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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.


  • Lectures rescheduled:
    Two additional lectures have been scheduled on wednesday 21/03 and wednesday 28/03. Both are from 9:00 to 11:00 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)
5 Fri 02/03 14:00-16:00 C Exercises:
unification, goal-oriented derivations

Induction and recursion:
well-founded relations, well-founded induction, mathematical induction
6 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
7 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
8 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
9 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
10 Thu 15/03 11:00-13:00 L1 Partial orders and fixpoints:
CPO of partial functions, monotonicity, continuity, Kleene's fixpoint theorem
11 Fri 16/03 14:00-16:00 C Exercises:
induction, recursion, posets

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

ghci session 3
16 Tue 27/03 14:00-16:00 L1 Exercises:
well-founded recursion, posets, denotational semantics, Haskell
17 Wed 28/03 09:00-11:00 L1 HOFL:
syntax, type system, type checking, type inference, principal type,
canonical forms, operational semantics
18 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
19 Thu 12/04 11:00-13:00 L1 HOFL:
lazy vs eager evaluation

Domain theory:
Integers with bottom, cartesian product, projections, switching lemma
20 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
21 Tue 17/04 14:00-16:00 L1 Denotational semantics of HOFL:
Type consistency, substitution lemma, compositionality and other properties
22 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
23 Fri 13/04 14:00-16:00 C Exercises:
HOFL, domains
24 Tue 24/04 14:00-16:00 L1 Erlang
Thu 31/05 11:00-13:00 L1 Second mid-term written exam
Registration to the exam is mandatory: exam registration system
Wed 13/06 14:00-16:00 L1 Exam
Registration to the exam is mandatory: exam registration system
Wed 04/07 14:00-16:00 L1 Exam
Registration to the exam is mandatory: exam registration system
Wed 25/07 14:00-16:00 C1 Exam
Registration to the exam is mandatory: exam registration system

magistraleinformatica/psc/start.txt · Ultima modifica: 19/04/2018 alle 09:53 (38 ore fa) da Roberto Bruni