Principles for Software Composition

PSC 2022/23 (375AA, 9 CFU)

Lecturer: Roberto Bruni
web - email - Microsoft Teams channel

Office hours: Tuesday 14:00-16:00 or by appointment

Objectives

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.

Prerequisites

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.

Textbook(s)

Main text:

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

Exam

The evaluation will be solely based on oral exams, which can involve the assignment of written exercises.

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.

Oral Exams: schedule

See the channel Exams in the Microsoft Teams platform

Announcements

the lecture of monday May 8 11-13 is canceled
the lecture of thursday April 20 14-16 (L1) is postponed to 16-18 (L1)
the lecture of thursday April 6 14-16 is canceled
as the course starts:
Each student must subscribe the Microsoft Teams channel of the course and then fill the form Students information to provide the following contact data and info about her/his background:
1. first name
2. last name
3. enrolment number (numero di matricola), optional
4. email
5. bachelor degree (course of study and university)
6. MSc course (if Computer Science, specify which curriculum)
then, fill the (optional) form about your familiarity with some of the subjects of the course: Familiar subjects

Lectures (1st part)

N	Date		Time	Room	Lecture notes	Links
1	Mon	20/02	11:00-13:00	L1	01 - Introduction to the course 02 - Preliminaries: from syntax to semantics, the role of formal semantics, SOS approach, small-step operational semantics, big-step operational semantics	Lecture 01 Lecture 02
2	Tue	21/02	16:00-18:00	L1	02 - Preliminaries (ctd): denotational semantics, compositionality principle, normalisation, determinacy, consistency, equivalence, congruence 03 - Unification: inference process, signatures, substitutions, unification problem, most general unifiers, unification algorithm 04 - Logical systems: logical systems, derivations, theorems	Lecture 02 Lecture 03 Lecture 04
3	Thu	23/02	14:00-16:00	L1	04 - Logical systems (ctd.): logic programs, goal-oriented derivations 05 - Induction: precedence relation, infinite descending chains, well-founded relations, well-founded induction, mathematical induction, proof of induction principle	Lecture 04 Lecture 05a
4	Mon	27/02	11:00-13:00	L1	Exercises: unification, goal-oriented derivations 05 - Induction (ctd.): structural induction, termination of arithmetic expressions, determinacy of arithmetic expressions, many-sorted signatures, arithmetic and boolean expressions, structural induction over many-sorted signatures, termination of boolean expressions, memories, update operation, operational semantics of commands	Exercises 01 Lecture 05a Lecture 05b
5	Tue	28/02	16:00-18:00	L1	05 - Induction (ctd.): divergence, rule for divergence, limits of structural induction, induction on derivations, rule induction, determinacy of commands	Lecture 05b Lecture 05c
6	Thu	02/03	14:00-16:00	L1	06 - Equivalence: operational equivalence, concrete equivalences, parametric equivalences, equivalence and divergence 07 - Induction and recursion: well-founded recursion, lexicographic precedence relation, Ackermann function, denotational semantics of arithmetic expressions, fixpoint equations	Lecture 06 Lecture 07
7	Mon	06/03	11:00-13:00	L1	Exercises: induction, termination, determinacy, divergence 07 - Induction and recursion (ctd.): consistency of operational and denotational semantics for arithmetic expressions 08 - Partial orders and fixpoints: partial orders, Hasse diagrams, chains, least element, minimal element, bottom element, upper bounds, least upper bound, limits, complete partial orders, powerset completeness, prefix independence	Exercises 02 Lecture 07 Lecture 08a
8	Tue	07/03	16:00-18:00	L1	08 - Partial orders and fixpoints (ctd.): CPO of partial functions, monotonicity, continuity, Kleene's fixpoint theorem	Lecture 08b
9	Thu	09/03	14:00-16:00	L1	08 - Partial orders and fixpoints (ctd.): McCarthy's 91 function, recursive definitions of partial functions as logical systems, immediate consequences operator, set of theorems as fixpoint 09 - Denotational semantics: lambda-notation, free variables, capture-avoiding substitutions, alpha-conversion, beta rule, conditionals, denotational semantics of commands, fixpoint computation	Lecture 08c Lecture 09
10	Mon	13/03	11:00-13:00	L1	10 - Consistency: denotational equivalence, congruence, compositionality principle, consistency of commands, correctness, completeness Exercises: posets, semantics, well-founded recursion, posets, semantics	Lecture 10 Exercises 03
11	Tue	14/03	16:00-18:00	L1	11 - Haskell: an overview Haskell ghci: basics, tuples, lists, list comprehension, guards, pattern matching, lambda, partial application, zip, exercises	Haskell Lecture 11 ghci session 01
12	Thu	16/03	14:00-16:00	L1	Haskell ghci (ctd): recursive definitions, tail recursion, let-in, where, map, filter, fixpoint operator, folds, exercises	Haskell ghci session 02
13	Mon	20/03	11:00-13:00	L1	Haskell ghci (ctd.): folds, application, function composition, data types, type classes, recursive data structures, derived instances, exercises	Haskell ghci session 03
14	Tue	21/03	16:00-18:00	L1	12 - HOFL: syntax, pre-terms, types, types judgements, type system, type checking, type inference, principal type	Lecture 12a
15	Thu	23/03	14:00-16:00	L1	Exercises: Haskell 12 - HOFL (ctd.): canonical forms, operational semantics, lazy vs eager evaluation	Exercises 04 Lecture 12b
16	Mon	27/03	11:00-13:00	L1	13 - Domain theory: Integers with bottom, cartesian product, projections, switching lemma, functional domains	Lecture 13a Lecture 13b
17	Tue	28/03	16:00-18:00	L1	13 - Domain theory (ctd.): lifting, let notation, continuity theorems, apply, fix 14 - Denotational semantics of HOFL: definition and examples, type consistency	Lecture 13c Lecture 14
18	Thu	30/03	14:00-16:00	L1	13 - Domain theory (ctd.): curry, uncurry 14 - Denotational semantics of HOFL (ctd.): substitution lemma, compositionality and other properties 15 - Consistency of HOFL: Counterexample to completeness, correctness of the operational semantics, operational convergence, denotational convergence, operational convergence implies denotational convergence (and vice versa), operational and denotational equivalence, correspondence for type int, unlifted semantics, lifted vs unlifted semantics Exercises: HOFL, domains	Lecture 13c Lecture 14 Lecture 15 Exercises 05
19	Mon	03/04	11:00-13:00	L1	Exercises: HOFL, domains Erlang erl: numbers, atoms, tuples, lists, terms, variables, term comparison, pattern matching, list comprehension, modules, functions, guards, higher order, recursion, pids, spawn, self, send, receive, examples	Exercises 05 Lecture 16 Erlang erl session
20	Tue	04/04	16:00-18:00	L1	17 - CCS: Syntax, operational semantics, value passing	Lecture 17a
-	Thu	06/04	14:00-16:00	L1	Canceled

Lectures (2nd part)

N	Date		Time	Room	Lecture notes	Links
21	Thu	13/04	14:00-16:00	L1	17 - CCS (ctd.): finitely branching processes, guarded processes 18 - Bisimulation: abstract semantics, graph isomorphism, trace equivalence, bisimulation game, strong bisimulation	Lecture 17b Lecture 18a Lecture 18b
22	Mon	17/04	11:00-13:00	L1	18 - Bisimulation (ctd.): strong bisimilarity, strong bisimilarity is an equivalence, strong bisimilarity is a bisimulation, strong bisimilarity is the coarsest strong bisimulation, strong bisimilarity is a congruence, some laws for strong bisimilarity, strong bisimilarity as a fixpoint, Phi operator, Phi is monotone, Phi is continuous (on finitely branching processes), Knaster-Tarski's fixpoint theorem	Lecture 18b Lecture 18c
23	Tue	18/04	16:00-18:00	L1	19 - Hennessy-Milner logic: modalities, HML syntax, formula satisfaction, converse of a formula, HML equivalence 20 - Weak Semantics: weak transitions, weak bisimulation, weak bisimilarity, weak bisimilarity is not a congruence, weak observational congruence, Milner's tau-laws 21 - CCS at work: modelling imperative programs with CCS, playing with CCS (using CAAL)	Lecture 19 Lecture 20
24	Thu	20/04	16:00-18:00	L1	21 - CCS at work (ctd.): modelling imperative programs with CCS, playing with CCS (using CAAL), modelling and verification of mutual exclusion algorithms with CCS and CAAL CAAL session (copy the text and paste it in the Edit panel)	Lecture 21 CAAL CAAL session
25	Mon	24/04	11:00-13:00	L1	Exercises: Erlang, CCS 22 - Temporal and modal logics: linear temporal logic (LTL), linear structures models, shifting, LTL satisfaction, equivalence of formulas, automata-like models	Exercises 06 Lecture 22a
26	Thu	27/04	14:00-16:00	L1	22 - Temporal and modal logics (ctd.): computational tree logic (CTL* and CTL), infinite trees, infinite paths, branching structure, CTL* satisfaction, equivalence of formulas, CTL formulas, expressiveness comparison, mu-calculus, positive normal form, least and greatest fixpoints, invariant properties, possibly properties, mu-calculus with labels	Lecture 22a Lecture 22b
27	Tue	02/05	16:00-18:00	L1	23 - GoogleGo: an overview GoogleGo playground: Go principles, variable declaration, type conversion, multiple assignments, type inference, imports, packages and public names, named return values, naked return, multiple results, conditionals and loops, pointers, struct, receiver arguments and methods, interfaces, goroutines, bidirectional channels, channel types, send, receive, asynchronous communication with buffering, close, select, communicating communication means, range, handling multiple senders, concurrent prime sieve	Lecture 23 Google Go go session
28	Thu	04/05	14:00-16:00	L1	24 - Pi-calculus: name mobility, free names, bound names, syntax and operational semantics, scope extrusion, early and late bisimilarities, weak semantics	Lecture 24
-	Mon	08/05	11:00-13:00	L1	canceled
29	Tue	09/05	16:00-18:00	L1	Exercises: logics, GoogleGo, pi-calculus 25 - Measure theory and Markov chains: probability space, random variables, stochastic processes, homogeneous Markov chains, DTMC, DTMC as matrices, DTMC as PTS, next state probability, ergodic DTMC, steady state distribution	Exercises 07 Lecture 25a
30	Thu	11/05	14:00-16:00	L1	25 - Measure theory and Markov chains (ctd): finite path probability, negative exponential distribution, CTMC, embedded DTMC, infinitesimal generator matrix, CTMC stationary distribution 26 - Probabilistic bisimilarities: bisimilarity revisited, reachability predicate, CTMC bisimilarity, DTMC bisimilarity, Markov chains with actions, probabilistic reactive systems, bisimilarity for reactive systems, Larsen-Skou logic	Lecture 25a Lecture 25b Lecture 26
31	Mon	15/05	11:00-13:00	L1	27 - PEPA: motivation, basic ideas, PEPA workflow, PEPA syntax, cooperation combinator, bounded capacity, apparent rate, PEPA operational semantics, performance analysis, reward structures	Lecture 27 PEPA
32	Tue	16/05	16:00-18:00	L1	Exercises: Markov chains, probabilistic systems, PEPA	Exercises 08
33	Thu	18/05	14:00-16:00	L1	Mini-projects discussion
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