Related papers: Towards Patterns for Heaps and Imperative Lambdas
We introduce a new nameless representation of lambda terms inspired by ordered logic. At a lambda abstraction, number and relative position of all occurrences of the bound variable are stored, and application carries the additional…
Metaprogramming enables the generation of performant code, while gradual typing facilitates the smooth migration from untyped scripts to robust statically typed programs. However, combining these features with imperative state -…
A system of linear dependent types for the lambda calculus with full higher-order recursion, called dlPCF, is introduced and proved sound and relatively complete. Completeness holds in a strong sense: dlPCF is not only able to precisely…
We extend the simply-typed guarded $\lambda$-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming…
The Lambek calculus can be considered as a version of non-commutative intuitionistic linear logic. One of the interesting features of the Lambek calculus is the so-called "Lambek's restriction," that is, the antecedent of any provable…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
Since more than three decades, interior-point methods proved very useful for optimization, from linear over semidefinite to conic (and partly beyond non-convex) programming; despite the fact that already in the semidefinite case (even when…
We address a problem connected to the unfolding semantics of functional programming languages: give a useful characterization of those infinite lambda-terms that are lambda_{letrec}-expressible in the sense that they arise as infinite…
Inspired by the trend on unifying theories of programming, this paper shows how the algebraic treatment of standard data dependency theory equips relational data with functional types and an associated type system which is useful for type…
This invited paper presents an overview of an ongoing research program aimed at extending the Curry-Howard-Lambek correspondence to quantum computation. We explore two key frameworks that provide both logical and computational foundations…
Working in point-free topology under the constraints of geometric logic, we prove the Fundamental Theorem of Calculus, and apply it to prove the usual rules for the derivatives of $x^\alpha$, $\gamma^x$, and $\log_\gamma x$.
We define a novel, extensional, three-valued semantics for higher-order logic programs with negation. The new semantics is based on interpreting the types of the source language as three-valued Fitting-monotonic functions at all levels of…
We introduce some new logics of imperfect information by adding atomic formulas corresponding to inclusion and exclusion dependencies to the language of first order logic. The properties of these logics and their relationships with other…
We develop a common semantic framework for the interpretation both of $\mathbf{IPC}$, the intuitionistic propositional calculus, and of logics weaker than $\mathbf{IPC}$ (substructural and subintuitionistic logics). This is done by proving…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
In a previous paper, a process algebra based on ACP (Algebra of Communicating Processes) was proposed in which processes involving data can be handled by means of features originating from imperative programming. In this paper, an extension…
Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…
We propose an implementation of lambda+, a recently introduced simply typed lambda-calculus with pairs where isomorphic types are made equal. The rewrite system of lambda+ is a rewrite system modulo an equivalence relation, which makes its…
We extend intersection types to a computational $\lambda$-calculus with algebraic operations \`a la Plotkin and Power. We achieve this by considering monadic intersections, whereby computational effects appear not only in the operational…
Finding a denotational semantics for higher order quantum computation is a long-standing problem in the semantics of quantum programming languages. Most past approaches to this problem fell short in one way or another, either limiting the…