Logic List Mailing Archive

Five-day minicourse on Lambada Calculus and Term Rewriting Systems

16-20 February 2009
Eindhoven, The Netherlands

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COURSE ANNOUNCEMENT

HIGHLIGHTS of Lambda Calculus and Term Rewriting Systems
by Henk Barendregt & Jan Willem Klop.
Five day mini-course, Monday February 16 - Friday February 20, 2009,
location: Technical University Eindhoven, The Netherlands.
Registration: www.win.tue.nl/math/eidma

BACKGROUND. Lambda Calculus and Combinatory Logic were instrumental
in codifying the  fundamental notion of computability, in the days of
Goedel,
Church, Kleene and Turing. Later on, these formal systems became the
heart
of functional programming. Typed lambda calculus, with the famous Curry-
Howard-de Bruijn  isomorphism, became the source of applications in the
realm of correctness of  formal proofs in mathematics and software,
with the
aid of proof assistants and  theorem provers. At a parallel track,
term rewriting
systems emerged, of which  Lambda Calculus and Combinatory Logic are
prominent examples. The development along this line was intertwined with
the emergence of the theory of  abstract data types. Recently,
infinitary
versions of both lambda calculus and  term rewriting are studied.

PROGRAMME (also at www.cs.ru.nl/~henk/LC-TRS.pdf)
This five day master class in lambda calculus and term rewriting is
centered
around some twenty of the main theorems, both classical and recent. Each
theorem is treated in a syllabus chapter of 10 pages, concluded with
a section
of exercises and notes for follow-up subjects and further reading.

Day 1. ABSTRACT REWRITING AND TERM REWRITING
(a) Newman?s Lemma and Decreasing Diagrams
(b) Critical Pair Completion
(c) Toyama?s Theorem; modularity
(d) Termination via Iterative Path Orders

Day 2. LAMBDA CALCULUS AND COMBINATORY LOGIC
(a) Computable functions on numbers and data types
(b) The fundamental theorems on reduction
(c) Combinators and lambda terms
(d) Reduction Strategies

Day 3. ORTHOGONAL TERM REWRITING
(a) The Erasure Lemma
(b) Root normal forms
(c) Reduction cycles
(d) Combinatory Reduction Systems

Day 4. TYPED LAMBDA CALCULI
(a) Strong normalization of simply typed lambda calculus
(b) Type algebras and intersection type structures
(c) The Curry-Howard-de Bruijn isomorphism
(d) Pure Type Systems

Day 5. INFINITARY REWRITING
(a) iTRSs and infinitary lambda calculus
(b) The infinitary unique normal form property; Boehm Trees
(c) Productivity of stream definitions
(d) Sequentiality and definability

To register as applicant, goto < www.win.tue.nl/math/eidma> .
Costs for (PhD) students: 300 Euro; participants of Dutch graduate
schools are entitled to 100 Euro reduction. A certificate of
attendance will be provided. Further course information can be
obtained from the lecturers: jwk@cs.vu.nl, henk@cs.ru.nl.
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