- Cite this paper as:
- Ahn K.Y., Sheard T., Fiore M., Pitts A.M. (2013) System Fi. In: Hasegawa M. (eds) Typed Lambda Calculi and Applications. TLCA 2013. Lecture Notes in Computer Science, vol 7941. Springer, Berlin, Heidelberg
We introduce a foundational lambda calculus, System Fi, for studying programming languages with term-indexed datatypes – higher-kinded datatypes whose indices range over data such as natural numbers or lists. System Fi is an extension of System Fω that introduces the minimal features needed to support term-indexing. We show that System Fi provides a theory for analysing programs with term-indexed types and also argue that it constitutes a basis for the design of logically-sound light-weight dependent programming languages. We establish erasure properties of Fi-types that capture the idea that term-indices are discardable in that they are irrelevant for computation. Index erasure projects typing in System Fi to typing in System Fω. So, System Fi inherits strong normalization and logical consistency from System Fω.
Keywordsterm-indexed data types generalized algebraic data types higher-order polymorphism type-constructor polymorphism higher- kinded types impredicative encoding strong normalization logical consistency
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