# Masks for array access in APL, and other sundries

*
*

As predicted, the APL Orchard did quickly provide alternative syntax for some of my expressions from Wedding Thanksgiving-Versary.

## Array access without `⍸`

The first suggested change came from Adam and it involves changing:

```
Years ← yr[⍸ {⍵>1977} yr]
```

into:

```
Years ← yr/⍨yr>1977 ⍝ Equivalent to (yr>1977)/yr
```

This was a well-deserved reminder that *replicate* (`/`

) is more ambiguous than many APL symbols -- it can be *either* a function or an operator.

I had completely forgotten about this behavioral variation of `/`

!

Essentially what happens is that we pass a series of `0`

s and `1`

s to the replicate function. The number of elements of this series must be the same as the number of elements in the structure we are accessing. `0`

means "leave the corresponding element out of the result". `1`

means "include one copy of the corresponding element in the result".

When used in this way, the term *compress* is generally used. If we were to provide an integer greater than `1`

, the corresponding element would appear that many times in the result. (There is also behavior for negative integers that varies across APL implementations.)

### Some background on *operators* vs *functions* in APL

Though `/`

is often used as a *monadic operator* in APL, it also exists as a *dyadic function* as well.

The distinction between *operator* and *function* in APL comes from it's origins as both a very early programming language (thus, before *operator* became a synonym for "built in function represented by a symbol") and as a mathematical notation (they are operators in the Heaviside sense of the word).

That is to say, an APL *operator* does nothing on it's own but is rather combined with a *function* in order to provide a modified version of that function. (J, an APL descendant, moved to calling operators *adverbs* and functions *verbs*, a distinction that may help to clarify).

A quick example of replicate in operator form:

```
+/ 3 4 5 ⍝ 12
```

This could be read aloud as "replicate the addition function across elements of the vector 3, 4, 5".

### Reverse it

The `⍨`

in the expression `yr/⍨yr>1977`

is useful in that it removes the need for parentheses in the expression. It also allows for an arguably more familiar "array access" syntax where the structure being accessed is on the left of the expression determining what pieces to access.

Using `⍨`

to avoid parentheses is a common idiom that nevertheless continues to trip me up. I'm therefore quite thankful to have this simple example to reflect upon.

## Dyalog dates are a bit magical

Another suggestion by the ever-helpful Adam was that I could avoid additional computation by using the Dyalog date format directly, rather than converting it into the human-readable day of the week form.

```
AnnDates/⍨5=7|1⎕DT AnnDates
```

Here we again see the same pattern with replicate and reverse. Looks like we will have to integrate this into our recognition capacities sooner rather than later!

The associated expression `5=7|1⎕DT AnnDates`

uses *residue* (dyadic `|`

) to get the remainder of division by `7`

. When that equals `5`

, we are looking at a Thursday!

## Easy ranges with `dfns.to`

Though only included in a footnote, I mentioned that the range `1978..2050`

could be constructed via `dfns.iotag`

.

It turns out that `dfns.to`

is a better fit for building a simple range like the one I require.

That said, I will once again be sticking to the vanilla approach in the updated program.

## Prettier output with `↑`

Lastly, the output can be improved by using *mix* (monadic `↑`

). Compared to my previously used `⍪`

, which outputs a 1-column matrix of 4-element vectors, `↑`

outputs a 4-column matrix.

## The revised program

Utilizing the above changes, the improved program now looks like:

```
⎕IO ← 0 ⍝ index origin of 0 means that the nth anniversary in our output table reads as expected
yr ← ⍳2050 ⋄ Years ← yr/⍨yr>1977
AnnDates ← Years ∘., ⊂11 26 ⍝ or Years,¨⊂11 26
AnnOnThursday ← 5=7|1⎕DT AnnDates
ThanksAnnDates ← AnnOnThursday/AnnDates
↑ ThanksAnnDates ,¨ ⍸AnnOnThursday
```

with the output:

```
1982 11 26 4
1993 11 26 15
1999 11 26 21
2004 11 26 26
2010 11 26 32
2021 11 26 43
2027 11 26 49
2032 11 26 54
2038 11 26 60
2049 11 26 71
```

Only one call to each (`¨`

), and it's only in our display code! Thanks again Adam and the whole APL Orchard crew.

*Update: That final each is removable by using a synonym! The expression:*

```
↑ ThanksAnnDates ,¨ ⍸AnnOnThursday
```

*is equivalent to:*

```
(↑ThanksAnnDates),⍸AnnOnThursday
```