Related papers: Exposition: Synthesis via Functional Interpretatio…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
Synthesizing programs from examples requires searching over a vast, combinatorial space of possible programs. In this search process, a key challenge is representing the behavior of a partially written program before it can be executed, to…
Modifiable combining functions are a synthesis of two common approaches to combining evidence. They offer many of the advantages of these approaches and avoid some disadvantages. Because they facilitate the acquisition, representation,…
Program synthesis from incomplete specifications (e.g. input-output examples) has gained popularity and found real-world applications, primarily due to its ease-of-use. Since this technology is often used in an interactive setting,…
These lecture notes contain a brief practical introduction to doing density functional theory calculations for crystals using the open source Quantum Espresso software. The level is aimed at graduate students who are studying condensed…
Program synthesis techniques construct or infer programs from user-provided specifications, such as input-output examples. Yet most specifications, especially those given by end-users, leave the synthesis problem radically ill-posed,…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…
Although hypothesis tests play a prominent role in Science, their interpretation can be challenging. Three issues are (i) the difficulty in making an assertive decision based on the output of an hypothesis test, (ii) the logical…
This article shows a correspondence between abstract interpretation of imperative programs and the refinement calculus: in the refinement calculus, an abstract interpretation of a program is a specification which is a function. This…
We present a method for synthesizing recursive functions that provably satisfy a given specification in the form of a polymorphic refinement type. We observe that such specifications are particularly suitable for program synthesis for two…
We describe the first results of a project of analyzing in which theories formal proofs can be ex- pressed. We use this analysis as the basis of interoperability between proof systems.
The aim of this work is to show how we can decompose a module (if decomposable) into an indecomposable module with the help of the minimization process.
Program synthesis is the task of automatically deriving a program that has been specified by a user in advance. Combining automated theorem proving with program synthesis enables the automated construction of proven-to-be-correct programs,…
In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory. This scientific…
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
The goal of this note is to show that continuous functions may be approximated using scattered translates of the Poisson kernel.
A introduction to the syntax and Semantics of Answer Set Programming intended as an handout to [under]graduate students taking Artificial Intlligence or Logic Programming classes.
The paper examines the construction of a course in mathematical analysis at a pedagogical university, aimed at developing the ability of future mathematics teachers to detect and solve problems related to finding proofs. Key words: teaching…
The goal of this paper is to offer a full support for universities and quality assessment committees in retrieving the feedback from their students regarding to their teaching staff. The computer based application presented before ([Cri07])…