Strong Normalization of the Typed λws-Calculus
- Cite this paper as:
- David R., Guillaume B. (2003) Strong Normalization of the Typed λws-Calculus. In: Baaz M., Makowsky J.A. (eds) Computer Science Logic. CSL 2003. Lecture Notes in Computer Science, vol 2803. Springer, Berlin, Heidelberg
The λws-calculus is a λ-calculus with explicit substitutions introduced in . It satisfies the desired properties of such a calculus: step by step simulation of β, confluence on terms with meta-variables and preservation of the strong normalization. It was conjectured in  that simply typed terms of λws are strongly normalizable. This was proved in  by Di Cosmo & al. by using a translation of λws into the proof nets of linear logic. We give here a direct and elementary proof of this result. The strong normalization is also proved for terms typable with second order types (the extension of Girard’s system F). This is a new result.
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