1.
Fear and Loathing
with APL

2.
Hi, my name is Yan Cui
aka @theburningmonk

3.
What is APL?
created at IBM in 1957, by Ken Iverson
designed to simplify math notations
“A Programming Language”

4.
What is APL?
famed for use of special symbols
array programming
influenced Mathematica, Matlab, etc.

5.
hey, I’m
learning
APL

6.
what the
hell is an
APL?

7.
have you
lost your
mind?

8.
Conway’s Game of Life
https://www.youtube.com/watch?v=a9xAKttWgP4

9.
“Beauty is in the Eye of the Beholder”
beauty doesn't exist on its own but is created by observers

10.
“…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

11.
“…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

12.
http://bit.ly/2eM3Qvr

13.
“A language that doesn't
affect the way you think
about programming, is not
worth knowing.”
- Alan Perlis

14.
“in an era of mainstream programming
languages, APL is a rare opportunity to
truly challenge the way you think about
programming”
- me

15.
Let’s learn some APL
http://tryapl.org/

16.
2 + 2
4
4 - 1
3
+ and - works the way you expect

17.
2 * 3
8
4 * 4
256
but * means power

18.
2 / 3
3 3
and / means replicate
it means replicate the scalar value 3, 2 times
and returns an array of 2 elements

19.
2 × 2
4
4 ÷ 2
2
multiplication (×) and division (÷)
just like in Maths!

20.
x ← 42
y ← 1 2 3 4
assignment (←)
variable names are case sensitive

21.
variables are mutable
x ← 42
x ← 1 2 3 4
x
1 2 3 4

22.
assign multiple values at once
(kinda like pattern matching)
x y z ← 1 2 3
x
1
y
2

23.
but the patterns must match
x y ← 1 2 3
LENGTH ERROR
x y ← 1 2 3

24.
1 2 3 - 3 2 1
¯2 0 2
1 2 3 × 3 2 1
3 4 3
arithmetic operations work on arrays too

25.
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

26.
4 ⌊ 2
2
4 ⌈ 2
4
min (⌊) and max (⌈)

27.
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

28.
dyadic
2 ⌈ 4
1 2 ⌈ 3 1
monadic
⌈ 2
⌈ 1 3

29.
⌊ 3 4.1 4.5 5.6
3 4 4 5
monadically, ⌊ means floor

30.
⌈ 3 4.1 4.5 5.6
3 5 5 6
and ⌈ means ceiling

31.
3 2 ⍴ 1 2 3 4 5 6
1 2
3 4
5 6
dyadically, ⍴ reshapes right hand side
rows
columns

32.
⍴ 1 2 3
3
⍴ (3 2 ⍴ 1 2 3 4 5 6)
3 2
monadically, ⍴ returns shape of argument

33.
3 2 ⍴ 1 2 3
1 2
3 1
2 3
⍴ recycles elements to fill space

34.
2 2 ⍴ 1 2 3 4 5 6
1 2
3 4
and ignores additional elements

35.
3 3 ⍴ 1 0 0 0
1 0 0
0 1 0
0 0 1
here’s a neat trick to get diagonals :-P

36.
⍴ 2 2 ⍴ 0 1 0
2 2
⍴ (2 2 ⍴ 0 1 0)
2 2
oh, and APL is read from RIGHT-TO-LEFT

37.
⍴ 2 2 ⍴ 0 1 0
2 2
⍴ (2 2 ⍴ 0 1 0)
2 2
oh, and APL is read from RIGHT-TO-LEFT

38.
+/ 1 2 3
6
btw, / also means reduce
ie, reduce over the array [1, 2, 3] with the plus function

39.
×/ 1 2 3 4 5
120
btw, / also means reduce
and here’s factorials!

40.
Defined Functions

41.
Avg ← { (+/ ⍵) ÷ ⍴⍵ }
anatomy of a defined function
function
name
assignment function
body

42.
Avg ← { (+/ ⍵) ÷ ⍴⍵ }
Avg 1 2 3
anatomy of a defined function
omega ⍵ represents the right argument

43.
Diff ← { (+/ ⍺) - (+/ ⍵) }
3 4 5 Diff 1 2 3
anatomy of a defined function
alpha ⍺ represents the left argument

44.
Plus ← { ⍺ + ⍵ }
Plus/ 1 2 3
6
defined functions can be used with / too

45.
Indexing an Array

46.
Xs ← 1 2 3
Xs[2]
2
APL is one-indexed!

47.
Xs[1 2 1]
1 2 1
Xs[2 2 ⍴ 1 2]
1 2
1 2
indices can be array too

48.
Xs[3 2] ← 6 4
Xs
1 4 6
updating an array

49.
⍳9
1 2 3 4 5 6 7 8 9
index generator

50.
Booleans

51.
1 < 2
1
1 2 3 < 3 2 1
1 0 0
1 is true, 0 is false
yup, works with arrays too ;-)

52.
~1
0
~1 0 1
0 1 0
monadically, ~ means negate

53.
(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 ∨

54.
(⍳10) > 7
0 0 0 0 0 0 0 1 1 1
+/ (⍳10) > 7
3
count no. of positives

55.
(⍳10) > 7
0 0 0 0 0 0 0 1 1 1
⍳10 > 7
?
are these two expression equivalent?

56.
(⍳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!

57.
(⍳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?

58.
Compression
(aka filtering)

59.
1 0 1 / 3 2 1
3 1
1 0 1 / 'iou'
i u
booleans can be used to as a mask

60.
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

61.
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

62.
1 2 3 ~ 3 4 3 5
1 2
‘ab’ ‘cd’ ‘ef’ ~ ‘cd’ ‘ef’
ab
dyadically, ~ means without

63.
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

64.
Phrase ← ‘hello world’
(Phrase ∊ 'aeiou') / Phrase
eoo
which vowels appeared in a phrase?

65.
2 2 ⍴ 1 2
1 2
1 2
∊ 2 2 ⍴ 1 2
1 2 1 2
monadically, ∊ flattens a matrix

66.
Take & Drop

67.
2 ↑ 1 2 3 4
1 2
2 2 ↑ (3 3 ⍴ ⍳9)
1 2
4 5
↑ to take items from an array
!?

68.
3 3 ⍴ ⍳9
1 2 3
4 5 6
7 8 9

69.
2 2 ↑ 3 3 ⍴ ⍳9
1 2 3
4 5 6
7 8 9
take a 2 (rows) by 2 (cols) matrix

70.
2 ↓ 1 2 3 4
3 4
2 2 ↓ (3 3 ⍴ ⍳9)
9
↓ to drop items from an array
!?

71.
3 3 ⍴ ⍳9
1 2 3
4 5 6
7 8 9

72.
2 2 ↓ 3 3 ⍴ ⍳9
1 2 3
4 5 6
7 8 9
drop first 2 rows and 2 cols

73.
¯2 ↑ 1 2 3 4
3 4
¯2 ↓ 1 2 3 4
1 2
use negative count to take/drop from
end of array

74.
¯2 2 ↑ (3 3 ⍴ ⍳9)
?
¯2 2 ↓ (3 3 ⍴ ⍳9)
?
what about these?
http://tryapl.org/ try it out yourself

75.
Mirrors &
Transportations

76.
3 3 ⍴ ⍳9
1 2 3
4 5 6
7 8 9
given a matrix

77.
3 3 ⍴ ⍳9
3 2 1
6 5 4
9 8 7
mirrors the matrix horizontally

78.
3 3 ⍴ ⍳9
7 8 9
4 5 6
1 2 3
mirrors the matrix vertically

79.
⍉ 3 3 ⍴ ⍳9
1 4 7
2 5 8
3 6 9
transposes the matrix⍉

80.
Outer Products

81.
cartesian product

82.
1 2 3 .+ 4 5 6
5 6 7
6 7 8
7 8 9
. creates a cartesian product

83.
1 2 3 .× 4 5 6
4 5 6
8 10 12
12 15 18
. creates a cartesian product

84.
(⍳3) .= (⍳3)
1 0 0
0 1 0
0 0 1
. creates a cartesian product

85.
(⍳3) .< (⍳3)
0 1 1
0 0 1
0 0 0
. creates a cartesian product

86.
(⍳3) .⌈ (⍳3)
1 2 3
2 2 3
3 3 3
. creates a cartesian product

87.
(⍳3) .+ (⍳3)
2 3 4
3 4 5
4 5 6
. creates a cartesian product

88.
what about this?
http://tryapl.org/ try it out yourself
∊ (⍳3) .× (⍳5)
?

89.
Demo Time…

90.
Conclusions

91.
should I learn APL?
absolutely! it’s the shock to the
system your brain needs

92.
is it gonna help my career?
does it matter?

93.
@theburningmonk
theburningmonk.com
github.com/theburningmonk