Type Systems for Distributed Programs: Components and Sessions by Ornela Dardha

Author:Ornela Dardha
Language: eng
Format: epub
Publisher: Atlantis Press, Paris

The following lemma gives an important result that relates the encoding of dual session types to dual linear -calculus channel types.

Lemma 6.3.7

(Encoding of Dual Session Types) If , then .

Proof

The proof is done by induction on the structure of session type T. We use the duality of session types defined in Fig. 5.​5 and the duality of standard -types defined in Fig. 4.​7.

By (E-End) we have and . It follows by duality of .

By (E-Out) we have . By duality of session types we have . By (T-In) we have . We conclude by the duality of -types.

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