Static typing for a faulty lambda calculus

David P. Walker, Lester Mackey, Jay Ligatti, George A. Reis, David I. August

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


A transient hardware fault occurs when an energetic particle strikes a transistor, causing it to change state. These faults do not cause permanent damage, but may result in incorrect program execution by altering signal transfers or stored values. While the likelihood that such transient faults will cause any significant damage may seem remote, over the last several years transient faults have caused costly failures in high-end machines at America Online, eBay, and the Los Alamos Neutron Science Center, among others [6, 44, 15]. Because susceptibility to transient faults is proportional to the size and density of transistors, the problem of transient faults will become increasingly important in the coming decades. This paper defines the first formal, type-theoretic framework for studying reliable computation in the presence of transient faults. More specifically, it defines λ zap, a lambda calculus that exhibits intermittent data faults. In order to detect and recover from these faults, λ zap programs replicate intermediate computations and use majority voting, thereby modeling software-based fault tolerance techniques studied extensively, but informally [10, 20, 30, 31, 32, 33, 41]. To ensure that programs maintain the proper invariants and use λ zap primitives correctly, the paper defines a type system for the language. This type system guarantees that well-typed programs can tolerate any single data fault. To demonstrate that λ zap can serve as an idealized typed intermediate language, we define a type-preserving translation from a standard simply-typed lambda calculus into λ zap.

Original languageEnglish (US)
Pages (from-to)38-49
Number of pages12
JournalSIGPLAN Notices (ACM Special Interest Group on Programming Languages)
Issue number9
StatePublished - Sep 2006

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Graphics and Computer-Aided Design


  • Fault tolerance
  • Lambda calculus
  • Reliable computing
  • Soft faults
  • Transient hardware faults
  • Type systems
  • Typed intermediate languages


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