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Typing Composite Subjects

Luca Aceto, Daniele Gorla, Stian Lybech

TL;DR

The purpose of this paper is to address the question of how to type composite subjects in a general fashion and shows an encoding in epi of a minimal OO language whose ``expectable'' type system exactly corresponds to the one induced by the proposed type system via the encoding.

Abstract

Many type systems have been presented in the literature for variants of the pi-calculus, but none of them are able to handle composite subjects such as those found in the language epi, which features polyadic synchronisation. The purpose of this paper is to address the question of how to type composite subjects in a general fashion. We assess the validity of our proposal by first proving the standard correctness results for a type system (i.e., subject reduction and type safety). Then, we follow the path opened by Sangiorgi in 1998 and show an encoding in epi of a minimal OO language called WC (While with \Classes) whose ``expectable'' type system exactly corresponds to the one induced by ours via the encoding. This comparison contributes to understanding the relationship between our types and conventional types for OO languages.

Typing Composite Subjects

TL;DR

The purpose of this paper is to address the question of how to type composite subjects in a general fashion and shows an encoding in epi of a minimal OO language whose ``expectable'' type system exactly corresponds to the one induced by the proposed type system via the encoding.

Abstract

Many type systems have been presented in the literature for variants of the pi-calculus, but none of them are able to handle composite subjects such as those found in the language epi, which features polyadic synchronisation. The purpose of this paper is to address the question of how to type composite subjects in a general fashion. We assess the validity of our proposal by first proving the standard correctness results for a type system (i.e., subject reduction and type safety). Then, we follow the path opened by Sangiorgi in 1998 and show an encoding in epi of a minimal OO language called WC (While with \Classes) whose ``expectable'' type system exactly corresponds to the one induced by ours via the encoding. This comparison contributes to understanding the relationship between our types and conventional types for OO languages.

Paper Structure

This paper contains 13 sections, 26 theorems, 26 equations, 10 figures.

Table of Contents

  1. Introduction
  2. On typing polyadic subjects
  3. The $\prescript{e}{}{\pi}$-calculus
  4. A simple type system for $\prescript{e}{}{\pi}$
  5. The language of types
  6. The type system
  7. Run-time errors, Safety, and Soundness results
  8. The WC language
  9. Syntax and (big-step) operational semantics
  10. Typed WC
  11. Encoding WC in $\prescript{e}{}{\pi}$
  12. On the quality of the encoding
  13. Conclusion and future works

Key Result

Theorem 1

If $\Gamma \vdash P$ then $\text{\normalfont\sffamily NSafe}_{\Gamma}\left(P\right)$.

Figures (10)

  • Figure 1: Early labelled semantics for the $\prescript{e}{}{\pi}$-calculus.
  • Figure 2: Type rules for values, subject vectors, and processes.
  • Figure 3: Error-predicate for processes.
  • Figure 4: The syntax of WC.
  • Figure 5: Semantics of WC declarations.
  • ...and 5 more figures

Theorems & Definitions (44)

  • Definition 1: Types
  • Theorem 1: Safety
  • proof
  • Definition 2: Well-typed label
  • Theorem 2: Subject reduction
  • Lemma 1: Weakening
  • Lemma 2: Strengthening
  • Definition 3: Well-typed substitution
  • Lemma 3: Substitution
  • Lemma 4: Safety for expressions
  • ...and 34 more