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- 2009 (2) (remove)

#### Keywords

- Lambda-Kalkül (2)
- Formale Semantik (1)
- Kontextuelle Gleichheit (1)
- Nichtdeterminismus (1)
- Operationale Semantik (1)
- Programmiersprache (1)
- contextual equivalence (1)
- non-determinism (1)
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- Counterexamples to simulation in non-deterministic call-by-need lambda-calculi with letrec (2009)
- This note shows that in non-deterministic extended lambda calculi with letrec, the tool of applicative (bi)simulation is in general not usable for contextual equivalence, by giving a counterexample adapted from data flow analysis. It also shown that there is a flaw in a lemma and a theorem concerning finite simulation in a conference paper by the first two authors.

- A finite simulation method in a non-deterministic call-by-need calculus with letrec, constructors and case (2009)
- The paper proposes a variation of simulation for checking and proving contextual equivalence in a non-deterministic call-by-need lambda-calculus with constructors, case, seq, and a letrec with cyclic dependencies. It also proposes a novel method to prove its correctness. The calculus’ semantics is based on a small-step rewrite semantics and on may-convergence. The cyclic nature of letrec bindings, as well as nondeterminism, makes known approaches to prove that simulation implies contextual equivalence, such as Howe’s proof technique, inapplicable in this setting. The basic technique for the simulation as well as the correctness proof is called pre-evaluation, which computes a set of answers for every closed expression. If simulation succeeds in finite computation depth, then it is guaranteed to show contextual preorder of expressions.