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diff --git a/docs/spec/primitive.html b/docs/spec/primitive.html index 74fb79d1..8f0dba65 100644 --- a/docs/spec/primitive.html +++ b/docs/spec/primitive.html @@ -113,6 +113,7 @@ <p><strong>Depth</strong> (<code><span class='Modifier2'>⚇</span></code>) is nearly a generalization of Each: <code><span class='Modifier'>¨</span></code> is equivalent to <code><span class='Modifier2'>⚇</span><span class='Number'>¯1</span></code>, except that <code><span class='Modifier2'>⚇</span><span class='Number'>¯1</span></code> doesn't enclose its result if all arguments are atoms. The list given by the right operand specifies how deeply to recurse into the arguments. A negative number <code><span class='Function'>-</span><span class='Value'>n</span></code> means to recurse <code><span class='Value'>n</span></code> times <em>or</em> until the argument is an atom, while a positive number <code><span class='Value'>n</span></code> means to recurse until the argument has depth <code><span class='Value'>n</span></code> or less. Recursion continues until all arguments have met the criterion for stopping. This recursion is guaranteed to stop because arrays are immutable, and form an inductive type.</p> <p><strong>Rank</strong> (<code><span class='Modifier2'>⎉</span></code>) applies the left operand to cells of the arguments of the specified ranks, forming a result whose cells are the results. <strong>Cells</strong> (<code><span class='Modifier'>˘</span></code>) is identical to <code><span class='Modifier2'>⎉</span><span class='Number'>¯1</span></code>, and applies to major cells of the arguments, where a value of rank less than 1 is considered its own major cell. All results must have the same shape, as with elements of the argument to Merge (<code><span class='Function'>></span></code>). The combined result is always an array, but results of the left operand can be atoms: an atom result will be enclosed to give a 0-cell. If a specified rank is a natural number <code><span class='Value'>n</span></code>, Rank applies the operand to <code><span class='Value'>n</span></code>-cells of the corresponding argument, or the entire argument if it has rank less than or equal to <code><span class='Value'>n</span></code>. If instead it's a negative integer <code><span class='Function'>-</span><span class='Value'>n</span></code>, then an effective rank of <code><span class='Number'>0</span><span class='Function'>⌈</span><span class='Value'>k</span><span class='Function'>-</span><span class='Value'>n</span></code> is used, so that the entire argument is used exactly when <code><span class='Value'>k</span><span class='Function'>=</span><span class='Number'>0</span></code>. Thus an atom will always be passed unchanged to the operand; in particular, Rank does not enclose it. Like Each, Rank matches cells of its arguments according to leading axis agreement, so that a cell of one argument might be paired with multiple cells of the other.</p> <p><strong>Fold</strong> (<code><span class='Modifier'>´</span></code>), <strong>Insert</strong> (<code><span class='Modifier'>˝</span></code>), and <strong>Scan</strong> (<code><span class='Modifier'>`</span></code>) repeatedly apply a function between parts of an array. Fold requires the argument to have rank 1 and applies the operand between its elements, while Insert requires it to have rank 1 or more and applies it between the cells. For each of these two functions, the operand is applied beginning at the end of the array, and an <a href="inferred.html#identities">identity</a> value is returned if the array is empty. While these functions reduce multiple values to a single result, Scan returns many results and preserves the shape of its argument. It requires the argument to have rank at least 1, and applies the function between elements along columns—that is, from one element in a major cell to the one in the same position of the next major cell. This application begins at the first major cell of the array. Scan never uses the identity element of its operand because if the argument is empty then the result, which has the same shape, will be empty as well.</p> +<p>A left argument for any of the three reduction-based modifiers indicates an initial value to be used, so that the first application of the operand function applies not to two values from <code><span class='Value'>𝕩</span></code> but instead to a value from <code><span class='Value'>𝕨</span></code> and a value from <code><span class='Value'>𝕩</span></code>. In Fold and Insert, the entire value <code><span class='Value'>𝕨</span></code> is the initial value, while in Scan, <code><span class='Value'>𝕨</span></code> is an array of initial values, which must have shape <code><span class='Number'>1</span><span class='Function'>↓≢</span><span class='Value'>𝕩</span></code>.</p> <p><strong>Repeat</strong> (<code><span class='Modifier2'>⍟</span></code>) applies the operand function, or its <a href="inferred.html#undo">inverse</a>, several times in sequence. The right operand must consist only of integer atoms (arranged in arrays of any depth), and each number there is replaced with the application of the left operand that many times to the arguments. If a left argument is present, then it's reused each time, as if it were bound to the operand function. For a negative number <code><span class='Function'>-</span><span class='Value'>n</span></code>, the function is "applied" <code><span class='Function'>-</span><span class='Value'>n</span></code> times by undoing it <code><span class='Value'>n</span></code> times. In both directions, the total number of times the function is applied is the maximum of all numbers present: results must be saved if intermediate values are needed.</p> <h3 id="restructuring">Restructuring</h3> <p><strong>Enclose</strong> (<code><span class='Function'><</span></code>) forms a unit array that contains its argument.</p> |