Curriculum Vitae. Prof. Antonino Salibra June 2008

Transcription

1 Curriculum Vitae Prof. Antonino Salibra June 2008 Address: Università Ca Foscari di Venezia Dipartimento di Informatica, Via Torino 155, Venezia, Italia salibra 1 Résumé Academic Positions: 1. Full Professor of Computer Science ( to date, Università Ca Foscari, Venezia); 2. Associate Professor of Computer Science ( , Università Ca Foscari, Venezia; , Università di Bari); 3. Research Associate ( , Università di Pisa); 4. Research grants, Italian Research Council ( , Università di Pisa). Responsability Positions (University of Venice): 1. Member of the Academic Senate 1 ( ). 2. Member of the Council of Faculty of Sciences ( ). 3. Member of the Educational Council of Faculty of Sciences ( to date). 4. Vice-Head of the Department of Computer Science ( ). 5. Member of the Council of Postgraduates Computer Science Courses ( to date). 6. Member of the Council of Undergraduates Computer Science Courses ( ). 7. President of the Commission approving the career of the students ( ). Sabbatical leaves: 1. Equipe PPS, Université Paris 7-Denis Diderot (2008, January-September); 2. Chargé de Recherche, LIX, École Polytechnique, Palaiseau (2007, two months); 3. Equipe PPS, Université Paris 7-Denis Diderot (2002, One-Month Professor; 2003, three months; 2004, three months; 2005, One-Month Professor; 2006, one month; 2007, One- Month Professor; supported by Université Paris 7, University of Venice, Italian Minister of University); 1 The Academic Senate is devoted to the political decisions of the University. It is constituted by the Head of the University and 17 other members. 1

2 4. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest (2003, one month; supported by European Community); 5. Mathematics Department, Victoria University of Wellington ( , three months; supported by Victoria University of Wellington); 6. Mathematics Department, Iowa State University (1992, two months; supported by NATO Senior Fellowships). Qualifications: 1. France: Qualification aux fonctions de Professeur des Universités, Section: 27 Informatique (period: 02/ /2009). 2 Research Field In this section I outline my research area and the scientific collaborations. Research Area: Logic and Theoretical Computer Science. Main Research Subjects: Mathematical Aspects of Computer Science; Programming. Detailed Research Subjects: Algebraic Semantics of Lambda Calculus; Model Theory of Lambda Calculus; Topology and Lambda Calculus; Abstract Data Types; Specification Formalisms; Equational Logic; Variable Binding; Universal Algebra; Abstract Model Theory; Algebraic Logic; Rewriting systems. Main Methodologies: Algebraic Methods. Secondary Methodologies: Topological and Combinatorial Methods. 2

3 Scientific Collaborations: Equipe PPS, Université Paris 7- Denis Diderot, France; LIX, École Polytechnique, Palaiseau; Department of Mathematics, Victoria University of Wellington, New Zealand; Department of Informatics, University of Twente, The Netherlands; Department of Mathematics, Iowa State University, USA; Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences, Hungary; Dipartimento di Informatica, University of Pisa, Italy. 3 Professional experience Undergraduate Courses: My teaching activity mainly was for the Undergraduate Courses on Computer Science Curriculum: Formal Methods ( , Venice), Computer Organization and Design ( , Venice), Theory of Computability ( , Venice), Formal Languages and Compilers ( , Bari), Computer Systems (1992, Bari and Bologna) Programming (1991, Pisa). In eighties I was assistant professor at the University of Pisa and my teaching activity mainly was for the Undergraduate Courses on Computer Science Curriculum: Theory of Computability and Formal Languages ( , Pisa), Foundation of Programming ( , Pisa), Programming ( , Pisa). Postgraduate Courses: [S-3] Algebraic and Topological Methods in Lambda Calculus, Hungarian Academy of Sciences, Budapest, 2003 [S-2] Lambda Calculus, Università Ca Foscari di Venezia, 2002 [S-1] Algebraic Semantics, Università di Bologna, 1995 PhD Thesis: I guided and am guiding the following students in preparing their graduation thesis. Stefania Lusin, Intersection Types, Lambda Abstraction Algebras and Lambda Theories, PhD thesis, Giulio Manzonetto, Models and theories of λ-calculus, PhD thesis, February Alberto Carraro, PhD thesis, Committees: I was a member of a PhD Committee (1993), University of Twente, Enschede, The Netherlands. I am a program committee member of the International Conference in Computer Science Logic (CSL-08), the annual conference of the European Association for Computer Science Logic (EACSL), Bologna-Bertinoro, Italy, September 15-20, Research Projects: Organization: Workshop of the national research project CoMeta Computational Metamodels held in December 2002 at University of Venice. Head project: International project TEMPUS (Trans-European Mobility Scheme for University Studies), Advanced joint european project for restructuring and upgrading the educational system at the Faculty of Electrical Engineering, Technical University of Budapest (1992). 3

4 Participant: MyThS Models and Types for Security in Mobile Distributed Systems, Contract IST , European project. (Head of the project: Vladimiro Sassone, University of Sussex) FOLLIA, FOndazioni Logiche di LInguaggi Astratti di Programmazione, (MURST, Italian Minister of University and Technological Research). (Head of the project: Simona Roinchi della Rocca, University of Torino). CoMeta Computational Metamodels (MURST, Italian Minister of University and Technological Research). (Head of the project: Furio Honsell, University of Udine). Metodi costruttivi in Topologia, Algebra e Analisi dei Programmi (MURST, Italian Minister of University and Technological Research). (Head of the project: G. Sambin, University of Padoa). Modelli e Metodi della Computazione e dei Linguaggi di Programmazione, MURST, Progetto Coordinato-CNR Programmazione Logica: Strumenti per Analisi e Trasformazione di Programmi; Tecniche di Ingegneria del Software; Estensioni con vincoli, concorrenza ed oggetti; Validazione ed Ottimizzazione di Programmi Logici Scientific Commettee: President of the scientific committee of the project MOOseo Virtuale delle fiabe: nuovi sviluppi e prospettive ( ), financial supported by Veneto Region ex art. 57 della Legge Regionale n. 1 del 2004 (finanziamenti a sostegno della scuola veneta). Member of the scientific committee of the project MOOseo Virtuale delle fiabe ( ), financial supported by Veneto Region ex art. 57 della Legge Regionale n. 1 del 2004 (finanziamenti a sostegno della scuola veneta). Invited Seminars: [S-16] March 2008: Joint Queen Mary/Imperial Seminar, Queen Mary College and Imperial College, London. [S-15] February 2008: Laboratoire LIPN, Univ. Paris 13, Villetaneuse (Paris). [S-14] November 2007: LIX, Ecole Polytechnique, Palaiseau. [S-13] Laboratoire PPS, Université Paris 7-Denis Diderot, Paris March 2007 May 2006; June 2005 (Workshop GEOCAL); June 2004; May 2004; June 2003; May [S-12] February 2003: Department of Mathematics, University of Padoa, Italy [S-11] June 2002: Department of Computer Science, University of Turin, Italy [S-10] February 2002: Department of Computer Science, University of Verona, Italy [S-9] January 1998: Department of Computer Science, University of Turin, Italy [S-8] Mathematical Institute of the Hungarian Academy of Sciences, Budapest, Hungary March 1996; 4

5 April 1996; February 1992; May [S-7] March 1996: Department of Mathematics, University of Padoa [S-6] June 1995: LADSEB, Italian National Council, Padoa [S-5] February 1992: Department of Computer Science, University of Bari [S-4] July 1991: Department of Mathematics, University of Colorado, Boulder, Colorado, Usa [S-3] June 1991: Department of Computer Science, University of Iowa, Iowa City, Iowa, Usa [S-2] June 1991: Department of Mathematics, Iowa State University, Ames, Iowa, USA [S-1] February 1990: Universitè de Paris-Sud, LRI, Orsay, France Invited Lectures: [L-12] Geometria della Logica (Incontro di studio di Logica Matematica, Filosofia e Informatica) Rome, Italy, April 2006 Lambda calculus: models and theories [L-11] AMiLP-3, Third AMAST Workshop on Algebraic Methods in Language Processing, Verona, Italy, August 2003 Lambda calculus: models and theories [L-10] Conference Logic, Algebra, Relativity held in Budapest (2002, November) in Honor of Istvan Nemeti Algebraic and topological methods in lambda calculus [L-9] Workshop on Abstract Algebraic Logic, Barcelona, Spain (July 1997) Categorical frames and Boolean algebras with operators in a category [L-8] Very Informal Conference on Theoretical Computer Science, Wellington, New Zealand (December 1996) Categorical Modal Logic [L-7] Conference on Modern Algebra and its Applications, Nashville, USA (May 1996) The algebraic logic of lambda calculus [L-6] Summer School on Algebraic Logic and Categorical Methods in Computer Science, Budapest, Hungary (July 1994) The abstract variable-binding calculus [L-5] XXXVIII Banach Semester on Algebraic Methods in Logic and Their Computer Science Applications, Varsaw, Poland (Sept. 1991) Lambda abstraction algebras: axiomatization and representability results [L-4] XXXVIII Banach Semester on Algebraic Methods in Logic and Their Computer Science Applications, Varsaw, Poland (Sept. 1991) Compactness and Löwenhein-Skolem properties in pre-institution categories [L-3] Meeting on algebraic logic, Mills College, Oakland, USA (June 1990) On atom Structures of Cylindric Algebras [L-2] Conference on Algebraic Logic, University of Colorado, Boulder, USA (May 1990) On atom Structures of Cylindric Algebras [L-1] Conference on Algebraic Logic, Budapest, Hungary (August 1988) A universal algebraic approach to languages, logic and semantics 5

6 Recent Lectures at Project Workshops [W-7] 12/2002: Workshop National Project CoMeta Metamodelli Computazionali MIUR , Venezia, December Title: Topologie nel lambda calcolo. [W-6] 03/2003: Workshop projet MathSTIC Logique et Smantique des Langages de Programmation, Equipe PPS, Universit Paris 7-Denis Diderot, Paris, March 16-17, Title: The lattice of lambda theories. [W-5] 12/2003: Workshop National Project CoMeta Metamodelli Computazionali MIUR , Udine, December Title: The sensible lambda theories of graph models. [W-4] 05/2005: Workshop National Project FOLLIA MIUR Geometria e strutture nelle prove e nei programmi, Roma, Maggio Title: Problemi aperti nella semantica del lambda calcolo puro. [W-3] 06/2005: Workshop International Project GEOCAL (Gometri du calcul) Sémantique du calcul, Equipe PPS, Universit Paris 7-Denis Diderot, Paris, Giugno Title: Visser versus Scott. [W-2] 01/2006: Workshop National Project FOLLIA MIUR Geometria e strutture nelle prove e nei programmi, Torino, January Title: Boolean algebras for lambda calculus. [W-1] 10/2006: Final Workshop National Project FOLLIA MIUR Geometria e strutture nelle prove e nei programmi, Bologna, October Title: Recursively Eenumerable lambda theories. Referee: I was the referee of the research project P162 of University of Padoa (1999). I acted as a referee for many journals and collections including: Journal of IGPL, Journal of Logic and Computation, Theoretical Computer Science, Fundamenta Informaticae, Information Processing Letters, Studia Logica, Algebra Universalis, Rendiconti del Seminario Matematico dell Università di Padova, Algebraic Logic (H. Andrèka, D. Monk, I. Nèmeti, eds.), etc. I acted as a referee for many conferences including: LICS (Logic in Computer Science), AMAST (Algebraic Methodology And Software Technology), MFCS (Mathematical Foundation of Computer Science), WADT (Workshop on Abstract Data Types), WoLLIC, ICLP, CIAK, JICSLP, ICTCS, TLCA, STACKS, CAAP, TAPSOFT, etc. 4 Former research activity In this section the detailed former research activities are described. 4.1 Extension of equational logic with type assignment Research subject: Abstract Data Types and Equational Logic. This research was developed in collaboration with V. Manca (University of Pisa) and G. Scollo (University of Twente), when I was research associate at University of Pisa. We have introduced and studied ET logic [34, 35, 16, 39, 15, 32], which is an extension of conditional equational logic by a binary predicate, which denotes a type assignment relation. We had interest towards such an extension because of limitations which were found in practice with the use of many-sorted conditional equational logic, e.g. for the specification of abstract data types with partial functions, polymorphic types, dependent types. In comparison to other formalisms, the main advantages of ET logic are 6

7 simplicity and unifying character, that is the fact that different problems find solution in a single formal system. The paper in [32] presents translation results for logics frequently found in the algebraic specification literature, thus corroborating the view of ET logic as having a unifying character. More precisely, sound and complete translations into ET logic are given for the following conditional logics: order-sorted equational logic, equational logic with partial algebras, (positive) Horn clausal logic. The translations proposed in [32] obey to a uniform scheme, which motivated the research started in [30] (see Section 4.4). ET conditional rewriting was studied in [16]. 4.2 Many-sorted equational logic Research subject: Abstract Data Types and Equational Logic. This research was developed in collaboration with V. Manca (University of Pisa), when I was research associate at University of Pisa. Many-sorted equational logic was used in the eighties and nineties as a formalism for specifying abstract data types, and it was shown in [17] enough powerful to represent first-order logic. Many-sorted equational logic is unsound when the possibility of having empty carrier sets is admitted. In [33, 15] a sound and complete calculus for many-sorted equational logic with possibly empty domains is provided. 4.3 The abstract variable-binding calculus Research subject: Variable Binding and Algebraic Logic. This research was developed in collaboration with Don Pigozzi (Iowa State University), when I was research associate at University of Pisa and then associate professor at University of Venice. I have initiated an investigation of substitution and variable-binding in the paper [38], which was presented at the Conference on Algebraic Logic held in Budapest in The pioneering paper [38] was developed in [37, 13], where it was introduced the abstract variable-binding calculus, which is modeled on the lambda calculus. In [13] an algebraic formulation of the variable-binding calculus is presented in which substitution is represented by an abstract operator. This gives rise to the variety (i.e., equational class) of polyadic VB-algebras. The main result of [13] is a functional representation theorem for polyadic VB-algebras which specializes to a completeness theorem for a number of familiar systems that can be formalized as variable-binding calculi. For example, the lambda calculus, the classical first-order predicate calculus, the theory of the generalized quantifier exists uncountable many and a fragment of Riemann integration. The theory of polyadic VB-algebras is also designed to provide a means of algebraizing first-order extensions, with the standard quantifiers, of a wide class of nonstandard propositional logics. We have obtained some results in this direction in [37], where the polyadic algebras of standard implicational calculi (SIC) are introduced. SIC s were considered by Rasiowa and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Lukasiewicz, modal logics that admit the rule of necessitation, BCK logic, etc. Each SIC S gives rise to the quasivariety of polyadic S-algebras. As a special case of the representation theorem presented in [13], the main result of [37] is a functional representation theorem for polyadic S-algebras that includes many of the known representation results for polyadic algebras over nonclassical logics. The algebraic techniques used in this research were exploited in the algebraization of lambda calculus (see Section 4.5 below). This research is related to the formalisms for variable binding introduced recently in Computer Science (See, for example, the Nominal Logic by Pitts: Nominal logic: A first order theory of names and binding, 4th International Symposium, TACS, 2001). 7

8 4.4 Algebraic and logical foundations of computing science Research subject: Abstract Model Theory and Specification Formalisms. This research was developed in collaboration with G. Scollo (University of Twente), when I was associate professor at University of Venice. The theory of institutions provides algebraic and logical specification with a very general framework, in fact a metatheory that proves useful to the classification and comparative analysis of several specification formalisms. However, that theory did not appear to be useful enough to formulate the expressiveness results obtained in [32]. In [12, 36, 26, 30] the concepts of pre-institution and of pre-institution transformation were introduced and the use of those concepts in the design of logical systems was analyzed. Moreover, a series of abstract model-theoretic results relating to pre-institution transformations were obtained. With [36], downward inheritance of model-theoretic properties along suitable pre-institution transformations turns out to be a wider phenomenon, generalizing the so-called reduction scheme in model-theoretic logics. Various instances of this phenomenon are investigated in [36], where the concepts of compact transformation and of cardinal pre-institution are introduced, yielding further results on downward inheritance of compactness and of Löwenheim-Skolem properties, and on the equivalence with first-order pre-institutions. New results on interpolation and Robinson properties are included in [12]. This research is up-to-date (see the papers by M. Aiguier and F. Barbier: An Institution-independent Proof of the Beth Definability Theorem, Studia Logica 85(3): , 2007; Structures for abstract rewriting, Journal of Automated Reasoning 38(4): , 2007). 4.5 The algebraic approach to Lambda Calculus Research subject: Algebraic Semantics, Universal Algebra, Model Theory of Lambda Calculus. This research was developed in collaboration with Don Pigozzi (Iowa State University), Robert Goldblatt (Victoria University of Wellington), Chantal Berline (University of Paris 7), Antonio Bucciarelli (University of Paris 7) and Giulio Manzonetto (University of Venice), when I was professor at University of Venice. Lambda Abstraction Algebras ([8, 4, 9, 10, 14, 28, 23, 29, 31]): I have launched in the nineties a research program for exploring lambda calculus using techniques of universal algebra and algebraic logic. The remark that the lattice of lambda theories is isomorphic to the congruence lattice of the term algebra of the least lambda theory λβ, is the starting point for studying the lambda calculus by universal algebraic methods. In [9] I have shown that the variety (i.e., equational class) generated by the term algebra of λβ is axiomatized by the finite schema of identities characterizing λ-abstraction algebras (LAAs). The variety of λ-abstraction algebras, introduced in [29, 31] at the beginning of nineties, constitutes a purely algebraic theory of the untyped lambda calculus, which keeps the lambda notation and hence all the functional intuitions. In [9] it is shown that, for every variety of LAAs, there exists exactly one lambda theory whose term algebra generates the variety. Thus, the properties of a lambda theory can be studied by means of the variety of LAAs generated by its term algebra. The natural LAAs, the ones the axioms were intended to characterize, are algebras of functions, which arise as expansions of lambda calculus models by the variables of lambda calculus in a natural way. Questions on the functional representation of various subclasses of lambda abstraction algebras were investigated in a series of papers [29, 31, 28, 14]. The main result in this research was obtained in collaboration with Goldblatt [10]: every lambda abstraction algebra is isomorphic to an algebra of functions arising from a model of lambda calculus. This theorem provides a completeness theorem for the infinitary lambda calculus, which arises in the study of infinite normal forms of lambda terms. Every infinitary lambda theory is the theory of 8

9 a suitable model of lambda calculus. I have recently shown in collaboration with Berline that there exists a congruence distributive variety of LAAs (see [4]). The existence of varieties of LAAs satisfying strong algebraic properties was an open problem since I proved in [8] that the variety LAA is not congruence modular. The existence of a congruence distributive variety of LAAs shows, against the common belief, that the lambda calculus satisfies strong algebraic properties. The main applications of the theory of LAAs are explained in the next paragraph. The Lattice of Lambda Theories ([5, 22, 3, 9]): There is a close relationship between the lattice of lambda theories and the variety LAA. In [9] I have shown that the lattice of lambda theories is isomorphic to the lattice of equational theories of LAAs. Not all lattices can be lattices of equational theories because the lattices of equational theories satisfy nontrivial quasi-identities in the language of lattices. The quasi-identities which hold in the lattice of lambda theories were investigated in [5]. I have conjectured at the end of the nineties that the lattice of lambda theories does not satisfy any nontrivial lattice identity. The first result in this area was obtained in [8], where it was shown that the non-modular pentagon N 5 embeds into the lattice of lambda theories. To support the conjecture I have shown in collaboration with Lusin (see [5]) that, for every nontrivial lattice identity e, there exists a natural number n such that e fails in the lattice of lambda theories in a language of λ-terms with n constants. One can ask whether the conjecture holds also for suitable fragments of the lattice of lambda theories: is there a lambda theory φ such that the interval sublattice [φ) = {ψ : φ ψ} is large and satisfies interesting lattice identities? In [4] it was shown that there exists a large and distributive interval sublattice [φ), where φ is a finitely axiomatizable lambda theory. This result is a consequence of the results described in the paragraph entitled Forcing. In collaboration with Manzonetto I have recently shown that, for every natural number n, there exists a lambda theory φ n such that the interval sublattice [φ n ) is isomorphic to the finite Boolean lattice with 2 n elements. The commutator ([5, 8]): General commutator theory originated from group theory and has to do with a binary operation, the commutator, that can be defined on the set of congruences of any algebra. The operation is very well behaved in congruence modular varieties. In [8] it was shown that the variety of lambda abstraction algebras and the variety of combinatory algebras are not congruence modular, as a consequence it is not possible to apply to them the nice properties of commutator developed for congruence modular varieties. I have also shown in collaboration with Lusin [5] the following results: (i) the commutator has a good behavior when one of the involved lambda theories is the inconsistent theory; (ii) a lattice identity holds in the congruence lattice of all LAAs if, and only if, it is trivial. Boolean algebras for lambda calculus ([20]): One of the milestones of modern algebra is the Stone representation theorem for Boolean algebras, which was generalized by Pierce to commutative rings with unit and next by Comer to the class of algebras with Boolean factor congruences. In collaboration with Manzonetto [20] I have generalized the Stone representation theorem to combinatory algebras. In every combinatory algebra there is a Boolean algebra of central elements (playing the role of idempotent elements in rings), whose operations are defined by suitable combinators. Central elements are used to represent any combinatory algebra as a Boolean product of directly indecomposable combinatory algebras (i.e., algebras which cannot be decomposed as the Cartesian product of two other nontrivial algebras). Applications of the Stone theorem to lambda calculus were given in [20]. The indecomposable semantics (i.e., the semantics of lambda calculus given in terms of models, which are directly indecomposable as combinatory algebras) includes the continuous semantics and its refinements, and the term models of all semisensible 9

10 lambda theories. The indecomposable semantics is equationally incomplete, and this incompleteness is as wide as possible: for every recursively enumerable lambda theory φ, there is a continuum of lambda theories including φ which are omitted by the indecomposable semantics. 4.6 The model theory of Lambda Calculus This research was developed in collaboration with Chantal Berline (University of Paris 7), Antonio Bucciarelli (University of Paris 7) and Giulio Manzonetto (University of Venice), when I was professor at University of Venice. Incompleteness ([24, 25, 6]): A semantics of lambda calculus is equationally incomplete if there exists a lambda theory which is not induced by any model in the semantics. In [24, 25, 6] I have introduced a new technique to prove in a uniform way the incompleteness of all denotational semantics of lambda calculus which have been proposed so far, including the strongly stable one, whose incompleteness had been conjectured by Bastonero, Gouy and Berline. The technique is applied to prove the incompleteness of any semantics of lambda calculus given in terms of partially ordered models with a bottom element. Further results are: (i) an incompleteness theorem for partially ordered models with finitely many connected components; (ii) an incompleteness theorem for topological models whose topology satisfies a suitable property of connectedness; (iii) a completeness theorem for topological models whose topology is non-trivial and metrizable. Absolutely Unorderable Combinatory Algebras ([6, 7]): By giving a partial answer to a question by Plotkin, I have characterized in collaboration with Lusin a wide class of combinatory algebras which are not absolutely unorderable. Graph Models of Lambda Calculus ([21, 4, 22, 3, 19]) 1. Sensible lambda theories ([3, 21, 22]): An interesting question is whether, given a class of models, there exist a minimal and maximal sensible lambda-theory represented by it. In collaboration with Bucciarelli I have given a positive answer to this question for the semantics of lambda calculus given in terms of graph models. The greatest sensible graph theory is characterized as the lambda-theory B generated by equating lambda terms with the same Böhm tree. This result is a consequence of the fact that all the equations between solvable lambda-terms, which have different Böhm trees, fail in every sensible graph model. Other results are: (i) the existence of a continuum of different sensible graph theories strictly included in B (this result positively answers a question by Berline); (ii) the nonexistence of a graph model whose equational theory is exactly the minimal lambda theory λβ (this result negatively answers a long standing open question for the class of graph models). 2. Forcing ([4]): Baeten and Boerboom s method of forcing is generalized to show that there exists a countable infinite sequence of easy lambda terms, that can be contemporaneously equated to any other countable infinite sequence of closed lambda terms. Lambda theories of effective lambda models ([19]): The question of whether the equational theory of an effective model of lambda calculus can be recursively enumerable (r.e. for brevity) is investigated. The following results have been obtained: (i) The equational theory of an effective model cannot be lambda-beta, lambda-beta-eta; (ii) The order theory of an effective model cannot be r.e.; (iii) No effective model living in the stable or strongly stable semantics has an r.e. equational theory. Concerning Scott s semantics, the class of graph models has been investigated and the following results were obtained, where graph theory is a shortcut for theory of a graph model : (iv) There exists a minimum order/equational graph theory; (v) 10

11 The minimum equational/order graph theory is the theory of an effective graph model; (vi) No order graph theory can be r.e. 5 Publications Submitted Papers [1] C. Berline, G. Manzonetto and A. Salibra. Effective Lambda Models Versus Recursively Enumerable Lambda Theories. Research report, 35 pp., January 2008, submitted. International Journals [2] G. Manzonetto and A. Salibra, Applying Universal Algebra to Lambda Calculus, January 2008, Journal of Logic and Computation (Special Issue of the International Conference on Order, Algebra and Logics), (to appear). [3] A. Bucciarelli, A. Salibra, Graph lambda theories, Mathematical Structures in Computer Science 2008 (to appear). [4] C. Berline, A. Salibra, Easiness in graph models, Theoretical Computer Science vol. 354, Issue 1 (2006), [5] S. Lusin, A. Salibra, The lattice of lambda theories. Journal of Logic and Computation, Vol. 14 n.3 (2004), [6] A. Salibra, Topological incompleteness and order incompleteness of the lambda calculus (Special Issue LICS 01), ACM Transactions on Computational Logic vol. 4 (2003), [7] S. Lusin, A. Salibra, A note on absolutely unorderable combinatory algebras, Journal of Logic and Computation, Vol. 13 n.4 (2003), [8] A. Salibra Nonmodularity results for lambda calculus, Fundamenta Informaticae, vol. 45 (2001), [9] A. Salibra On the algebraic models of lambda calculus, Theoretical Computer Science, vol. 249 (2000), [10] A. Salibra, R. Goldblatt, A finite equational axiomatization of the functional algebras for the lambda calculus, Information and Computation vol. 148 (1999), [11] D. Pigozzi, A. Salibra, Lambda abstraction algebras: coordinatizing models of lambda calculus, Fundamenta Informaticae vol. 33 (1998), [12] A. Salibra, G. Scollo, Interpolation and Compactness in categories of pre-institutions, Mathematical Structures in Computer Science vol. 6 (1996), [13] D. Pigozzi, A. Salibra, The abstract variable-binding calculus, Studia Logica, vol. 55, n. 1 (1995), [14] D. Pigozzi, A. Salibra, Lambda abstraction algebras: representation theorems, Theoretical Computer Science, vol. 140 (1995),

12 [15] V. Manca, A. Salibra, Soundness and Completeness of the Birkhoff Equational Calculus for Many-sorted Algebras with Possibly Empty Carrier Sets, Theoretical Computer Science vol. 94 (1992), [16] V. Manca, A. Salibra, G. Scollo, Equational Type Logic, Theoretical Computer Science vol. 77 (1990), [17] V. Manca, A. Salibra, First-order Theories as Many-sorted Algebras, Notre Dame Journal of Formal Logic vol. 25 (1984), International Conferences [18] G. Manzonetto and A. Salibra, From Lambda Calculus to Universal Algebra and Back, 33rd International Symposium on Mathematical Foundations of Computer Science, Torun, Poland, LNCS, Springer-Verlag, [19] C. Berline, G. Manzonetto, A. Salibra, Lambda theories of effective lambda models, Proc. of 16th EACSL Annual Conference on Computer Science and Logic (CSL 07), LNCS 4646, pp , Springer-Verlag (2007). [20] G. Manzonetto, A. Salibra, Boolean algebras for lambda calculus, Proceedings of 21st Annual IEEE Symposium on Logic in Computer Science (LICS 06), Seattle, Washington, USA, August 12th 15th, IEEE Computer Society Publications. [21] A. Bucciarelli, A. Salibra, The sensible graph theories of lambda calculus, Proceedings of 19th Annual IEEE Symposium on Logic in Computer Science (LICS 04), Turku, Finland, July 13 18, 2004, IEEE Computer Society Publications, [22] A. Bucciarelli, A. Salibra The minimal graph model of lambda calculus, Proc. 27th International Symposium on Mathematical Foundations of Computer Science, LNCS 2747, Springer- Verlag (2003), [23] A. Salibra Lambda calculus: models and theories (Invited Lecture), Proceedings of the Third AMAST Workshop on Algebraic Methods in Language Processing (AMiLP-2003), F. Spoto, G. Scollo and A. Nijhol eds., TWLT Proceedings Series n.21, University of Twente (2003), [24] A. Salibra A continuum of theories of lambda calculus without semantics, Proceedings of 16th Annual IEEE Symposium on Logic in Computer Science (LICS 01), Boston, USA, June 16 19, 2001, IEEE Computer Society Publications, [25] A. Salibra Towards lambda calculus order-incompleteness, Workshop on Böhm theorem: applications to Computer Science Theory (BOTH 2001), Electronics Notes in Theoretical Computer Science Vol. 50 No. 2, Elsevier Science B, V., 2001, [26] A. Salibra On categorical frames, universal algebra and Boolean algebras with operators in a category, Proc. Workshop on Abstract Algebraic Logic Bellaterra, Spain, July 1 5, (J. Font, R. Jansana, D. Pigozzi eds.), CRM Quaderns num. 10/ gener 1998, (Invited Lecture). [27] A. Salibra, The variety of lambda abstraction algebras does not admit n-permutable congruences for all n, 4th International Seminar RelMiCS, (Ewa Orlowska and Andrzej Szalas eds.), Warsaw, Poland, Septermber 14-20,

13 [28] D. Pigozzi, A. Salibra, Dimension-complemented lambda abstraction algebras, Proc. 3rd International Conference on Algebraic Methodology and Software Technology (AMAST 93), Enschede, Olanda, June 1993, (M. Nivat, C. Rattray, T. Rus, G. Scollo eds.), Workshops in Computing, Springer-Verlag, London, 1994, [29] D. Pigozzi, A. Salibra, A representation theorem for lambda abstraction algebras, Proc. 18th International Symposium on Mathematical Foundations of Computer Science, (A.M. Borzyszkowski, S. Sokolowski eds.) Lecture Notes in Computer Science vol. 711, Springer-Verlag, 1993, [30] A. Salibra, G. Scollo, A soft stairway to institutions, Recent Trends in Data Type Specification, (M. Bidoit, C. Choppy eds.), Lecture Notes in Computer Science vol. 655, Springer-Verlag, 1993, [31] D. Pigozzi, A. Salibra, Introduction to lambda abstraction algebras, Proceedings of the IX Latin American Symposium on Mathematical Logic, (Baha Blanca, 1992) Notas de Logica Matematica vol. 38 (1993), [32] V. Manca, A. Salibra, G. Scollo, On the Expressiveness of Equational Type Logic, Proc. Conference on The Unified Computation Laboratory: Modelling, Specifications and Tools, (C.M.I. Rattray, R.G. Clarke eds.), Oxford University Press, 1992, [33] V. Manca, A. Salibra, Equational Calculi for Many-sorted Algebras with Empty Carrier Sets, Proc. 15th International Symposium on Mathematical Foundation of Computer Science (MFCS 90), (B. Rovan ed.), Lecture Notes in Computer Science vol. 452, Springer-Verlag, 1990, [34] V. Manca, A. Salibra, G. Scollo, On the nature of TELLUS (a Typed Equational Logic Look over Uniform Specification), Proc. 14th International Symposium on Mathematical Foundation of Computer Science (MFCS 89), (A. Kreczmar, G. Mirkowska eds.), Lecture Notes in Computer Science vol. 379, Springer-Verlag, 1989, [35] V. Manca, A. Salibra, G. Scollo, DELTA: a Deduction system integrating Equational Logic and Type Assignment, Proc. of the first International Conference on Algebraic Methodology and Software Technology, Iowa City, Iowa, May 23 25, 1989, Papers in Collections [36] A. Salibra, G. Scollo, Compactness and Löwenheim-Skolem properties in pre-institution categories, Algebraic Methods in Logic and in Computer Science, (C. Rauszer ed.), Banach Center Publications vol. 28, Inst. Math. Polish Acad. Sci., Warszawa, 1993, [37] D. Pigozzi, A. Salibra, Polyadic algebras over non-classical logics, Algebraic Methods in Logic and in Computer Science, (C. Rauszer ed.), Banach Center Publications vol. 28, Polish Academy of Sciences, Warszawa, 1993, [38] A. Salibra, A General Theory of Algebras with Quantifiers, Algebraic Logic, (H. Andréka, J.D. Monk, I. Németi eds.), Colloq. Math. Soc. J. Bolyai vol. 54, North-Holland Publishing Co., Amsterdam, 1991, [39] V. Manca, A. Salibra, On the Power of Equational Logic: Applications and Extensions, Algebraic Logic, (H. Andréka, J.D. Monk, I. Németi eds.), Colloq. Math. Soc. J. Bolyai vol. 54, North-Holland Publishing Co., Amsterdam, 1991,

14 Italian Conferences [40] A. Salibra, Universal Algebraic Semantics, Atti degli Incontri di Logica Matematica, Università di Siena, Siena, [41] V. Manca, A. Salibra, Algebra Universale e Logica in Computer Science, Atti degli Incontri di Logica Matematica, Università di Siena, Siena, Books [42] S. Antonelli, V. Manca, A. Salibra, Logica del Primo Ordine, Editrice Tecnico Scientifica, Pisa, [43] S. Antonelli, V. Manca, A. Salibra, Logica, Editrice Tecnico Scientifica, Pisa, Abstracts [44] A. Salibra, Boolean algebras and lambda calculus (abstract), International Conference on Algebraic and Topological Methods in Non-Classical Logics III (TANCL 07), University of Oxford, Oxford, England, August 5-9, [45] A. Salibra, Algebra and topology in lambda calculus (abstract), accepted as one of the ten Plenary Presentations at International Conference on Order, Algebra and Logics, Nashville, USA, June 12-17, oal2007/viewabstracts.php [46] A. Salibra, G. Scollo, A reduction scheme by pre-institution transformations (abstract), Journal of Symbolic Logic vol. 58 (1993), [47] V. Manca, A. Salibra, G. Scollo, Introducing equational type logic (abstract), Journal of Symbolic Logic vol. 56 (1991), Reviews [48] A. Salibra, Review for Zentralblatt MATH of the paper: Z.M. Arola, S. Blom, Skew confluence and the lambda calculus with letrec, Annals of Pure and Applied Logic, vol. 117 (2002) [49] A. Salibra, Review for Zentralblatt MATH of the paper: P. Hofstra and J. van Oosten, Ordered partial combinatory algebras, Math. Proc. Cambridge Phil. Soc., vol. 134 (2003) [50] A. Salibra, Review for Zentralblatt MATH of the paper: M. Dezani-Ciancaglini, S. Ghilezan, and S. Likavec. Behavioural inverse limit models. Theoret. Comput. Sci., 316(1-3):49-74, [51] A. Salibra, Review for Zentralblatt MATH of the paper: F. Alessi, M. Dezani-Ciancaglini and S. Lusin. Intersection types and domain operators. Theoret. Comput. Sci., 316(1-3):25-47, [52] A. Salibra, Review for Zentralblatt MATH of the paper: P. O Hearn, On bunched typing, Journal of Functional Programming, vol. 13 (2003)

15 Technical Reports [53] A. Salibra, Algebraic and topological methods in lambda calculus. In the unpublished booklet entitled Logic, Algebra, Relativity Papers dedicated to Istvan Nemeti, Alfred Renyi Institute of Mathematics, Budapest, November The booklet was prepared for the conference in honor of Istvan Nemeti, program committee: M. Ferenczi, A. Kurucz, G. Sagi, and I. Sain. [54] E. Jabara, A. Salibra, Una nota sui gruppoidi topologici (in italian). Research Report CS , Universita Ca Foscari, Venezia, [55] A. Salibra Modularity in lambda calculus, Appia-Gulp-Prode 2000, La Habana, Cuba, December [56] A. Salibra The algebraic categorical modal logic of deductive systems and universal algebra, Research Report CS97-14, Università Ca Foscari, Venezia, [57] A. Salibra Categorical frames and Boolean algebras with operators in a category, Participants Handout of the Workshop on Abstract Algebraic Logic. (J. Font, R. Jansana, D. Pigozzi eds.), Internal Report, University of Barcelona, Barcelona, Spain, [58] A. Salibra, Cylindric semilattices generating atom structures of cylindric algebras, Research Report CS95-2, Università Ca Foscari, Venezia, [59] A. Salibra, G. Scollo, Polymorphies = Categories + Algebras, Partecipants Handout of the 10th Workshop on Abstract Data Type. (E. Astesiano, M. Cerioli, G. Reggio eds.), Internal Report, University of Genova, Department of Computer Science, [60] V. Manca, A. Salibra, G. Scollo, ADT specification constructs for equational type logic, Partecipants Handout of the 7th Workshop on Specification of Abstract Data Type, (K.P. Jantke, H. Reichel eds.), Internal Report University of Leipzig, Department of Computer Science, [61] V. Ambriola, A. Salibra, Tree Sequential Term Rewriting Systems, Research Report TR 40/89, Dipartimento di Informatica, Università di Pisa, Dicembre [62] V. Manca, A. Salibra, Soundness and Completeness of the Birkhoff Many-Sorted Equational Calculus, Partecipants Handhout of the 5th Workshop on Specification of Abstract Data Types, (Don Sannella ed.), Report No. ECS-LFCS-87-41, University of Edinburgh, Department of Computer Science, [63] R. Barbuti, A. Salibra, The integration of logic negation and negation as failure in logic programming, Research Report, Dipartimento di Informatica, Università di Pisa, ottobre [64] V. Manca, A. Salibra, High-order algebras, Research Report, Dipartimento di Informatica, Università di Pisa, settembre [65] V. Manca, A. Salibra, Sviluppi algebrici della nozione di struttura nella semantica dei linguaggi, Research Report, Dipartimento di Informatica, Università di Pisa, marzo [66] V. Manca, A. Salibra, Algebraic semantics through based algebras, Research Report, Dipartimento di Informatica, Università di Pisa, ottobre [67] S. Antonelli, V. Manca, A. Salibra, A deduction system based on the analytic tableaux, Research Report, Dipartimento di Informatica, Università di Pisa, ottobre [68] V. Manca, A. Salibra, Σ-formalisms: an extension of the many-sorted algebras, Research Report, Dipartimento di Informatica, Università di Pisa, giugno

16 [69] V. Manca, A. Salibra, Un approccio algebrico allo studio dei formalismi, Research Report, Dipartimento di Informatica, Università di Pisa, novembre