Related papers: A modal typing system for self-referential program…
Reflective systems allow their own structures to be altered from within. Here we are concerned with a style of reflection, called linguistic reflection, which is the ability of a running program to generate new program fragments and to…
Existing computer algebra packages do not fully support quantum mechanics calculations in Dirac's notation. I present the foundation for building such support: a mathematical system for the symbolic manipulation of expressions used in the…
We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode…
Polarization of types in call-by-push-value naturally leads to the separation of inductively defined observable values (classified by positive types), and coinductively defined computations (classified by negative types), with adjoint…
The objective of this paper is to present general, mechanically verified, refinement rules for reasoning about recursive programs and while loops in the context of concurrency. Unlike many approaches to concurrency, we do not assume that…
When a user finds an interesting recommendation in a recommender system, the user may want to recall related items recommended in the past to reconsider or to enjoy them again. If the system can pick up such "recalled" items at each user's…
We consider a general prescriptive type system with parametric polymorphism and subtyping for logic programs. The property of subject reduction expresses the consistency of the type system w.r.t. the execution model: if a program is…
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…
This paper presents and extends our type theoretical framework for a compositional treatment of natural language semantics with some lexical features like coercions (e.g. of a town into a football club) and copredication (e.g. on a town as…
Covering and elimination inequalities are central to combinatorial optimization, yet their role has largely been studied in problem-specific settings or via no-good cuts. This paper introduces a unified perspective that treats these…
Dynamic languages are praised for their flexibility and expressiveness, but static analysis often yields many false positives and verification is cumbersome for lack of structure. Hence, unit testing is the prevalent incomplete method for…
Current representations used in reasoning steps of large language models can mostly be categorized into two main types: (1) natural language, which is difficult to verify; and (2) non-natural language, usually programming code, which is…
We present a framework which allows a uniform approach to the recently introduced concept of pseudo-repetitions on words in the morphic case. This framework is at the same time more general and simpler. We introduce the concept of a…
We present natural deduction systems and associated modal lambda calculi for the necessity fragments of the normal modal logics K, T, K4, GL and S4. These systems are in the dual-context style: they feature two distinct zones of…
System F, the polymorphic lambda calculus, features the principle of impredicativity: polymorphic types may be (explicitly) instantiated at other types, enabling many powerful idioms such as Church encoding and data abstraction.…
We present a semi-automated framework to construct and reason about programs in a deeply-embedded while-language. The while-language we consider is a simple computation model that can simulate (and be simulated by) Turing Machines with a…
It is discussed a practical possibility of a provable programming of mathematics basing on intuitionism and the dependent types feature of a programming language.The principles of constructive mathematics and provable programming are…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…
Logic programming has traditiLogic programming has traditionally lacked devices for expressing iterative tasks. To overcome this problem, this paper proposes iterative goal formulas of the form $\seqandq{x}{L} G$ where $G$ is a goal, $x$ is…
Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate…