Manuel Maarek

Restoring Natural Language as a Computerised Mathematics Input Method

Methods for computerised mathematics have found little appeal among mathematicians because they call for additional skills which are not available to the typical mathematician. We herein propose to reconcile computerised mathematics to mathematicians by restoring natural language as the primary medium for mathematical authoring. Our method associates portions of text with grammatical argumentation roles and computerises the informal mathematical style of the mathematician. Typical abbreviations like the aggregation of equations a = b > c, are not usually accepted as input to computerised languages. We propose specific annotations to explicate the morphology of such natural language style, to accept input in this style, and to expand this input in the computer to obtain the intended representation (i.e., a = b and b > c). We have named this method syntax souringin contrast to the usual syntax sugaring. All results have been implemented in a prototype editor developed on top of

Flexible Encoding of Mathematics on the Computer

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MathLang: Experience-driven Development of a New Mathematical Language

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Liability in software engineering: overview of the LISE approach and illustration on a case study

as a GUI for the core grammatical aspect of MathLang, a framework developed by the ULTRA group to computerise and formalise mathematics.

Liability issues in software engineering: the use of formal methods to reduce legal uncertainties

This paper reports on refinements and extensions to the MathLang framework that add substantial support for natural language text. We show how the extended framework supports multiple views of mathematical texts, including natural language views using the exact text that the mathematician wants to use. Thus, MathLang now supports the ability to capture the essential mathematical structure of mathematics written using natural language text. We show examples of how arbitrary mathematical text can be encoded in MathLang without needing to change any of the words or symbols of the texts or their order. In particular, we show the encoding of a theorem and its proof that has been used by Wiedijk for comparing many theorem prover representations of mathematics, namely the irrationality of \(\sqrt{2}\) (originally due to Pythagoras). We encode a 1960 version by Hardy and Wright, and a more recent version by Barendregt.

Experience in using a typed functional language for the development of a security application

Computerizing mathematical texts to allow software access to some or all of the texts’ semantic content is a long and tedious process that currently requires much expertise. We believe it is useful to support computerization that adds some structural and semantic information, but does not require jumping directly from the word-processing level (e.g., LATEX) to full formalization (e.g., Mizar, Coq, etc.). Although some existing mathematical languages are aimed at this middle ground (e.g., MathML, OpenMath, OMDoc), we believe they miss features needed to capture some important aspects of mathematical texts, especially the portion written with natural language. For this reason, we have been developing MathLang, a language for representing mathematical texts that has weak type checking and support for the special mathematical use of natural language. MathLang is currently aimed at only capturing the essential grammatical and binding structure of mathematical text without requiring full formalization. The development of MathLang is directly driven by experience encoding real mathematical texts. Based on this experience, this paper presents the changes that yield our latest version of MathLang. We have restructured and simplified the core of the language, replaced our old notion of “context” by a new system of blocks and local scoping, and made other changes. Furthermore, we have enhanced our support for the mathematical use of nouns and adjectives with object-oriented features so that nouns now correspond to classes, and adjectives to mixins.

Attack Modeling for System Security Analysis

Abstract In this paper we report on the design of a new mathematical language and our method of designing it, driven by the encoding of mathematical texts. MathLang is intended to provide support for checking basic well-formedness of mathematical text without requiring the heavy and diffcult-to- use machinery of full type theory or other forms of full formalization. At the same time, it is intended to allow the addition of fuller formalization to a document as time and effort permits. MathLang is intended to, ultimately, be useful in providing better software support for authoring mathematics, reading mathematics, and organizing and distributing mathematics. The preliminary language presented in this paper is intended only for machine manipulation and for debugging of the design of MathLang.

Avoiding security pitfalls with functional programming: a report on the development of a secure XML validator

LISE is a multidisciplinary project involving lawyers and computer scientists with the aim to put forward a set of methods and tools to (1) define software liability in a precise and unambiguous way and (2) establish such liability in case of incident. This paper provides an overview of the overall approach taken in the project based on a case study. The case study illustrates a situation where, in order to reduce legal uncertainties, the parties to a contract wish to include in the agreement specific clauses to define as precisely as possible the share of liabilities between them for the main types of failures of the system.

Improving predictability, efficiency and trust of model-based proof activity

This paper reports on the results of a multidisciplinary project involving lawyers and computer scientists with the aim to put forward a set of methods and tools to (1) define software liability in a precise and unambiguous way and (2) establish such liability in case of incident. The overall approach taken in the project is presented through an electronic signature case study. The case study illustrates a situation where, in order to reduce legal uncertainties, the parties wish to include in the contract specific clauses to define as precisely as possible the share of liabilities between them for the main types of failures of the system.