Slides for Ruby Manor 4 talk

1. on Discovering Joy
Francis Fish (@fjfish)

2. Fish?
NOT COMPUTER SCIENTIST
LIKE PROGRAMMING
LEARN NEW LANGUAGE LONG TIME
NOW
KNOW NOTHING, YOU MUCH CLEVERER
THAN ME
DISCOVERING JOY - NOT EXPERT!

3. Blame Braithwaite
Appendix
Finding joy in
combinators

4. Combinators

5. Combinator?
http://en.wikipedia.org/wiki/Combinator
A combinator is a higher-order function that uses
only function application and earlier defined
combinators to define a result from its arguments.
(no parameters, functions as arguments)

6. Joy Resources
http://en.wikipedia.org/wiki/Joy_(programmin
Invented by Manfred von Thun of La Trobe
University in Melbourne, Australia (retired)
Purely functional, combinatorial, stack based
Mirror
http://www.kevinalbrecht.com/code/joy-mirror

7. Interesting
Program is data (like Lisp)
Stack based - no parameters
Post-fix (goes with stack)
Does functional stuff well
Combinators - take what’s on the stack and do
stuff - including combining other combinators
Not Forth - no dictionary - functional

8. Stack Based?
Let’s go see

9. Example: Square
5 dup * .
- will print 25 and leave the stack empty
(as a function)
square == dup *
(== is the only infix operator - not runtime)

10. WAT?

11. Parameters, None
A stack of combinators
Code acts on the stack
dup *
Copy it and multiply the top 2 elements
together

12. Cube - you tell
me :)

13. 5 dup dup * *.
5#5
dup # 5 5
dup # 5 5 5
* # 5 25
* # 125
125

14. Programs
Joy programs are built from smaller programs by
just two operations: concatenation and quotation.

15. Quoted Programs
[bob alice]
Is a list, but also a quoted program
You can plug it into things and then execute
Built in functions, anonymous Y combinator
etc.
Fill in the blanks

16. Types
character, file, float, integer, list, set, string,
truth
What else do you need?
(Except maybe hash)
And sets are weird

17. Combinators
ifte - if then else
The ifte combinator expects three quoted programs on the stack, an if-part, a then-part and an else-part,
in that order, with the else-part on top
dip
dip combinator expects a program on top of the stack and below that another value. It saves the value,
executes the program on the remainder of the stack and then restores the saved value.
i
identity - run the quoted program on the top of the stack

18. Combinators
concat
Join two aggregates together
cons - lisp
Add the top thing to the aggregate behind it on the stack
dup
Duplicate the stack top
swap
cause a flight of penguins

19. Combinators
Not talking about:
construct, dupd, map, popd, rolldown, rolldownd,
rollup, rollupd, rotate, succ, pred, swap, swapd,
swons, times, take, ternary, treegenrec, unswons,
x, first ...

20. Example:
Factorial
Factorial

21. Linear Recursion
5 [null] [succ] [dup pred] [*] linrec .
["null" false]
linrec : [P] [T] [R1] [R2] -> ....Executes P. If that yields true, executes T.Else execu
["dup pred" 4 5]
["null" false 5]
["null" false 3 4 5]
["*" 6 4 5]
...["*" 120]
["linrec" 120]
120

22. Primitive Recursion
5 [1] [*] primrec .
["R0" 1 1 2 3 4 5]
["*" 1 2 3 4 5] primrec : X [I] [C] -> R.Executes I to obtain
["*" 2 3 4 5] an initial value R0.For integer X uses increasing
positive integers to X, combines by C for new
["*" 6 4 5] R.For aggregate X uses successive members and
["*" 24 5] combines by C for new R.
["*" 120]
120
(HINT: it’s not recursion)

23. Y-Combinator
5
[ [pop 0 =] [pop pop 1] [[dup 1 -] dip i *] ifte ]
[dup cons] swap concat dup cons i

24. Explanation
5 Cond Else Then
[ [pop 0 =] [pop pop 1] [[dup 1 -] dip i *] ifte ]
[dup cons] swap concat dup cons i

25. If the top of the stack is 0
discard the copied program and the 0 left and
push 1
else
duplicate the top of the stack and subtract 1 from
the top value
then dip and call the copy of yourself underneath
the stack top
on return apply *
* the value below with the one you calculated

26. [dup cons] swap concat program and the integer on
(We already have the quoted dup cons i
the top of the stack)
(We push a quoted dup cons onto the stack)
run whats comes out of:
Take the stack top and cons to aggregate underneath
dup the aggregate
concat them together swap with whatever’s on the stack
top
We end up with the previous quoted program on the stack
top and run it

27. ['1 false 4 5]
['3 2 3 4 5] Just for laffs
['6 [[dup cons [pop 0 =] [pop pop 1] [[dup 1 -] dip i *] ifte] dup cons [pop 0 =] [pop pop 1]
[[dup 1 -] dip i *] ifte] 2 3 4 5]
['1 false 3 4 5]
['3 1 2 3 4 5]
['6 [[dup cons [pop 0 =] [pop pop 1] [[dup 1 -] dip i *] ifte] dup cons [pop 0 =] [pop pop 1]
[[dup 1 -] dip i *] ifte] 1 2 3 4 5]
['1 false 2 3 4 5]
['3 0 1 2 3 4 5]
['6 [[dup cons [pop 0 =] [pop pop 1] [[dup 1 -] dip i *] ifte] dup cons [pop 0 =] [pop pop 1]
[[dup 1 -] dip i *] ifte] 0 1 2 3 4 5]
['1 true 1 2 3 4 5]
['2 1 1 2 3 4 5]
['5 1 1 2 3 4 5]

28. What Have I discovered?

29. Ruby Practice
How do we do recursion?
We can see the stack, this reminds us of
things we had forgotten
Recursion can always be recast as iteration
Quick poll - how many people know this?
How many had forgotten?
Can make difficult problems more tractable

30. Ruby Practice
Program is data?
Method missing/symbols
Dispatch tables etc.
ERB - macro languages

31. THings to think about
Can we use stacks and combinators to solve
problems more easily?
Can we create DSL’s that do this?
Would we want to :)

32. Building a web app
Who needs HAML when we could have:
[
[
[
["Hello" div]
] body
]
[
[
[“My App” title]
[“main.js” script]
] head]
] html

33. Next?
http://programjoy.eu - £1.40 :)
Will front a runtime and links to the mirror
Will run the tutorial
If you want to help - contact me
More fun to work on rather than <corporate-
bs>next big ecommerce social doo dah
site</corporate-bs>

34. Finis/Questions
Francis Fish (@fjfish)
www.francisfish.com
www.leanpub.com/fjfish