On weak and strong normalisations

With the help of continuations, we first construct a transformation T which transforms every Aterm t into a AJ-term T(t). Then we apply the conservation theorem in A-calculus to show that t is strongly normalisable if T(t) has a /J-normal form. In this way, we succeed in establishing the equivalence between weak and strong normalisation theorems in various typed A-calculi. This not only enhances the understanding between weak and strong normalisations, but also presents an elegant approach to proving strong normalisation theorems via the notion of weak normalisations.

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