DLπ is an Agda formalization of the linear π-calculus with dependent pairs. It allows for the modeling of structured conversations in which processes and types depend on the content of exchanged messages.
This folder contains the full formalization of DLπ. Below is an outline of the files and of their purpose. While looking at the code, use of Fira Code is recommended as it contains several ligatures that make the Agda code much more pleasant to read.
- Language.agda Data types for representing
terms and processes. Search no further if you're looking
for
Name,TermandProcess. This module also includes the definition ofMultiplicity,TypeandContext, as well as theNullpredicate and theScaleandSplitrelations for multiplicities, types and contexts. - Congruence.agda Definition of structural pre-congruence and related type preservation result.
- Reduction.agda Definition of labelled reduction and corresponding typing preservation result.
- Common.agda Some general purpose functions, properties and axioms (extensionality).
- Split.agda Properties of splitting for multiplicities, types and contexts.
- Scale.agda Properties of scaling for multiplicities, types and contexts.
- Swap.agda Some auxiliary properties about swapping names in a context.
- Weaken.agda Definition of
Weaken, weakening and strengthening properties for terms and processes. - Substitution.agda Type-preserving substitution of terms for variables in processes.
- Lookup.agda Proof that a name not occurring in a well-typed process has an unrestricted type.
- PrefixNormalForm.agda Proof that every process can be rewritten in prefix-normal-form using structural pre-congruence.
- PrefixedBy.agda Predicate that holds when a process has an unguarded input/output prefix for a given channel.
- ReducibleNormalForm.agda Proof that every process with both an input and an output prefix for a given channel can be rewritten in reducible normal form using structural pre-congruence. In this normal form, the two prefixes sit next to each other, so the process is ready to reduce.
- Results.agda This module collects all the properties stated in Section 4 of the paper. Compared to their formulation in the paper, the statements are slightly differnt and/or simpler to account for the fact that terms and processes are intrinsically typed.
- Main.agda Container for a few examples, but mostly useful as root file that triggers the type checking of everything.
This folder contains encoding functions from (dependent) session type languages to DLπ types. The folder is organized as follows:
- Common.agda imports the extensionality
principle and defines the
Typedata type for representing finite DLπ types. - FinLabels contains the encoding of
non-dependent, labeled session types with n-ary branches and
choices. Labels are elements of the
Fin ndata type. - LinearLogic contains the encoding of dependent session types à la Toninho, Caires & Pfenning 2011. These session types subsume the original non-dependent ones by Honda.
- LabelDependent contains the encoding of label-dependent session types defined by Thiemann & Vasconcelos 2020.
Each subfolder is organized as follows:
Types.agdadefines session types and auxiliary data types, including the notion of bisimilarity used for proving that decoding is the inverse of encoding.Encoding.agdadefines a predicate onTypethat characterizes the image of the encoding.Encode.agdadefines the encoding function and proves that it satisfies theEncodingpredicate.Decode.agdadefines the decoding function.Proofs.agdacontains the proofs that encoding and decoding are one the inverse of the other modulo bisimilarity.Equalities.agda, if present, contains examples illustrating the fact that the encoding function is not injective.
The formalization of DLπ is described in the paper A Dependently Typed Linear π-Calculus in Agda, which appears in the proceedings of PPDP 2020. A preprint version of the paper can be found here.