Related papers: Handling polymorphic algebraic effects
A new totally algebraic formalism based on general, abstract ladder operators has been proposed. This approach heavily grounds in the superoperator formalism of Primas. However it is necessary to introduce many improvements in his…
In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those. In this…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
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…
Influence diagrams provide a compact graphical representation of decision problems. Several algorithms for the quick computation of their associated expected utilities are available in the literature. However, often they rely on a full…
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…
A formalism for the study of highly interacting electronic systems is presented. The proposed scheme is based on two key concepts: composite operators and algebra constraints. Composite field operators, that naturally appear as a…
Modal types -- types that are derived from proof systems of modal logic -- have been studied as theoretical foundations of metaprogramming, where program code is manipulated as first-class values. In modal type systems, modality corresponds…
This work exploits the logical foundation of session types to determine what kind of type discipline for the pi-calculus can exactly capture, and is captured by, lambda-calculus behaviours. Leveraging the proof theoretic content of the…
We propose algebraic protocols that enable the definition of protocol templates and session types analogous to the definition of domain-specific types with algebraic datatypes. Parameterized algebraic protocols subsume all regular as well…
Designing programming languages that enable intuitive and safe manipulation of data structures is a critical research challenge. Conventional destructive memory operations using pointers are complex and prone to errors. Existing type…
We present a call-by-need $\lambda$-calculus that enables strong reduction (that is, reduction inside the body of abstractions) and guarantees that arguments are only evaluated if needed and at most once. This calculus uses explicit…
The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while…
The purpose of this paper is to give a characterisation of divided power algebras over a reduced operad. Such a characterisation is given in terms of polynomial operations, following the classical example of divided power algebras. We…
Higher-order representations of objects such as programs, proofs, formulas and types have become important to many symbolic computation tasks. Systems that support such representations usually depend on the implementation of an intensional…
We present a mathematical framework for quantum mechanics in which the basic entities and operations have physical significance. In this framework the primitive concepts are states and effects and the resulting mathematical structure is a…
Interactive behaviors are ubiquitous in modern cryptography, but are also present in $\lambda$-calculi, in the form of higher-order constructions. Traditionally, however, typed $\lambda$-calculi simply do not fit well into cryptography,…
Effect systems are lightweight extensions to type systems that can verify a wide range of important properties with modest developer burden. But our general understanding of effect systems is limited primarily to systems where the order of…
The objective of this paper is to develop a functional programming language for quantum computers. We develop a lambda calculus for the classical control model, following the first author's work on quantum flow-charts. We define a…
In this paper, we introduce product interactions, an algebraic formalism in which neural network layers are constructed from compositions of a multiplication operator defined over suitable algebras. Product interactions provide a principled…