Frege Tutorial at JavaOne 2015
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This document discusses the benefits of purely functional programming using the Frege programming language. Some key points made include: - Frege is based on principles of pure functional programming and avoids side effects through its type system and lack of assignments. - Functions in Frege are pure by design and can be reasoned about locally through equational reasoning. This makes code more robust and refactorable. - Frege supports features like currying, pattern matching, lazy evaluation, and list comprehensions to enable a functional style of programming. - Examples are given showing how concepts from category theory like natural transformations can be expressed and checked via the type system for robustness. - Interoperability with Java
![Lazy Evaluation
frege> times 0 (length [1..])
0
endless sequence
evaluation would never stop
Pattern matching and
non-strict evaluation
to the rescue!](https://image.slidesharecdn.com/fregeatjavaone-151027203519-lva1-app6892/85/Frege-Tutorial-at-JavaOne-2015-19-320.jpg)
![Magic (?)
Think of a generic function
f :: [a] -> [a]
and any specific function
g :: a -> b](https://image.slidesharecdn.com/fregeatjavaone-151027203519-lva1-app6892/85/Frege-Tutorial-at-JavaOne-2015-24-320.jpg)
![Magic (?)
[a] [a]
[b] [b]
f
f
map g map g](https://image.slidesharecdn.com/fregeatjavaone-151027203519-lva1-app6892/85/Frege-Tutorial-at-JavaOne-2015-25-320.jpg)
![Magic (?)
[1,2,3] [3,2,1]
[2,4,6] [6,4,2]
reverse
reverse
map (*2) map (*2)
Commutative square of natural transformations.](https://image.slidesharecdn.com/fregeatjavaone-151027203519-lva1-app6892/85/Frege-Tutorial-at-JavaOne-2015-26-320.jpg)
![Zipping
addzip [] _ = []
addzip _ [] = []
addzip (x:xs) (y:ys) =
(x + y : addzip xs ys )](https://image.slidesharecdn.com/fregeatjavaone-151027203519-lva1-app6892/85/Frege-Tutorial-at-JavaOne-2015-38-320.jpg)
![Zipping
addzip [] _ = []
addzip _ [] = []
addzip (x:xs) (y:ys) =
(x + y : addzip xs ys )
use as
addzip [1,2,3]
[1,2,3]
== [2,4,6]
Pattern matching
feels like Prolog
Why only for the (+) function?
We could be more general…](https://image.slidesharecdn.com/fregeatjavaone-151027203519-lva1-app6892/85/Frege-Tutorial-at-JavaOne-2015-39-320.jpg)
![High Order Functions
zipWith f [] _ = []
zipWith f _ [] = []
zipWith f (x:xs) (y:ys) =
(f x y : zipWith xs ys )](https://image.slidesharecdn.com/fregeatjavaone-151027203519-lva1-app6892/85/Frege-Tutorial-at-JavaOne-2015-40-320.jpg)
![High Order Functions
zipWith f [] _ = []
zipWith f _ [] = []
zipWith f (x:xs) (y:ys) =
(f x y : zipWith xs ys )
use as
zipWith (+) [1,2,3]
[1,2,3]
== [2,4,6]
and, yes we can now define
addzip =
zipWith (+)
invented by Gottlob Frege](https://image.slidesharecdn.com/fregeatjavaone-151027203519-lva1-app6892/85/Frege-Tutorial-at-JavaOne-2015-41-320.jpg)
![Fizzbuzz Imperative
public class FizzBuzz{
public static void main(String[] args){
for(int i= 1; i <= 100; i++){
if(i % 15 == 0{
System.out.println(„FizzBuzz");
}else if(i % 3 == 0){
System.out.println("Fizz");
}else if(i % 5 == 0){
System.out.println("Buzz");
}else{
System.out.println(i);
} } } }](https://image.slidesharecdn.com/fregeatjavaone-151027203519-lva1-app6892/85/Frege-Tutorial-at-JavaOne-2015-43-320.jpg)
![Fizzbuzz Logical
fizzes = cycle ["", "", "fizz"]
buzzes = cycle ["", "", "", "", "buzz"]
pattern = zipWith (++) fizzes buzzes
numbers = map show [1..]
fizzbuzz = zipWith max pattern numbers
main _ = do
for (take 100 fizzbuzz) println](https://image.slidesharecdn.com/fregeatjavaone-151027203519-lva1-app6892/85/Frege-Tutorial-at-JavaOne-2015-44-320.jpg)
![List Comprehension
Pythagorean triples: a2 + b2 = c2
pyth n = [
(x,y,z)
| x <- [1..n], y <- [1..n], z <- [1..n],
x*x + y*y == z*z
]](https://image.slidesharecdn.com/fregeatjavaone-151027203519-lva1-app6892/85/Frege-Tutorial-at-JavaOne-2015-46-320.jpg)
![List Comprehension
Pythagorean triples: a2 + b2 = c2
pyth n = [
(x,y,z)
| x <- [1..n], y <- [1..n], z <- [1..n],
x*x + y*y == z*z
]
select from
where
„brute force“ or „executable specification“.
A more efficient solution:](https://image.slidesharecdn.com/fregeatjavaone-151027203519-lva1-app6892/85/Frege-Tutorial-at-JavaOne-2015-47-320.jpg)
![List Comprehension
Pythagorean triples: a2 + b2 = c2
[ (m*m-n*n, 2*m*n, m*m+n*n)
| m <- [2..], n <- [1..m-1]
]
endless production think „nested loop“
„select“
functions
dynamic
„from“
empty
„where“](https://image.slidesharecdn.com/fregeatjavaone-151027203519-lva1-app6892/85/Frege-Tutorial-at-JavaOne-2015-48-320.jpg)
Frege Tutorial at JavaOne 2015
- 1. Purely functional programming - the red pill JavaOne 2015
- 3. Takeaway Frege is fundamentally different based on science made for practical use
- 4. Why do we care? a = 1 b = 2 c = b b = a a = c 1 1 2 1 2 2 1 1 22 1 2 time1 time2 time3 state1 state2 state3
- 5. Operational Reasoning a = 1 b = 2 c = b b = a a = c 1 1 2 1 2 2 1 1 2 2 1 2 time1 time2 time3 state1 state2 state3 We need a debugger!
- 7. Using functions a = 1 b = 2 1 1 2 2 1 swap(a,b) = (b,a)
- 8. The Key Idea Assignments change state and introduce time. Statements do side effects. Let’s just program without assignments or statements!
- 12. Define a Function frege> times a b = a * b frege> (times 3) 4 12 frege> :type times Num α => α ->(α -> α) no types declared function appl. left associative tell the inferred type typeclass only 1 parameter! return type is a function! thumb: „two params of same numeric type returning that type“ no comma
- 13. Reference a Function frege> twotimes = times 2 frege> twotimes 3 6 frege> :t twotimes Int -> Int
- 14. Reference a Function frege> twotimes = times 2 frege> twotimes 3 6 frege> :t twotimes Int -> Int No second argument! „Currying“, „schönfinkeling“, or „partial function application“. Concept invented by Gottlob Frege. inferred types are more specific
- 16. Function Composition frege> twotimes (threetimes 2) 12 frege> sixtimes = twotimes . threetimes frege> sixtimes 2 frege> :t sixtimes Int -> Int f(g(x)) more about this later (f ° g) (x)
- 18. Pattern Matching frege> times 0 (threetimes 2) 0 frege> times 0 b = 0 unnecessarily evaluated shortcuttingpattern matching
- 19. Lazy Evaluation frege> times 0 (length [1..]) 0 endless sequence evaluation would never stop Pattern matching and non-strict evaluation to the rescue!
- 20. Pure Functions Java T foo(Pair<T,U> p) {…} Frege foo :: (α,β) -> α What could possibly happen? What could possibly happen?
- 21. Pure Functions Java T foo(Pair<T,U> p) {…} Frege foo :: (α,β) -> α Everything! State changes, file or db access, missile launch,… a is returned
- 22. can be cached (memoized) can be evaluated lazily can be evaluated in advance can be evaluated concurrently can be eliminated in common subexpressions can be optimized Pure Functions
- 23. Is my method pure? Let the type system find out!
- 25. Magic (?) [a] [a] [b] [b] f f map g map g
- 26. Magic (?) [1,2,3] [3,2,1] [2,4,6] [6,4,2] reverse reverse map (*2) map (*2) Commutative square of natural transformations.
- 27. Robust Refactoring Changing the order of operations Requires purity. 100% safe if the type system can detect natural transformations Applied Category Theory credits: Phil Wadler, Tech Mesh 2012 - Faith, Evolution, and Programming Languages
- 29. Java Interoperability do not mix OO and FP combine them
- 30. Java -> Frege Scripting: JSR 223 Service: compile *.fr file call static method simple
- 31. pure native encode java.net.URLEncoder.encode :: String -> String encode “Dierk König“ native millis java.lang.System.currentTimeMillis :: () -> IO Long millis () millis () past = millis () - 1000 Does not compile! Frege -> Java This is a key distinction between Frege and other JVM languages! even Java can be pure
- 32. allows calling Java but never unprotected! is explicit about effects just like Haskell Frege
- 33. Type System Global type inference and thus more safety and less work for the programmer You don’t need to specify any types at all! But sometimes you do anyway…
- 34. Mutable I/O Mutable Mutable Keep the mess out! Pure Computation Pure Computation Pure Computation
- 35. Mutable I/O Mutable Mutable Keep the mess out! Pure Computation Pure Computation Pure Computation Ok, these are Monads. Be brave. Think of them as contexts that the type system propagates and makes un-escapable. Thread- safe by design! Checked by compiler
- 36. Java Java Java Service Based Design Frege Frege Frege A typical integration option: use Frege code for services
- 37. Some Cool Stuff
- 39. Zipping addzip [] _ = [] addzip _ [] = [] addzip (x:xs) (y:ys) = (x + y : addzip xs ys ) use as addzip [1,2,3] [1,2,3] == [2,4,6] Pattern matching feels like Prolog Why only for the (+) function? We could be more general…
- 41. High Order Functions zipWith f [] _ = [] zipWith f _ [] = [] zipWith f (x:xs) (y:ys) = (f x y : zipWith xs ys ) use as zipWith (+) [1,2,3] [1,2,3] == [2,4,6] and, yes we can now define addzip = zipWith (+) invented by Gottlob Frege
- 45. Fizzbuzz Comparison Imperative Logical Conditionals 4 0 Operators 7 1 Nesting level 3 0 Sequencing sensitive transparent Maintainability - - - +
- 46. List Comprehension Pythagorean triples: a2 + b2 = c2 pyth n = [ (x,y,z) | x <- [1..n], y <- [1..n], z <- [1..n], x*x + y*y == z*z ]
- 47. List Comprehension Pythagorean triples: a2 + b2 = c2 pyth n = [ (x,y,z) | x <- [1..n], y <- [1..n], z <- [1..n], x*x + y*y == z*z ] select from where „brute force“ or „executable specification“. A more efficient solution:
- 48. List Comprehension Pythagorean triples: a2 + b2 = c2 [ (m*m-n*n, 2*m*n, m*m+n*n) | m <- [2..], n <- [1..m-1] ] endless production think „nested loop“ „select“ functions dynamic „from“ empty „where“
- 49. History Java promise: „No more pointers!“ But NullPointerExceptions (?)
- 50. Frege is different No More But state no state (unless declared) statements expressions (+ „do“ notation) assignments definitions variables ST monad as „agent“ interfaces type classes classes & objects algebraic data types inheritance parametric polymorphism null references Maybe NullPointerExceptions Bottom, error
- 52. Frege in comparison Java Groovy Frege Haskell concept by Simon Peyton-Jones Frege makes the Haskell spirit accessible to the Java programmer and provides a new level of safety. apply logic run computers practical robust
- 53. Unique in Frege Explicit effects Purity = no effects Guarantees extend into Java calls Laziness enforces purity and immutable values (no assignments) Global type inference requires a purely functional language (only expressions, no statements)
- 54. Why Frege Robustness under parallel execution Robustness under composition Robustness under increments Robustness under refactoring Enables local and equational reasoning Best way to learn FP
- 55. Why FP matters Enabling incremental development www.canoo.com/blog/fp1 Brush up computational fundamentals „An investment in knowledge always pays the best interest.“ —Benjamin Franklin
- 56. Why Frege it is just a pleasure to work with
- 57. How? http://www.frege-lang.org @fregelang stackoverflow „frege“ tag edX FP101 MOOC (still possible to join!)
- 58. Gottlob Frege "As I think about acts of integrity and grace, I realise that there is nothing in my knowledge that compares with Frege’s dedication to truth… It was almost superhuman.“ —Bertrand Russel "Not many people managed to create a revolution in thought. Frege did.“ —Graham Priest Lecture on Gottlob Frege: http://www.youtube.com/watch?v=foITiYYu2bc
- 59. Dierk König Canoo mittie Please vote at the machine!