Cost-Aware Type Theory

Niu, Yue; Harper, Robert

doi:10.48550/arxiv.2011.03660

Cited by 2 publications

(7 citation statements)

References 35 publications

(54 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In contrast the same method in a framework for pure behavioral properties becomes a technical device for definition that does not provide further insight into the defined program. As observed in Niu and Harper [2020], the cost-aware setting evinces a synergetic relationship between cost analysis itself and programming with general recursion that is further amplified in calf: cost structure enables one to effectively encode general recursion, and general recursion gives rise to programs with interesting cost structure.…”

Section: Analyzing the Cost Of General Recursive Functionsmentioning

confidence: 99%

“…Finally, we mention the work of Niu and Harper [2020] on a cost-aware computational type theory CATT in the Nuprl tradition. Unlike the type theory of Constable and Crary [2002], CATT only internalizes cost structure, which leads to a framework that is more directly applicable to cost analysis.…”

Section: Type Systems For Cost Analysismentioning

confidence: 99%

“…Unlike the type theory of Constable and Crary [2002], CATT only internalizes cost structure, which leads to a framework that is more directly applicable to cost analysis. In particular, Niu and Harper [2020] introduce a connective łfuntimež that internalizes cost specification on functions types and prove a novel refinement rule for funtime by appealing to the specified cost bound, constituting an induction principle based on cost structure. Our observation that cost analysis may be used to encode general recursion in calf is inspired by the work on CATT, as is the idea of using a cost-aware dependent function type to specify cost signatures.…”

Section: Type Systems For Cost Analysismentioning

confidence: 99%

“…Our observation that cost analysis may be used to encode general recursion in calf is inspired by the work on CATT, as is the idea of using a cost-aware dependent function type to specify cost signatures. Niu and Harper [2020] do not develop a formal proof theory for CATT, a fact that appears to pose significant challenges for its mechanization.…”

Section: Type Systems For Cost Analysismentioning

confidence: 99%

“…As mentioned in Section 1.6, Bove and Capretta's accessibility predicates provide a way to express general recursive definitions in type theory. Inspired by Niu and Harper [2020], we provide an alternative approach in calf that exploits the cost structure of programs: one can use the cost bound of a given algorithm to safely define the algorithm in question. Instead of accessibility predicates, we may parameterize every program by a clock that represents the amount of fuel available for recursion.…”

Section: Recursionmentioning

confidence: 99%

See 4 more Smart Citations

A cost-aware logical framework

Niu

Sterling

Grodin

et al. 2022

Proc. ACM Program. Lang.

Self Cite

View full text Add to dashboard Cite

We present calf , a c ost- a ware l ogical f ramework for studying quantitative aspects of functional programs. Taking inspiration from recent work that reconstructs traditional aspects of programming languages in terms of a modal account of phase distinctions , we argue that the cost structure of programs motivates a phase distinction between intension and extension . Armed with this technology, we contribute a synthetic account of cost structure as a computational effect in which cost-aware programs enjoy an internal noninterference property: input/output behavior cannot depend on cost. As a full-spectrum dependent type theory, calf presents a unified language for programming and specification of both cost and behavior that can be integrated smoothly with existing mathematical libraries available in type theoretic proof assistants. We evaluate calf as a general framework for cost analysis by implementing two fundamental techniques for algorithm analysis: the method of recurrence relations and physicist’s method for amortized analysis . We deploy these techniques on a variety of case studies: we prove a tight, closed bound for Euclid’s algorithm, verify the amortized complexity of batched queues, and derive tight, closed bounds for the sequential and parallel complexity of merge sort, all fully mechanized in the Agda proof assistant. Lastly we substantiate the soundness of quantitative reasoning in calf by means of a model construction.

show abstract

Section: Analyzing the Cost Of General Recursive Functionsmentioning

confidence: 99%

Section: Type Systems For Cost Analysismentioning

confidence: 99%

Section: Type Systems For Cost Analysismentioning

confidence: 99%

Section: Type Systems For Cost Analysismentioning

confidence: 99%

Section: Recursionmentioning

confidence: 99%

See 3 more Smart Citations

A cost-aware logical framework

Niu

Sterling

Grodin

et al. 2022

Proc. ACM Program. Lang.

Self Cite

View full text Add to dashboard Cite

show abstract

A cost-aware logical framework

Niu¹,

Sterling²,

Grodin³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

We present calf, a cost-aware logical framework for studying quantitative aspects of functional programs. Taking inspiration from recent work that reconstructs traditional aspects of programming languages in terms of a modal account of phase distinctions, we argue that the cost structure of programs motivates a phase distinction between intension and extension. Armed with this technology, we contribute a synthetic account of cost structure as a computational effect in which cost-aware programs enjoy an internal noninterference property: input/output behavior cannot depend on cost. As a full-spectrum dependent type theory, calf presents a unified language for programming and specification of both cost and behavior that can be integrated smoothly with existing mathematical libraries available in type theoretic proof assistants.We evaluate calf as a general framework for cost analysis by implementing two fundamental techniques for algorithm analysis: the method of recurrence relations and physicist's method for amortized analysis. We deploy these techniques on a variety of case studies: we prove a tight, closed bound for Euclid's algorithm, verify the amortized complexity of batched queues, and derive tight, closed bounds for the sequential and parallel complexity of merge sort, all fully mechanized in the Agda proof assistant. Lastly we substantiate the soundness of quantitative reasoning in calf by means of a model construction.

show abstract

Cost-Aware Type Theory

Cited by 2 publications

References 35 publications

A cost-aware logical framework

A cost-aware logical framework

A cost-aware logical framework

Contact Info

Product

Resources

About