Use "unit" or "rank-0" instead of "scalar"

1 files changed, 4 insertions, 4 deletions

diff --git a/doc/couple.md b/doc/couple.md
index 3cc1ac8f..f78d441c 100644
--- a/doc/couple.md
+++ b/doc/couple.md
@@ -30,7 +30,7 @@ In all cases what these functions do is more like reinterpreting existing data t
         ⥊ ⥊¨ a
         ∾ ⥊ ⥊¨ a
 
-The way this happens, and the constraint that all inner arrays have the same shape, is closely connected to the concept of an array, and like Table `⌜`, Merge might be considered a fundamental way to build up multidimensional arrays from lists. In both cases scalars are somewhat special. They are the identity element of a function with Table, and can be produced by Merge inverse, `>⁼` **on a list**, which forces either the outer or inner shape to be empty (BQN chooses `>⁼` to be `<`, but only on an array, as `>` cannot produce non-arrays). Merge has another catch as well: it cannot produce arrays with a `0` in the shape, except at the end, without some sort of prototype system.
+The way this happens, and the constraint that all inner arrays have the same shape, is closely connected to the concept of an array, and like Table `⌜`, Merge might be considered a fundamental way to build up multidimensional arrays from lists. In both cases rank-0 or unit arrays are somewhat special. They are the identity element of a function with Table, and can be produced by Merge inverse, `>⁼` **on a list**, which forces either the outer or inner shape to be empty (BQN chooses `>⁼` to be `<`, but only on an array, as `>` cannot produce non-arrays). Merge has another catch as well: it cannot produce arrays with a `0` in the shape, except at the end, without some sort of prototype system.
 
         ⊢ e ← ⟨⟩¨ ↕3
         ≢ > e
@@ -38,9 +38,9 @@ The way this happens, and the constraint that all inner arrays have the same sha
 
 Above we start with a list of three empty arrays. After merging once we get a shape `3‿0` array, sure, but what happens next? The shape added by another merge is the shared shape of that array's elements—and there aren't any! If the nested list kept some type information around then we might know, but extra type information is essentially how lists pretend to be arrays. True dynamic lists simply can't represent multidimensional arrays with a `0` in the middle of the shape. In this sense, arrays are a richer model than nested lists.
 
-## Coupling scalars
+## Coupling units
 
-A note on the topic of Solo and Couple applied to scalars. As always, one axis will be added, so that the result is a list (strangely, J's [laminate](https://code.jsoftware.com/wiki/Vocabulary/commaco#dyadic) differs from Couple in this one case, as it will add an axis to get a shape `2‿1` result). For Solo, this is interchangeable with Deshape (`⥊`), and either primitive might be chosen for stylistic reasons. For Couple, it is equivalent to Join-to (`∾`), but this is an irregular form of Join-to because it is the only case where Join-to adds an axis to both arguments instead of just one. Couple should be preferred in this case.
+A note on the topic of Solo and Couple applied to units. As always, one axis will be added, so that the result is a list (strangely, J's [laminate](https://code.jsoftware.com/wiki/Vocabulary/commaco#dyadic) differs from Couple in this one case, as it will add an axis to get a shape `2‿1` result). For Solo, this is interchangeable with Deshape (`⥊`), and either primitive might be chosen for stylistic reasons. For Couple, it is equivalent to Join-to (`∾`), but this is an irregular form of Join-to because it is the only case where Join-to adds an axis to both arguments instead of just one. Couple should be preferred in this case.
 
 The pair function, which creates a list from its arguments, can be written `Pair ← ≍○<`, while `≍` in either valence is `>∘Pair`. As an interesting consequence, `≍ ←→ >∘≍○<`, and the same relationship holds for `Pair`.
 
@@ -49,6 +49,6 @@ The pair function, which creates a list from its arguments, can be written `Pair
 
 ## Definitions
 
-As discussed above, `≍` is equivalent to `>{⟨𝕩⟩;⟨𝕨,𝕩⟩}`. To complete the picture we should describe Merge fully. Merge is defined on an array argument `𝕩` such that there's some shape `s` satisfying `∧´⥊(s≡≢)¨𝕩`. If `𝕩` is empty then any shape satisfies this expression; `s` should be chosen based on known type information for `𝕩` or otherwise assumed to be `⟨⟩`. If `s` is empty then `𝕩` is allowed to contain atoms as well as array scalars, and these will be implicitly promoted to arrays by the `⊑` indexing used later. We construct the result by combining the outer and inner axes of the argument with Table; since the outer axes come first they must correspond to the left argument and the inner axes must correspond to the right argument. `𝕩` is a natural choice of left argument, and because no concrete array can be used, the right argument will be `↕s`, the array of indices into any element of `𝕩`. To get the appropriate element corresponding to a particular choice of index and element of `𝕩` we should select using that index. The result of Merge is `𝕩⊑˜⌜↕s`.
+As discussed above, `≍` is equivalent to `>{⟨𝕩⟩;⟨𝕨,𝕩⟩}`. To complete the picture we should describe Merge fully. Merge is defined on an array argument `𝕩` such that there's some shape `s` satisfying `∧´⥊(s≡≢)¨𝕩`. If `𝕩` is empty then any shape satisfies this expression; `s` should be chosen based on known type information for `𝕩` or otherwise assumed to be `⟨⟩`. If `s` is empty then `𝕩` is allowed to contain atoms as well as unit arrays, and these will be implicitly promoted to arrays by the `⊑` indexing used later. We construct the result by combining the outer and inner axes of the argument with Table; since the outer axes come first they must correspond to the left argument and the inner axes must correspond to the right argument. `𝕩` is a natural choice of left argument, and because no concrete array can be used, the right argument will be `↕s`, the array of indices into any element of `𝕩`. To get the appropriate element corresponding to a particular choice of index and element of `𝕩` we should select using that index. The result of Merge is `𝕩⊑˜⌜↕s`.
 
 Given this definition we can also describe Rank (`⎉`) in terms of Each (`¨`) and the simpler monadic function Enclose-Rank `<⎉k`. We assume effective ranks `j` for `𝕨` (if present) and `k` for `𝕩` have been computed. Then the correspondence is `𝕨F⎉k𝕩 ←→ >(<⎉j𝕨)F¨(<⎉k𝕩)`.