@conference {810, title = {Galois: A Language for Proofs Using Galois Connections and Fork Algebras}, booktitle = { PLMMS{\textquoteright}09 - ACM SIGSAM 2009 International Workshop on Programming Languages for Mechanized Mathematics Systems}, year = {2009}, month = {August}, address = {Munich, Germany}, abstract = {<p>Galois is a domain specific language supported by the Galculator interactive proof-assistant prototype. Galculator uses an equational approach based on Galois connections with indirect equality as an additional inference rule. Galois allows for the specification of different theories in a point-free style by using fork algebras, an extension of relation algebras with expressive power of first-order logic. The language offers sub-languages to derive proof rules from Galois connections, to express proof tactics, and to organize axioms and theorems into modular definitions.</p> <p>In this paper, we describe how the algebraic theory underlying the proof-method drives the design of the Galois language. We provide the syntax and semantics of important fragments of Galois and show how they are hierarchically combined into a complete language.</p> }, attachments = {https://haslab.uminho.pt/sites/default/files/pfsilva/files/plmms09.pdf}, author = {Paulo Silva and Joost Visser and Jos{\'e} Nuno Oliveira} }