Abstract
Structural language features are those that introduce new kinds of declarations as opposed to those that only add expressions. They pose a significant challenge when representing languages in meta-languages such as standard formats like OMDoc or logical frameworks like LF. It is desirable to use shallow representations where a structural language feature is represented by the analogous feature of the meta-language, but the richness of structural language features in practical languages makes this difficult. Therefore, the current state of the art is to encode unrepresentable structural language features in terms of more elementary ones, but that makes the representations difficult to reuse and verify. This challenge is exacerbated by the fact that many languages allow users to add new structural language features that are elaborated into a small trusted kernel, which allows for a large and growing set of features.
In this paper we extend the Mmt representation framework with a generic concept of structural features. This allows defining exactly the language features needed for elegant shallow embeddings of object languages. The key achievement here is to make this concept expressive enough to cover complex practical features while retaining the simplicity of existing meta-languages. We exemplify our framework with representations of various important structural features including datatype definitions and theory instantiations.
The authors were supported by DFG grant RA-1872/3-1, KO 2428/13-1 OAF and EU grant Horizon 2020 ERI 676541 OpenDreamKit.
D. Müller—The author was supported by a postdoc fellowship of the German Academic Exchange Service (DAAD).
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Notes
- 1.
These listings show our actual formalizations in concrete syntax and use a few semantically inessential features that go beyond the syntax introduced in Fig. 1. Most notably, # introduces a notation and
separates declaration components. - 2.
For notational simplicity, we only consider the case of unary constructors; the generalization to n-ary constructors is clear.
- 3.
For simplicity, we restrict ourselves to the case where \(D_{ind}\) elaborates into a single inductive type (ignoring mutual induction).
separates declaration components.References
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Müller, D., Rabe, F., Rothgang, C., Kohlhase, M. (2020). Representing Structural Language Features in Formal Meta-languages. In: Benzmüller, C., Miller, B. (eds) Intelligent Computer Mathematics. CICM 2020. Lecture Notes in Computer Science(), vol 12236. Springer, Cham. https://doi.org/10.1007/978-3-030-53518-6_13
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