相关论文: Initiality for Typed Syntax and Semantics

Syntax is a latent hierarchical structure which underpins the robust and compositional nature of human language. In this work, we explore the hypothesis that syntactic dependencies can be represented in language model attention…

As the name suggests, type-logical grammars are a grammar formalism based on logic and type theory. From the prespective of grammar design, type-logical grammars develop the syntactic and semantic aspects of linguistic phenomena…

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…

We present a type system that combines, in a controlled way, first-order polymorphism with intersectiontypes, union types, and subtyping, and prove its safety. We then define a type reconstruction algorithm that issound and terminating.…

Many variants of type theory extend a basic theory with additional primitives or properties like univalence, guarded recursion or parametricity, to enable constructions or proofs that would be harder or impossible to do in the original…

This work introduces the novel concept of kind refinement, which we develop in the context of an explicitly polymorphic ML-like language with type-level computation. Just as type refinements embed rich specifications by means of…

A coercion semantics of a programming language with subtyping is typically defined on typing derivations rather than on typing judgments. To avoid semantic ambiguity, such a semantics is expected to be coherent, i.e., independent of the…

We present an extension of the second-order logic AF2 with iso-style inductive and coinductive definitions specifically designed to extract programs from proofs a la Krivine-Parigot by means of primitive (co)recursion principles. Our logic…

Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we…

A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…

We present an approach to type theory in which the typing judgments do not have explicit contexts. Instead of judgments of shape "Gamma |- A : B", our systems just have judgments of shape "A : B". A key feature is that we distinguish free…

We develop the usage of certain type theories as specification languages for algebraic theories and inductive types. We observe that the expressive power of dependent type theories proves useful in the specification of more complicated…

We present a two-level theory to formalize constructive mathematics as advocated in a previous paper with G. Sambin. One level is given by an intensional type theory, called Minimal type theory. This theory extends the set-theoretic version…

Harnessing the power of dependently typed languages can be difficult. Programmers must manually construct proofs to produce well-typed programs, which is not an easy task. In particular, migrating code to these languages is challenging.…

Semantic properties are domain-specific specification constructs used to augment an existing language with richer semantics. These properties are taken advantage of in system analysis, design, implementation, testing, and maintenance…

Several explanation methods such as Integrated Gradients (IG) can be characterised as path-based methods, as they rely on a straight line between the data and an uninformative baseline. However, when applied to language models, these…

Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…

In recent work we have shown how it is possible to define very precise type systems for object-oriented languages by abstractly compiling a program into a Horn formula f. Then type inference amounts to resolving a certain goal w.r.t. the…

Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…

A categorial grammar assigns one of several syntactic categories to each symbol of the alphabet, and the category of a string is then deduced from the categories assigned to its symbols using two simple reduction rules. This paper…