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compiler_design.html
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1//EN"
"http://www.w3.org/TR/xhtml11/DTD/xhtml11.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head>
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<meta name="generator" content="AsciiDoc 8.6.9" />
<title>Fasto 2015 Compiler Design Document</title>
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<body class="article">
<div id="header">
<h1>Fasto 2015 Compiler Design Document</h1>
</div>
<div id="content">
<div id="preamble">
<div class="sectionbody">
<div class="paragraph"><p>This documents describes the overall design of the Fasto compiler for
the 2015 iteration of the course Introduction to Compilers at DIKU.</p></div>
<div class="paragraph"><p>The Fasto compiler is implemented in Standard ML and consists of a
number of modules, each implementing one analysis or transformation
step. A <em>driver program</em> is responsible for reading Fasto source
programs from the file system, passing the text to the parser, passing
the resulting AST through various compiler passes, and finally writing
the generated assembly code back to a file. The Fasto compiler does
not itself contain an assembler, but instead produces assembly code
suitable for use in the MARS MIPS
simulator.<span class="footnote"><br />[<a href="http://courses.missouristate.edu/KenVollmar/MARS/">http://courses.missouristate.edu/KenVollmar/MARS/</a>]<br /></span></p></div>
</div>
</div>
<div class="sect1">
<h2 id="_description_of_the_fasto_compiler_modules">Description of the Fasto compiler modules</h2>
<div class="sectionbody">
<div class="paragraph"><p>This section introduces the compiler’s structure and explains some
details and reasons for particular choices.</p></div>
<div class="sect2">
<h3 id="_lexer_parser_and_symbol_table">Lexer, Parser and Symbol Table</h3>
<div class="paragraph"><p>The lexer and parser are implemented in files <code>Lexer.lex</code> and
<code>Parser.grm</code>, respectively. The lexical rules and grammar have
already been described in the main project document.</p></div>
<div class="paragraph"><p>File <code>SymTab.sml</code> provides a polymorphic implementation of the symbol
table. The symbol table is simply a list of tuples, in which the
first term is a string, denoting the name of a variable/function, and
the second term is the information associated to that name. The type
of the second term is polymorphic, i.e. different types of information
will be stored in different tables during processing. The main
functions are: (i) <code>bind</code>, which adds a name-value pair to the symbol
table (potentially hiding an older entry), and (ii) <code>lookup</code>.
Function <code>lookup</code> receives as input the name of a variable, <code>n</code>, and
searches the symbol table to find the closest binding for <code>n</code>. If no
such binding exists then option <code>NONE</code> is returned, otherwise <code>SOME
m</code>, where <code>m</code> is the information associated with <code>n</code>.</p></div>
</div>
<div class="sect2">
<h3 id="_abstract_syntax_representation">Abstract Syntax Representation</h3>
<div class="paragraph"><p>The abstract syntax representation is defined in the file Fasto.sml:
the entire program has either type <code>Fasto.UnknownTypes.Prog</code> or
<code>Fasto.KnownTypes.Prog</code>, depending on which phase the compiler is in.
A program is a list of function declarations. A function declaration
has type <code>FunDec</code>. Expressions and types are built by the
constructors of types <code>Exp</code> and <code>Type</code>, respectively.</p></div>
<div class="paragraph"><p><code>Exp</code>, <code>FunDec</code>, <code>Prog</code> and other central constructors are located
inside the <code>FastoFn</code> functor. This means that whenever <code>TypeAnnot</code>
occurs, the actual type is <code>unit</code> (the SML type of the value <code>()</code>) if
they are used in the <code>UnknownTypes</code> structure, or <code>Type</code> if in the
<code>KnownTypes</code> structure. After parsing, a program uses the
<code>UnknownTypes</code> version of <code>TypeAnnot</code>, namely <code>unit</code>, and after type
checking, a program uses the <code>KnownTypes</code> version — <code>Type</code>.</p></div>
<div class="paragraph"><p>Note that several type constructors of <code>Exp</code> contain <code>Type</code> nodes.
For instance the indexing constructor is declared as <code>Index of string
* Exp * TypeAnnot * pos</code>. These type nodes are replaced by the
correct type by the type checker, and used in the MIPS code generation
phase. For example, generating MIPS code for array indexing (<code>a[i]</code>)
requires to know whether the element type is stored in one byte or in
one word (four bytes), i.e. whether to use a load-byte or load-word
instruction.</p></div>
<div class="paragraph"><p><code>Fasto.sml</code> also provides functions to pretty print a program
(prettyPrint) a function (ppFun), a type (ppType), or an expression
(ppExp). Pretty printing can be used for user-friendlier error
messages and for debugging.</p></div>
</div>
<div class="sect2">
<h3 id="_interpreter">Interpreter</h3>
<div class="paragraph"><p>The interpreter is implemented in file <code>Interpret.sml</code>. The entry
point is function <code>evalPgm</code>, which builds the symbol table for
functions and starts the interpretation of the program by interpreting
function <code>main</code>.</p></div>
<div class="paragraph"><p>Interpreting a (call to a) function is implemented by function
<code>callFun</code>, which: (i) evaluates the function arguments, (ii) creates a
new symbol table for variables and binds the evaluated arguments to
the function’s formal arguments, and (iii) continues by interpreting
the expression that corresponds to the body of the function.</p></div>
<div class="paragraph"><p>Finally, interpreting an expression is implemented by <code>evalExp</code>
via case analysis on the type constructors of <code>Exp</code>.</p></div>
</div>
<div class="sect2">
<h3 id="_type_checking">Type Checking</h3>
<div class="paragraph"><p>The type checker is implemented in file <code>Type.sml</code>. The entry point is</p></div>
<div class="paragraph"><p><code>checkProgram : Fasto.UnknownTypes.Prog -> Fasto.KnownTypes.Prog</code></p></div>
<div class="paragraph"><p>which verifies that all functions in the program have the declared
type and annotates the nodes.</p></div>
<div class="paragraph"><p>Type checking a function means to verify that the result type of the
function matches the type of the function-body expression, given the
formal parameters have the declared types. Typechecking a function
<em>application</em> means to verify that the types of the actual and the
formal parameters match.</p></div>
<div class="paragraph"><p>Expressions are type-checked recursively, building types in a bottom-up fashion.
For instance, type-checking an <code>if-then-else</code> means to
check that the condition is boolean, and to determine the types of the <code>then</code>
and <code>else</code> sub-expressions and to verify that these types are the same.</p></div>
<div class="paragraph"><p>Type checking an expression is mainly implemented by <code>expType</code> via
case analysis on the type constructors of <code>Exp</code>. <em>Your changes to the
type checker will mainly extend <code>expType</code>'s implementation.</em></p></div>
<div class="paragraph"><p>As mentioned, type information also needs to be passed to the MIPS
code generator, especially for arrays and for the built-in <code>write</code>
function. Therefore, <code>checkProgram</code> builds a new abstract-syntax
representation in which the type information of various
<code>Fasto.UnknownTypes.Exp</code> constructors are changed to the correct
types, represented in <code>Fasto.KnownTypes.Exp</code> (for instance the type of
the array for array-indexing <code>a[i]</code>).</p></div>
</div>
<div class="sect2">
<h3 id="_high_level_optimisations">High-Level Optimisations</h3>
<div class="paragraph"><p>An optimising compiler is typically organised as a set of <em>passes</em>,
each of which take as input a program, and produce as output an
equivalent - but optimised - program. The Fasto compiler follows this
design, and implements each pass as a distinct module. All but one of
these are fully implemented for you, but will be covered for
completeness.</p></div>
<div class="sect3">
<h4 id="_code_callgraph_code"><code>CallGraph</code></h4>
<div class="paragraph"><p>This module is not an optimisation pass per se, but is a module
containing facilities for computing the <em>call graph</em> of a Fasto
program, which is used in some optimisations. The call graph contains
information about which functions are called directly or indirectly by
a given function. As an important special case, if a function is
recursive (even indirectly), the call graph will register it as
calling itself.</p></div>
</div>
<div class="sect3">
<h4 id="_code_inlining_code"><code>Inlining</code></h4>
<div class="paragraph"><p>Function inlining is a transformation in which the body of a function
is substituted for a call to the function. This has two main
benefits: first, it removes the overhead of the function call.
Second, and more importantly, it acts as an <em>enabling optimisation</em>,
in that most optimisations are not able to cross function call
boundaries, and thus may only be applicable once a function has been
inlined.</p></div>
<div class="paragraph"><p>Inlining is not free, and can result in a expontential increase in
code size, which can negatively impact performance. Production
compilers use heuristics to determine when inlining should happen
(usually based on the size of the function), but in Fasto we are more
liberal: we aggressively inline all non-recursive functions.</p></div>
<div class="listingblock">
<div class="title">Before inlining</div>
<div class="content"><!-- Generator: GNU source-highlight 3.1.8
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre><tt><span style="font-weight: bold"><span style="color: #0000FF">fun</span></span> <span style="color: #009900">int</span> f<span style="color: #990000">(</span><span style="color: #009900">int</span> x<span style="color: #990000">,</span> <span style="color: #009900">int</span> y<span style="color: #990000">)</span> <span style="color: #990000">=</span>
<span style="color: #990000">(</span>x<span style="color: #990000">+</span><span style="color: #993399">2</span><span style="color: #990000">)</span> <span style="color: #990000">*</span> <span style="color: #990000">(</span>y<span style="color: #990000">-</span><span style="color: #993399">2</span><span style="color: #990000">)</span>
<span style="font-weight: bold"><span style="color: #0000FF">fun</span></span> <span style="color: #009900">int</span> main<span style="color: #990000">()</span> <span style="color: #990000">=</span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> a <span style="color: #990000">=</span> read<span style="color: #990000">(</span><span style="color: #009900">int</span><span style="color: #990000">)</span> <span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> b <span style="color: #990000">=</span> f<span style="color: #990000">(</span>a<span style="color: #990000">,</span> <span style="color: #993399">2</span><span style="color: #990000">)</span> <span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
c</tt></pre></div></div>
<div class="listingblock">
<div class="title">After inlining</div>
<div class="content"><!-- Generator: GNU source-highlight 3.1.8
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre><tt><span style="font-weight: bold"><span style="color: #0000FF">fun</span></span> <span style="color: #009900">int</span> f<span style="color: #990000">(</span><span style="color: #009900">int</span> x<span style="color: #990000">,</span> <span style="color: #009900">int</span> y<span style="color: #990000">)</span> <span style="color: #990000">=</span>
<span style="color: #990000">(</span>x<span style="color: #990000">+</span><span style="color: #993399">2</span><span style="color: #990000">)</span> <span style="color: #990000">*</span> <span style="color: #990000">(</span>y<span style="color: #990000">-</span><span style="color: #993399">2</span><span style="color: #990000">)</span>
<span style="font-weight: bold"><span style="color: #0000FF">fun</span></span> <span style="color: #009900">int</span> main<span style="color: #990000">()</span> <span style="color: #990000">=</span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> a <span style="color: #990000">=</span> read<span style="color: #990000">(</span><span style="color: #009900">int</span><span style="color: #990000">)</span> <span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> b <span style="color: #990000">=</span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> x <span style="color: #990000">=</span> a <span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> y <span style="color: #990000">=</span> <span style="color: #993399">2</span> <span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
<span style="color: #990000">(</span>x <span style="color: #990000">+</span> <span style="color: #993399">2</span><span style="color: #990000">)</span> <span style="color: #990000">*</span> <span style="color: #990000">(</span>y <span style="color: #990000">-</span> <span style="color: #993399">2</span><span style="color: #990000">)</span>
<span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
b</tt></pre></div></div>
<div class="paragraph"><p>The figure above illustrates the process of inlining a function <code>f</code> -
note that the original function still exists in the program, and that
the resulting code is somewhat awkward. It is the job of later
optimisations to clean this up.</p></div>
</div>
<div class="sect3">
<h4 id="_code_copyconstpropfold_code"><code>CopyConstPropFold</code></h4>
<div class="paragraph"><p>This module contains two conceptually separate, but
implementation-wise heavily linked optimisations: <em>copy propagation</em>
and <em>constant folding</em>. In copy propagation, we react to bindings
such as <code>let x = a</code> or <code>let y = 2</code>, which merely "copy" a variable or
constant, and replace subsequent uses of <code>x</code> and <code>y</code> with <code>a and `2</code>
respectively. In constant folding, we simplify expressions whose
value can be determined at compile-time. In the running example, once
we have performed the substitution <code>y => 2</code> in the expression <code>y-2</code>,
we obtain <code>2-2</code>, which, since it contains only constants, can be
evaluated at compile-time to <code>0</code>. In the original expression <code>(x + 2)
* (y - 2)</code> we thus produce <code>(x + 2) * 0</code>, which can again be
constant-folded to <code>0</code>.</p></div>
<div class="listingblock">
<div class="title">Before copy/const prop/fold</div>
<div class="content"><!-- Generator: GNU source-highlight 3.1.8
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre><tt><span style="font-weight: bold"><span style="color: #0000FF">fun</span></span> <span style="color: #009900">int</span> f<span style="color: #990000">(</span><span style="color: #009900">int</span> x<span style="color: #990000">,</span> <span style="color: #009900">int</span> y<span style="color: #990000">)</span> <span style="color: #990000">=</span>
<span style="color: #990000">(</span>x<span style="color: #990000">+</span><span style="color: #993399">2</span><span style="color: #990000">)</span> <span style="color: #990000">*</span> <span style="color: #990000">(</span>y<span style="color: #990000">-</span><span style="color: #993399">2</span><span style="color: #990000">)</span>
<span style="font-weight: bold"><span style="color: #0000FF">fun</span></span> <span style="color: #009900">int</span> main<span style="color: #990000">()</span> <span style="color: #990000">=</span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> a <span style="color: #990000">=</span> read<span style="color: #990000">(</span><span style="color: #009900">int</span><span style="color: #990000">)</span> <span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> b <span style="color: #990000">=</span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> x <span style="color: #990000">=</span> a <span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> y <span style="color: #990000">=</span> <span style="color: #993399">2</span> <span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
<span style="color: #990000">(</span>x <span style="color: #990000">+</span> <span style="color: #993399">2</span><span style="color: #990000">)</span> <span style="color: #990000">*</span> <span style="color: #990000">(</span>y <span style="color: #990000">-</span> <span style="color: #993399">2</span><span style="color: #990000">)</span>
<span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
b</tt></pre></div></div>
<div class="listingblock">
<div class="title">After copy/const prop/fold</div>
<div class="content"><!-- Generator: GNU source-highlight 3.1.8
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre><tt><span style="font-weight: bold"><span style="color: #0000FF">fun</span></span> <span style="color: #009900">int</span> f<span style="color: #990000">(</span><span style="color: #009900">int</span> x<span style="color: #990000">,</span> <span style="color: #009900">int</span> y<span style="color: #990000">)</span> <span style="color: #990000">=</span>
<span style="color: #990000">(</span>x<span style="color: #990000">+</span><span style="color: #993399">2</span><span style="color: #990000">)</span> <span style="color: #990000">*</span> <span style="color: #990000">(</span>y<span style="color: #990000">-</span><span style="color: #993399">2</span><span style="color: #990000">)</span>
<span style="font-weight: bold"><span style="color: #0000FF">fun</span></span> <span style="color: #009900">int</span> main<span style="color: #990000">()</span> <span style="color: #990000">=</span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> a <span style="color: #990000">=</span> read<span style="color: #990000">(</span><span style="color: #009900">int</span><span style="color: #990000">)</span> <span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> x <span style="color: #990000">=</span> a <span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> y <span style="color: #990000">=</span> <span style="color: #993399">2</span> <span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> b <span style="color: #990000">=</span> <span style="color: #993399">0</span>
<span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
b</tt></pre></div></div>
<div class="paragraph"><p>Note that the program still contains the now-unused bindings for <code>a</code>,
<code>x</code> and <code>y</code> - these are removed in the next pass.</p></div>
<div class="paragraph"><p><strong>This pass has not been fully implemented in the handed-out code, and
its completion is the subject of Task 3.</strong></p></div>
</div>
<div class="sect3">
<h4 id="_code_deadbindingremoval_code"><code>DeadBindingRemoval</code></h4>
<div class="paragraph"><p>The purpose of this optimization is to remove variable bindings that
are not used. This is conceptually quite simple, but complicated by
the fact that we cannot remove bindings whose expressions perform IO,
as this would change the semantics of the program.</p></div>
<div class="listingblock">
<div class="title">Before dead variable removal</div>
<div class="content"><!-- Generator: GNU source-highlight 3.1.8
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre><tt><span style="font-weight: bold"><span style="color: #0000FF">fun</span></span> <span style="color: #009900">int</span> f<span style="color: #990000">(</span><span style="color: #009900">int</span> x<span style="color: #990000">,</span> <span style="color: #009900">int</span> y<span style="color: #990000">)</span> <span style="color: #990000">=</span>
<span style="color: #990000">(</span>x<span style="color: #990000">+</span><span style="color: #993399">2</span><span style="color: #990000">)</span> <span style="color: #990000">*</span> <span style="color: #990000">(</span>y<span style="color: #990000">-</span><span style="color: #993399">2</span><span style="color: #990000">)</span>
<span style="font-weight: bold"><span style="color: #0000FF">fun</span></span> <span style="color: #009900">int</span> main<span style="color: #990000">()</span> <span style="color: #990000">=</span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> a <span style="color: #990000">=</span> read<span style="color: #990000">(</span><span style="color: #009900">int</span><span style="color: #990000">)</span> <span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> x <span style="color: #990000">=</span> a <span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> y <span style="color: #990000">=</span> <span style="color: #993399">2</span> <span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> b <span style="color: #990000">=</span> <span style="color: #993399">0</span>
<span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
b</tt></pre></div></div>
<div class="listingblock">
<div class="title">After dead variable removal</div>
<div class="content"><!-- Generator: GNU source-highlight 3.1.8
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre><tt><span style="font-weight: bold"><span style="color: #0000FF">fun</span></span> <span style="color: #009900">int</span> f<span style="color: #990000">(</span><span style="color: #009900">int</span> x<span style="color: #990000">,</span> <span style="color: #009900">int</span> y<span style="color: #990000">)</span> <span style="color: #990000">=</span>
<span style="color: #990000">(</span>x<span style="color: #990000">+</span><span style="color: #993399">2</span><span style="color: #990000">)</span> <span style="color: #990000">*</span> <span style="color: #990000">(</span>y<span style="color: #990000">-</span><span style="color: #993399">2</span><span style="color: #990000">)</span>
<span style="font-weight: bold"><span style="color: #0000FF">fun</span></span> <span style="color: #009900">int</span> main<span style="color: #990000">()</span> <span style="color: #990000">=</span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> a <span style="color: #990000">=</span> read<span style="color: #990000">(</span><span style="color: #009900">int</span><span style="color: #990000">)</span> <span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
<span style="font-weight: bold"><span style="color: #0000FF">let</span></span> b <span style="color: #990000">=</span> <span style="color: #993399">0</span>
<span style="font-weight: bold"><span style="color: #0000FF">in</span></span>
b</tt></pre></div></div>
<div class="paragraph"><p>While dead binding removable is rarely useful on directly