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Comparing type systems for deadlock freedom 1 1 Introduction 1 2 Session π-calculus 4 2.1 Process model 4 2.2 Type system 5 2.3 Deadlock freedom 6 3 Two approaches to deadlock freedom 7 3.1 Linear logic foundations of session types 7 3.2 Deadlock freedom by encodability 8 3.2.1 The dyadic π-calculus 8 Syntax. 8 Reduction semantics. 9 3.2.2 Types with usages 9 3.2.3 Properties 12 3.2.4 On deadlock freedom by encoding 13 4 Separating classes of deadlock-free typed processes 14 4.1 Classes of deadlock-free processes 14 4.1.1 The classes L and K 14 4.1.2 The class μK 15 4.2 Main results 16 5 Translating K into L 18 5.1 Characteristic processes and catalyzers 19 5.2 Translating K into L 20 5.2.1 Properties 22 5.3 Discussion: translating K into L exploiting value dependencies 23 6 Discussion 25 7 Related work 26 8 Concluding remarks 27 Declaration of competing interest 27 Acknowledgements 28 Appendix A Omitted proofs for § 4 28 A.1 Proof of Theorem 4.1 (Page 18) 28 Appendix B Omitted proofs for § 5 33 B.1 Proof of Lemma 5.1 33 B.2 Proof of Theorem 5.1 34 B.3 Proof of Theorem 5.2 (Page 23) 37 References 42