Contents of the Course

• Foundations of functional programming:
  • Expressions and their evaluation
  • Function definition by recursive equations
  • Pattern matching
  • Evaluation, reduction, normalform
  • Higher order functions, currying
  • Polymorphism
  • Type correctness and type inference
• Types:
  • Algebraic data types
  • Standard data types (Lists, Cartesian products, lifting) and
    standard functions (fold, map, filter)
  • Trees
  • Graphs
• Structuring and Specification:
  • Modules
  • Interfaces
  • Abstract data types
  • Signatures and axioms
• Theoretic aspects:
  • Denotational semantics
  • Referential transparency
  • Term rewriting and lambda calculus
  • Proof by structural induction
  • Program development by transformation
• Advanced functional programming:
  • Monads
  • Funktional I/O with Monads
  • Overloading, type classes, constructor classes
  • Polymorphic recursion
  • Strict and lazy evaluation
  • Infinite data types, co-induction
  • Extensions of the type system