Haskell in Motion An Introduction to FRP

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Haskell in Motion An Introduction to FRP

• Zhanyong Wan, Yale University
• 3/23/2001

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What Is FRP

• A Domain-Specific Language
• Not general-purpose
• For hybrid reactive systems
• Embedded in Haskell
• Isnt compiled by a compiler written in Haskell
• Isnt compiled into Haskell
• Is a collection of Haskell data types and
  functions

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General-Purpose vs. Domain-Specific

• General-purpose programming languages
• Want to solve all problems in one framework
• Have to make trade-offs when designing the
  language
• Expressiveness vs. Efficiency
• Do not possess domain knowledge
• Can not always make the right trade-offs
• Not abstract enough
• Not optimized for the domain

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Writing Animation in GP Languages

• 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
• A better way exists!

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Domain-Specific Languages

• DSLs
• Not intended to be general-purpose
• Aimed at solving problems in a particular domain
• Why DSLs?
• Designed with the problem domain in mind
• Capture the right abstraction
• Let the programmer concentrate on the problem,
  not low-level details
• Examples
• HTML, SQL, Shell in UNIX, Perl, Prolog

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Domain-Specific Languages (contd)

• Haskell as the vehicle for DSLs
• Flexible syntax
• User-defined operators, infix usage of functions
• Powerful type system
• Higher-order
• Control structures
• Referentially transparent imperative programming
  via monads
• Polymorphic
• Abstract code
• Reusable
• Declarative
• Quick prototyping
• Good for testing new language constructs and
  design ideas
• Embedded DSL inherits Haskells syntax and type
  system

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Reactive Programming

• Reactive systems
• Continuously react to stimuli
• Environment cannot wait
• Conceptually, values can change over continuous
  time
• Examples
• Interactive animation
• GUI
• Robotics
• Control systems
• Traditional languages do a poor job
• Discrete sampling
• The animation example

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Benefits of FRP

• High-level, declarative
• Concise code
• Executable spec
• new! Time is continuous

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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 GUI

moveXY (sin timeB) 0 charlotte charlotte
importBitmap charlotte.bmp
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Essential Haskell Features Used

• Higher-order functions
• Lazy streams
• Infix operators
• Type classes
• Multi-parameter type classes
• Functional dependency
• IO monad
• Interaction with the environment
• Memoization
• Monads
• Tasks

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Using FRP

• Resources
• http//haskell.org/frp
• Manual http//haskell.org/frp/manual.html
• How to use
• In the Zoo
• /usr/local/bin/rugs
• /usr/local/hugs/frp/
• /usr/local/hugs/frob/
• At home
• Copy the files from Zoo
• On Linux rugs
• On Windows hugs -98

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Basic Concepts

• Behaviors (Behavior i a)
• Reactive, continuous-time-varying values
• timeB Behavior i Time
• mouseB GuiInput i gt Behavior i Point2
• Events (Event i a)
• Streams of discrete event occurrences
• lbpE GuiInput i gt Event i ()
• Switching
• b1 till lbpE -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
• timeB Behavior i Time
• Input
• mouseB GuiInput i gt Behavior i Point2
• Integration
• integralB Behavior i FRPReal
• -gt Behavior i FRPReal
• (integralB timeB)
• Constant behaviors
• lift0 a -gt Behavior i a
• (lift0 5)

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Lifting

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

time
time
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Simplify the Syntax

• Can we make lifting implicit?
• lift2 () (lift0 1) (lift1 sin timeB)
• gt 1 sin timeB
• Sometimes, Yes!

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Demo Simple Behaviors
demo

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

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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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Demo Spatial Transformations
demo

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

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Demo Spatial Composition
demo

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

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Demo 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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Demo Recursive Behaviors (contd)
demo

• FRP Code
• moveTo po ball
• where
• ks 1
• kf 0.8
• d mouseB .-. po
• a ks d kf v
• v integralB a
• po vector2ToPoint2 integralB v
• Declarative
• Concise
• Recursive

d pm po a ksd kfv v ? a dt po ? v dt
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Events

• User events
• lbpE GuiInput i gt Event i ()
• Predicate events
• whenE Behavior i Bool -gt Event i ()
• Trivial events
• neverE Event i a

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Events (contd)

• Composite events
• (..) Event i a -gt Event i a -gt Event i a
• bothE Event i a -gt Event i b -gt Event i
  (a,b)
• filterE Event i a -gt (a -gt Bool) -gt Event i a
• (gt) Event i a -gt (a -gt b) -gt Event i b
• (-gt) Event i a -gt b -gt Event i b
• e -gt b e gt const b
• onceE Event i a -gt Event i a
• accumE a -gt Event i (a-gta) -gt Event i a
• snapshotE Event i a -gt Behavior i b
• -gt Event i (a,b)

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Switching

• Mode switching
• A common pattern in reactive systems
• Till
• till Behavior i a -gt Event i (Behavior i a)
• -gt Behavior i a
• Switch
• switch Behavior i a -gt Event i (Behavior i a)
• -gt Behavior i a
• Higher-order events
• Event algebra

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Demo Switching
demo

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

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Demo Event Merging
demo

• Making choices
• main9 animate
• withColor (green switch
• (lbpE -gt blue .. rbpE -gt red))
• mouseBall
• Higher-order events help

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Other Demos
demo

• Paddle ball
• Simulates robots
• Large
• 100 pure FRP

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Inside Haskell the Numeric
demo

• Case study
• f Int -gt Bool
• g Double -gt Bool
• f 5 -- well-typed
• g 5 -- well-typed
• f 5.6 -- ill-typed!
• g 5.6 -- well-typed
• How does this work?
• 5 ?
• 5.6 ?
• No C/Java style implicit coercion in Haskell
• 5 Int ?
• 5 Double ?

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Inside Haskell the Numeric (contd)

• Numbers are polymorphic!
• 5 Num a gt a
• 5.6 Fractional a gt a
• Numeric operators are polymorphic too
• () Num a gt a -gt a -gt a
• sin Floating a gt a -gt a
• Numeric classes
• class Num a
• class Num a gt Fractional a
• class Fractional a gt Floating a
• instance Num Int/Integer/Float/Double/
  ...
• instance Fractional Float/Double/...
• instance Floating Float/Double/...

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How Does This Work?

• Numbers are polymorphic
• 5 Num a gt a
• Haskells open-world assumption
• always possible to add new instances to a class
• Numeric literals must work for new Num instances!
• Binary numbers
• data Bit Zero One
• newtype Bin Bin Bit
• instance Num Bin
• Should accept 5 where a Bin is expected!
• But how?

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Inside Haskell the Numeric (contd)
demo

• Haskell treats numbers in a special way
• 5 is shorthand for fromInteger 5
• 5.6 is shorthand for fromRational 5.6
• And so on
• Implementing Bin
• instance Num Bin where
• ...
• fromInteger 0 Bin Zero
• fromInteger 1 Bin One
• fromInteger n
• n lt 0
• error "Bin negative number not
  supported."
• fromInteger n Bin (bits bit) where
• Bin bits fromInteger (n div 2)
• Bin bit fromInteger (n mod 2)

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Simplify Lifting Syntax

• Numeric literals lift themselves
• instance Num a gt Num (Behavior i a) where
• fromInteger lift0 . fromInteger
• instance Fractional a gt Fractional (Behavior i
  a) where
• fromRational lift0 . fromRational
• Numeric operators lift themselves too
• instance Num a gt Num (Behavior i a) where
• () lift2 ()
• instance Floating a gt Floating (Behavior i a)
  where
• sin lift1 sin
• Now possible
• lift2 () (lift0 1) (lift1 sin timeB)
• gt 1 sin timeB

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Overloading Not Always Possible

• Built-in operators/functions
• () Eq a gt a -gt a -gt Bool
• Lifted
• () Eq a gt
• Behavior i a -gt Behavior i a -gt Bool
• Not
• () Eq a gt
• Behavior i a -gt Behavior i a -gt Behavior i
  Bool
• The -suffix convention
• () Eq a gt
• Behavior i a -gt Behavior i a -gt Behavior i
  Bool
• User-defined operators/functions
• Polymorphic definition
• Explicit lifting

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End of Lecture

• Slides available at
• http//haskell.org/frp/frp-intro.ppt