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<div class="nav"><a href="https://github.com/mlochbaum/BQN">BQN</a></div>
<h1 id="specification-bqn-literal-notation">Specification: BQN literal notation</h1>
<p>A <em>literal</em> is a single <a href="token.html">token</a> that indicates a fixed character, number, or array. While literals indicate values of a data type, <a href="primitive.html">primitives</a> indicate values of an operation type: function, 1-modifier, or 2-modifier.</p>
<p>Two types of literal deal with text. As the source code is considered to be a sequence of unicode code points ("characters"), and these code points are also used for BQN's character <a href="types.html">data type</a>, the representation of a text literal is very similar to its value. In a text literal, the newline character is always represented using the ASCII line feed character, code point 10. A <em>character literal</em> is enclosed with single quotes <code>'</code> and its value is identical to the single character between them. A <em>string literal</em> is enclosed in double quotes <code>"</code>, and any double quotes between them must come in pairs, as a lone double quote marks the end of the literal. The value of a string literal is a rank-1 array whose elements are the characters in between the enclosing quotes, after replacing each pair of double quotes with only one such quote.</p>
<p>The format of a <em>numeric literal</em> is more complicated. From the <a href="token.html">tokenization rules</a>, a numeric literal consists of a numeric character (one of <code><span class='Number'>¯∞π.0123456789</span></code>) followed by any number of numeric or alphabetic characters. Some numeric literals are <em>valid</em> and indicate a number, while others are invalid and cause an error. The grammar for valid numbers is given below in a <a href="https://en.wikipedia.org/wiki/Backus%E2%80%93Naur_form">BNF</a> variant. Only four alphabetic characters are allowed: "i", which separates the real and imaginary components of a complex number, "e", which functions as in scientific notation, and the uppercase versions of these letters.</p>
<pre><span class='Value'>number</span> <span class='Function'>=</span> <span class='Value'>component</span> <span class='Paren'>(</span> <span class='Paren'>(</span> <span class='String'>"i"</span> <span class='Function'>|</span> <span class='String'>"I"</span> <span class='Paren'>)</span> <span class='Value'>component</span> <span class='Paren'>)</span><span class='Value'>?</span>
<span class='Value'>component</span> <span class='Function'>=</span> <span class='Value'>mantissa</span> <span class='Paren'>(</span> <span class='Paren'>(</span> <span class='String'>"e"</span> <span class='Function'>|</span> <span class='String'>"E"</span> <span class='Paren'>)</span> <span class='Value'>exponent</span> <span class='Paren'>)</span><span class='Value'>?</span>
<span class='Value'>exponent</span> <span class='Function'>=</span> <span class='String'>"¯"</span><span class='Value'>?</span> <span class='Value'>digit</span><span class='Function'>+</span>
<span class='Value'>mantissa</span> <span class='Function'>=</span> <span class='String'>"¯"</span><span class='Value'>?</span> <span class='Paren'>(</span> <span class='String'>"∞"</span> <span class='Function'>|</span> <span class='String'>"π"</span> <span class='Function'>|</span> <span class='Value'>digit</span><span class='Function'>+</span> <span class='Paren'>(</span> <span class='String'>"."</span> <span class='Value'>digit</span><span class='Function'>+</span> <span class='Paren'>)</span><span class='Value'>?</span> <span class='Paren'>)</span>
<span class='Value'>digit</span> <span class='Function'>=</span> <span class='String'>"0"</span> <span class='Function'>|</span> <span class='String'>"1"</span> <span class='Function'>|</span> <span class='String'>"2"</span> <span class='Function'>|</span> <span class='String'>"3"</span> <span class='Function'>|</span> <span class='String'>"4"</span> <span class='Function'>|</span> <span class='String'>"5"</span> <span class='Function'>|</span> <span class='String'>"6"</span> <span class='Function'>|</span> <span class='String'>"7"</span> <span class='Function'>|</span> <span class='String'>"8"</span> <span class='Function'>|</span> <span class='String'>"9"</span>
</pre>
<p>The digits or arabic numerals correspond to the numbers from 0 to 9 in the conventional way (also, each corresponds to its code point value minus 48). A sequence of digits gives a natural number by evaluating it in base 10: the number is 0 for an empty sequence, and otherwise the last digit's numerical value plus ten times the number obtained from the remaining digits. The symbol <code><span class='Number'>∞</span></code> indicates infinity and <code><span class='Number'>π</span></code> indicates the ratio <a href="https://en.wikipedia.org/wiki/Pi_(mathematics)">pi</a> of a circle's circumference to its diameter (or, for modern mathematicians, the smallest positive real number at which the function <code><span class='Brace'>{</span><span class='Function'>⋆</span><span class='Number'>0j1</span><span class='Function'>×</span><span class='Value'>𝕩</span><span class='Brace'>}</span></code> attains a real part of 0). The <a href="https://aplwiki.com/wiki/High_minus">high minus</a> symbol <code><span class='Number'>¯</span></code> indicates that the number containing it is to be negated.</p>
<p>When an exponent is provided (with <code><span class='Value'>e</span></code> or <code><span class='Function'>E</span></code>), the corresponding mantissa is multiplied by ten to that power, giving the value <code><span class='Value'>mantissa</span><span class='Function'>×</span><span class='Number'>10</span><span class='Function'>⋆</span><span class='Value'>exponent</span></code>. If a second component is present (using <code><span class='Value'>i</span></code> or <code><span class='Function'>I</span></code>), that component's value is multiplied by the <a href="https://en.wikipedia.org/wiki/Imaginary_unit">imaginary unit</a> <em>i</em> and added to the first component; otherwise the value is the first component's value without modification. If complex numbers are not supported, then <code><span class='Value'>i</span></code> should not be allowed in numeric literals, even when followed by 0.</p>
<p>The above specification describes exactly a complex number with extended real components. To obtain a BQN number, each component is rounded to its nearest representative by the rules of the number system used: for IEEE 754, smallest distance, with ties rounding to the option with even mantissa.</p>
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