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Principles for Software Composition

PSC 2017/18 (375AA, 9 CFU)

Lecturer: Roberto Bruni
web - email - phone 050 2212785 - fax 050 2212726

Office hours: Wednesday 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:

Other readings:

External resources:


The evaluation will be based on written and oral exams.

The written exam is not necessary if the two (written) mid-terms exams are evaluated positively.

  • First (written) mid-term exam: 5/4/2018
  • Second (written) mid-term exam: 31/5/2018

Registration to written exams (mandatory): Exams registration system

In the written exam the student must demonstrate

  • knowledge: his/her knowledge of the course material
  • problem solving: the ability to solve some exercises, and
  • organisation: the ability to organise an effective and correctly written reply.

During the oral exam the student must demonstrate

  • knowledge: his/her knowledge of the course material, and
  • understanding: the ability to discuss the reading matter thoughtfully and with propriety of expression.

Oral Exams: schedule

Date Time Name
Thu 26/7 10:30 Colombo Michele


  • Lectures rescheduled:
    Two additional lectures have been scheduled on wednesday 16/05 and wednesday 23/05. Both are from 9:00 to 11:00 in room L1.
  • Lecture canceled:
    The lecture of friday 27/04 is canceled. It will be rescheduled later on.
  • Lectures rescheduled:
    Two additional lectures have been scheduled on wednesday 21/03 and wednesday 28/03. Both are from 9:00 to 11:00 in room L1.
  • Lecture canceled:
    The lecture of thursday 01/03 is canceled. It will be rescheduled later on.
  • Lecture canceled:
    The lecture of friday 23/02 is canceled. It will be rescheduled in March.
  • as the course starts:
    Each student should send an email to the professor from his/her favourite email account with subject PSC17-18 and the following data
    (by doing so, the account will be included in the class mailing-list, where important announcements can be sent):
    1. first name and last name (please clarify which is which, to avoid ambiguities)
    2. enrolment number (numero di matricola)
    3. bachelor degree (course of study and university)
    4. your favourite topics in computer science (optional)

Lectures (1st part)

N Date Time Room Lecture notes Links
1 Tue 20/02 14:00-16:00 L1 Introduction to the course
2 Thu 22/02 11:00-13:00 L1 Preliminaries:
formal semantics, logical systems, derivations
- Fri 23/02 14:00-16:00 C Canceled
3 Tue 27/02 14:00-16:00 L1 Preliminaries:
signatures, unification problem, logic programs
goal-oriented derivations
- Thu 01/03 11:00-13:00 L1 Canceled (weather condition alert)
4 Fri 02/03 14:00-16:00 C Exercises:
unification, goal-oriented derivations

Induction and recursion:
well-founded relations, well-founded induction, mathematical induction
5 Tue 06/03 14:00-16:00 L1 Induction and recursion:
proof of induction principle, structural induction,
termination of arithmetic expressions, determinacy of arithmetic expressions
6 Thu 08/03 11:00-13:00 L1 Induction and recursion:
structural induction over many-sorted signatures, termination of boolean expressions,
operational semantics of commands, divergence
7 Fri 09/03 14:00-16:00 C Induction and recursion:
induction on derivations, rule induction, determinacy of commands,
well-founded recursion, lexicographic precedence relation, Ackermann function,
denotational semantics of arithmetic expressions, fixpoint equations
8 Tue 13/03 14:00-16:00 L1 Exercises:
induction and recursion, consistency of arithmetic expressions

Partial orders and fixpoints:
partial orders, Hasse diagrams, least upper bound, chains, limits,
complete partial orders, bottom element, powerset completeness
9 Thu 15/03 11:00-13:00 L1 Partial orders and fixpoints:
CPO of partial functions, monotonicity, continuity, Kleene's fixpoint theorem
10 Fri 16/03 14:00-16:00 C Exercises:
induction, recursion, posets

Partial orders and fixpoints:
immediate consequences operator, denotational semantics of commands
11 Tue 20/03 14:00-16:00 L1 Partial orders and fixpoints:
fixpoint computation, consistency of commands, semantic equivalence
12 Wed 21/03 09:00-11:00 L1 Haskell:
an overview
ghci session 1
13 Thu 22/03 11:00-13:00 L1 Haskell:
recursion, folds, application, function composition
ghci session 2
14 Fri 23/03 14:00-16:00 C Haskell:
data types, type classes, recursive data structures, derived instances,
IO actions, errors

ghci session 3
15 Tue 27/03 14:00-16:00 L1 Exercises:
well-founded recursion, posets, denotational semantics, Haskell
16 Wed 28/03 09:00-11:00 L1 HOFL:
syntax, type system, type checking, type inference, principal type,
canonical forms, operational semantics
17 Thu 05/04 11:00-13:00 L1 First mid-term written exam
Extra-ordinary exam (MOD)

Lectures (2nd part)

N Date Time Room Lecture notes Links
18 Thu 12/04 11:00-13:00 L1 HOFL:
lazy vs eager evaluation

Domain theory:
Integers with bottom, cartesian product, projections, switching lemma
19 Fri 13/04 14:00-16:00 C Domain theory:
functional domains, lifting, continuity theorems, apply, fix, let notation

Consistency of HOFL:
Counterexample to completeness
20 Tue 17/04 14:00-16:00 L1 Denotational semantics of HOFL:
Type consistency, substitution lemma, compositionality and other properties
21 Thu 19/04 11:00-13:00 L1 Consistency of HOFL:
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
22 Fri 20/04 14:00-16:00 C Exercises:
HOFL, domains
23 Tue 24/04 14:00-16:00 L1 Erlang:
an overview
erl session
24 Thu 26/04 11:00-13:00 L1 CCS:
Syntax, operational semantics, abstract semantics, graph isomorphism,
trace equivalence, bisimulation game
- Fri 27/04 14:00-16:00 C Canceled
25 Thu 03/05 11:00-13:00 L1 CCS:
strong bisimulation, strong bisimilarity, strong bisimilarity is an equivalence
26 Fri 04/05 14:00-16:00 C CCS:
strong bisimilarity as a fixpoint, finitely branching processes, guarded processes,
Knaster-Tarski's fixpoint theorem, Hennessy-Milner logic
27 Tue 08/05 14:30-16:00 L1 CCS:
strong bisimilarity is a congruence, some equational laws for strong bisimilarity,
weak bisimilarity, weak observational congruence, Milner's tau-laws, value passing,
modelling with CCS
- Thu 10/05 11:00-13:00 L1 Canceled
for allowing participation to the course on Formal Methods for Program Verification
28 Fri 11/05 14:00-16:00 C Exercises:
Erlang, CCS
29 Tue 15/05 14:00-16:00 L1 CCS:
modelling and playing with CCS (using CAAL)
CAAL examples (copy the text and paste it in the Edit panel)
30 Wed 16/05 09:00-11:00 L1 Temporal and modal logics:
linear temporal logic (LTL), computational tree logic (CTL* and CTL), mu-calculus
31 Thu 17/05 11:00-13:00 L1 Temporal and modal logics:
mu-calculus examples

an overview
Google Go
32 Fri 18/05 14:00-16:00 C GoogleGo:
an overview

syntax and operational semantics, examples
33 Tue 22/05 14:00-16:00 L1 Pi-calculus:
abstract semantics, early and late bisimilarities, weak bisimilarities

logics, GoogleGo
34 Wed 23/05 09:00-11:00 L1 Exercises:

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
35 Thu 24/05 11:00-13:00 L1 Measure theory and Markov chains:
ergodic DTMC and steady state distribution, exponential distribution, CTMC,
infinitesimal generator matrix, embedded DTMC,
bisimilarity revisited, reachability predicate, CTMC bisimilarity, DTMC bisimilarity
36 Fri 25/05 14:00-16:00 C Markov chains with actions:
reactive systems, bisimilarity for reactive systems, Larsen-Skou logic

PEPA syntax, apparent rate, PEPA operational semantics,
performance analysis
37 Tue 29/05 14:00-16:00 L1 Exercises:
probabilistic systems
38 Thu 31/05 11:00-13:00 L1 Second mid-term written exam
39 Wed 13/06 14:00-16:00 L1 Exam
40 Wed 04/07 14:00-16:00 L1 Exam
41 Wed 25/07 14:00-16:00 C1 Exam
42 Tue 11/09 14:00-16:00 N1 Exam
Registration to the exam is mandatory: exam registration system

magistraleinformatica/psc/start.txt · Ultima modifica: 25/07/2018 alle 21:10 (4 settimane fa) da Roberto Bruni