Logique linéaire et paradigmes logiques du calcul

Course 2-1 offered within MPRI.

A brief discription of this course is available in French.


Instructors: Michele Pagani, Delia Kesner, Beniamino Accattoli, and Dale Miller.


During 2019, lectures will be on Fridays from 8h45 - 11h45. The lecture should be in a room in b√Ętiment S. Germain. Miller will lecture (in English) on the following dates: February 1, 8, 15, 22.

Lecture Notes

The lecture notes for most of the first four lectures are collected in the draft monograph ``Logic programming and its proof theory''. Parts of this book will be made available as the lectures proceed.


The exam for the second part of this course will be on 8 March 2019. To prepare for the exam, read the lecture notes and do the exercises in them.

References and Links

Below are some documents available via the web that may be of use in this class.

  1. Linear Logic, by Roberto Di Cosmo and Dale Miller, The Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.).
  2. Logic for Computer Science: Foundations of Automatic Theorem Proving, by Jean Gallier, Wiley, pp. 511 (1986). This book is now out of print but available for free download.
  3. Proofs and Types by Jean-Yves Girard, Paul Taylor, and Yves Lafont. Cambridge University Press. This book is now available from a number of sources for free download. Try the link above to find locations for downloading. Also available here.
  4. Proof Theory as an Alternative to Model Theory by Dale Miller. Argues that the theory of proofs should also be considered a foundations for the design and justification of logic programming.
  5. Logic, Higher-order, by Dale Miller. A short article for the Encyclopedia of Artificial Intelligence: Second Edition, edited by S. Shapiro, 1992. (DVI, PDF).
  6. Programming with Higher-Order Logic by Dale Miller and Gopalan Nadathur, published by Cambridge University Press in June 2012 (available via Amazon). This book covers the design and applications of the λProlog programming language.