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This paper proposes bimorphic recursion, which is restricted polymorphic recursion such that every recursive call in the body of a function definition has the same type. Bimorphic recursion allows us to assign two different types to a…
We propose a generalization of Categorial Grammar in which lexical categories are defined by means of recursive constraints. In particular, the introduction of relational constraints allows one to capture the effects of (recursive) lexical…
We introduce the task of expressive speech retrieval, where the goal is to retrieve speech utterances spoken in a given style based on a natural language description of that style. While prior work has primarily focused on performing speech…
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…
Boyer and Moore have discussed a recursive function that puts conditional expressions into normal form [1]. It is difficult to prove that this function terminates on all inputs. Three termination proofs are compared: (1) using a measure…
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…
We present an efficient and robust reference resolution algorithm in an end-to-end state-of-the-art information extraction system, which must work with a considerably impoverished syntactic analysis of the input sentences. Considering this…
The authors' ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-definable…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
In this paper we adapt the definitions and results from Apt and Vermeulen on `First order logic as a constraint programming language' (in: Proceedings of LPAR2001, Baaz and Voronkov (eds.), Springer LNAI 2514) to include important ideas…
We present a compositional framework for certifying resource bounds in typed programs. Terms are typed with synthesized bounds drawn from an abstract resource lattice, enabling uniform treatment of time, memory, gas, and domain-specific…
We develop a static complexity analysis for a higher-order functional language with structural list recursion. The complexity of an expression is a pair consisting of a cost and a potential. The former is defined to be the size of the…
We set up a parametrised monadic translation for a class of call-by-value functional languages, and prove a corresponding soundness theorem. We then present a series of concrete instantiations of our translation, demonstrating that a number…
Recursive calls over recursive data are useful for generating probability distributions, and probabilistic programming allows computations over these distributions to be expressed in a modular and intuitive way. Exact inference is also…
This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html). The logical vocabulary of the system consists of…
Nominal algebra includes $\alpha$-equality and freshness constraints on nominal terms endowed with a nominal set semantics that facilitates reasoning about languages with binders. Nominal unification is decidable and unitary, however, its…
We present semantic correctness proofs of forward-mode Automatic Differentiation (AD) for languages with sources of partiality such as partial operations, lazy conditionals on real parameters, iteration, and term and type recursion. We…
We present a fully abstract model of a call-by-value language with higher-order functions, recursion and natural numbers, as an exponential ideal in a topos. Our model is inspired by the fully abstract models of O'Hearn, Riecke and…
Constructive type theory combines logic and programming in one language. This is useful both for reasoning about programs written in type theory, as well as for reasoning about other programming languages inside type theory. It is…
Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…