Lambda-Cálculo e Lógica Combinatória

2013.2

Ementa e Programa

Instrutores: Ruy de Queiroz e Anjolina de Oliveira

Horário e Sala de Aula
4^a 08-10h, Sala D-224
6^a 10-12h, Sala A-014

Forum: Lambda Cálculo 2013.2

Ementa: O lambda-cálculo. Estrutura de termos e substituição. Redução. Lógica Combinatória. Redução fraca. O Poder Expressivo de Lambda e dos Combinadores. O teorema do ponto-fixo. Representando as funções recursivas. O teorema da indecidibilidade. Lambda-cálculo com tipos. Isomorfismo de Curry-Howard.

Livro-Texto:

Lambda-Calculus and Combinators: An Introduction, J. Roger Hindley & Jonathan P. Seldin, Cambridge University Press, 2nd edition (August 11, 2008), ISBN-10: 0521898854. (Primeira edição: Introduction to Combinators and Lambda-Calculus, London Mathematical Society Student Texts 1, CUP, 1986.)

Outros recursos bibliográficos:

1. An introduction to lambda calculi and arithmetic, Harold Simmons.

2. http://www.safalra.com/science/lambdacalculus/index.html

3. On-line books, aulaure notes, etc (Lambda Calculus)

4. Barendregt and Barendsen's shorter introduction to the lambda calculus

5. Alonzo Church Papers

6. Church, Alonzo, An unsolvable problem of elementary number theory, American Journal of Mathematics, 58 (1936), pp. 345.363. (This paper contains the proof that the equivalence of lambda expressions is in general not decidable.)

7. Church, Alonzo, The calculi of lambda-conversion. Imprint: Princeton, Princeton University Press, 1941 [i.e. 1963]. (Series: Annals of mathematical studies, no. 6)

8. Lambda-Calculus, Types and Models, by J.L. Krivine, Masson, Paris, 1993 (English xlation) ISBN 0-13-062407-1.

Leitura adicional:

1. `Funktion und Begriff', Vortrag, gehalten in der Sitzung vom 9. Januar 1891 der Jenaischen Gesellschaft für Medizin und Naturwissenschaft, Jena: Hermann Pohle. Translated as `Function and Concept' by P. Geach in Translations from the Philosophical Writings of Gottlob Frege, P. Geach and M. Black (eds. and trans.), Oxford: Blackwell, third edition, 1980.

2. Grundgesetze der Arithmetik, Jena: Verlag Hermann Pohle, Band I, 1893. Partial translation as The Basic Laws of Arithmetic by M. Furth, Berkeley: U. of California Press, 1964.