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 - **Absolute Value** (`|`)
 - **Modulus** (`|`) is an extension of modular division to real numbers. As it uses floor instead of truncation, it's not the same as the `%` operator from C or other languages when `𝕨<0`.
 - Comparisons **Less Than** (`<`), **Greater Than** (`>`), **Greater Than or Equal to** (`≥`), and **Not Equals** (`≠`) are defined in terms of the two provided comparisons.
+
+### Iteration modifiers
+
+Modifiers for iteration are defined in layers 1, 2, and 4. Two 2-modifiers, `⚇` and `⎉`, use a list of numbers obtained by applying the right operand to the arguments in order to control application. This list has one to three elements: if all three are given then they correspond to the monadic, left, and right arguments; if one is given then it controls all three; and if two are given then they control the left argument, and the right and monadic arguments.
+
+**Table** (`⌜`) and **Each** (`¨`) map over the elements of arrays to produce result elements. They convert atom arguments to unit arrays. With one argument, the two modifiers are the same; with two, they differ in how they pair elements. Table pairs every element of the left argument with every element of the right, giving a result shape `𝕨∾○≢𝕩`. Each uses leading axis agreement: it requires one argument's shape to be a prefix of the other's (if the arguments have the same rank, then the shapes must match and therefore be mutual prefixes). This causes each element of the lower-rank argument to correspond to a cell of the higher-rank one; it's repeated to pair it with each element of that cell. The result shape is the shape of the higher-rank argument.
+
+**Depth** (`⚇`) is nearly a generalization of Each: `¨` is equivalent to `⚇¯1`, except that `⚇¯1` 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 `-n` means to recurse `n` times *or* until the argument is an atom, while a positive number `n` means to recurse until the argument has depth `n` or less. Recursion continues until all arguments have met the criterion for stopping.
+
+**Rank** (`⎉`) applies the left operand to cells of the arguments of the specified ranks, forming a result whose cells are the results. **Cells** (`˘`) is identical to `⎉¯1`, 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 (`>`). 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 `n`, Rank applies the operand to `n`-cells of the corresponding argument, or the entire argument if it has rank less than or equal to `n`. If instead it's a negative integer `-n`, then an effective rank of `0⌈k-n` is used, so that the entire argument is used exactly when `k=0`. 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.
+
+**Fold** (`´`), **Insert** (`˝`), and **Scan** (`` ` ``) 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 [identity](inferred.md#identities) 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.
+
+**Repeat** (`⍟`) applies the operand function, or its [inverse](inferred.md#undo), 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 `-n`, the function is "applied" `-n` times by undoing it `n` 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.