CS429 Functional Programming, Syllabus

• Introduction to Haskell and Lazy, Functional Programming
  • tuples
  • polymorphism
  • higher order functions
  • strings & characters
  • lazy evaluation
• Datatypes
  • Data-Type declarations
  • Defining functions over datatypes using patterns,
  • Enumerations,
  • The Shape Datatype of the text.
• Programs and Proofs
  • Program Manipulation
  • Comparing the functional paradigm
  • Actions and Haskell,
  • Monads,
• Simple Graphics.
  • Using the graphics primitives,
  • Drawing Primitive Shapes,
  • Sierpinski’s Triangle,
  • Snow-flake,
  • Coordinate Systems,
  • Position independent shapes,
  • Drawing the Shape Data-type.
• Polymorphism
  • Polymorphic Functions,
  • Polymorphic datatypes,
  • Type Constructors define polymorphic Constructor functions,
  • Recursive datatypes,
  • Higher Order functions,
  • Perimeters of Shapes.
• Trees
  • Kinds of trees - branching factor,
  • functions over trees,
  • patterns of recursion - the fold for trees,
  • Arithmetic expressions,
  • Infinite trees.
• Regions
  • Sets and characteristic functions,
  • Regions,
  • Is a point in a Region?,
  • Currying,
  • Sections,
  • Anonymous functions,
  • function composition.
• Pictures
  • Low level graphics bit-maps: G.Region,
  • From Region to G.Region,
  • Shape to G.Region,
  • Drawing G.Region,
  • Reactive Pictures.
• Proofs by Induction
  • Review of Proofs by calculation,
  • Structure of Proofs by induction over lists,
  • Proofs by induction with case analysis,
  • Proofs by structural Induction,
  • Proofs by induction over Trees.
  • Prooving two functions are equal.
  • Proving things about Monadic expressions
• The Haskell Class System
  • Classes as predicates on types
  • Instance declarations,
  • Inheritance and dependent classes,
  • Derived instances,
  • The Show class,
  • The Fix operator from homework #5.
• Simple Animations
  • Buffered graphics,
  • Animations in Haskell,
  • Complex animations,
  • Lifting primitives to animations,
  • Behaviors,
  • Type classes animations and Behaviors,
  • Time translation.
• Infinite Lists and Streams
  • Infinite lists v.s. Streams,
  • Normal order evaluation,
  • Recursive streams,
  • Stream Diagrams,
  • Lazy patterns,
  • Memoization,
  • Inductive properties of infinite lists.
• Reactive Animations
  • Simple Animations - Review.
  • Reactive animations.
  • Vocabulary for reactive animations
  • Introduction by Examples.
  • Implementation of behaviors and events.
• File IO, Channels and Concurrency
  • Files, Channels, and Handles.
  • IO exception handling.
  • First Class Channels.
  • Concurrency and ForkIO.
• Higher Order Types
  • Type constructors that take types as arguments.
  • Functor,
  • Monad,
  • MonadPlus and MonadZero.
• Functional Music
  • Haskore System.
  • The Music datatype.
  • MIDI Instruments.
  • Pitch & absolute Pitch.
  • Composing Music:
  • Delay,
  • Repeating,
  • Transposing.
  • Manipulating Music: Duration, Cutting, Reversing.
  • Percussion.
  • Presentation and the MIDI file format
• Interpreting Music
  • Performance
  • Linearizing music
  • MidiFile structure

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