Arithmetical proofs of strong normalization results for symmetric lambda calculi

A revised completeness result for the simply typed λµ-calculus using realizability semantics.. Karim Nour,

The Main Theorem Putting together the matching between LO β-steps and mul- tiplicative transitions (Theorem 2), the quadratic bound on the exponentials via the multiplicatives

The proof of Theorem 65 consists of two parts: proving first that the untyped µµ ′ -calculus is strongly normalizing, the demonstration of the strong normalization of the typed case

De Groote (2001) introduced the typed λµ ∧∨ -calculus to code the classical natural deduction system, and showed that it enjoys the main important properties: the strong

Since it has been understood that the Curry-Howard isomorphism relating proofs and programs can be extended to classical logic, various systems have been introduced: the λ c

The strong normalization of a typed λµ-calculus can be deduced from the one of the corresponding typed λ-calculus by using CPS translations. See, for example, [14] for such

In section 5, we give an example showing that the proofs of strong normalization using candidates of reducibility must somehow be different from the usual ones and we show that, in

This follows immediately from the strong normalization of the calculus of substitution (i.e. all the rules except b) which is proved in [4]2. We have stated the previous lemma in