M SEMINARIO MATEMATICO Università' e Politecnico Torino

' ; K «i

Fascicoli speciali pubblicati

Stochastic Problems in Mechanics Linear Partial and Pseudo differential Operators Differential Geometry on Homogeneous Spaces Special Functions: Theory and Computation Algebraic Varieties of Small Dimension Linear and Non-linear Mathematica! Control Theory

Distribuzione in Italia ROSENBERG & SELLIER, Editori in Torino Via Andrea Doria, 14 10123 TORINO

Italia Europa Extraeuropa

Abbonamento 1987 (3 Fascicoli ordinari 105.000 140.000 200.000 e 2 speciali) Fascicolo speciale (separatamente) 50.000 70.000 90.000

Inviare assegno bancario sbarrato o effettuare versamento sul ccp 11571106 intestato a Rosenberg & Sellier Editori in Torino, specificando la causale del versamento: "Rendicon­ti del Seminario Matematico, abbonamento 1987". Le annate arretrate si vendono al prezzo dell'abbonamento in corso. Per abbonamenti, cambi di indirizzi, informazioni scrivere a Rosenberg.

COMITATO DI REDAZIONE

Triennio 1984-1987

F. RICCI (Direttore), G. LOLLI (Vice Direttore), N. BELLOMO A. CONTE, L. GATTESCHI, G. GEYMONAT, S. GRECO G. MONEGATO, M. STOKA, F. TRICERRI (Segretario)

SEMINARIO MATEMATICO Università' e Politecnico

Convegno su LOGIC AND COMPUTER SCIENCE: NEW TRENDS AND APPLICATIONS

FASCICOLO SPECIALE 1987

Proprietà letteraria riservata

PREFACE

Logic and computer science: new trends and application

Torino, Villa Gualino, 13-15 ottobre 1986

In the fall of 1984 the Seminario Matematico dell'Università e del Politecni­co di Torino decided to dedicate one of its next conferences to the topic of Mathematical Logic. It was immediately apparent, given the kind of research pursued in this field in our University, that the conference should focus on the relationship between this well established discipline and the new problems emerging from computer science, where the demand for logie is growing.

Computer science is a challenge to logie in a wide spectrum going from traditional fields such as recursion theory, now becoming computational complexity, to new logicai languages and logicai calculi in functional and logie programming. And an entirely novel logie approàch is requested by present day models of computation as well as by specific implemented pro­cedure such as that of negation by failure.

We decided not to restrict the conference topics to just one argument, but to offer a wide, if not exhaustive panorama of problems and researches: new logics suggested by parallelism, a survey of classical automatic deduction and of applications of expert systems, computational complexity of logie pro-grams, semantics of functional and logie languages; we didn't forget the im­pact ori mathematics itself, as exemplified by recursive algebra, and on the very foundations of mathematics, at least in the program of reverse mathematics,

We hoped at the time that this choice would result in a more lively confe­rence, and we were right; we hope now that the present volume will be of interest to a wider audience, as a unique opportunity to have a survey of what is going on in logie and in the foundations of computer science, and some of its reflexes on mathematics.

The conference was held in october 1986, from the 13th to the 15th, in Villa Gualino, on the hills prospecting the town, where is the residence of

VI

the Institute for Scientific Interchange. The invited leetures have been given in the following order:

J.-Y. Girard, Linear Logic, A. Nerode, Complexity The oretic Algebra, A. Scedrov, Semantical Metbods for Polymorphism, G. Longo, From Gòdel-Numbering to Higher-Types and Higher-Order, M. Beeson, Normalization ofTerms in Logic and Computer Science, S.G. Simpson, Reverse Matbematics, W. Sieg, Kònig's Lemma, E. Eder, Tbeorem Proving and the Connection Method - The State of the Art, C. Cellucci, Using Full First Order Logic as a Programming Language, R. Platek, Practical Verification, J. Makowski, How to Choose your Logic for Computer Science, E. Bòrger, Logicai and Computational Complexity of Classes of Logic Pro-grams.

Ali of them, but for those of Beeson, Simpson and Platek are presented in this volume, sometimes with a few variations. Beeson's contribution will be hopefully made available elsewhere; Simpson's work in reverse mathematics is well known and easily accessible; Platek's talk has been a presentation of the activity of Odissey Research Associates, and of its philosophy.

The conference has had the generous financial support of italian CNR and of the Institute for Scientific Interchange of Torino; ISI has also given active help in the organization, and we are very grateful to its President T. Regge, to M. Rasetti and to the secretary Ms. T. Bertoletti.

Torino, novembre 1987

Gabriele Lolli

Organizing Commitee:

G. Lolli F. Arzarello A. Martelli F. Previale

C O N T E N T S

Preface Pag.

List of invited speakers

List of Participants

INVITED LECTURES

A. Nerode-J.B. Remmel, Complexìty theoretic algebra I. Vector spaces over finite fields

J.-Y. Girard, Multiplicatives

A. Scedrov, The mie of computable choice for constructively provable

functionals of finite type "

G. Longo, From numbered sets to type theories "

W. Sieg, Provably recursive functionals of theories with Koenig's lemma " E. Eder, Theorem proving and the connection method - The state of the

art

C. Cellucci, Using full first order logie as a programming language "

E. Bòrger, Logicai and computational complexìty of classes of logie programs »

E. Dahlhaus-J. A. Makowsky, Computable directory queries "

LIST OF INVITED SPEAKERS

M. J. BEESON, Department of Mathematics and Computer Science, San Jose State Univ., San Jose, CA 95192

E. BÒRGER, Dipartimento di Informatica, Università, Corso Italia 40, 56100 Pisa, Italia C. CELLUCCI, Dipartimento di Filosofia, Università La Sapienza, 00100 IRoma, Italia

G. LONGO, Dipartimento di Informatica, Università, Corso Italia 40, 56100 Pisa, Italia

J.-Y. GIRARD, Equipe de Logique, Département de Mathématiques, T 45-55, 5 étage, Université, Paris VII, 2 place Jussieux, 75251 Paris CEDEX 05, France

J.A. MAKOWSKI, Department of Computer Science, Israel Institute of Technology, Haifa, Israel

A. NERODE, Department of Mathematics, White Hall, Cornell University, Ithaca, NY 14853

E. EDER, Fachbereich Informatile, Universitàt Dortmund, D4600, Dorthmund, 50, F.R. Germany

R. PLATEK, Odyssey Res. Associates, 1283 Trumansburg Rd., Ithaca, NY 14850

A SCEDROV, Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104

W. SIEG, Department of Philosophy, Carnegie-Mellon University, Pittsburg, PA 15213

S.G. SIMPSON, Department or Mathematics, McAllister Bldg, Pennsylvania State Universi­ty, University Park, PA 16802

X

LIST OF PARTICIPANTS

S. TULIPANI (Camerino)

A. FERRO (Catania)

E. MOGGI (Edinburgo)

M.V ABRUSCI (Firenze)

A. CANTINI (Firenze)

G. CORSI (Firenze)

E. BALLO (Milano)

P. MIGLIOLI (Milano)

M. ORNAGHI (Milano)

U. SOLITRO (Milano)

L. ALOISIO (Napoli)

R. FERRO (Padova)

S. VALENTINI (Padova)

A. DI COSMO (Pisa)

R. AMADIO (Pisa)

E. MORICONI (Pisa)

G. MORINI (Pisa)

A. SALIBRA (Pisa)

G. DI GIANNANTONIO (Roma)

G. MASCARI (Roma)

A. VINCENZI (Savona)

C. BERNARDI (Siena)

S. SORBI (Siena)

S. STEFANI (Siena)

F. ARZARELLO (Torino)

A. MARCONE (Torino)

P. ODIFREDDI (Torino)

F. PARLAMENTO (Torino)

F. PREVIALE (Torino)

L. ANTONELLI (Torino)

D. MARCONI (Torino)

F. CARDONE (Torino)

M. COPPO (Torino)

B. DEMO (Torino)

M. DEZANI (Torino)

P. GIANNINI (Torino)

E. GIOVANNETTI (Torino) G. LOLLI (Torino) A. MARTELLI (Torino) S. RONCHI DELLA ROCCA (Torino) P. TORASSO (Torino) B. VENNERI (Torino) M. ZACCHI (Torino) A. MARCJA (Trento)

Finito di stampare nell'ottobre 1988 dalla "Precisa" TORINO

per conto del

SEMINARIO MATEMATICO DELL'UNIVERSITÀ' E DEL POLITECNICO DI TORINO

Via Carlo Alberto, 10 -10123 TORINO

INDICAZIONI PER GLI AUTORI

I lavori destinati alla pubblicazione sui Rendiconti del Seminario Mate­matico dell'Università e del Politecnico di Torino devono essere inviati in duplice copia al seguente indirizzo :

Seminario Matematico dell'Università e del Politecnico di Torino Via Carlo Alberto 10

10123 Torino

I lavori presentati devono essere dattiloscritti e una delle due copie deve contenere le eventuali indicazioni per il tipografo.

I lavori devono essere inoltre completi di bibliografia e corredati della classificazione AMS.

Gli autori riceveranno gratuitamente 50 estratti per ogni articolo. Even­tuali richieste di ulteriori estratti a pagamento devono essere presentate all'atto della restituzione delle prime bozze.

Di regola le seconde bozze non vengono inviate agli autori per la corre­zione.

ISSN 0373-1243