The completeness of typing for context-semantics

Journal article, 2007

We present a variation of Hindley's completeness theorem for simply typed lambda-calculus. It is based on a Kripke semantics where the worlds are contexts, called context-semantics. This variation was obtained indirectly by simplifying an analysis of a fragment of polymorphic lambda-calculus [2]. We relate in this way works done in proof theory [4, 14] with a fundamental result in lambda-calculus.