haskell allows us to define invariants which will be enforced by the tool. Liquid Haskell is a research project that is still in development. As such, it has some rough spots, however it’s still very much capable of helping us with our problem here. But before we begin, we need to get the tool installed.

To install the tool, execute:

``cabal install liquidhaskell``

…simple right? Unfortunately, we’re not quite done. We need to install an SMT solver. This tool is used by Liquid Haskell. Currently, the tool defaults to Z3. I’m not sure how to use a different solver (and Z3 works just fine), so I suggest you you Z3. You’ll have to build Z3, and place the binary somewhere on the `PATH`. After this is done, and assuming your `.cabal/bin` directory is also on the `PATH`, testing your source file is a simple as:

``liquid [FILE].hs``

## Let’s Have A Look

Create a haskell source file that contains the following:

``````headInTail :: [a] -> [a]

``liquid [YOUR_FILE].hs``

A bunch of stuff should scroll by, then in a second you’ll see something similar to the following:

``````**** UNSAFE *********************************************

Doop.hs:5:22: Error: Liquid Type Mismatch
Inferred type
VV : [a] | VV == l && len VV >= 0

not a subtype of Required type
VV : [a] | len VV > 0

In Context
VV : [a] | VV == l && len VV >= 0
l  : [a] | len l >= 0``````

If you go to the line and column indicated, you’ll find the argument to tail. Conveniently, it seems that Liquid Haskell comes pre-loaded with definitions for some library functions. Normally, you’ll have to define those yourself. In fact, let’s do just that.

The next logical step here is to write a specification for our function. This specification is a statement about what sorts of values the function can take. Add the following to your source file, in the line above the signature for headInTail:

``{-@ headInTail :: {l:[a] | len l > 0} -> [a] @-}``

If you re-run `liquid` on your source file, you’ll see that the warning went away, and the program now indicates that your source is “SAFE”. So, what does this refinement mean?

Basically, these refinements are machine-checked comments. They have no impact on the program, they exist for Liquid Haskell. Think of it as being like an enhanced type signature. Like a normal type signature, we start with the name of the function, then two colons. This part, however:

``{l:[a] | len l > 0}``

…should be new. Basically, this part says that the list should not be empty. You should read it as “l is a [a] such that len l is greater than zero.” A lot of the notation used by Liquid Haskell comes from formal logic. Let’s break this down some more:

``l:[a]``

Here we bind a symbol, l, to the first list argument. At any point to the right of this symbol until the end of the scope defined by `{}`, we can reference this symbol.

``{... | ...}``

The pipe symbol indicates that we are going to make some statement about the type on the left hand side.

``len l > 0``

Here we state that the length of l must be greater than 0. It looks like we are calling a function, and we sort of are; len is a measure which is a special function that is used in specifications. However, the subject of measures is a post for another day.

You may now be thinking: “Well this is all well and good, but what’s to stop me from calling this function on an empty list?” To answer that, let’s implement main:

``````main =
do i <- getLine

Add this to your source file, and then run `liquid [YOUR_FILE].hs` and you’ll notice that Liquid Haskell has a problem with your attempt to call `headInTail`:

``````**** UNSAFE *********************************************

Doop.hs:3:29: Error: Liquid Type Mismatch
Inferred type
VV : [Char] | VV == i && len VV >= 0

not a subtype of Required type
VV : [Char] | len VV > 0

In Context
VV : [Char] | VV == i && len VV >= 0
i  : [Char] | len i >= 0``````

Liquid Haskell is telling you that it can’t prove that the length of `i` is greater than 0. If you execute your main function, you should see that it works as expected. Type in a string, and it’ll do the right thing. Push enter right away and you’ll get an exception.

``````*Main> main
hello
elloh
*Main> main

*** Exception: Prelude.tail: empty list``````

…ick… Let’s fix this:

``````main =
do i <- getLine
case i of
``````*Main> main