magistraleinformatica:psc:start

**PSC 2020/21 (375AA, 9 CFU)**

Lecturer: **Roberto Bruni**

web - email - Microsoft Teams channel

Office hours: **Tuesday 15:00-17:00 or by appointment**

The objective of the course is to present:

- different models of computation,
- their programming paradigms,
- their mathematical descriptions, both
*concrete*and*abstract*, - some intellectual tools/techniques for reasoning on models.

The course will cover the basic techniques for assigning meaning to programs with higher-order, concurrent and probabilistic features (e.g., domain theory, logical systems, well-founded induction, structural recursion, labelled transition systems, Markov chains, probabilistic reactive systems, stochastic process algebras) and for proving their fundamental properties, such as termination, normalisation, determinacy, behavioural equivalence and logical equivalence. Temporal and modal logics will also be studied for the specification and analysis of programs. In particular, some emphasis will be posed on modularity and compositionality, in the sense of guaranteeing some property of the whole by proving simpler properties of its parts.

There are no prerequisites, but the students are expected to have some familiarity with discrete mathematics, first-order logic, context-free grammars, and code fragments in imperative and functional style.

Main text:

- Roberto Bruni, Ugo Montanari, “Models of Computation”, Springer Texts in Computer Science, 2017.

Other readings:

- Graham Hutton, “Programming in Haskell”, 2nd edition, Cambridge University Press (2016). Chapters: 1-8, 14, 15.
- Joe Armstrong, Programming Erlang, 2nd edition. The Pragmatic Bookshelf (2013). Chapters: 1-5, 8, 10-12.
- Caleb Doxsey, Introducing Go, O'Reilly Media (2016). Chapters: 1-4, 6-7, 10.
- Robin Milner, “Communication and Concurrency”, Prentice Hall (1989). Chapters: 1-7, 10.
- Luca Aceto, et al, “Reactive Systems”, Cambridge University Press (2011). Chapters: 1-7.
- Jane Hillston, A Compositional Approach to Performance Modelling, Cambridge University Press (1996). Chapters 1-3.

External resources:

Normally, the evaluation would have been based on written and oral exams.

Due to the covid-19 countermeasures, for the current period, the evaluation will be solely based on oral exams.

Registration to exams (mandatory): Exams registration system

During the oral exam the student must demonstrate

- knowledge: his/her knowledge of the course material, and
- problem solving: the ability to solve some simple exercises, and
- understanding: the ability to discuss the reading matter thoughtfully and with propriety of expression.

Date | Time | Name | Place | |
---|---|---|---|---|

weekday | DD/MM | HH:MM | Student Name | Microsoft Teams |

- Due to the covid-19 emergency situation, there will be no
**mid-term exams**

- as the course starts:

Each student must subscribe the Microsoft Teams channel of the course and then send an email to the professor from his/her favourite email account with subject**PSC20-21**and the following data

(by doing so, the account will be included in the class mailing-list, where important announcements can be sent):**first name**and**last name**(please clarify which is which, to avoid ambiguities)**enrolment number**(numero di matricola)- bachelor degree (
**course of study**and**university**) - your favourite topics in computer science (optional)

Virtual classroom: To join a lecture enter the course team on Microsoft Teams, go to the Lectures channel and click on the scheduled lecture.

N | Date | Time | Room | Lecture notes | Links | |
---|---|---|---|---|---|---|

1 | Mon | 15/02 | 16:00-18:00 | Teams | 01 - Introduction to the course | Lecture 01 |

2 | Wed | 17/02 | 14:00-16:00 | Teams | 02 - Preliminaries:from syntax to semantics, the role of formal semantics, SOS approach, small-step operational semantics, big-step operational semantics | Lecture 02 |

3 | Fri | 21/02 | 14:00-16:00 | Teams | 02 - Preliminaries (ctd.):denotational semantics, compositionality principle, normalisation, determinacy, consistency, equivalence, congruence, signatures03 - Unification: inference process, signatures, substitutions,unification problem, unification algorithm | Lecture 03 |

4 | Mon | 22/02 | 16:00-18:00 | Teams | 04 - Logical systems:logical systems, derivations, logic programs, goal-oriented derivations | Lecture 04 |

5 | Wed | 24/02 | 14:00-16:00 | Teams | 05 - Induction and recursion:precedence relation, infinite descending chains, well-founded relations, well-founded induction, mathematical induction, proof of induction principle, structural induction, termination of arithmetic expressions, determinacy of arithmetic expressions | Lecture 05a |

6 | Fri | 26/02 | 14:00-16:00 | Teams | 05 - Induction and recursion:termination of arithmetic expressionsExercises: unification, goal-oriented derivations | Exercises 01 |

7 | Mon | 01/03 | 16:00-18:00 | Teams | 05 - Induction and recursion:determinacy of arithmetic expressions, structural induction over many-sorted signatures, termination of boolean expressions, operational semantics of commands, divergence, induction on derivations | |

8 | Wed | 03/03 | 14:00-16:00 | Teams | 05 - Induction and recursion:rule induction, determinacy of commands, well-founded recursion, denotational semantics of arithmetic expressions, consistency of operational and denotational semantics for arithmetic expressions lexicographic precedence relation, Ackermann function, fixpoint equations | |

9 | Fri | 05/03 | 14:00-16:00 | Teams | Exercises:induction and recursion, termination, determinacy, divergencePartial orders and fixpoints: partial orders, Hasse diagrams, chains, least element, minimal element, bottom element, upper bounds, least upper bound, chains, limits | |

10 | … | … | … | Teams | Partial orders and fixpoints:complete partial orders, powerset completeness, CPO of partial functions, monotonicity, continuity, Kleene's fixpoint theorem | |

11 | … | … | … | Teams | Partial orders and fixpoints:immediate consequences operator, denotational semantics of commands, fixpoint computation, semantic equivalence, consistency of commands correctness | |

12 | … | … | … | Teams | Exercises:well-founded recursion, posets, semanticsPartial orders and fixpoints: consistency of commands, completeness | |

13 | … | … | … | Teams | Lambda-notation:free variables, capture-avoiding substitutionsHaskell: an overviewghci session 1 | Haskell |

14 | … | … | … | Teams | Haskell:lambda, guards, pattern matching, recursion, exercisesghci session 2 | |

15 | … | … | … | Teams | Haskell:recursive definitions, folds, application, function compositionghci session 3 | |

16 | … | … | … | Teams | Haskell:data types, type classes, recursive data structures, derived instancesghci session 4 Exercises: Haskell | |

17 | … | … | … | Teams | Exercises:Haskellghci session 5 HOFL: syntax, type system, type checking, type inference, principal type | |

18 | … | … | … | Teams | HOFL:canonical forms, operational semantics, lazy vs eager evaluationDomain theory: Integers with bottom, cartesian product, projections | |

19 | … | … | … | Teams | Self-assessment test |

N | Date | Time | Room | Lecture notes | Links | |
---|---|---|---|---|---|---|

20 | … | … | … | Teams | Correction of self-assessment test | |

21 | … | … | … | Teams | Domain theory:switching lemma, functional domains, lifting | |

22 | … | … | … | Teams | Domain theory:continuity theorems, apply, fix, let notationDenotational semantics of HOFL: definition and examples, type consistency | |

23 | … | … | … | Teams | Denotational semantics of HOFL:substitution lemma, compositionality and other propertiesConsistency of HOFL: Counterexample to completeness, correctness of the operational semantics, operational convergence, denotational convergence, operational convergence implies denotational convergence, denotational convergence implies operational convergence (optional), operational and denotational equivalence, correspondence for type int, unlifted semantics | |

24 | … | … | … | Teams | Exercises:HOFL, domains | |

25 | … | … | … | Teams | Erlang:an overviewerl session | Erlang |

26 | … | … | … | Teams | CCS:Syntax, operational semantics, finitely branching processes, guarded processes, value passing, abstract semantics, graph isomorphism | |

27 | … | … | … | Teams | CCS:trace equivalence, bisimulation game, strong bisimulation, strong bisimilarity, strong bisimilarity is an equivalence, strong bisimilarity as a fixpoint | |

28 | … | … | … | Teams | CCS:strong bisimilarity as a fixpoint, Knaster-Tarski's fixpoint theorem, strong bisimilarity is a congruence, some laws for strong bisimilarity, Hennessy-Milner logic | |

29 | … | … | … | Teams | CCS:weak bisimulation, weak bisimilarity, weak observational congruence, Milner's tau-laws, modelling with CCS | |

30 | … | … | … | Teams | CCS:modelling and playing with CCS (using CAAL)CAAL session (copy the text and paste it in the Edit panel) | CAAL |

31 | … | … | … | Teams | Exercises:Erlang, CCSTemporal and modal logics: linear temporal logic (LTL) | |

32 | … | … | … | Teams | Temporal and modal logics:computational tree logic (CTL* and CTL), mu-calculus | |

33 | … | … | … | Teams | GoogleGo:an overviewgo-session | Google Go |

34 | … | … | … | Teams | Pi-calculus:syntax and operational semantics, examples | |

35 | … | … | … | Teams | Exercises:logics, GoogleGo, pi-calculusPi-calculus: early and late bisimilarities, weak bisimilarities | |

36 | … | … | … | Teams | Measure theory and Markov chains:probability space, random variables, stochastic processes, homogeneous Markov chains, DTMC, DTMC as matrices, DTMC as PTS, next state probability, finite path probability, ergodic DTMC, steady state distribution, negative exponential distribution | |

37 | … | … | … | Teams | Measure theory and Markov chains:CTMC, embedded DTMC, infinitesimal generator matrix,CTMC stationary distribution, bisimilarity revisited, reachability predicate, CTMC bisimilarity, DTMC bisimilarity Markov chains with actions: reactive systems, bisimilarity for reactive systems, Larsen-Skou logicPEPA: motivation, basic ideas, PEPA workflow | |

38 | … | … | … | Teams | PEPA:PEPA syntax, apparent rate, PEPA operational semantics,performance analysis Exercises: probabilistic systems | PEPA |

End | ||||||

- | … | … | … | Teams | Oral Exam Exams registration system | |

- | … | … | … | Teams | Oral Exam Exams registration system | |

- | … | … | … | Teams | Oral Exam Exams registration system | |

- | … | … | … | Teams | Oral Exam Exams registration system | |

- | … | … | … | Teams | Oral Exam Exams registration system | |

- | … | … | … | Teams | Oral Exam Exams registration system |

magistraleinformatica/psc/start.txt · Ultima modifica: 26/02/2021 alle 15:13 (2 giorni fa) da Roberto Bruni