agda-calf

Niu, Yue; Sterling, Jonathan; Grodin, Harrison; Harper, Robert

doi:10.1145/3462303

Cited by 2 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a type theory, calf naturally supports a compositional style of verification. When localized to quantitative properties of programs, calf evinces the notion of a cost signature [Acar and Blelloch 2019], the cost-aware counterpart to the functional specification of a data structure. In calf, we may specify the quantitative properties of a data structure by using cost-aware dependent functions (𝑎 : 𝐴) 𝑐 − → 𝐵, an application of the hasCost refinement from Section 1.4:…”

Section: Compositional Cost Analysismentioning

confidence: 99%

“…Fortunately, both programmers can be supplied with suitable implementations: edge sets for Alice and adjacency matrices for Bob. Although somewhat artificial, this example shows that calf is able to formalize the notion of a cost signature as used by Acar and Blelloch [2019], paving the way to verified, cost-aware development of large-scale programs.…”

Section: Compositional Cost Analysismentioning

confidence: 99%

See 1 more Smart Citation

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: Compositional Cost Analysismentioning

confidence: 99%

Section: Compositional Cost Analysismentioning

confidence: 99%

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

Decalf: A Directed, Effectful Cost-Aware Logical Framework

Grodin,

Niu,

Sterling

et al. 2024

Proc. ACM Program. Lang.

View full text Add to dashboard Cite

We present decalf , a d irected, e ffectful c ost- a ware l ogical f ramework for studying quantitative aspects of functional programs with effects. Like calf , the language is based on a formal phase distinction between the extension and the intension of a program, its pure behavior as distinct from its cost measured by an effectful step-counting primitive. The type theory ensures that the behavior is unaffected by the cost accounting. Unlike calf , the present language takes account of effects , such as probabilistic choice and mutable state. This extension requires a reformulation of calf ’s approach to cost accounting: rather than rely on a ”separable” notion of cost, here a cost bound is simply another program . To make this formal, we equip every type with an intrinsic preorder, relaxing the precise cost accounting intrinsic to a program to a looser but nevertheless informative estimate. For example, the cost bound of a probabilistic program is itself a probabilistic program that specifies the distribution of costs. This approach serves as a streamlined alternative to the standard method of isolating a cost recurrence and readily extends to higher-order, effectful programs. The development proceeds by first introducing the decalf type system, which is based on an intrinsic ordering among terms that restricts in the extensional phase to extensional equality, but in the intensional phase reflects an approximation of the cost of a program of interest. This formulation is then applied to a number of illustrative examples, including pure and effectful sorting algorithms, simple probabilistic programs, and higher-order functions. Finally, we justify decalf via a model in the topos of augmented simplicial sets.

show abstract

agda-calf

Cited by 2 publications

References 0 publications

A cost-aware logical framework

A cost-aware logical framework

Decalf: A Directed, Effectful Cost-Aware Logical Framework

Contact Info

Product

Resources

About