The <a href="library/">scripts</a> used to generate the knowledge base of
Matita can be <a href="library/">browsed on line</a>.
</p>
+ <p>
+ The experimental <a href="nlibrary/">scripts</a> for the next major version of Matita can also be <a href="nlibrary/">browsed on line</a>.
+ </p>
<br/>
<h1>Large Developments</h1>
+ <h2>Certified Complexity (CerCo)<a name="cerco"></a></h2>
+ <p>Matita is being used to certify a cost preserving compiler from a
+ large subset of C into the 8051 machine code. The compiler does not
+ only produce the target code, but it also instruments the source code
+ with precise cost declarations for the execution of O(1) code
+ fragments. This induced cost model for the source language is
+ inherently non compositional since it is affected by the compilation
+ strategy: the same instructions are compiled in different ways in
+ different contexts, yielding different costs.
+ </p>
+ <p>The final aim of the CerCo project is to formally reason on
+ intensional properties on the C code -- e.g. to show that some hard
+ deadline is always met
+ -- and to be sure that the property holds also for the target code.
+ </p>
+ <p>The CerCo project is a FET Open IST project funded by the EU
+ community in the 7th Framework Programme. More informations on the
+ project and the code of the Matita formalization can be found
+ on the <a href="cerco.cs.unibo.it">CerCo Web site</a>
+ </p>
+
+ <h2>The Basic Picture<a name="sambin"></a></h2>
+ <p>
+ The <a href="library/formal_topology">scripts</a> present a formalization
+ of some results from the forthcoming book <a href="http://www.oup.com/us/catalog/general/subject/Mathematics/Logic/?view=usa&ci=9780199232888">The Basic Picture - Structures for Constructive Topology</a> by Giovanni Sambin.
+ </p>
+ <p>The formalization has been the result of a three years long
+ collaboration between mathematicians from the University of Padova
+ and computer scientists from the University of
+ Bologna, sponsored by the University of Padova. In particular,
+ the groups that collaborated are headed respectively by Prof. Sambin
+ in Padua (formal topology and constructive type theory)
+ and by Prof. Asperti in Bologna (constructive type theory and interactive
+ theorem proving).
+ </p>
+ <p>
+ In particular the <a href="library/formal_topology">scripts</a> present:
+ </p>
+ <ul>
+ <li>the category of Basic Pairs, that are generalizations of
+ topological spaces</li>
+ <li>the category of Basic Topologies, that are generalizations of
+ formal topologies</li>
+ <li>the existence of a categorical embedding of the former category
+ into the latter. The embedding is an improvement on the usual
+ adjunction between topological spaces and locales</li>
+ </ul>
+ <p>
+ All the results are presented constructively and in the predicative
+ fragment of Matita, without any reference to choice axioms.
+ </p>
+ In order to reason conformtably on the previous concrete categories and
+ functors, we also present algebraic versions of all the introduced
+ notions, as well as categorical embedding of the concrete categories in
+ the algebraized ones. In particular we formalized:
+ </p>
+ <ul>
+ <li>the large category of Overlap Algebras, that extend locales with an
+ axiomatized (= algebraized) overlap binary predicate. The
+ concrete overlap predicate states positively
+ (i.e. without using negation) the existence (in the intuitionistic
+ sense) of a point in the intersection of two sets.
+ The natural morphism over Overlap Algebras are functions for the
+ existential and universal pre and post images of a relation.
+ </li>
+ <li>the large category of O-Basic Pairs, that algebraize Basic
+ Pairs by means of Overlap Algebras</li>
+ <li>the large category of O-Basic Topologies, that algebraize Basic
+ Topologies by means of Overlap Algebras</li>
+ <li>the categorical embedding of Basic Pairs into O-Basic Pairs and
+ of Basic Topologies into O-Basic Topologies</li>
+ <li>the existence of a categorical embedding of the category
+ of O-Basic Pairs into the category of O-Basic Topologies</li>
+ </ul>
+ <p>
+ More information will be available in a forthcoming paper by
+ Claudio Sacerdoti Coen and Enrico Tassi to be
+ published in the Mathematical Structures in Computer Science journal.
+ </p>
+
<h2>Freescale<a name="freescale"></a></h2>
<p>
The <a href="freescale/">scripts</a> present:
for more information.
</p>
+ <h1>Small Developments</h1>
+
+ <h2>Pointed regular expressions<a name="freescale"></a></h2>
+ <p>
+ The <a href="re/">script</a> present:
+ </p>
+
+ <ul>
+ <li>a formalization of the syntax and semantics of pointed regular
+ expressions, that are regular expressions where points are put
+ in front of atoms to describe where the next character recognized
+ by the expression should be. Multiple points represent the union
+ of multiple languages. A pointed regular expression corresponds
+ to a state of a regular automaton for the regular expression
+ obtained erasing all points.</li>
+ <li>a formalization of the construction of the automaton for a regular
+ expression by means of iterative computation of pointed regular
+ expressions.</li>
+ <li>a proof of correctness of the construction (to be completed)</li>
+ </ul>
+
+ <p>The development requires the SVN version of Matita to be executed.</p>
+
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