Related papers: A Calculus of Inheritance
The Curry-Howard correspondence is often described as relating proofs (in intutionistic natural deduction) to programs (terms in simply-typed lambda calculus). However this narrative is hardly a perfect fit, due to the computational content…
Driven by the interest of reasoning about probabilistic programming languages, we set out to study a notion of unicity of normal forms for them. To provide a tractable proof method for it, we define a property of distribution confluence…
Operational semantics have been enormously successful, in large part due to its flexibility and simplicity, but they are not compositional. Denotational semantics, on the other hand, are compositional but the lattice-theoretic models are…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
In this paper, we present a linear and reversible programming language with inductives types and recursion. The semantics of the languages is based on pattern-matching; we show how ensuring syntactical exhaustivity and non-overlapping of…
We provide here a computational interpretation of first-order logic based on a constructive interpretation of satisfiability w.r.t. a fixed but arbitrary interpretation. In this approach the formulas themselves are programs. This contrasts…
The lambda calculus is a universal programming language. It can represent the computable functions, and such offers a formal counterpart to the point of view of functions as rules. Terms represent functions and this allows for the…
The study of polarity in computation has revealed that an "ideal" programming language combines both call-by-value and call-by-name evaluation; the two calling conventions are each ideal for half the types in a programming language. But…
We introduce a first proofs-as-parallel-programs correspondence for classical logic. We define a parallel and more powerful extension of the simply typed lambda calculus corresponding to an analytic natural deduction based on the excluded…
computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable…
The main goal of concept-oriented programming (COP) is describing how objects are represented and accessed. It makes references (object locations) first-class elements of the program responsible for many important functions which are…
Taha and Nielsen have developed a multi-stage calculus {\lambda}{\alpha} with a sound type system using the notion of environment classifiers. They are special identifiers, with which code fragments and variable declarations are annotated,…
We propose a presentation of classical propositional tableaux elaborated by application of methods that are noteworthy in program design, namely program derivation with separation of concerns. We start by deriving from a straightforward…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
Recollements of derived module categories are investigated, using a new technique, ladders of recollements, which are mutation sequences. The position in the ladder is shown to control whether a recollement restricts from unbounded to…
We develop the integral calculus for quasi-standard smooth functions defined on the ring of Fermat reals. The approach is by proving the existence and uniqueness of primitives. Besides the classical integral formulas, we show the…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
We develop a compositional approach for automatic and symbolic differentiation based on categorical constructions in functional analysis where derivatives are linear functions on abstract vectors rather than being limited to scalars,…
A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics…
We introduce a set of eight universal Rules of Inference by which computer programs with known properties (axioms) are transformed into new programs with known properties (theorems). Axioms are presented to formalize a segment of Number…