Program Semantics, Verification, and Construction
(Previous instance: 2007/2008)
2008/2009
Course coordinator: Nelma Moreira (nam(AT)ncc(DOT)up(DOT)pt
)
Lecture 1
Lambda Calculus
Date:
07/10/08
Notes:
*
Lcalc.pdf
Lecture 2
Deduction Systems and Intuitionism
Date:
13/10/08
Notes:
* psvc02.pdf
Lecture 3
Type systems and the Curry-Howard isomorphism
Date:
21/10/08 (tuesday, 15h-18h)
Notes:
Lecture 4
Operational Semantics
Bibliography:
Semantics with Applications, H. Nielson and F. Nielson. (online version)
Date:
27/10/08 (Monday, 10h-13h) Sala 1
Lecture 5
Denotational Semantics
Date:
03/11/08 (Monday, 10h-13h) Sala 1
Bibliography:
Semantics with Applications, H. Nielson and F. Nielson. (online version)
Lecture 6
Proof assistants based on type theory
Date:
11/11/08 (tuesday, 15h-18h) Sala 1
Notes:
Lecture 7
Extensions of Pure Type Systems
The Coq proof assistant
Date:
17/11/08 (Monday, 10h-13h) Sala 1
Notes:
Material:
Lecture 8
Functional Program Verification in Coq
Date:
24/11/08 (Monday, 10h-13h) Sala 1
Notes:
Lecture 9
Hoare logic and interface specification languages
Date:
15/12/00 (Monday, 10h-13h) Sala 1
Slides:
(see next lecture)
Lecture 10
Verification conditions and program verification in practice
Date:
5/01/09 (Monday, 10h-13h) Sala 1
Lecture 11
Introduction to the mathematics of program construction
Date:
12/01/09 (Monday, 10h-13h) Sala 1
Topics:Overview of the scientific method applied to software design.Correct by verification versus correct by construction. Calculate versus invent & verify.The e=m+c equation: description versus calculation. Point-free (PF) and point-wise (PW) notations. PF-transform for (algebraic) reasoning.
Analogy with the Laplace transform (historical perspective).
Binary relations as a building block for logic in computer science.
Introduction to the binary relation calculus.
Notes:
- Theory and applications of the PF-transform Lectures 1-2 (01-56) (slides of the LerNET? doctoral school at Piriapolis, Uruguay, 2008)
- Full tutorial paper: (LNCS)
Lecture 12
PF-transform: when everything becomes a relation
Date:
19/01/09 (Monday, 10h-13h) Sala 1
Topics:
Taxonomy of binary relations. Functions.
Conditions and coreflexives. PF-transform of n-ary
relations. Products and Sums. Universal
constructions and properties.
Extended static checking (ESC) in the
PF-style. Induction-free calculation of preconditions
and invariants. Three case studies.
Notes:
Lecture 13
Constructive proofs and program calculation
Date:
26/01/09 (Monday, 10h-13h) Sala 1
Topics:
A PF-approach to polymorphic type checking. Reynolds' relation on
functions. The free-theorem of polymorphic functions in one equation.
Inductive predicates and relations. The catamorphism concept.
Universal property and its corollaries.
Mutual recursion. Calculation of for/while loops from systems of mutually recursive equations over linear types.
Notes:
- Theorems for free: a (calculational) introduction (slides)
- Relational algebra: a Kleene algebra central to the mathematics of program construction (slides)