Towards Generic Programming with Sized Types

Abel, Andreas

doi:10.1007/11783596_4

Cited by 3 publications

(2 citation statements)

References 37 publications

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“…Another notion of polarity arises from considering the (co-, contra-, in-)variance of type constructors. It is used by Abel [2006] to give a version of F ω with subtyping, and Dolan and Mycroft [2017] apply this version of polarity to give a complete type inference algorithm for an ML-style language with subtyping. Our polarized subtyping judgment is closest in spirit to the work of Zeilberger [2009].…”

Section: Discussion and Related Workmentioning

confidence: 99%

Sound and complete bidirectional typechecking for higher-rank polymorphism with existentials and indexed types

Dunfield

Krishnaswami

2019

Proc. ACM Program. Lang.

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Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its applicability to a variety of type systems, its error reporting, and its ease of implementation. Following principles from proof theory, bidirectional typing can be applied to many type constructs. The principles underlying a bidirectional approach to indexed types (generalized algebraic datatypes) are less clear. Building on proof-theoretic treatments of equality, we give a declarative specification of typing based on focalization. This approach permits declarative rules for coverage of pattern matching, as well as support for first-class existential types using a focalized subtyping judgment. We use refinement types to avoid explicitly passing equality proofs in our term syntax, making our calculus similar to languages such as Haskell and OCaml. We also extend the declarative specification with an explicit rules for deducing when a type is principal, permitting us to give a complete declarative specification for a rich type system with significant type inference. We also give a set of algorithmic typing rules, and prove that it is sound and complete with respect to the declarative system. The proof requires a number of technical innovations, including proving soundness and completeness in a mutually recursive fashion. CCS Concepts: • Software and its engineering → Data types and structures; • Theory of computation → Type theory;

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Section: Discussion and Related Workmentioning

confidence: 99%

Sound and complete bidirectional typechecking for higher-rank polymorphism with existentials and indexed types

Dunfield

Krishnaswami

2019

Proc. ACM Program. Lang.

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“…It is conveniently coded with a generalized recursor fix µ n , which recurses on the n + 1st argument and is definable from fix µ [3]. In the corecursive call to comp ν , the first argument is casted from SP s k A B to SP ∞ A B using subtyping of inductive types.…”

Section: Example: Composition Of Stream Processorsmentioning

confidence: 99%

Mixed Inductive/Coinductive Types and Strong Normalization

Abel¹

Programming Languages and Systems

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Abstract. We introduce the concept of guarded saturated sets, saturated sets of strongly normalizing terms closed under folding of corecursive functions. Using this tool, we can model equi-inductive and equicoinductive types with terminating recursion and corecursion principles. Two type systems are presented: Mendler (co)iteration and sized types. As an application we show that we can directly represent the mixed inductive/coinductive type of stream processors with associated recursive operations.

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Strong Normalization and Equi-(Co)Inductive Types

Abel¹

2007

Lecture Notes in Computer Science

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heprtment of gomputer ieneD niversity of wunih yettingenstrFTUD hEVHSQV wünhenD qermny abel@tcs.ifi.lmu.deAbstract. e type system for the lmdElulus enrihed with reurE sive nd oreursive funtions over equiEindutive nd Eoindutive types is presented in whih ll wellEtyped progrms re strongly normlizingF he hoie of equiEindutive typesD insted of the more ommon isoE indutive typesD in)uenes oth redution rules nd the strong normlE iztion proofF fy emedding isoE into equiEtypesD the ltter ones re reognized s more fundmentlF e model sed on orthogonlity is onE struted where semntil type orresponds to set of oservtionsD nd soundness of the type system is provenF

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Towards Generic Programming with Sized Types

Cited by 3 publications

References 37 publications

Sound and complete bidirectional typechecking for higher-rank polymorphism with existentials and indexed types

Sound and complete bidirectional typechecking for higher-rank polymorphism with existentials and indexed types

Mixed Inductive/Coinductive Types and Strong Normalization

Strong Normalization and Equi-(Co)Inductive Types

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