Having Fun with Functions How you can use functions to: write interactive animation, control robots,

1
Having Fun with Functions How you can use
functions to write interactive
animation, control robots, and compose music.

• Zhanyong Wan, Yale UniversitySeptember, 2001
• Acknowledgement Part of the slides provided by
  Paul Hudak

2
Roadmap

• ? Programming languages research at Yale
• Introduction to Haskell
• Domain specific languages
• FRP
• Haskore
• Conclusions and video

3
Alan Perlis Epigrams in Programming

• A programming language is low level when its
  programs require attention to the irrelevant.
• If a listener nods his head when you're
  explaining your program, wake him up.
• Optimization hinders evolution.
• Once you understand how to write a program get
  someone else to write it.
• The use of a program to prove the 4-color theorem
  will not change mathematics - it merely
  demonstrates that the theorem, a challenge for a
  century, is probably not important to
  mathematics.
• There are two ways to write error-free programs
  only the third one works.
• A language that doesn't affect the way you think
  about programming, is not worth knowing.

4
PL Research at Yale

• Faculty members (a partial list)
• Paul Hudak functional programming (Haskell),
  domain specific languages, language theory.
• John Peterson functional programming (Haskell),
  domain specific languages, compilation
• Zhong Shao functional programming (ML), type
  theory, compilation techniques, proof-carrying
  code.
• Carsten Schuermann logical frameworks, theorem
  proving, type theory, functional programming.

5
Having Fun at Yale
audio

• John Peterson
• Rock climbing
• Skiing
• Kayaking
• Paul Hudak
• Music
• Soccer coaching
• Skiing
• Rock climbing
• Kayaking

6
Roadmap

• Programming languages research at Yale
• ? Introduction to Haskell
• Domain specific languages
• FRP
• Haskore
• Conclusions and video

7
Haskell by Examples

• Higher-order functions
• Functions are first-class values
• Currying
• max (Int,Int) ? Intmax (x,y) if x gt y then
  x else ymax(5,6) ? 6
• max Int ? (Int ? Int)max x y if x gt y then
  x else ymax 5 6 ? 6
• m5 Int ? Intm5 max 5 ltgt m5 y if 5 gt y
  then 5 else ym5 4 ? 5m5 6 ? 6

In C, this would be int max(int, int)
8
Haskell by Examples

• Recursion
• sum 0sum (xxs) x sum xs
• prod 1prod (xxs) x prod xs
• Higher-order functions improve modularization
• Modularization is the key to successful
  programming!
• fold f a afold f a (xxs) f x (fold f a
  xs)
• sum fold () 0
• prod fold () 1
• allTrue fold () True
• anyTrue fold () False

9
Haskell by Examples

• Lazy evaluation
• Call-by-need
• f x y if x gt 0 then x else y f e1 e2
• Infinite data structures
• ones 1 ones ? 1 1 1 1 1
• numsFrom n n numsFrom (n1) ? n n1
  n2 n3
• squares map (2) (numsFrom 0) ? 0 1 4
  9 16 25 36
• take 5 squares ? 0, 1, 4, 9, 16
• fib 1 1 zipWith () fib (tail fib) ?
  1 1 2 3 5 8 13 () 1 2
  3 5 8 13 21 ---------------------
  ----------------1 1 2 3 5 8 13 21
  34

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Haskell by Examples

• Lazy evaluation
• Another powerful tool for improving modularity
• sort xs take n xs smallest n x take n
  (sort x)
• Only practical for lazy languages
• Need-driven no unnecessary computation
• No large intermediate data structure

11
Haskell by Examples

• Advanced type systems
• Polymorphic
• zipWith ?a,b,c. (a?b?c) ? a ? b ? c
• Type inference
• zipWith f _ zipWith f _ zipWith f
  (xxs) (yys) f x y zipWith f xs ys
• a ? b ? c ? d refine ?a ? b ? e ? d
  refine ?(b ? e ? d) ? b ? e ? d rename
  ?(a ? b ? c) ? a ? b ? c

12
Roadmap

• Programming languages research at Yale
• Introduction to Haskell
• ? Domain specific languages
• FRP
• Haskore
• Conclusions and video

13
Animation in a General-Purpose Language

• Sketch of the code (taken from Elliotts Fran
  manual)
• allocate and initialize window, various drawing
  surfaces and bitmaps
• repeat until quit
• get time ( t )
• clear back buffer
• for each sprite (back to front)
• compute position, scale, etc. at t
• draw to back buffer
• flip back buffer to the screen
• deallocate bitmaps, drawing surfaces, window
• Lots of tedious, low-level code that you have to
  write yourself
• There is a better way!

14
We Need Domain Specificity

• A domain-specific language (or DSL) is a language
  that precisely captures a domain semantics no
  more, and no less.
• Examples
• SQL, UNIX shells, Perl, Prolog
• FRP, Haskore

15
Advantages of DSL Approach

• Programs in the target domain are
• more concise
• quicker to write
• easier to maintain
• easier to reason about
• can often be written by non-programmers

Contribute to higher programmer productivity
Dominant cost in large SW systems
Verification, transform- ation, optimization
These are the same arguments in favor of any
high-level language. But in addition
Helps bridge gap between developer and user
16
The Bottom Line

Conventional
Total SW Cost
Methodology

C2

Start
-
up
DSL
-
based

Costs

Methodology
C1



Software Life-Cycle
17
DSLs Allow Faster Prototyping
Using the Spiral Model of Software Development
specify
specify
design
design
build
test
test
build
With DSL
Without DSL
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Roadmap

• Programming languages research at Yale
• Introduction to Haskell
• Domain specific languages
• ? FRP
• Haskore
• Conclusions and video

19
Reactive Programming

• Reactive systems
• Continually react to stimuli
• Environment cannot wait system must respond
  quickly
• Run forever
• Examples
• Computer animation
• GUI
• Robotics
• Vision
• Control systems
• Real-time systems

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Functional Reactive Programming

• Functional Reactive Programming (FRP)
• Focuses on model instead of presentation
• Continuous time domain
• Discrete time domain
• Recursion higher-order functions
• Originally embedded in Haskell
• Continuous/discrete signals
• Behaviors values varying over time
• Events discrete occurrences
• Reactivity b1 until ev -gt b2
• Combinators until, switch, when, integral, etc

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What Is FRP Good for?

• Applications of FRP
• Fran Elliott and Hudak Interactive animation
• Frob Peterson, Hager, Hudak and Elliott
  Robotics
• FVision Reid, Peterson, Hudak and Hager Vision
• Frappé Courtney Java
• FranTk Sage, Fruit Courtney GUI

moveXY (sin time) 0 charlotte charlotte
importBitmap charlotte.bmp
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Basic Concepts

• Behaviors (Behavior a)
• Reactive, continuous-time-varying values
• time Behavior Time
• mouse Behavior Point2
• Events (Event a)
• Streams of discrete event occurrences
• lbp Event ()
• Switching
• b1 till lbp -gt b2
• Combinators
• Behaviors and events are both first-class
• Passed as arguments
• Returned by functions
• Composed using combinators

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Behaviors

• Time
• time Behavior Time
• Input
• mouse Behavior Point2
• Integration
• integral Behavior Double
• -gt Behavior Double
• (integral time)
• Constant behaviors
• lift0 a -gt Behavior a
• (lift0 5)

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Lifting

• Static value -gt behavior
• lift0 a -gt Behavior a
• lift1 (a -gt b) -gt Behavior a -gt Behavior b
• lift2 (a -gt b -gt c)
• -gt Behavior a -gt Behavior b -gt Behavior c
• ...
• Examples
• lift1 sin time
• ? sin time
• lift2 () (lift0 1) (lift1 sin time)
• ? 1 sin time

time
time
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Simple Behaviors
demo

• Hello, world!
• hello Behavior Picture
• hello text lift0 "Hello, world!"
• main1 animate hello
• Interaction mouse-following
• main2 animate moveTo mouse hello
• Time
• main3 animate text lift1 show time

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Geometry in FRP

• 2-D
• Points
• Vectors
• Common shapes
• Circle, line, polygon, arc, and etc
• Affine transformations
• Rotation
• Translation
• Reflection
• Scaling
• Shear
• Composition of the above
• 3-D as well

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Spatial Transformations
demo

• Spatial transformations -- dancing ball
• ball Behavior Picture
• ball withColor red stretch 0.1 circle
• wiggle, waggle
• Behavior Double -gt Behavior Double
• wiggle omega sin (omegatime)
• waggle omega cos (omegatime)
• main4 om1 om2 animate
• moveXY (wiggle om1) (waggle om2)
  
• moveTo mouse ball

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Spatial Composition
demo

• Spatial composition -- dancing ball text
• main5 animate moveTo mouse
• moveXY (wiggle 4) (waggle 4) ball over
• moveXY (wiggle 7) (waggle 3) hello

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Recursive Behaviors

• Damped motion of a mass dragged with a spring
• Integral equations
• Recursive

d pm po a ksd kfv v ? a dt po ? v dt
d
pm
v
po
ks d
-kf v
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Recursive Behaviors (contd)
demo

• FRP Code
• main6 animate
• moveTo po ball over withColor blue (line
  mouseB po)
• where
• ks 1
• kf 0.8
• d mouse .-. po
• a ks d kf v
• v integral a
• po vector2ToPoint2 integral v
• Declarative
• Concise
• Recursive

d pm po a ksd kfv v ? a dt po ? v dt
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Switching
demo

• Switching of behaviors
• color Behavior Color
• color red till lbp -gt blue
• mouseBall Behavior Picture
• mouseBall moveTo mouse stretch 0.5 circle
• main7 animate withColor color mouseBall
• Recursive switching
• cycle3 c1 c2 c3 c1 till lbp
• -gt cycle3 c2 c3 c1
• main8 animate
• withColor (cycle3 red green blue) mouseBall

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Paddle Ball in 17 Lines
video

• paddleball vel walls over paddle over pball
  velwalls let upper paint blue (translate (
  0,1.7) (rec 4.4 0.05))             left  paint
  blue (translate (-2.2,0) (rec 0.05
  3.4))            right paint blue (translate (
  2.2,0) (rec 0.05 3.4))         in upper over
  left over rightpaddle paint red (translate
  (fst mouse, -1.7) (rec 0.5 0.05))pball vel  
  let xvel    vel stepAccum xbounce -gtgt
  negate      xpos    integral xvel     
  xbounce when (xpos gt 2 xpos lt -2)     
  yvel    vel stepAccum ybounce -gtgt
  negate      ypos    integral yvel     
  ybounce when (ypos gt 1.5                  
  ypos between (-2.0,-1.5)                
         fst mouse between (xpos-0.25,xpos0.25))
    in paint yellow (translate (xpos, ypos) (ell
  0.2 0.2))x between (a,b) x gt a x lt b

33
Crouching Robots, Hidden Camera

• RoboCup
• Team controllers written in FRP
• Embedded robot controllers written in C(our
  goal use FRP instead)

camera
Team B controller
Team A controller
radio
radio
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A Point-tracking Control System

• Input
• xd, yd, ?d desired position heading
• x, y, ? actual position heading
• Output
• u forward speed
• v rotational speed

?d
(xd,yd)
u
?
v
(x,y)
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A Point-tracking System
video

• u u_d - k1 z1
• v k2 derivativeB theta_d dTheta - r1
  z1 - r2 z2
• dTheta lift1 normalizeAngle theta -
  theta_d
• u_d derivativeB x_d cos theta_d
  derivativeB y_d sin theta_d
• z1 (x x_d) cos theta (y y_d) sin
  theta
• z2 (x x_d) sin theta (y y_d) cos
  theta
• r1 ifZ (abs dTheta lt 0.01) 0 (u_d(1 -
  cos dTheta)/dTheta)
• r2 ifZ (abs dTheta lt 0.01) (-u_d)
  (-u_d sin dTheta / dTheta)

36
Roadmap

• Programming languages research at Yale
• Introduction to Haskell
• Domain specific languages
• FRP
• ? Haskore
• Conclusions and video

37
Haskore

• Motivation
• Traditional music notation has many limitations
• Unable to express a composers intentions.
• Biased toward music that is humanly performable.
• Unable to express notions of algorithmic
  composition.Haskore (Haskell Score) is a
  library of Haskellfunctions and datatypes for
  composing music.

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Basic Haskore Structure
type Pitch (PitchClass, Octave) data
PitchClass Cf C Cs Df D Ds Ef E
Es Ff F Fs Gf G Gs
Af A As Bf B Bs type Octave
Int data Music Note Pitch Dur --
a note Rest Dur -- a rest
Music Music -- sequential composition
Music Music -- parallel composition
Tempo Int Int Music -- scale the tempo
Trans Int Music -- transposition
Instr IName Music -- instrument
label type Dur Float -- in whole notes type
IName String type PName String
39
Gloveby Tom Makucevichwith help from Paul
HudakComposed using Haskore, a Haskell DSL,and
rendered using csound.
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Roadmap

• Programming languages research at Yale
• Introduction to Haskell
• Domain specific languages
• FRP
• Haskore
• ? Conclusions and video

41
Conclusions
video

• Haskell has changed the way many people think
  about programming. It is worth knowing!
• Functional programming community have some good
  ideas. Lets start using them!
• Functional programming is fun!
• Check out our web-site!
• Haskell http//haskell.org/
• FRP http//haskell.org/frp/
• Haskore http//haskell.org/haskore/
• Hugs http//haskell.org/hugs/
• Life at Yale is fun! (See the video)