<html><head><meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1"><title>2.3. Using Precedences</title><link rel="stylesheet" href="fptools.css" type="text/css"><meta name="generator" content="DocBook XSL Stylesheets V1.73.2"><link rel="start" href="index.html" title="Happy User Guide"><link rel="up" href="sec-using.html" title="Chapter 2. Using Happy"><link rel="prev" href="sec-sequences.html" title="2.2. Parsing sequences"><link rel="next" href="sec-type-signatures.html" title="2.4. Type Signatures"></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">2.3. Using Precedences</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec-sequences.html">Prev</a> </td><th width="60%" align="center">Chapter 2. Using <span class="application">Happy</span></th><td width="20%" align="right"> <a accesskey="n" href="sec-type-signatures.html">Next</a></td></tr></table><hr></div><div class="sect1" lang="en"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="sec-Precedences"></a>2.3. Using Precedences</h2></div></div></div><a class="indexterm" name="id2496239"></a><a class="indexterm" name="id2496246"></a><p>Going back to our earlier expression-parsing example,
wouldn't it be nicer if we didn't have to explicitly separate
the expressions into terms and factors, merely to make it
clear that <code class="literal">'*'</code> and <code class="literal">'/'</code>
operators bind more tightly than <code class="literal">'+'</code> and
<code class="literal">'-'</code>?</p><p>We could just change the grammar as follows (making the
appropriate changes to the expression datatype too):</p><pre class="programlisting">
Exp : let var '=' Exp in Exp { Let $2 $4 $6 }
| Exp '+' Exp { Plus $1 $3 }
| Exp '-' Exp { Minus $1 $3 }
| Exp '*' Exp { Times $1 $3 }
| Exp '/' Exp { Div $1 $3 }
| '(' Exp ')' { Brack $2 }
| int { Int $1 }
| var { Var $1 }
</pre><p>but now Happy will complain that there are shift/reduce
conflicts because the grammar is ambiguous - we haven't
specified whether e.g. <code class="literal">1 + 2 * 3</code> is to be
parsed as <code class="literal">1 + (2 * 3)</code> or <code class="literal">(1 + 2) *
3</code>. Happy allows these ambiguities to be resolved by
specifying the <em class="firstterm">precedences</em> of the
operators involved using directives in the
header<sup>[<a name="id2496328" href="#ftn.id2496328" class="footnote">2</a>]</sup>:</p><pre class="programlisting">
...
%right in
%left '+' '-'
%left '*' '/'
%%
...
</pre><a class="indexterm" name="id2496348"></a><a class="indexterm" name="id2496359"></a><a class="indexterm" name="id2496371"></a><p>The <code class="literal">%left</code> or <code class="literal">%right</code>
directive is followed by a list of terminals, and declares all
these tokens to be left or right-associative respectively. The
precedence of these tokens with respect to other tokens is
established by the order of the <code class="literal">%left</code> and
<code class="literal">%right</code> directives: earlier means lower
precedence. A higher precedence causes an operator to bind more
tightly; in our example above, because <code class="literal">'*'</code>
has a higher precedence than <code class="literal">'+'</code>, the
expression <code class="literal">1 + 2 * 3</code> will parse as <code class="literal">1
+ (2 * 3)</code>.</p><p>What happens when two operators have the same precedence?
This is when the <em class="firstterm">associativity</em> comes into
play. Operators specified as left associative will cause
expressions like <code class="literal">1 + 2 - 3</code> to parse as
<code class="literal">(1 + 2) - 3</code>, whereas right-associative
operators would parse as <code class="literal">1 + (2 - 3)</code>. There
is also a <code class="literal">%nonassoc</code> directive which indicates
that the specified operators may not be used together. For
example, if we add the comparison operators
<code class="literal">'>'</code> and <code class="literal">'<'</code> to our
grammar, then we would probably give their precedence as:</p><pre class="programlisting">...
%right in
%nonassoc '>' '<'
%left '+' '-'
%left '*' '/'
%%
...</pre><p>which indicates that <code class="literal">'>'</code> and
<code class="literal">'<'</code> bind less tightly than the other
operators, and the non-associativity causes expressions such as
<code class="literal">1 > 2 > 3</code> to be disallowed.</p><div class="sect2" lang="en"><div class="titlepage"><div><div><h3 class="title"><a name="how-precedence-works"></a>2.3.1. How precedence works</h3></div></div></div><p>The precedence directives, <code class="literal">%left</code>,
<code class="literal">%right</code> and <code class="literal">%nonassoc</code>,
assign precedence levels to the tokens in the declaration. A
rule in the grammar may also have a precedence: if the last
terminal in the left hand side of the rule has a precedence,
then this is the precedence of the whole rule.</p><p>The precedences are used to resolve ambiguities in the
grammar. If there is a shift/reduce conflict, then the
precedence of the rule and the lookahead token are examined in
order to resolve the conflict:</p><div class="itemizedlist"><ul type="disc"><li><p>If the precedence of the rule is higher, then the
conflict is resolved as a reduce.</p></li><li><p>If the precedence of the lookahead token is higher,
then the conflict is resolved as a shift.</p></li><li><p>If the precedences are equal, then</p><div class="itemizedlist"><ul type="circle"><li><p>If the token is left-associative, then reduce</p></li><li><p>If the token is right-associative, then shift</p></li><li><p>If the token is non-associative, then fail</p></li></ul></div></li><li><p>If either the rule or the token has no precedence,
then the default is to shift (these conflicts are reported
by Happy, whereas ones that are automatically resolved by
the precedence rules are not).</p></li></ul></div></div><div class="sect2" lang="en"><div class="titlepage"><div><div><h3 class="title"><a name="context-precedence"></a>2.3.2. Context-dependent Precedence</h3></div></div></div><p>The precedence of an individual rule can be overriden,
using <em class="firstterm">context precedence</em>. This is
useful when, for example, a particular token has a different
precedence depending on the context. A common example is the
minus sign: it has high precedence when used as prefix
negation, but a lower precedence when used as binary
subtraction.</p><p>We can implement this in Happy as follows:</p><pre class="programlisting">%right in
%nonassoc '>' '<'
%left '+' '-'
%left '*' '/'
%left NEG
%%
Exp : let var '=' Exp in Exp { Let $2 $4 $6 }
| Exp '+' Exp { Plus $1 $3 }
| Exp '-' Exp { Minus $1 $3 }
| Exp '*' Exp { Times $1 $3 }
| Exp '/' Exp { Div $1 $3 }
| '(' Exp ')' { Brack $2 }
| '-' Exp %prec NEG { Negate $2 }
| int { Int $1 }
| var { Var $1 }</pre><a class="indexterm" name="id2496675"></a><p>We invent a new token <code class="literal">NEG</code> as a
placeholder for the precedence of our prefix negation rule.
The <code class="literal">NEG</code> token doesn't need to appear in
a <code class="literal">%token</code> directive. The prefix negation
rule has a <code class="literal">%prec NEG</code> directive attached,
which overrides the default precedence for the rule (which
would normally be the precedence of '-') with the precedence
of <code class="literal">NEG</code>.</p></div><div class="footnotes"><br><hr width="100" align="left"><div class="footnote"><p><sup>[<a name="ftn.id2496328" href="#id2496328" class="para">2</a>] </sup>Users of <code class="literal">yacc</code> will find
this familiar, Happy's precedence scheme works in exactly the
same way.</p></div></div></div><div class="navfooter"><hr><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec-sequences.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec-using.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec-type-signatures.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">2.2. Parsing sequences </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> 2.4. Type Signatures</td></tr></table></div></body></html>
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