Tutorial 1 – 18.10.2006

Lambda Calculus

  • Lambda terms

    • inductive definition
    • recursive functions: size, free variables, closed terms
    • structural induction: proving a simple property |fv(t)| <= size(t)
    • concrete syntax: strings of characters
    • abstract syntax: abstract syntax trees
  • Reduction relation (call-by-value)

    • inductive definition
    • values = abstractions
    • deterministic – without proof
      (i.e induction on the structure of the derivation)
  • Evaluation Relation

    • reflexive transitive closure of the reduction relation
    • success evaluation -> value
    • stuckness – only for open terms here
    • divergence – omega

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