# Service Equivalence via Multiparty Session Type Isomorphisms

## TL;DR

This paper introduces a novel approach using multiparty session type isomorphisms to determine service equivalence and facilitate adaptation in service-oriented architectures, leveraging trace semantics and equational theory.

## Contribution

It proposes a new formal framework for assessing service substitutability via MPST isomorphisms, including a constructive method for service adapter code.

## Key findings

- Develops a trace semantics-based approach for MPST isomorphisms
- Introduces an equational theory for MPST isomorphisms
- Enables formal assessment of service substitutability

## Abstract

This paper addresses a problem found within the construction of Service Oriented Architecture: the adaptation of service protocols with respect to functional redundancy and heterogeneity of global communication patterns. We utilise the theory of Multiparty Session Types (MPST). Our approach is based upon the notion of a multiparty session type isomorphism, utilising a novel constructive realisation of service adapter code to establishing equivalence. We achieve this by employing trace semantics over a collection of local types and introducing meta abstractions over the syntax of global types. We develop a corresponding equational theory for MPST isomorphisms. The main motivation for this line of work is to define a type isomorphism that affords the assessment of whether two components/services are substitutables, modulo adaptation code given software components formalised as session types.