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Structured recursion schemes such as folds and unfolds have been widely used for structuring both functional programs and program semantics. In this context, it has been customary to implement denotational semantics as folds over an…
We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…
We present a recursive formulation of the Horn algorithm for deciding the satisfiability of propositional clauses. The usual presentations in imperative pseudo-code are informal and not suitable for simple proofs of its main properties. By…
While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of…
Reversible computing is motivated by both pragmatic and foundational considerations arising from a variety of disciplines. We take a particular path through the development of reversible computation, emphasizing compositional reversible…
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…
This paper constructively proves the existence of an effective procedure generating a computable (total) function that is not contained in any given effectively enumerable set of such functions. The proof implies the existence of machines…
We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class $\operatorname{PTIME}$ of languages computable in polynomial time in terms of differential…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
This paper investigates some issues arising in categorical models of reversible logic and computation. Our claim is that the structural (coherence) isomorphisms of these categorical models, although generally overlooked, have decidedly…
A fertile field of research in theoretical computer science investigates the representation of general recursive functions in intensional type theories. Among the most successful approaches are: the use of wellfounded relations,…
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…
We present algorithms that learn certain classes of function-free recursive logic programs in polynomial time from equivalence queries. In particular, we show that a single k-ary recursive constant-depth determinate clause is learnable.…
A set is introreducible if it can be computed by every infinite subset of itself. Such a set can be thought of as coding information very robustly. We investigate introreducible sets and related notions. Our two main results are that the…
We compare three notions of effectiveness on uncountable structures. The first notion is that of a $\real$-computable structure, based on a model of computation proposed by Blum, Shub, and Smale, which uses full-precision real arithmetic.…
The recent approaches of extending the GRAPHPLAN algorithm to handle more expressive planning formalisms raise the question of what the formal meaning of "expressive power" is. We formalize the intuition that expressive power is a measure…
This paper formalizes and proves correct a compilation scheme for mutually-recursive definitions in call-by-value functional languages. This scheme supports a wider range of recursive definitions than previous methods. We formalize our…
A syntactical proof is given that all functions definable in a certain affine linear typed lambda-calculus with iteration in all types are polynomial time computable. The proof provides explicit polynomial bounds that can easily be…
Experimental science usually relies on laboratory procedures that, after finitely many steps, terminate with numerical reports on physical quantities. This paper argues that such procedures can be understood as algorithmic once the…