Editing and links

1 files changed, 8 insertions, 8 deletions

diff --git a/doc/indices.md b/doc/indices.md
index 105b9ee7..62122175 100644
--- a/doc/indices.md
+++ b/doc/indices.md
@@ -2,9 +2,9 @@
 
 # Indices
 
-One-dimensional arrays such as K lists or Python arrays have only one kind of index, a single number that refers to an element. For multidimensional arrays using the [leading axis theory](leading.md), there are several types of indexing that can be useful. Historically, nested APL designs have equivocated between these, which I believe can lead to subtle errors when programming. BQN focuses on single-number (atomic) indices, which can refer to list elements or array major cells (or more generally indexing along any particular axis). When using atomic indices to select elements, the indexed array has to be a list. In contrast, elements of any array can be indicated by list indices with length equal to that array's rank. Only two BQN primitives use these list indices: Range (`↕`), which returns an array of them if given a list argument, and Pick (`⊑`), where the depth-1 components of an array left argument are list indices.
+One-dimensional arrays such as K lists or Python arrays have only one kind of index, a single number that refers to an element. For multidimensional arrays using the [leading axis theory](leading.md), there are several types of indexing that can be useful. Historically, nested APL designs have equivocated between these, which I believe can lead to subtle errors when programming. BQN focuses on single-number (atomic) indices, which can refer to list elements or array major cells (or more generally indexing along any particular axis). When using atomic indices to select elements, the indexed array has to be a list. In contrast, elements of any array can be indicated by list indices with length equal to that array's rank. Only two BQN primitives use these list indices: [Range](range.md) (`↕`), which returns an array of them if given a list argument, and [Pick](pick.md) (`⊑`), where the depth-1 components of an array left argument are list indices.
 
-The following functions take or return indices. Except where marked, the indices are in the result; this is by far the most common type of index use. `⊔` is given two rows as it falls into both cases. Note that in the result case, there is usually no possibility for the programmer to select the format of indices. Instead, the language should be carefully designed to make sure that the kind of index returned is as useful as possible.
+The following functions take or return indices. Except where marked, the indices are in the result; this is by far the most common type of index use. [Group](group.md) (`⊔`) is given two rows as it falls into both cases. Note that in the result case, there is usually no possibility for the programmer to select the format of indices. Instead, the language should be carefully designed to make sure that the kind of index returned is as useful as possible.
 
 | Monad | Dyad | Where   | How
 |-------|------|---------|--------------------------
@@ -20,23 +20,23 @@ The following functions take or return indices. Except where marked, the indices
 |       | `⊏`  | `𝕨`     | Major cell or along-axis number
 |  `⍉`  |      |         | Axis number
 
-Dyadic Transpose (`⍉`) uses indices into the right argument axes in its left argument, but since array shape is 1-dimensional, there is only one sensible choice for this, a single number.
+In Dyadic [Transpose](transpose.md#dyadic-transpose) (`⍉`), `𝕨` is made up of indices into axes of `𝕩`. Since array shape is 1-dimensional, there is only one sensible choice for these elements, a single number each.
 
 ## Element indices
 
 In general, the index of an element of an array is a list whose length matches the array rank. It is also possible to use a number for an index into a list, as the list index is a singleton, but this must be kept consistent with the rest of the language. NARS-family APLs make the Index Generator (`↕` in BQN) return a numeric list when the argument has length 1 but a nested array otherwise. This means that the depth of the result depends on the shape of the argument, inverting the typical hierarchy. BQN shouldn't have such an inconsistency.
 
-Functions `↕`, `/`, `⊔`, and `⊑` naturally deal with element indices. Each of these can be defined to use list indices. However, this usually rules out the possibility of using atomic indices, which makes these functions harder to use both with generic array manipulation and with the major cell indices discussed in the next section. For this reason BQN restricts `⊔` and monadic `/` to use atomic indices, which comes with the requirement that the arguments to monadic `/` and `⊔`, and the result of monadic `⊔`, must be lists. For dyadic `⊔` the depth-1 elements of the left argument are lists of indices along axes of the result; see [the documentation](group.md#multidimensional-grouping). The restriction that comes from using single-number indices is that all axes must be treated independently, so that for example it isn't possible to group elements along diagonals without preprocessing. However, this restriction also keeps Group from having to use an ordering on list indices.
+Functions [Range](range.md) (`↕`), [Indices](replicate.md) (`/`), [Group](group.md) (`⊔`), and [Pick](pick.md) (`⊑`) naturally deal with element indices. Each of these can be defined to use list indices. However, this usually rules out the possibility of using atomic indices, which makes these functions harder to use both with generic array manipulation and with the major cell indices discussed in the next section. For this reason BQN restricts `⊔` and `/` to use atomic indices, which comes with the requirement that the arguments to Group and Indices, and the result of Group Indices, must be lists. For dyadic Group the depth-1 elements of `𝕨` are arrays of indices along axes of the result ([multi-axis documentation](group.md#multidimensional-grouping)). This means each axis of `𝕩` can only be related to one axis of the result.
 
-Unlike `/` and `⊔`, `↕` and `⊑` do use list element indices. For `↕` this is because the output format can be controlled by the argument format: if passed a single number, the result uses atomic indices (so it's a numeric list); if passed a list, it uses list indices and the result has depth 2 (the result depth is always one greater than the argument depth). For `⊑`, list indices are chosen because `⊏` handles atomic indices well already. When selecting multiple elements from a list, they would typically have to be placed in an array, which is equivalent to `⊏` with a numeric list left argument. An atomic left argument to `⊑` is converted to a list, so it can be used to select a single element if only one is wanted. To select multiple elements, `⊑` uses each depth-1 array in the left argument as an index and replaces it with that element from the right argument. Because this uses elements as elements (not cells), it is impossible to have conformability errors where elements do not fit together. Ill-formed index errors are of course still possible, and the requirements on indices are quite strict. They must exactly match the structure of the right argument's shape, with no units or higher-rank arrays allowed. Atoms also cannot be used in this context, as it would create ambiguity: is a one-element list an index, or does it contain an index?
+Unlike `/` and `⊔`, `↕` and `⊑` do use list element indices. For `↕` this is because the output format can be controlled by the argument format: if passed a single number, the result uses atomic indices (so it's a numeric list); if passed a list, it uses list indices and the result has depth 2 (the result depth is always one greater than the argument depth). For `⊑`, list indices are chosen because [Select](select.md) (`⊏`) handles atomic indices well already. When selecting multiple elements from a list, they would typically have to be placed in an array, which is equivalent to `⊏` with a numeric list `𝕨`. An atom `𝕨` in Pick is converted to a list, so it can be used to select a single element if only one is wanted. To select multiple elements, `⊑` uses each depth-1 array in `𝕨` as an index and replaces it with that element from the right argument. Because this uses elements as elements (not cells), it is impossible to have conformability errors where elements do not fit together (invalid index errors are of course still possible). Atoms also cannot be used in this context, as it would create ambiguity: is a one-element list an index, or does it contain an index?
 
 ## Major cell indices
 
-One of the successes of the [leading axis model](https://aplwiki.com/wiki/Leading_axis_theory) is to introduce a kind of index for multidimensional arrays that is easier to work with than list indices. The model introduces [cells](https://aplwiki.com/wiki/Cell), where a cell index is a list of any length up to the containing array's rank. General cell indices are discussed in the next section; first we introduce a special case, indices into major cells or ¯1-cells. These cells naturally form a list, so the index of a major cell is a single number. These indices can also be considered indices along the first axis, since an index along any axis is a single number.
+One of the successes of the [leading axis model](https://aplwiki.com/wiki/Leading_axis_theory) is to introduce a kind of index for multidimensional arrays that is easier to work with than list indices. The model introduces [cells](https://aplwiki.com/wiki/Cell), where a cell index is a list of any length up to the containing array's rank. General cell indices are discussed in the next section; first we introduce a special case, indices into major cells or ¯1-cells. These cells naturally form a list, so the index of a major cell is a single number. Such an index can also be considered to select along the first axis, since an index along any axis is a single number.
 
-Ordering-based functions `⍋`, `⍒`, `⊐`, and `⊒` only really make sense with major cell indices: while it's possible to order other indices as ravel indices, this probably isn't useful from a programming standpoint. Note that `⊐` only uses the ordering in an incidental way, because it's defined to return the *first* index where a right argument cell is found. A mathematician would be more interested in a "pre-image" function that returns the set of all indices where a particular value appears. However, programming usefulness and consistency with the other search functions makes searching for the first index a reasonable choice.
+[Ordering](order.md) functions `⍋⍒` and [search](search.md)/[self-comparison](selfcmp.md) functions `⊐⊒` that depend on cell ordering only really make sense with major cell indices: while other indices have an ordering, it's not very natural. Note that `⊐` only uses the ordering in an incidental way, because it's defined to return the *first* index where a cell in `𝕩` is found. A mathematician would be more interested in a "pre-image" function that returns the set of all indices where a particular value appears. However, programming usefulness and consistency with the other search functions makes searching for the first index a reasonable choice.
 
-Only one other function—but an important one!—deals with cells rather than elements: `⊏`, cell selection. Like dyadic `↑↓↕⌽⍉` (depth 0) and `/⊔` (depth 1), Select allows either a simple first-axis case where the left argument has depth 1 or less (a depth-0 argument is automatically enclosed), and a multi-axis case where it is a list of depth-1 elements. In each case the depth-1 arrays index along a single axis.
+Only one other function—but an important one!—deals with cells rather than elements: [Select](select.md) (`⊏`). Select [allows](leading.md#multiple-axes) either a simple first-axis case where `𝕨` has depth 1 or less (a depth-0 argument is automatically enclosed), and a multi-axis case where it is a list of depth-1 elements. In each case the depth-1 arrays index along a single axis.
 
 ## General cell indices