Related papers: Full Abstraction for a Recursively Typed Lambda Ca…
We develop a dependent type theory that is based purely on inductive and coinductive types, and the corresponding recursion and corecursion principles. This results in a type theory with a small set of rules, while still being fairly…
This is a short paper about the relationship between logic and computation. More specifically, it is about a relationship between the completeness proof for intuitionistic propositional logic within the form of proof-theoretic semantics…
Statutory reasoning refers to the application of legislative provisions to a series of case facts described in natural language. We re-frame statutory reasoning as an analogy task, where each instance of the analogy task involves a…
The postulates of comprehension and extensionality in set theory are based on an inversion principle connecting set-theoretic abstraction and the property of having a member. An exactly analogous inversion principle connects functional…
We investigate program equivalence for linear higher-order(sequential) languages endowed with primitives for computational effects. More specifically, we study operationally-based notions of program equivalence for a linear…
The intrinsic treatment of binding in the lambda calculus makes it an ideal data structure for representing syntactic objects with binding such as formulas, proofs, types, and programs. Supporting such a data structure in an implementation…
Probabilistic applicative bisimulation is a recently introduced coinductive methodology for program equivalence in a probabilistic, higher-order, setting. In this paper, the technique is applied to a typed, call-by-value, lambda-calculus.…
The sequent calculus is a proof system which was designed as a more symmetric alternative to natural deduction. The {\lambda}{\mu}{\mu}-calculus is a term assignment system for the sequent calculus and a great foundation for compiler…
For the lambda-calculus with surjective pairing and terminal type, Curien and Di Cosmo were inspired by Knuth-Bendix completion, and introduced a confluent rewriting system that (1) extends the naive rewriting system, and (2) is stable…
We consider the notion of a vacuous reduct semantics for abstract argumentation frameworks, which, given two abstract argumentation semantics {\sigma} and {\tau}, refines {\sigma} (base condition) by accepting only those {\sigma}-extensions…
The Functional Machine Calculus (Heijltjes 2022) is a new approach to unifying the imperative and functional programming paradigms. It extends the lambda-calculus, preserving the key features of confluent reduction and typed termination, to…
This paper presents simple, syntactic strong normalization proofs for the simply-typed lambda-calculus and the polymorphic lambda-calculus (system F) with the full set of logical connectives, and all the permutative reductions. The…
This paper is a concise and painless introduction to the $\lambda$-calculus. This formalism was developed by Alonzo Church as a tool for studying the mathematical properties of effectively computable functions. The formalism became popular…
We describe a mathematical structure that can give extensional denotational semantics to higher-order probabilistic programs. It is not limited to discrete probabilities, and it is compatible with integration in a way the models that have…
Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…
We consider the probabilistic applicative bisimilarity (PAB), a coinductive relation comparing the applicative behaviour of probabilistic untyped lambda terms according to a specific operational semantics. This notion has been studied with…
We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…
In sequential functional languages, sized types enable termination checking of programs with complex patterns of recursion in the presence of mixed inductive-coinductive types. In this paper, we adapt sized types and their metatheory to the…
In a previous paper the authors applied the Abstract Interpretation approach for approximating the probabilistic semantics of biological systems, modeled specifically using the Chemical Ground Form calculus. The methodology is based on the…
Confluence in abstract parallel category systems is established for net class-rewriting in iterative closed multilevel quotient graph structures with uncountable node arities by multi-dimensional transducer operations in topological metrics…