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Lazy evaluation is a powerful tool for functional programmers. It enables the concise expression of on-demand computation and a form of compositionality not available under other evaluation strategies. However, the stateful nature of lazy…
The existing call-by-need lambda calculi describe lazy evaluation via equational logics. A programmer can use these logics to safely ascertain whether one term is behaviorally equivalent to another or to determine the value of a lazy…
Amortized analysis is a program cost analysis technique for data structures in which the cost of operations is specified in aggregate, under the assumption of continued sequential use. Typically, amortized analyses are presented…
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 elegant theory of the call-by-value lambda-calculus relies on weak evaluation and closed terms, that are natural hypotheses in the study of programming languages. To model proof assistants, however, strong evaluation and open terms are…
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…
Lazy evaluation is a powerful technique that can optimize code execution by deferring evaluations until their results are required, thus enhancing efficiency. In most modern programming languages, like R, lazy evaluation is commonly applied…
The theory of the call-by-value lambda-calculus relies on weak evaluation and closed terms, that are natural hypotheses in the study of programming languages. To model proof assistants, however, strong evaluation and open terms are…
The call-by-need lambda calculus provides an equational framework for reasoning syntactically about lazy evaluation. This paper examines its operational characteristics. By a series of reasoning steps, we systematically unpack the…
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…
Amortised analysis is a technique for proving a combined time bound for a batch of operations on a data structure, even if some of those operations are expensive. But the traditional method of amortised analysis yields incorrect time bounds…
Amortized analysis is a cost analysis technique for data structures in which cost is studied in aggregate: rather than considering the maximum cost of a single operation, one bounds the total cost encountered throughout a session.…
To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…
We present $\textbf{calf}$, a $\textbf{c}$ost-$\textbf{a}$ware $\textbf{l}$ogical $\textbf{f}$ramework for studying quantitative aspects of functional programs. Taking inspiration from recent work that reconstructs traditional aspects of…
The lambda calculus since more than half a century is a model and foundation of functional programming languages. However, lambda expressions can be evaluated with different reduction strategies and thus, there is no fixed cost model nor…
The goal of this lecture is to show how modern theorem provers---in this case, the Coq proof assistant---can be used to mechanize the specification of programming languages and their semantics, and to reason over individual programs and…
The assessment of reactive power demand plays an instrumental role in power system planning. This paper presents a methodology for calculating reactive power demand based on a two-step approach. Unlike existing methodologies in the…
Linguistic theories formulated in the architecture of {\sc hpsg} can be very precise and explicit since {\sc hpsg} provides a formally well-defined setup. However, when querying a faithful implementation of such an explicit theory, the…
We introduce a framework for automatically choosing data structures to support efficient computation of analytical workloads. Our contributions are twofold. First, we introduce a novel low-level intermediate language that can express the…
Latent or continuous chain-of-thought methods replace explicit textual rationales with a number of internal latent steps, but these intermediate computations are difficult to evaluate beyond correlation-based probes. In this paper, we view…