Related papers: Denotational cost semantics for functional languag…
A standard informal method for analyzing the asymptotic complexity of a program is to extract a recurrence that describes its cost in terms of the size of its input, and then to compute a closed-form upper bound on that recurrence. We give…
A typical way of analyzing the time complexity of functional programs is to extract a recurrence expressing the running time of the program in terms of the size of its input, and then to solve the recurrence to obtain a big-O bound. For…
The main way of analyzing the complexity of a program is that of extracting and solving a recurrence that expresses its running time in terms of the size of its input. We develop a method that automatically extracts such recurrences from…
With one exception, our previous work on recurrence extraction and denotational semantics has focused on a source language that supports inductive types and structural recursion. The exception handles general recursion via an initial…
We present a semantics based framework for analysing the quantitative behaviour of programs with regard to resource usage. We start from an operational semantics equipped with costs. The dioid structure of the set of costs allows for…
This paper introduces a new methodology for the complexity analysis of higher-order functional programs, which is based on three components: a powerful type system for size analysis and a sound type inference procedure for it, a ticking…
We develop a static complexity analysis for a higher-order functional language with structural list recursion. The complexity of an expression is a pair consisting of a cost and a potential. The former is defined to be the size of the…
Decomposition and abstraction is an essential component of computational thinking, yet it is not always emphasized in introductory programming courses. In addition, as generative AI further reduces the focus on syntax and increases the…
In this short paper, we consider a form of higher-order rewriting with a call-by-value evaluation strategy so as to model call-by-value programs. We briefly present a cost-size semantics to call-by-value rewriting: a class of algebraic…
This paper introduces a new methodology for the complexity analysis of higher-order functional programs, which is based on three ingredients: a powerful type system for size analysis and a sound type inference procedure for it, a ticking…
We present a new method for inferring complexity properties for a class of programs in the form of flowcharts annotated with loop information. Specifically, our method can (soundly and completely) decide if computed values are polynomially…
Although computational complexity is a fundamental aspect of program behavior, it is often at odds with common type theoretic principles such as function extensionality, which identifies all functions with the same $\textit{input-output}$…
We show how the complexity of higher-order functional programs can be analysed automatically by applying program transformations to a defunctionalized versions of them, and feeding the result to existing tools for the complexity analysis of…
We study a cost-aware programming language for higher-order recursion dubbed $\textbf{PCF}_\mathsf{cost}$ in the setting of synthetic domain theory (SDT). Our main contribution relates the denotational cost semantics of…
Recurrence equations have played a central role in static cost analysis, where they can be viewed as abstractions of programs and used to infer resource usage information without actually running the programs with concrete data. Such…
This article presents a type-based analysis for deriving upper bounds on the expected execution cost of probabilistic programs. The analysis is naturally compositional, parametric in the cost model, and supports higher order functions and…
Some type-based approaches to termination use sized types: an ordinal bound for the size of a data structure is stored in its type. A recursive function over a sized type is accepted if it is visible in the type system that recursive calls…
In David Schmidt's PhD work he explored the use of denotational semantics as a programming language. It was part of an effort to not only treat formal semantics as specifications but also as interpreters and input to compiler generators.…
Describing systems in terms of choices and their resulting costs and rewards offers the promise of freeing algorithm designers and programmers from specifying how those choices should be made; in implementations, the choices can be realized…
A reliable technique for deductive program verification should be proven sound with respect to the semantics of the programming language. For each different language, the construction of a separate soundness proof is often a laborious…