Fear and loathing with APL (oredev)

Fear and Loathing with APL

Hi, my name is Yan Cuiaka @theburningmonk

What is APL?

created at IBM in 1957, by Ken Iverson

designed to simplify math notations

“A Programming Language”

What is APL?

famed for use of special symbols

array programming

influenced Mathematica, Matlab, etc.

hey, I’m learning

APL

what the hell is an

APL?

have you lost your

mind?

Conway’s Game of Life

https://www.youtube.com/watch?v=a9xAKttWgP4

“Beauty is in the Eye of the Beholder”

beauty doesn't exist on its own but is created by observers

“…We followed up with two studies on the accuracy rates of novices using a total of six programming languages: Ruby, Java, Perl, Python, Randomo, and Quorum. Randomo was designed by randomly choosing some keywords from the ASCII table (a metaphorical placebo). To our surprise, we found that languages using a more traditional C-style syntax (both Perl and Java) did not afford accuracy rates significantly higher than a language with randomly generated keywords, …”

“An Empirical Investigation into Programming Language Syntax”- Andreas Stefik and Susanna Siebert

“…We followed up with two studies on the accuracy rates of novices using a total of six programming languages: Ruby, Java, Perl, Python, Randomo, and Quorum. Randomo was designed by randomly choosing some keywords from the ASCII table (a metaphorical placebo). To our surprise, we found that languages using a more traditional C-style syntax (both Perl and Java) did not afford accuracy rates significantly higher than a language with randomly generated keywords, …”

“An Empirical Investigation into Programming Language Syntax”- Andreas Stefik and Susanna Siebert

http://bit.ly/2eM3Qvr

“A language that doesn't affect the way you think

about programming, is not worth knowing.”

- Alan Perlis

“in an era of mainstream programming languages, APL is a rare opportunity to truly challenge the way you think about

programming”

- me

Let’s learn some APL

http://tryapl.org/

2 + 2 4

4 - 1 3

+ and - works the way you expect

2 * 3 8

4 * 4 256

but * means power

2 / 3 3 3

and / means replicate

it means replicate the scalar value 3, 2 timesand returns an array of 2 elements

2 × 2 4 4 ÷ 2 2

multiplication (×) and division (÷)

just like in Maths!

x ← 42 y ← 1 2 3 4

assignment (←)

variable names are case sensitive

variables are mutable

x ← 42 x ← 1 2 3 4 x

1 2 3 4

assign multiple values at once(kinda like pattern matching)

x y z ← 1 2 3 x

1 y

2

but the patterns must match

x y ← 1 2 3 LENGTH ERROR x y ← 1 2 3

1 2 3 - 3 2 1 ¯2 0 2

1 2 3 × 3 2 1 3 4 3

arithmetic operations work on arrays too

1 2 3 + 1 2 3 4

2 × 1 2 3 2 4 6

if one side is scalar then the other side can be any shape

4 ⌊ 2 2 4 ⌈ 2 4

min (⌊) and max (⌈)

1 2 3 4 5 ⌈ 4 4 4 4 4 5 1 2 3 ⌈ 3 2 1 3 2 3

min (⌊) and max (⌈)

same rules apply for arrays

dyadic

2 ⌈ 4 1 2 ⌈ 3 1

monadic

⌈ 2 ⌈ 1 3

⌊ 3 4.1 4.5 5.6 3 4 4 5

monadically, ⌊ means floor

⌈ 3 4.1 4.5 5.6 3 5 5 6

and ⌈ means ceiling

3 2 ⍴ 1 2 3 4 5 6 1 2 3 4 5 6

dyadically, ⍴ reshapes right hand side

rows

columns

⍴ 1 2 3 3 ⍴ (3 2 ⍴ 1 2 3 4 5 6)

3 2

monadically, ⍴ returns shape of argument

3 2 ⍴ 1 2 3 1 2 3 1 2 3

⍴ recycles elements to fill space

2 2 ⍴ 1 2 3 4 5 6 1 2 3 4

and ignores additional elements

3 3 ⍴ 1 0 0 0 1 0 0 0 1 0 0 0 1

here’s a neat trick to get diagonals :-P

⍴ 2 2 ⍴ 0 1 0 2 2 ⍴ (2 2 ⍴ 0 1 0)

2 2

oh, and APL is read from RIGHT-TO-LEFT

⍴ 2 2 ⍴ 0 1 0 2 2 ⍴ (2 2 ⍴ 0 1 0)

2 2

oh, and APL is read from RIGHT-TO-LEFT

+/ 1 2 3 6

btw, / also means reduce

ie, reduce over the array [1, 2, 3] with the plus function

×/ 1 2 3 4 5 120

btw, / also means reduce

and here’s factorials!

Defined Functions

Avg ← { (+/ ⍵) ÷ ⍴⍵ }

anatomy of a defined functionfunction name

assignment function body

Avg ← { (+/ ⍵) ÷ ⍴⍵ }

Avg 1 2 3

anatomy of a defined function

omega ⍵ represents the right argument

Diff ← { (+/ ⍺) - (+/ ⍵) }

3 4 5 Diff 1 2 3

anatomy of a defined function

alpha ⍺ represents the left argument

Plus ← { ⍺ + ⍵ } Plus/ 1 2 3

6

defined functions can be used with / too

Indexing an Array

Xs ← 1 2 3 Xs[2]

2

APL is one-indexed!

Xs[1 2 1] 1 2 1

Xs[2 2 ⍴ 1 2] 1 2 1 2

indices can be array too

Xs[3 2] ← 6 4 Xs

1 4 6

updating an array

⍳9 1 2 3 4 5 6 7 8 9

index generator

Booleans

1 < 2 1

1 2 3 < 3 2 1 1 0 0

1 is true, 0 is false

yup, works with arrays too ;-)

~1 0

~1 0 1 0 1 0

monadically, ~ means negate

(1 2 3 < 3 2 1) ∧ (1 1 1) 1 0 0

(1 2 3 < 3 2 1) ∨ (1 1 1) 1 1 1

logical AND ∧ and logical OR ∨

(⍳10) > 7 0 0 0 0 0 0 0 1 1 1

+/ (⍳10) > 7 3

count no. of positives

(⍳10) > 7 0 0 0 0 0 0 0 1 1 1 ⍳10 > 7

?

are these two expression equivalent?

(⍳10) > 7 0 0 0 0 0 0 0 1 1 1 ⍳10 > 7

1

are these two expression equivalent?

nope! remember, APL reads from RIGHT-TO-LEFT!

(⍳10) > 7 0 0 0 0 0 0 0 1 1 1

7 < ⍳10 0 0 0 0 0 0 0 1 1 1

are these two expression equivalent?

Compression (aka filtering)

1 0 1 / 3 2 1 3 1

1 0 1 / 'iou' i u

booleans can be used to as a mask

Values ← 1 3 5 7 9 Values > 4

0 0 1 1 1 (Values > 4) / Values

5 7 9

a LINQ-style Where can be written as

Values > 4 0 0 1 1 1 ⍳⍴Values

1 2 3 4 5 (Values > 4) / (⍳⍴Values)

3 4 5

and to get the indices instead

1 2 3 ~ 3 4 3 5 1 2

‘ab’ ‘cd’ ‘ef’ ~ ‘cd’ ‘ef’ ab

dyadically, ~ means without

1 1 3 5 3 7 ∊ 1 2 3 1 1 1 0 1 0

'hello world' ∊ 'aeiou' 0 1 0 0 1 0 0 1 0 0 0

dyadically, ∊ checks for membership

Phrase ← ‘hello world’ (Phrase ∊ 'aeiou') / Phrase

eoo

which vowels appeared in a phrase?

2 2 ⍴ 1 2 1 2 1 2

∊ 2 2 ⍴ 1 2 1 2 1 2

monadically, ∊ flattens a matrix

Take & Drop

2 ↑ 1 2 3 4 1 2

2 2 ↑ (3 3 ⍴ ⍳9) 1 2 4 5

↑ to take items from an array

!?

3 3 ⍴ ⍳9 1 2 3 4 5 6 7 8 9

2 2 ↑ 3 3 ⍴ ⍳9 1 2 3 4 5 6 7 8 9

take a 2 (rows) by 2 (cols) matrix

2 ↓ 1 2 3 4 3 4

2 2 ↓ (3 3 ⍴ ⍳9) 9

↓ to drop items from an array

!?

3 3 ⍴ ⍳9 1 2 3 4 5 6 7 8 9

2 2 ↓ 3 3 ⍴ ⍳9 1 2 3 4 5 6 7 8 9

drop first 2 rows and 2 cols

¯2 ↑ 1 2 3 4 3 4

¯2 ↓ 1 2 3 4 1 2

use negative count to take/drop from end of array

¯2 2 ↑ (3 3 ⍴ ⍳9) ?

¯2 2 ↓ (3 3 ⍴ ⍳9) ?

what about these?

http://tryapl.org/ try it out yourself

Mirrors & Transportations

3 3 ⍴ ⍳9 1 2 3 4 5 6 7 8 9

given a matrix

3 3 ⍴ ⍳9 3 2 1 6 5 4 9 8 7

mirrors the matrix horizontally

3 3 ⍴ ⍳9 7 8 9 4 5 6 1 2 3

mirrors the matrix vertically

⍉ 3 3 ⍴ ⍳9 1 4 7 2 5 8 3 6 9

transposes the matrix⍉

Outer Products

cartesian product

1 2 3 .+ 4 5 6 5 6 7 6 7 8 7 8 9

. creates a cartesian product

1 2 3 .× 4 5 6 4 5 6 8 10 12 12 15 18

. creates a cartesian product

(⍳3) .= (⍳3) 1 0 0 0 1 0 0 0 1

. creates a cartesian product

(⍳3) .< (⍳3) 0 1 1 0 0 1 0 0 0

. creates a cartesian product

(⍳3) .⌈ (⍳3) 1 2 3 2 2 3 3 3 3

. creates a cartesian product

(⍳3) .+ (⍳3) 2 3 4 3 4 5 4 5 6

. creates a cartesian product

what about this?

http://tryapl.org/ try it out yourself

∊ (⍳3) .× (⍳5) ?

Demo Time…

Conclusions

should I learn APL?

absolutely! it’s the shock to the system your brain needs

is it gonna help my career?

does it matter?

@theburningmonktheburningmonk.comgithub.com/theburningmonk