MPRI

- Fondements des systemes de preuves / Foundations of proof systems (24h, 3 ECTS)

Fondements des systemes de preuves / Foundations of proof systems (24h, 3 ECTS)

This course focuses on the notion of formal proof in mathematics and in informatics. It presents several logical theories, including type theories used in several proof systems such as Coq, Agda, HOL, Isabelle, PVS. In particular we will treat in depth the articulation between reasoning and computation.

When and where ?

The lectures are each Tuesday from 8:45 to 12:00, in the Sophie Germain Building, room 1013

Schedule

September 10th: Inductive definitions. Natural deduction
September 17th: Logical and axiomatic cuts - Arithmetic
September 24th: Normalization of simply typed lambda-calculus and System T
October 1st: Higher-Order Logic
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Exam

Tuesday, Nov. 19th 2019, 9h-11h30, 1013. Course notes and personal documents allowed

Prerequisites

The notion of inductive definition
The notions of free and bound variables, alphabetic equivalence, and substitution
The syntax of (many-sorted) predicate logic
The natural deduction
The untyped lambda-calculus
The simply typed lambda-calculus
The expression of computable functions in arithmetic, in the language of rewrite rules and in the lambda-calculus