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| <main> |
| <h1 id="background-topics"><a class="header" href="#background-topics">Background topics</a></h1> |
| <p>This section covers a numbers of common compiler terms that arise in |
| this guide. We try to give the general definition while providing some |
| Rust-specific context.</p> |
| <p><a id="cfg"></a></p> |
| <h2 id="what-is-a-control-flow-graph"><a class="header" href="#what-is-a-control-flow-graph">What is a control-flow graph?</a></h2> |
| <p>A control-flow graph (CFG) is a common term from compilers. If you’ve ever |
| used a flow-chart, then the concept of a control-flow graph will be |
| pretty familiar to you. It’s a representation of your program that |
| clearly exposes the underlying control flow.</p> |
| <p>A control-flow graph is structured as a set of <strong>basic blocks</strong> |
| connected by edges. The key idea of a basic block is that it is a set |
| of statements that execute “together” – that is, whenever you branch |
| to a basic block, you start at the first statement and then execute |
| all the remainder. Only at the end of the block is there the |
| possibility of branching to more than one place (in MIR, we call that |
| final statement the <strong>terminator</strong>):</p> |
| <pre><code class="language-mir">bb0: { |
| statement0; |
| statement1; |
| statement2; |
| ... |
| terminator; |
| } |
| </code></pre> |
| <p>Many expressions that you are used to in Rust compile down to multiple |
| basic blocks. For example, consider an if statement:</p> |
| <pre><code class="language-rust ignore">a = 1; |
| if some_variable { |
| b = 1; |
| } else { |
| c = 1; |
| } |
| d = 1;</code></pre> |
| <p>This would compile into four basic blocks in MIR. In textual form, it looks like |
| this:</p> |
| <pre><code class="language-mir">BB0: { |
| a = 1; |
| if some_variable { |
| goto BB1; |
| } else { |
| goto BB2; |
| } |
| } |
| |
| BB1: { |
| b = 1; |
| goto BB3; |
| } |
| |
| BB2: { |
| c = 1; |
| goto BB3; |
| } |
| |
| BB3: { |
| d = 1; |
| ... |
| } |
| </code></pre> |
| <p>In graphical form, it looks like this:</p> |
| <pre><code> BB0 |
| +--------------------+ |
| | a = 1; | |
| +--------------------+ |
| / \ |
| if some_variable else |
| / \ |
| BB1 / \ BB2 |
| +-----------+ +-----------+ |
| | b = 1; | | c = 1; | |
| +-----------+ +-----------+ |
| \ / |
| \ / |
| \ BB3 / |
| +----------+ |
| | d = 1; | |
| | ... | |
| +----------+ |
| </code></pre> |
| <p>When using a control-flow graph, a loop simply appears as a cycle in |
| the graph, and the <code>break</code> keyword translates into a path out of that |
| cycle.</p> |
| <p><a id="dataflow"></a></p> |
| <h2 id="what-is-a-dataflow-analysis"><a class="header" href="#what-is-a-dataflow-analysis">What is a dataflow analysis?</a></h2> |
| <p><a href="https://cs.au.dk/~amoeller/spa/"><em>Static Program Analysis</em></a> by Anders Møller |
| and Michael I. Schwartzbach is an incredible resource!</p> |
| <p><em>Dataflow analysis</em> is a type of static analysis that is common in many |
| compilers. It describes a general technique, rather than a particular analysis.</p> |
| <p>The basic idea is that we can walk over a <a href="#cfg">control-flow graph (CFG)</a> and |
| keep track of what some value could be. At the end of the walk, we might have |
| shown that some claim is true or not necessarily true (e.g. “this variable must |
| be initialized”). <code>rustc</code> tends to do dataflow analyses over the MIR, since MIR |
| is already a CFG.</p> |
| <p>For example, suppose we want to check that <code>x</code> is initialized before it is used |
| in this snippet:</p> |
| <pre><code class="language-rust ignore">fn foo() { |
| let mut x; |
| |
| if some_cond { |
| x = 1; |
| } |
| |
| dbg!(x); |
| }</code></pre> |
| <p>A CFG for this code might look like this:</p> |
| <pre><code class="language-txt"> +------+ |
| | Init | (A) |
| +------+ |
| | \ |
| | if some_cond |
| else \ +-------+ |
| | \| x = 1 | (B) |
| | +-------+ |
| | / |
| +---------+ |
| | dbg!(x) | (C) |
| +---------+ |
| </code></pre> |
| <p>We can do the dataflow analysis as follows: we will start off with a flag <code>init</code> |
| which indicates if we know <code>x</code> is initialized. As we walk the CFG, we will |
| update the flag. At the end, we can check its value.</p> |
| <p>So first, in block (A), the variable <code>x</code> is declared but not initialized, so |
| <code>init = false</code>. In block (B), we initialize the value, so we know that <code>x</code> is |
| initialized. So at the end of (B), <code>init = true</code>.</p> |
| <p>Block (C) is where things get interesting. Notice that there are two incoming |
| edges, one from (A) and one from (B), corresponding to whether <code>some_cond</code> is true or not. |
| But we cannot know that! It could be the case the <code>some_cond</code> is always true, |
| so that <code>x</code> is actually always initialized. It could also be the case that |
| <code>some_cond</code> depends on something random (e.g. the time), so <code>x</code> may not be |
| initialized. In general, we cannot know statically (due to <a href="https://en.wikipedia.org/wiki/Rice%27s_theorem">Rice’s |
| Theorem</a>). So what should the value of <code>init</code> be in block (C)?</p> |
| <p>Generally, in dataflow analyses, if a block has multiple parents (like (C) in |
| our example), its dataflow value will be some function of all its parents (and |
| of course, what happens in (C)). Which function we use depends on the analysis |
| we are doing.</p> |
| <p>In this case, we want to be able to prove definitively that <code>x</code> must be |
| initialized before use. This forces us to be conservative and assume that |
| <code>some_cond</code> might be false sometimes. So our “merging function” is “and”. That |
| is, <code>init = true</code> in (C) if <code>init = true</code> in (A) <em>and</em> in (B) (or if <code>x</code> is |
| initialized in (C)). But this is not the case; in particular, <code>init = false</code> in |
| (A), and <code>x</code> is not initialized in (C). Thus, <code>init = false</code> in (C); we can |
| report an error that “<code>x</code> may not be initialized before use”.</p> |
| <p>There is definitely a lot more that can be said about dataflow analyses. There is an |
| extensive body of research literature on the topic, including a lot of theory. |
| We only discussed a forwards analysis, but backwards dataflow analysis is also |
| useful. For example, rather than starting from block (A) and moving forwards, |
| we might have started with the usage of <code>x</code> and moved backwards to try to find |
| its initialization.</p> |
| <p><a id="quantified"></a></p> |
| <h2 id="what-is-universally-quantified-what-about-existentially-quantified"><a class="header" href="#what-is-universally-quantified-what-about-existentially-quantified">What is “universally quantified”? What about “existentially quantified”?</a></h2> |
| <p>In math, a predicate may be <em>universally quantified</em> or <em>existentially |
| quantified</em>:</p> |
| <ul> |
| <li><em>Universal</em> quantification: |
| <ul> |
| <li>the predicate holds if it is true for all possible inputs.</li> |
| <li>Traditional notation: ∀x: P(x). Read as “for all x, P(x) holds”.</li> |
| </ul> |
| </li> |
| <li><em>Existential</em> quantification: |
| <ul> |
| <li>the predicate holds if there is any input where it is true, i.e., there |
| only has to be a single input.</li> |
| <li>Traditional notation: ∃x: P(x). Read as “there exists x such that P(x) holds”.</li> |
| </ul> |
| </li> |
| </ul> |
| <p>In Rust, they come up in type checking and trait solving. For example,</p> |
| <pre><code class="language-rust ignore">fn foo<T>()</code></pre> |
| <p>This function claims that the function is well-typed for all types <code>T</code>: <code>∀ T: well_typed(foo)</code>.</p> |
| <p>Another example:</p> |
| <pre><code class="language-rust ignore">fn foo<'a>(_: &'a usize)</code></pre> |
| <p>This function claims that for any lifetime <code>'a</code> (determined by the |
| caller), it is well-typed: <code>∀ 'a: well_typed(foo)</code>.</p> |
| <p>Another example:</p> |
| <pre><code class="language-rust ignore">fn foo<F>() |
| where for<'a> F: Fn(&'a u8)</code></pre> |
| <p>This function claims that it is well-typed for all types <code>F</code> such that for all |
| lifetimes <code>'a</code>, <code>F: Fn(&'a u8)</code>: <code>∀ F: ∀ 'a: (F: Fn(&'a u8)) => well_typed(foo)</code>.</p> |
| <p>One more example:</p> |
| <pre><code class="language-rust ignore">fn foo(_: dyn Debug)</code></pre> |
| <p>This function claims that there exists some type <code>T</code> that implements <code>Debug</code> |
| such that the function is well-typed: <code>∃ T: (T: Debug) and well_typed(foo)</code>.</p> |
| <p><a id="variance"></a></p> |
| <h2 id="what-is-a-de-bruijn-index"><a class="header" href="#what-is-a-de-bruijn-index">What is a de Bruijn Index?</a></h2> |
| <p><a href="https://en.wikipedia.org/wiki/De_Bruijn_index">De Bruijn indices</a> are a way of representing, using only integers, |
| which variables are bound in which binders. They were originally invented for |
| use in lambda calculus evaluation (see <a href="https://en.wikipedia.org/wiki/De_Bruijn_index">this Wikipedia article</a> for |
| more). In <code>rustc</code>, we use de Bruijn indices to <a href="../ty_module/generic_arguments.html">represent generic types</a>.</p> |
| <p>Here is a basic example of how de Bruijn indices might be used for closures (we |
| don’t actually do this in <code>rustc</code> though!):</p> |
| <pre><code class="language-rust ignore">|x| { |
| f(x) // de Bruijn index of `x` is 1 because `x` is bound 1 level up |
| |
| |y| { |
| g(x, y) // index of `x` is 2 because it is bound 2 levels up |
| // index of `y` is 1 because it is bound 1 level up |
| } |
| }</code></pre> |
| <h2 id="what-are-co--and-contra-variance"><a class="header" href="#what-are-co--and-contra-variance">What are co- and contra-variance?</a></h2> |
| <p>Check out the subtyping chapter from the |
| <a href="https://doc.rust-lang.org/nomicon/subtyping.html">Rust Nomicon</a>.</p> |
| <p>See the <a href="../variance.html">variance</a> chapter of this guide for more info on how |
| the type checker handles variance.</p> |
| <p><a id="free-vs-bound"></a></p> |
| <h2 id="what-is-a-free-region-or-a-free-variable-what-about-bound-region"><a class="header" href="#what-is-a-free-region-or-a-free-variable-what-about-bound-region">What is a “free region” or a “free variable”? What about “bound region”?</a></h2> |
| <p>Let’s describe the concepts of free vs bound in terms of program |
| variables, since that’s the thing we’re most familiar with.</p> |
| <ul> |
| <li>Consider this expression, which creates a closure: <code>|a, b| a + b</code>. |
| Here, the <code>a</code> and <code>b</code> in <code>a + b</code> refer to the arguments that the closure will |
| be given when it is called. We say that the <code>a</code> and <code>b</code> there are <strong>bound</strong> to |
| the closure, and that the closure signature <code>|a, b|</code> is a <strong>binder</strong> for the |
| names <code>a</code> and <code>b</code> (because any references to <code>a</code> or <code>b</code> within refer to the |
| variables that it introduces).</li> |
| <li>Consider this expression: <code>a + b</code>. In this expression, <code>a</code> and <code>b</code> refer to |
| local variables that are defined <em>outside</em> of the expression. We say that |
| those variables <strong>appear free</strong> in the expression (i.e., they are <strong>free</strong>, |
| not <strong>bound</strong> (tied up)).</li> |
| </ul> |
| <p>So there you have it: a variable “appears free” in some |
| expression/statement/whatever if it refers to something defined |
| outside of that expressions/statement/whatever. Equivalently, we can |
| then refer to the “free variables” of an expression – which is just |
| the set of variables that “appear free”.</p> |
| <p>So what does this have to do with regions? Well, we can apply the |
| analogous concept to type and regions. For example, in the type <code>&'a u32</code>, <code>'a</code> appears free. But in the type <code>for<'a> fn(&'a u32)</code>, it |
| does not.</p> |
| <h1 id="further-reading-about-compilers"><a class="header" href="#further-reading-about-compilers">Further Reading About Compilers</a></h1> |
| <blockquote> |
| <p>Thanks to <code>mem</code>, <code>scottmcm</code>, and <code>Levi</code> on the official Discord for the |
| recommendations, and to <code>tinaun</code> for posting a link to a <a href="https://web.archive.org/web/20181230012554/https://twitter.com/graydon_pub/status/1039615569132118016">twitter thread from |
| Graydon Hoare</a> |
| which had some more recommendations!</p> |
| <p>Other sources: https://gcc.gnu.org/wiki/ListOfCompilerBooks</p> |
| <p>If you have other suggestions, please feel free to open an issue or PR.</p> |
| </blockquote> |
| <h2 id="books"><a class="header" href="#books">Books</a></h2> |
| <ul> |
| <li><a href="https://www.cis.upenn.edu/~bcpierce/tapl/">Types and Programming Languages</a></li> |
| <li><a href="https://www.cs.rochester.edu/~scott/pragmatics/">Programming Language Pragmatics</a></li> |
| <li><a href="https://www.cs.cmu.edu/~rwh/pfpl/">Practical Foundations for Programming Languages</a></li> |
| <li><a href="https://www.pearson.com/us/higher-education/program/Aho-Compilers-Principles-Techniques-and-Tools-2nd-Edition/PGM167067.html">Compilers: Principles, Techniques, and Tools, 2nd Edition</a></li> |
| <li><a href="https://www.cs.kent.ac.uk/people/staff/rej/gcbook/">Garbage Collection: Algorithms for Automatic Dynamic Memory Management</a></li> |
| <li><a href="https://www.amazon.com/Linkers-Kaufmann-Software-Engineering-Programming/dp/1558604960">Linkers and Loaders</a> (There are also free versions of this, but the version we had linked seems to be offline at the moment.)</li> |
| <li><a href="https://www.goodreads.com/book/show/887908.Advanced_Compiler_Design_and_Implementation">Advanced Compiler Design and Implementation</a></li> |
| <li><a href="https://www.goodreads.com/book/show/2063103.Building_an_Optimizing_Compiler">Building an Optimizing Compiler</a></li> |
| <li><a href="http://www.craftinginterpreters.com/">Crafting Interpreters</a></li> |
| </ul> |
| <h2 id="courses"><a class="header" href="#courses">Courses</a></h2> |
| <ul> |
| <li><a href="https://www.cs.uoregon.edu/research/summerschool/archives.html">University of Oregon Programming Languages Summer School archive</a></li> |
| </ul> |
| <h2 id="wikis"><a class="header" href="#wikis">Wikis</a></h2> |
| <ul> |
| <li><a href="https://en.wikipedia.org/wiki/List_of_programming_languages_by_type">Wikipedia</a></li> |
| <li><a href="https://esolangs.org/wiki/Main_Page">Esoteric Programming Languages</a></li> |
| <li><a href="https://plato.stanford.edu/index.html">Stanford Encyclopedia of Philosophy</a></li> |
| <li><a href="https://ncatlab.org/nlab/show/HomePage">nLab</a></li> |
| </ul> |
| <h2 id="misc-papers-and-blog-posts"><a class="header" href="#misc-papers-and-blog-posts">Misc Papers and Blog Posts</a></h2> |
| <ul> |
| <li><a href="https://www.cse.chalmers.se/research/group/logic/book/">Programming in Martin-Löf’s Type Theory</a></li> |
| <li><a href="https://dl.acm.org/doi/10.1145/3093333.3009882">Polymorphism, Subtyping, and Type Inference in MLsub</a></li> |
| </ul> |
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