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<meta name="description" content="Today we’ll talk about unary operators, namely unary plus (+) and unary minus (-) operators. A lot of today’s material is based on the material from the previous article, so if you need a refresher just head back to Part 7 and go over it again. Remember: repetition is the …" />
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<meta property="og:description" content="Today we’ll talk about unary operators, namely unary plus (+) and unary minus (-) operators. A lot of today’s material is based on the material from the previous article, so if you need a refresher just head back to Part 7 and go over it again. Remember: repetition is the …"/>
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<i class="fa fa-calendar"></i><time datetime="2016-01-18T06:10:00-05:00"> Mon, January 18, 2016</time>
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<p>Today we’ll talk about <strong>unary operators</strong>, namely unary plus (+) and unary minus (-) operators.</p>
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<p>A lot of today’s material is based on the material from the previous article, so if you need a refresher just head back to <a href="../lsbasi-part7/index.html" title="Part 7">Part 7</a> and go over it again. Remember: repetition is the mother of all learning.</p>
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<p>Having said that, this is what you are going to do today:</p>
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<ul>
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<li>extend the grammar to handle unary plus and unary minus operators</li>
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<li>add a new <em>UnaryOp</em> <span class="caps">AST</span> node class</li>
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<li>extend the parser to generate an <span class="caps">AST</span> with <em>UnaryOp</em> nodes</li>
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<li>extend the interpreter and add a new <em>visit_UnaryOp</em> method to interpret unary operators</li>
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</ul>
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<p>Let’s get started, shall we?</p>
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<p>So far we’ve worked with binary operators only (+, -, *, /), that is, the operators that operate on two operands.</p>
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<p>What is a unary operator then? A <em>unary operator</em> is an operator that operates on one <em>operand</em> only.</p>
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<p>Here are the rules for unary plus and unary minus operators:</p>
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<ul>
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<li>The unary minus (-) operator produces the negation of its numeric operand</li>
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<li>The unary plus (+) operator yields its numeric operand without change</li>
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<li>The unary operators have higher precedence than the binary operators +, -, *, and /</li>
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</ul>
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<p>In the expression “+ - 3” the first ‘+’ operator represents the unary plus operation and the second ‘-‘ operator represents the unary minus operation. The expression “+ - 3” is equivalent to “+ (- (3))” which is equal to -3. One could also say that <strong>-3</strong> in the expression is a negative integer, but in our case we treat it as a unary minus operator with 3 as its positive integer operand:</p>
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<p><img alt="" src="lsbasi_part8_exp1.png" width="640"></p>
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<p>Let’s take a look at another expression, “5 - - 2”:</p>
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<p><img alt="" src="lsbasi_part8_exp2.png" width="640"></p>
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<p>In the expression “5 - - 2” the first ‘-‘ represents the <em>binary</em> subtraction operation and the second ‘-‘ represents the <em>unary</em> minus operation, the negation.</p>
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<p>And some more examples:</p>
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<p><img alt="" src="lsbasi_part8_exp3.png" width="640"></p>
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<p><img alt="" src="lsbasi_part8_exp4.png" width="640"></p>
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<p>Now let’s update our grammar to include unary plus and unary minus operators. We’ll modify the <em>factor</em> rule and add unary operators there because unary operators have higher precedence than binary +, -, * and / operators.</p>
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<p>This is our current <em>factor</em> rule:</p>
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<p><img alt="" src="lsbasi_part8_factor_before.png" width="640"></p>
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<p>And this is our updated <em>factor</em> rule to handle unary plus and unary minus operators:</p>
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<p><img alt="" src="lsbasi_part8_factor_after.png" width="640"></p>
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<p>As you can see, I extended the <em>factor</em> rule to reference itself, which allows us to derive expressions like “- - - + - 3”, a legitimate expression with a lot of unary operators.</p>
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<p>Here is the full grammar that can now derive expressions with unary plus and unary minus operators:</p>
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<p><img alt="" src="lsbasi_part8_grammar.png" width="640"></p>
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<p>The next step is to add an <span class="caps">AST</span> node class to represent unary operators.</p>
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<p>This one will do:</p>
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<div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">UnaryOp</span><span class="p">(</span><span class="n">AST</span><span class="p">):</span>
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<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">op</span><span class="p">,</span> <span class="n">expr</span><span class="p">):</span>
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<span class="bp">self</span><span class="o">.</span><span class="n">token</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">op</span> <span class="o">=</span> <span class="n">op</span>
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<span class="bp">self</span><span class="o">.</span><span class="n">expr</span> <span class="o">=</span> <span class="n">expr</span>
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</pre></div>
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<p>The constructor takes two parameters: <em>op</em>, which represents the unary operator token (plus or minus) and <em>expr</em>, which represents an <span class="caps">AST</span> node.</p>
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<p>Our updated grammar had changes to the <em>factor</em> rule, so that’s what we’re going to modify in our parser - the <em>factor</em> method. We will add code to the method to handle the “(<span class="caps">PLUS</span> | <span class="caps">MINUS</span>) factor” sub-rule:</p>
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<div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">factor</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
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<span class="sd">"""factor : (PLUS | MINUS) factor | INTEGER | LPAREN expr RPAREN"""</span>
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<span class="n">token</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">current_token</span>
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<span class="k">if</span> <span class="n">token</span><span class="o">.</span><span class="n">type</span> <span class="o">==</span> <span class="n">PLUS</span><span class="p">:</span>
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<span class="bp">self</span><span class="o">.</span><span class="n">eat</span><span class="p">(</span><span class="n">PLUS</span><span class="p">)</span>
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<span class="n">node</span> <span class="o">=</span> <span class="n">UnaryOp</span><span class="p">(</span><span class="n">token</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">factor</span><span class="p">())</span>
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<span class="k">return</span> <span class="n">node</span>
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<span class="k">elif</span> <span class="n">token</span><span class="o">.</span><span class="n">type</span> <span class="o">==</span> <span class="n">MINUS</span><span class="p">:</span>
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<span class="bp">self</span><span class="o">.</span><span class="n">eat</span><span class="p">(</span><span class="n">MINUS</span><span class="p">)</span>
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<span class="n">node</span> <span class="o">=</span> <span class="n">UnaryOp</span><span class="p">(</span><span class="n">token</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">factor</span><span class="p">())</span>
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<span class="k">return</span> <span class="n">node</span>
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<span class="k">elif</span> <span class="n">token</span><span class="o">.</span><span class="n">type</span> <span class="o">==</span> <span class="n">INTEGER</span><span class="p">:</span>
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<span class="bp">self</span><span class="o">.</span><span class="n">eat</span><span class="p">(</span><span class="n">INTEGER</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">Num</span><span class="p">(</span><span class="n">token</span><span class="p">)</span>
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<span class="k">elif</span> <span class="n">token</span><span class="o">.</span><span class="n">type</span> <span class="o">==</span> <span class="n">LPAREN</span><span class="p">:</span>
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<span class="bp">self</span><span class="o">.</span><span class="n">eat</span><span class="p">(</span><span class="n">LPAREN</span><span class="p">)</span>
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<span class="n">node</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">expr</span><span class="p">()</span>
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<span class="bp">self</span><span class="o">.</span><span class="n">eat</span><span class="p">(</span><span class="n">RPAREN</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">node</span>
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</pre></div>
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<p><br/>
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And now we need to extend the <em>Interpreter</em> class and add a <em>visit_UnaryOp</em> method to interpret unary nodes:</p>
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<div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">visit_UnaryOp</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">):</span>
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<span class="n">op</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">op</span><span class="o">.</span><span class="n">type</span>
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<span class="k">if</span> <span class="n">op</span> <span class="o">==</span> <span class="n">PLUS</span><span class="p">:</span>
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<span class="k">return</span> <span class="o">+</span><span class="bp">self</span><span class="o">.</span><span class="n">visit</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">expr</span><span class="p">)</span>
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<span class="k">elif</span> <span class="n">op</span> <span class="o">==</span> <span class="n">MINUS</span><span class="p">:</span>
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<span class="k">return</span> <span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">visit</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">expr</span><span class="p">)</span>
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</pre></div>
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<p>Onward!</p>
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<p>Let’s manually build an <span class="caps">AST</span> for the expression “5 - - - 2” and pass it to our interpreter to verify that the new <em>visit_UnaryOp</em> method works. Here is how you can do it from the Python shell:</p>
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<div class="highlight"><pre><span></span><span class="o">>>></span> <span class="kn">from</span> <span class="nn">spi</span> <span class="kn">import</span> <span class="n">BinOp</span><span class="p">,</span> <span class="n">UnaryOp</span><span class="p">,</span> <span class="n">Num</span><span class="p">,</span> <span class="n">MINUS</span><span class="p">,</span> <span class="n">INTEGER</span><span class="p">,</span> <span class="n">Token</span>
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<span class="o">>>></span> <span class="n">five_tok</span> <span class="o">=</span> <span class="n">Token</span><span class="p">(</span><span class="n">INTEGER</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
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<span class="o">>>></span> <span class="n">two_tok</span> <span class="o">=</span> <span class="n">Token</span><span class="p">(</span><span class="n">INTEGER</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
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<span class="o">>>></span> <span class="n">minus_tok</span> <span class="o">=</span> <span class="n">Token</span><span class="p">(</span><span class="n">MINUS</span><span class="p">,</span> <span class="s1">'-'</span><span class="p">)</span>
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<span class="o">>>></span> <span class="n">expr_node</span> <span class="o">=</span> <span class="n">BinOp</span><span class="p">(</span>
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<span class="o">...</span> <span class="n">Num</span><span class="p">(</span><span class="n">five_tok</span><span class="p">),</span>
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<span class="o">...</span> <span class="n">minus_tok</span><span class="p">,</span>
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<span class="o">...</span> <span class="n">UnaryOp</span><span class="p">(</span><span class="n">minus_token</span><span class="p">,</span> <span class="n">UnaryOp</span><span class="p">(</span><span class="n">minus_token</span><span class="p">,</span> <span class="n">Num</span><span class="p">(</span><span class="n">two_tok</span><span class="p">)))</span>
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<span class="o">...</span> <span class="p">)</span>
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<span class="o">>>></span> <span class="kn">from</span> <span class="nn">spi</span> <span class="kn">import</span> <span class="n">Interpreter</span>
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<span class="o">>>></span> <span class="n">inter</span> <span class="o">=</span> <span class="n">Interpreter</span><span class="p">(</span><span class="bp">None</span><span class="p">)</span>
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<span class="o">>>></span> <span class="n">inter</span><span class="o">.</span><span class="n">visit</span><span class="p">(</span><span class="n">expr_node</span><span class="p">)</span>
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<span class="mi">3</span>
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</pre></div>
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<p>Visually the above <span class="caps">AST</span> tree looks like this:</p>
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<p><img alt="" src="lsbasi_part8_ast.png" width="420"></p>
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<p>Download the full source code of the interpreter for this article directly from <a href="https://github.com/rspivak/lsbasi/blob/master/part8/python/spi.py">GitHub</a>. Try it out and see for yourself that your updated tree-based interpreter properly evaluates arithmetic expressions containing unary operators.</p>
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<p>Here is a sample session:</p>
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<div class="highlight"><pre><span></span>$ python spi.py
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spi> - <span class="m">3</span>
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-3
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spi> + <span class="m">3</span>
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<span class="m">3</span>
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spi> <span class="m">5</span> - - - + - <span class="m">3</span>
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<span class="m">8</span>
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spi> <span class="m">5</span> - - - + - <span class="o">(</span><span class="m">3</span> + <span class="m">4</span><span class="o">)</span> - +2
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<span class="m">10</span>
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</pre></div>
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<p><br/>
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I also updated the <a href="https://github.com/rspivak/lsbasi/blob/master/part8/python/genastdot.py">genastdot.py</a> utility to handle unary operators. Here are some of the examples of the generated <span class="caps">AST</span> images for expressions with unary operators:</p>
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<div class="highlight"><pre><span></span>$ python genastdot.py <span class="s2">"- 3"</span> > ast.dot <span class="o">&&</span> dot -Tpng -o ast.png ast.dot
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</pre></div>
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<p><img alt="" src="lsbasi_part8_genastdot_01.png"></p>
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<div class="highlight"><pre><span></span>$ python genastdot.py <span class="s2">"+ 3"</span> > ast.dot <span class="o">&&</span> dot -Tpng -o ast.png ast.dot
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</pre></div>
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<p><img alt="" src="lsbasi_part8_genastdot_02.png"></p>
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<div class="highlight"><pre><span></span>$ python genastdot.py <span class="s2">"5 - - - + - 3"</span> > ast.dot <span class="o">&&</span> dot -Tpng -o ast.png ast.dot
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</pre></div>
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<p><img alt="" src="lsbasi_part8_genastdot_03.png"></p>
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<div class="highlight"><pre><span></span>$ python genastdot.py <span class="s2">"5 - - - + - (3 + 4) - +2"</span> <span class="se">\</span>
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> ast.dot <span class="o">&&</span> dot -Tpng -o ast.png ast.dot
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</pre></div>
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<p><img alt="" src="lsbasi_part8_genastdot_04.png"></p>
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<p><br/>
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<br/>
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And here is a new exercise for you:</p>
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<p><img alt="" src="lsbasi_part8_exercises.png" width="280"></p>
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<ul>
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<li>Install <a href="http://www.freepascal.org/">Free Pascal</a>, compile and run <a href="https://github.com/rspivak/lsbasi/blob/master/part8/python/testunary.pas">testunary.pas</a>, and verify that the results are the same as produced with your <a href="https://github.com/rspivak/lsbasi/blob/master/part8/python/spi.py">spi</a> interpreter.</li>
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</ul>
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<p><br/>
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That’s all for today. In the next article, we’ll tackle assignment statements. Stay tuned and see you soon.</p>
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<p><br/>
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Here is a list of books I recommend that will help you in your study of interpreters and compilers:</p>
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<ol>
|
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<li>
|
||
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<p><br/>
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<strong>All articles in this series:</strong>
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<ul>
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<li>
|
||
<a href="../lsbasi-part1/index.html">Let's Build A Simple Interpreter. Part 1.</a>
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</li>
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<li>
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<a href="../lsbasi-part2/index.html">Let's Build A Simple Interpreter. Part 2.</a>
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<li>
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<a href="../lsbasi-part3/index.html">Let's Build A Simple Interpreter. Part 3.</a>
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<li>
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<a href="../lsbasi-part4/index.html">Let's Build A Simple Interpreter. Part 4.</a>
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<li>
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<a href="../lsbasi-part5/index.html">Let's Build A Simple Interpreter. Part 5.</a>
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<li>
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<a href="../lsbasi-part6/index.html">Let's Build A Simple Interpreter. Part 6.</a>
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<li>
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<a href="../lsbasi-part7/index.html">Let's Build A Simple Interpreter. Part 7: Abstract Syntax Trees</a>
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<li>
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<a href="index.html">Let's Build A Simple Interpreter. Part 8.</a>
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<a href="../lsbasi-part9/index.html">Let's Build A Simple Interpreter. Part 9.</a>
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<li>
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<a href="../lsbasi-part10/index.html">Let's Build A Simple Interpreter. Part 10.</a>
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<a href="../lsbasi-part11/index.html">Let's Build A Simple Interpreter. Part 11.</a>
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<a href="../lsbasi-part12/index.html">Let's Build A Simple Interpreter. Part 12.</a>
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<a href="../lsbasi-part13.html">Let's Build A Simple Interpreter. Part 13: Semantic Analysis</a>
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<a href="../lsbasi-part14/index.html">Let's Build A Simple Interpreter. Part 14: Nested Scopes and a Source-to-Source Compiler</a>
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<a href="../lsbasi-part15/index.html">Let's Build A Simple Interpreter. Part 15.</a>
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<a href="../lsbasi-part16/index.html">Let's Build A Simple Interpreter. Part 16: Recognizing Procedure Calls</a>
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<a href="../lsbasi-part17.html">Let's Build A Simple Interpreter. Part 17: Call Stack and Activation Records</a>
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<a href="../lsbasi-part18/index.html">Let's Build A Simple Interpreter. Part 18: Executing Procedure Calls</a>
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<a href="../lsbasi-part19/index.html">Let's Build A Simple Interpreter. Part 19: Nested Procedure Calls</a>
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