|Unit||Credits||Academic sector||Period||Academic staff|
Introduction of the mathematical logic and its connection with other topics. Distinction between syntax and semantics. Formalization of properties in a formal language. Proof theory. Derivation and counter examples.
The aim of the course is to present the theoretical basis of programming languages. A number of paradigmatic untyped and typed languages will be introduced. The entire course will focus on the concepts of operational semantics and type system. Formal techniques for verifying the behaviour of programs will be introduced.
Levels of reference. Language and meta-language.
Propositional and predicative logic(classic and intuitionistic).
Sequent calculus and definitional equations.
Systems LJ e LK. Cut elimination. Proof search.
Classical evaluation of formulae, both propositional and predicative.
Soundness, Completeness and Compactness for LK.
Decidability for predicative calculus.
(i) Mathematical induction over the natural numbers;
(ii) Structural induction;
(iii) Rule induction.
Big step and small step semantics for simple languages including
• Exp, Bool, languages for arithmetic and Boolean expressions
• the imperative language of while commands While
• the functional languages Fun and Lambda and simple variations on them; call-by-name and call-by-value semantics.
(i) Typing assignments for the languages Fun and Lambda
(ii) Progress and preservation.
(iii) For Lambda you should be familiar with the computational consequences of using types; in particular the need for explicit fixpoint operators.
Written and oral test.
The exam consists of a written and oral test.
|Andrea Asperti, Agata Ciabattoni||Logica a Informatica||McGraw-Hill||2007|
|Carl A. Gunter||Semantics of Programming Languages||MIT Press||1992||0262570955|
|G. Winskel||The formal Semantics of Programming Languages||MIT Press||1993|