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Teaching haskell to juggle
This document discusses teaching Haskell for juggling notation and simulation. It covers siteswap notation for encoding juggling patterns, space-time diagrams for visualizing ball trajectories, and state diagrams for modeling valid throw sequences. Haskell is proposed for its type safety, isolation of side effects, and succinct programming features like pattern matching and higher-order functions. Code examples are presented for generating valid siteswaps and animating simulations using OpenGL. Finally, representing siteswaps at the type level in Haskell is proposed to leverage the type system for validity checking.
Teaching haskell to juggle
- 1. Teaching Haskell ToJuggle Phil Freeman
- 2. Agenda • Theory • Finding valid patterns and their states • Why Haskell? • If there’s time: – Animating siteswaps with HOpenGL – Type level siteswaps
- 3. Siteswap Notation • Encodestiming of throws • Ignores hand positions • E.g. – 3-ball cascade ‘3,3,3,3,…’ – 3-ball shower ‘5,1,5,1,…’ – 4-ball fountain ‘4,4,4,4,…’
- 4. Siteswap Notation • Handsalternate – Even numbers indicate throws to the same hand – Odd numbers indicate throws to the other hand • Current ball will be thrown again after N-1 beats • Period = length (* 2) • Number of props = average value • 0 is a pause with an empty hand
- 5. Space Time Diagrams •Tracks the orbit of each balls between the hands • Axes represent – Time – Ball position • Time axis is divided into beats
- 6. Space Time Diagrams LH 333 RH LH 15 RH LH 423 RH
- 7. State Diagrams • Tracks when balls in the air will land • An × indicates a ball scheduled to land • A - indicates a free hand • E.g. – 3-ball cascade: ×××-- – 3-ball shower: ×-×-× → ××-×- → ×-×-× – 4-ball fountain: ××××-
- 8. State Diagrams • To“throw” a 0, shift the pattern to the left: – -×××- →0 ×××-- • To throw to height N, shift and insert an × at the Nth place: – ×××-- →5 ××--× • State diagrams and heights form the vertices and edges of a directed graph. • Valid siteswaps are cycles in this graph.
- 9. State Diagrams ×××-- ××-×- -×××- ×-××- E.g. 3 props, maximum height 4
- 10. Translation Siteswap Space Time State Diagram Period Length (* 2) Tiling Period Cycle Length (* 2) # of Props Average # of Orbits # of ×’s Height Value Horizontal Max node label Distance length
- 11. Why Haskell? • Typesafety • Side effects are isolated • Succinct – Pattern matching – Polymorphism – Higher order functions
- 12. Code Break • Finding Valid Siteswaps • throw, throwMany, foldM • graph, generateGraph • E.g. all patterns decorating a 3-cascade • E.g. over combinator
- 13. HOpenGL • Provides ahigh-level interface to the OpenGL bindings. • Computations take place in IO • E.g. preservingMatrix :: IO a -> IO a • Use powerful existing tools, e.g. mapM
- 14. Code Break • AnimatingSiteswaps • IORef • E.g. insert
- 15. Type Level Siteswaps •Idea: Can we use the type system to identify valid siteswaps? • E.g. Can we improve on the type of (++) for concatenating patterns? • Use singleton types, type classes and fundeps to encode the state graph in the type system.
- 16. Code Break • TypeLevel Siteswaps
- 17.