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PRISM Manual | ThePRISMLanguage / Expressions
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<p><a class='wikilink' href='Main.html'>The PRISM Language</a> /
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</p><h1>Expressions</h1>
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<p>The definition of the <code>area</code> constant, in the example above, uses an <em>expression</em>.
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We now define more precisely what types of expression are supported by PRISM.
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Expressions can contain literal values (12, 3.141592, <code><strong>true</strong></code>, <code><strong>false</strong></code>, etc.),
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identifiers (corresponding to variables, constants, etc.) and operators from the following list:
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</p>
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<div class='vspace'></div><ul><li><code>-</code> (unary minus)
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</li><li><code>*</code>, <code>/</code> (multiplication, division)
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</li><li><code>+</code>, <code>-</code> (addition, subtraction)
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</li><li><code><</code>, <code><=</code>, <code>>=</code>, <code>></code> (relational operators)
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</li><li><code>=</code>, <code>!=</code> (equality operators)
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</li><li><code>!</code> (negation)
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</li><li><code>&</code> (conjunction)
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</li><li><code>|</code> (disjunction)
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</li><li><code><=></code> (if-and-only-if)
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</li><li><code>=></code> (implication)
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</li><li><code>?</code> (condition evaluation: <code>condition ? a : b</code> means "if <code>condition</code> is true then <code>a</code> else <code>b</code>")
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</li></ul><p class='vspace'>All of these operators except <code>?</code> are left associative
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(i.e. they are evaluated from left to right).
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The precedence of the operators is as found in the list above,
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most strongly binding operators first.
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Operators on the same line (e.g. <code>+</code> and <code>-</code>) are of equal precedence.
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</p>
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<p class='vspace'>Much of the notation for expressions is hence essentially equivalent to that of C/C++ or Java.
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One notable exception to this is that the division operator <code>/</code> always performs floating point, not integer, division,
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i.e. the result of <code>22/7</code> is 3.142857... not 3.
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All expressions must evaluate correctly in terms of type (integer, double or Boolean).
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</p>
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<p class='vspace'><strong>Built-in Functions</strong>
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</p>
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<p class='vspace'>Expressions can make use of several built-in functions:
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</p>
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<div class='vspace'></div><ul><li><code>min(...)</code> and <code>max(...)</code>, which select the minimum and maximum value, respectively, of two or more numbers;
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</li><li><code>floor(x)</code> and <code>ceil(x)</code>, which round <code>x</code> down and up, respectively, to the nearest integer;
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</li><li><code>pow(x,y)</code> which computes <code>x</code> to the power of <code>y</code>;
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</li><li><code>mod(i,n)</code> for integer modulo operations;
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</li><li><code>log(x,b)</code>, which computes the logarithm of <code>x</code> to base <code>b</code>.
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</li></ul><p class='vspace'>Examples of their usage are:
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</p>
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<div class='vspace'></div>
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<div class='sourceblock ' id='sourceblock1'>
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<div class='sourceblocktext'><div class="prism"><span class="prismkeyword">min</span>(<span class="prismident">x</span>+<span class="prismnum">1</span>, <span class="prismident">x_max</span>)<br/>
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<span class="prismkeyword">max</span>(<span class="prismident">a</span>,<span class="prismident">b</span>,<span class="prismident">c</span>)<br/>
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<span class="prismident">floor</span>(<span class="prismnum">13.5</span>)<br/>
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<span class="prismident">ceil</span>(<span class="prismnum">13.5</span>)<br/>
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<span class="prismident">pow</span>(<span class="prismnum">2</span>, <span class="prismnum">8</span>)<br/>
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<span class="prismident">pow</span>(<span class="prismnum">9.0</span>, <span class="prismnum">0.5</span>)<br/>
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<span class="prismident">mod</span>(<span class="prismnum">1977</span>, <span class="prismnum">100</span>)<br/>
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<span class="prismident">log</span>(<span class="prismnum">123</span>, <span class="prismnum">2.71828183</span>)<br/>
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</div></div>
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<div class='sourceblocklink'><a href='http://www.prismmodelchecker.org/manual/ThePRISMLanguage/Expressions?action=sourceblock&num=1' type='text/plain'>[$[Get Code]]</a></div>
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</div>
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<p class='vspace'>For compatibility with older versions of PRISM, all functions can also be expressed via the <code><strong>func</strong></code> keyword, e.g. <code>func(floor, 13.5)</code>.
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</p>
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<p class='vspace'><strong>Use of Expressions</strong>
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</p>
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<p class='vspace'>Expressions can be used in a wide range of places in a PRISM language description, e.g.:
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</p>
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<div class='vspace'></div><ul><li>constant definitions
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</li><li>lower/upper bounds and initial values for variables
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</li><li>guards
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</li><li>probabilities/rates
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</li><li>updates
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</li></ul><p class='vspace'>This allows, for example, the probability in a command to be dependent on the current state:
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</p>
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<div class='vspace'></div>
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<div class='sourceblock ' id='sourceblock2'>
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<div class='sourceblocktext'><div class="prism"> [] (<span class="prismident">x</span>>=<span class="prismnum">1</span> & <span class="prismident">x</span><=<span class="prismnum">10</span>) -> <span class="prismident">x</span>/<span class="prismnum">10</span> : (<span class="prismident">x</span>'=<span class="prismkeyword">max</span>(<span class="prismnum">1</span>,<span class="prismident">x</span>-<span class="prismnum">1</span>)) + <span class="prismnum">1</span>-<span class="prismident">x</span>/<span class="prismnum">10</span> : (<span class="prismident">x</span>'=<span class="prismkeyword">min</span>(<span class="prismnum">10</span>,<span class="prismident">x</span>+<span class="prismnum">1</span>)) <br/>
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</div></div>
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<div class='sourceblocklink'><a href='http://www.prismmodelchecker.org/manual/ThePRISMLanguage/Expressions?action=sourceblock&num=2' type='text/plain'>[$[Get Code]]</a></div>
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<h3><a class='wikilink' href='../Main/Main.html'>PRISM Manual</a></h3>
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<p><strong><a class='wikilink' href='Main.html'>The PRISM Language</a></strong>
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</p><ul><li><a class='wikilink' href='Main.html'>Introduction</a>
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