Mœbius: metaprogramming using contextual types: the stage where system f can pattern match on itself

Jang, Junyoung; Gélineau, Samuel; Monnier, Stefan; Pientka, Brigitte

doi:10.1145/3498700

Cited by 14 publications

(18 citation statements)

References 26 publications

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“…We believe it is not difficult to apply polymorphic context types to dual-context CMTT, although we do not explore it in this paper. CMTT provides a basis for several metaprogramming languages [9,20,26]. We expect that λ ∀[] will contribute to future designs of metaprogramming languages as well.…”

Section: Related Workmentioning

confidence: 99%

“…Pattern matching against code Analytic metaprogramming that allows pattern matching against code values is considered beneficial and explored recently [18,28,9]. Especially, Moebius [9] provides a contextual modal type system capable of pattern matching against open code with polymorphic types. It should be feasible to extend λ ∀[] to allow pattern matching against code values, but it is left for future work.…”

Section: Related Workmentioning

confidence: 99%

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Contextual Modal Type Theory with Polymorphic Contexts

Murase

Nishiwaki²,

Igarashi

2023

Lecture Notes in Computer Science

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Modal types—types that are derived from proof systems of modal logic—have been studied as theoretical foundations of metaprogramming, where program code is manipulated as first-class values. In modal type systems, modality corresponds to a type constructor for code types and controls free variables and their types in code values. Nanevski et al. have proposed contextual modal type theory, which has modal types with fine-grained information on free variables: modal types are explicitly indexed by contexts—the types of all free variables in code values.This paper presents $$\lambda _{\forall []}$$ λ ∀ [ ] , a novel extension of contextual modal type theory with parametric polymorphism over contexts. Such an extension has been studied in the literature but, unlike earlier proposals, $$\lambda _{\forall []}$$ λ ∀ [ ] is more general in that it allows multiple occurrence of context variables in a single context. We formalize $$\lambda _{\forall []}$$ λ ∀ [ ] with its type system and operational semantics given by $$\beta $$ β -reduction and prove its basic properties including subject reduction, strong normalization, and confluence. Moreover, to demonstrate the expressive power of polymorphic contexts, we show a type-preserving embedding from a two-level fragment of Davies’ $$\lambda _{\bigcirc }$$ λ ◯ , which is based on linear-time temporal logic, to $$\lambda _{\forall []}$$ λ ∀ [ ] .

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Contextual Modal Type Theory with Polymorphic Contexts

Murase

Nishiwaki²,

Igarashi

2023

Lecture Notes in Computer Science

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“…There are several modal multi-stage systems which support runtime code generation but not staged compilation, such as those based on S4 modalities (e.g. [Davies and Pfenning 2001]) or contextual modalities ( [Jang et al 2022]).…”

Section: Related Workmentioning

confidence: 99%

Staged compilation with two-level type theory

Kovács

2022

Proc. ACM Program. Lang.

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The aim of staged compilation is to enable metaprogramming in a way such that we have guarantees about the well-formedness of code output, and we can also mix together object-level and meta-level code in a concise and convenient manner. In this work, we observe that two-level type theory (2LTT), a system originally devised for the purpose of developing synthetic homotopy theory, also serves as a system for staged compilation with dependent types. 2LTT has numerous good properties for this use case: it has a concise specification, well-behaved model theory, and it supports a wide range of language features both at the object and the meta level. First, we give an overview of 2LTT's features and applications in staging. Then, we present a staging algorithm and prove its correctness. Our algorithm is "staging-by-evaluation", analogously to the technique of normalization-by-evaluation, in that staging is given by the evaluation of 2LTT syntax in a semantic domain. The staging algorithm together with its correctness constitutes a proof of strong conservativity of 2LLT over the object theory. To our knowledge, this is the first description of staged compilation which supports full dependent types and unrestricted staging for types.

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“…In recent years, modal type systems based on this dual-context style have received renewed attention and provided insights into a wide range of seemingly unconnected areas: from reasoning about universes in homotopy type theory [28,36] to mechanizing meta-theory [34,35], to reasoning about effects [38], and meta-programming [25]. This line of work builds on the dual-context formulation of Pfenning and Davies.…”

Section: Introductionmentioning

confidence: 99%

A Categorical Normalization Proof for the Modal Lambda-Calculus

Hu¹,

Pientka²

2023

Electronic Notes in Theoretical Informatics and Computer Science

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We investigate a simply typed modal $\lambda$-calculus, $\lambda^{\to\square}$, due to Pfenning, Wong and Davies, where we define a well-typed term with respect to a context stack that captures the possible world semantics in a syntactic way. It provides logical foundation for multi-staged meta-programming. Our main contribution in this paper is a normalization by evaluation (NbE) algorithm for $\lambda^{\to\square}$ which we prove sound and complete. The NbE algorithm is a moderate extension to the standard presheaf model of simply typed $\lambda$-calculus. However, central to the model construction and the NbE algorithm is the observation of Kripke-style substitutions on context stacks which brings together two previously separate concepts, structural modal transformations on context stacks and substitutions for individual assumptions. Moreover, Kripke-style substitutions allow us to give a formulation for contextual types, which can represent open code in a meta-programming setting. Our work lays the foundation for extending the logical foundation by Pfenning, Wong, and Davies towards building a practical, dependently typed foundation for meta-programming.

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Mœbius: metaprogramming using contextual types: the stage where system f can pattern match on itself

Cited by 14 publications

References 26 publications

Contextual Modal Type Theory with Polymorphic Contexts

Contextual Modal Type Theory with Polymorphic Contexts

Staged compilation with two-level type theory

A Categorical Normalization Proof for the Modal Lambda-Calculus

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