1 <!--#include virtual="xhtml-header.shtml" -->
3 <html xmlns="http://www.w3.org/1999/xhtml">
5 <title>Matita - Library</title>
6 <!--#include virtual="xhtml-meta.shtml" -->
9 <!--#include virtual="menubar.shtml" -->
11 <h1>Matita Library</h1>
13 <h2>Scripts<a name="scripts"></a></h2>
15 The <a href="library/">scripts</a> used to generate the knowledge base of
16 Matita can be <a href="library/">browsed on line</a>.
19 The experimental <a href="nlibrary/">scripts</a> for the next major version of Matita can also be <a href="nlibrary/">browsed on line</a>.
24 <h1>Large Developments</h1>
26 <h2>Certified Complexity (CerCo)<a name="cerco"></a></h2>
27 <p>Matita is being used to certify a cost preserving compiler from a
28 large subset of C into the 8051 machine code. The compiler does not
29 only produce the target code, but it also instruments the source code
30 with precise cost declarations for the execution of O(1) code
31 fragments. This induced cost model for the source language is
32 inherently non compositional since it is affected by the compilation
33 strategy: the same instructions are compiled in different ways in
34 different contexts, yielding different costs.
36 <p>The final aim of the CerCo project is to formally reason on
37 intensional properties on the C code -- e.g. to show that some hard
38 deadline is always met
39 -- and to be sure that the property holds also for the target code.
41 <p>The CerCo project is a FET Open IST project funded by the EU
42 community in the 7th Framework Programme. More informations on the
43 project and the code of the Matita formalization can be found
44 on the <a href="cerco.cs.unibo.it">CerCo Web site</a>
47 <h2>The Basic Picture<a name="sambin"></a></h2>
49 The <a href="library/formal_topology">scripts</a> present a formalization
50 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.
52 <p>The formalization has been the result of a three years long
53 collaboration between mathematicians from the University of Padova
54 and computer scientists from the University of
55 Bologna, sponsored by the University of Padova. In particular,
56 the groups that collaborated are headed respectively by Prof. Sambin
57 in Padua (formal topology and constructive type theory)
58 and by Prof. Asperti in Bologna (constructive type theory and interactive
62 In particular the <a href="library/formal_topology">scripts</a> present:
65 <li>the category of Basic Pairs, that are generalizations of
66 topological spaces</li>
67 <li>the category of Basic Topologies, that are generalizations of
68 formal topologies</li>
69 <li>the existence of a categorical embedding of the former category
70 into the latter. The embedding is an improvement on the usual
71 adjunction between topological spaces and locales</li>
74 All the results are presented constructively and in the predicative
75 fragment of Matita based on the minimalist type theory
76 by Maietti and Sambin, where choice axioms are not valid.
78 In order to reason conformtably on the previous concrete categories and
79 functors, we also present algebraic versions of all the introduced
80 notions, as well as categorical embedding of the concrete categories in
81 the algebraized ones. In particular we formalized:
84 <li>the large category of Overlap Algebras, that extend locales with an
85 axiomatized (= algebraized) overlap binary predicate. The
86 concrete overlap predicate states positively
87 (i.e. without using negation) the existence (in the intuitionistic
88 sense) of a point in the intersection of two sets.
89 The natural morphism over Overlap Algebras are functions for the
90 existential and universal pre and post images of a relation.
92 <li>the large category of O-Basic Pairs, that algebraize Basic
93 Pairs by means of Overlap Algebras</li>
94 <li>the large category of O-Basic Topologies, that algebraize Basic
95 Topologies by means of Overlap Algebras</li>
96 <li>the categorical embedding of Basic Pairs into O-Basic Pairs and
97 of Basic Topologies into O-Basic Topologies</li>
98 <li>the existence of a categorical embedding of the category
99 of O-Basic Pairs into the category of O-Basic Topologies</li>
102 More information will be available in a forthcoming paper by
103 Claudio Sacerdoti Coen and Enrico Tassi to be
104 published in the Mathematical Structures in Computer Science journal.
107 <h2>Freescale<a name="freescale"></a></h2>
109 The <a href="freescale/">scripts</a> present:
113 <li>an executable formalization of the operational semantics of
114 any <a href="http://www.freescale.com">Freescale</a>
115 micro-controller of the <a href="http://www.freescale.com/webapp/sps/site/homepage.jsp?nodeId=0162468449&tid=FSH">HC05/HC08/RS08/HCS08 families</a>
117 <li>a compiler from assembly language (pseudocodes + operands) to
119 <li>several automatic checks for unhandled opcodes, memory accesses,
120 correctness of ALU logic, etc.</li>
121 <li>three examples of assembly programs (string reverse, counting sort
122 and perfect numbers sieve) with sets of data to run them</li>
125 <p>The execution in the executable formalization has been compared
126 to real world execution using the <a href="http://www.freescale.com/webapp/sps/site/overview.jsp?code=784_LPBBNEWTOOL&fsrch=1">USB SPYDER08</a>
131 The code (in <a href="http://caml.inria.fr">OCaml</a>)
132 of an executable <a href="freescale/freescale_ocaml">emulator</a>,
133 automatically generated from the scripts above. On the tests above,
134 it runs at about 29% of the speed of the
135 <a href="http://www.freescale.com/codewarrior">CodeWarrior</a>
139 <p>The formalization has been the Undergraduate Thesis of
140 Mr. Cosimo Oliboni. The manuscript (italian only) can be found
141 <a href="http://matita.cs.unibo.it/documentation.shtml#freescale">
145 <h2>The Formal System λδ (lambda-delta)<a name="lambda-delta"></a></h2>
147 <p>The formal system λδ is a typed λ-calculus that
148 pursues the unification of terms, types, environments and contexts
150 λδ takes some features from the Automath-related
151 λ-calculi and some from the pure type systems, but differs
152 from both in that it does not include the Π construction while it
153 provides for an abbreviation mechanism at the level of terms.
156 <p> The development presents the proofs of some important properties that
157 λδ enjoys. In particular:
158 <ul> <li> the confluence of reduction </li>
159 <li> the correctness of types </li>
160 <li> the uniqueness of types up to conversion </li>
161 <li> the subject reduction of the type assignment </li>
162 <li> the strong normalization of the typed terms </li>
163 <li> the decidability of type inference problem </li>
168 See the <a href="http://helm.cs.unibo.it/lambda-delta/">λδ home page</a>
169 for more information.
172 <h1>Small Developments</h1>
174 <h2>Pointed regular expressions<a name="freescale"></a></h2>
176 The <a href="re/">script</a> present:
180 <li>a formalization of the syntax and semantics of pointed regular
181 expressions, that are regular expressions where points are put
182 in front of atoms to describe where the next character recognized
183 by the expression should be. Multiple points represent the union
184 of multiple languages. A pointed regular expression corresponds
185 to a state of a regular automaton for the regular expression
186 obtained erasing all points.</li>
187 <li>a formalization of the construction of the automaton for a regular
188 expression by means of iterative computation of pointed regular
190 <li>a proof of correctness of the construction (to be completed)</li>
193 <p>The development requires the SVN version of Matita to be executed.</p>
195 <!--#include virtual="bottombar.shtml" -->