The Completeness of Typing for Context-Semantics

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.