Elaboration in Dependent Type Theory

Moura, Leonardo de; Avigad, Jeremy; Kong, Soonho; Roux, Cody

doi:10.48550/arxiv.1505.04324

Cited by 4 publications

(4 citation statements)

References 24 publications

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“…To the best of our knowledge, none of the ITPs listed in the introduction support hygienic elaboration extensions of this kind, but we will show how to extend their common elaboration scheme in that way in this section. Elaboration 11 can be thought of as a function elabTerm : Syntax → ElabM Expr in an appropriate monad ElabM 12 from a (concrete or abstract) surface-level syntax tree type Syntax to a fully-specified core term type Expr [dMAKR15]. We have presented the (concrete) definition of Syntax in Lean 4 in Section 4; the particular definition of Expr is not important here.…”

Section: Integrating Macros Into Elaborationmentioning

confidence: 99%

Beyond Notations: Hygienic Macro Expansion for Theorem Proving Languages

Ullrich¹,

Moura²

2022

Logical Methods in Computer Science

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In interactive theorem provers (ITPs), extensible syntax is not only crucial to lower the cognitive burden of manipulating complex mathematical objects, but plays a critical role in developing reusable abstractions in libraries. Most ITPs support such extensions in the form of restrictive "syntax sugar" substitutions and other ad hoc mechanisms, which are too rudimentary to support many desirable abstractions. As a result, libraries are littered with unnecessary redundancy. Tactic languages in these systems are plagued by a seemingly unrelated issue: accidental name capture, which often produces unexpected and counterintuitive behavior. We take ideas from the Scheme family of programming languages and solve these two problems simultaneously by proposing a novel hygienic macro system custom-built for ITPs. We further describe how our approach can be extended to cover type-directed macro expansion resulting in a single, uniform system offering multiple abstraction levels that range from supporting simplest syntax sugars to elaboration of formerly baked-in syntax. We have implemented our new macro system and integrated it into the new version of the Lean theorem prover, Lean 4. Despite its expressivity, the macro system is simple enough that it can easily be integrated into other systems.

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Section: Integrating Macros Into Elaborationmentioning

confidence: 99%

Beyond Notations: Hygienic Macro Expansion for Theorem Proving Languages

Ullrich¹,

Moura²

2022

Logical Methods in Computer Science

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“…Other Proof Assistants. Other languages/proof assistants based on intensional type theory include Coq [31], Idris [8], Lean [11] and Matita [7]. All of them handle code that we created based on Example 2.1 adequately, but they fail to type check code that we created based on Example 2.2.…”

Section: Lemma 52 the Rule Schemas Defined In §33 Respect The Open-wo...mentioning

confidence: 99%

Practical dependent type checking using twin types

Juan

Danielsson

2020

Proceedings of the 5th ACM SIGPLAN International Workshop on Type-Driven Development

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People writing proofs or programs in dependently typed languages can omit some function arguments in order to decrease the code size and improve readability. Type checking such a program involves filling in each of these implicit arguments in a type-correct way. This is typically done using some form of unification.One approach to unification, taken by Agda, involves sometimes starting to unify terms before their types are known to be equal: in some cases one can make progress on unifying the terms, and then use information gleaned in this way to unify the types. This flexibility allows Agda to solve implicit arguments that are not found by several other systems. However, Agda's implementation is buggy: sometimes the solutions chosen are ill-typed, which can cause the type checker to crash.With Gundry and McBride's twin variable technique one can also start to unify terms before their types are known to be equal, and furthermore this technique is accompanied by correctness proofs. However, so far this technique has not been tested in practice as part of a full type checker.We have reformulated Gundry and McBride's technique without twin variables, using only twin types, with the aim of making the technique easier to implement in existing type checkers (in particular Agda). We have also introduced a type-agnostic syntactic equality rule that seems to be useful in practice. The reformulated technique has been tested in a type checker for a tiny variant of Agda. This type checker handles at least one example that Coq, Idris, Lean and Matita cannot handle, and does so in time and space comparable to that used by Agda. This suggests that the reformulated technique is usable in practice.

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“…The Lean mathematical library mathlib [23] has settled on the use of the typeclass [25] pattern for representing structures, implemented through Lean's mechanism of instance parameters [7,8]. Typeclasses were invented by Wadler to provide ad hoc polymorphism in Haskell [25].…”

Section: Introductionmentioning

confidence: 99%

Use and abuse of instance parameters in the Lean mathematical library

Baanen¹

2022

Preprint

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The Lean mathematical library mathlib features extensive use of the typeclass pattern for organising mathematical structures, based on Lean's mechanism of instance parameters. Related mechanisms for typeclasses are available in other provers including Agda, Coq and Isabelle with varying degrees of adoption. This paper analyses representative examples of design patterns involving instance parameters in the current Lean 3 version of mathlib, focussing on complications arising at scale and how the mathlib community deals with them.

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Elaboration in Dependent Type Theory

Cited by 4 publications

References 24 publications

Beyond Notations: Hygienic Macro Expansion for Theorem Proving Languages

Beyond Notations: Hygienic Macro Expansion for Theorem Proving Languages

Practical dependent type checking using twin types

Use and abuse of instance parameters in the Lean mathematical library

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