Corrado Böhm. Corrado Böhm Technology Programming Logics λ 25 January / 25
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1 Corrado Böhm Corrado Böhm Technology Programming Logics λ 25 January / 25
2 Technology 1951: Corrado Böhm Technology Programming Logics λ 25 January / 25
3 Technology 1951: Corrado Böhm Technology Programming Logics λ 25 January / 25
4 Technology 1951: a compiler that can compile the language in which it is written Corrado Böhm Technology Programming Logics λ 25 January / 25
5 Technology 1951: a compiler that can compile the language in which it is written a meta-circular compiler Corrado Böhm Technology Programming Logics λ 25 January / 25
6 Technology 1951: a compiler that can compile the language in which it is written a meta-circular compiler five years before FORTRAN was defined Corrado Böhm Technology Programming Logics λ 25 January / 25
7 Technology 1951: a compiler that can compile the language in which it is written a meta-circular compiler five years before FORTRAN was defined seven years before LISP was defined Corrado Böhm Technology Programming Logics λ 25 January / 25
8 Technology Corrado Böhm Technology Programming Logics λ 25 January / 25
9 Technology Corrado Böhm Technology Programming Logics λ 25 January / 25
10 Technology Corrado Böhm Technology Programming Logics λ 25 January / 25
11 Technology Corrado Böhm Technology Programming Logics λ 25 January / 25
12 Technology Corrado Böhm Technology Programming Logics λ 25 January / 25
13 Technology Corrado Böhm Technology Programming Logics λ 25 January / 25
14 Technology Corrado Böhm Technology Programming Logics λ 25 January / 25
15 Programming 1966: Corrado Böhm Technology Programming Logics λ 25 January / 25
16 Programming 1966: Böhm-Jacopini theorem Corrado Böhm Technology Programming Logics λ 25 January / 25
17 Programming 1966: Böhm-Jacopini theorem the theoretical basis of structured programming Corrado Böhm Technology Programming Logics λ 25 January / 25
18 Programming Corrado Böhm Technology Programming Logics λ 25 January / 25
19 Programming Corrado Böhm Technology Programming Logics λ 25 January / 25
20 Programming Corrado Böhm Technology Programming Logics λ 25 January / 25
21 Programming Corrado Böhm Technology Programming Logics λ 25 January / 25
22 Programming Corrado Bo hm Technology Programming Logics λ 25 January / 25
23 Programming Corrado Böhm Technology Programming Logics λ 25 January / 25
24 Programming Corrado Böhm Technology Programming Logics λ 25 January / 25
25 Logics 1968: Corrado Böhm Technology Programming Logics λ 25 January / 25
26 Logics 1968: Böhm s theorem Corrado Böhm Technology Programming Logics λ 25 January / 25
27 Logics 1968: Böhm s theorem equivalence of programs represented by λ-terms in β-η-normal form is decidable Corrado Böhm Technology Programming Logics λ 25 January / 25
28 Logics 1968: Böhm s theorem equivalence of programs represented by λ-terms in β-η-normal form is decidable two syntactically different β-η-normal forms can be separated by applying them to the same sequence of λ-terms Corrado Böhm Technology Programming Logics λ 25 January / 25
29 Logics 1968: Böhm s theorem equivalence of programs represented by λ-terms in β-η-normal form is decidable two syntactically different β-η-normal forms can be separated by applying them to the same sequence of λ-terms two terms of λ-calculus having syntactically different normal forms with respect to β-η-reduction cannot be consistently equated Corrado Böhm Technology Programming Logics λ 25 January / 25
30 Logics Corrado Bo hm Technology Programming Logics λ 25 January / 25
31 Logics Corrado Böhm Technology Programming Logics λ 25 January / 25
32 Logics Corrado Böhm Technology Programming Logics λ 25 January / 25
33 Logics Corrado Böhm Technology Programming Logics λ 25 January / 25
34 Logics Böhm-out technique SELECT(k, i) 1 i k = i ROTATE(k) 1 k a = a 1 k Corrado Böhm Technology Programming Logics λ 25 January / 25
35 Logics Böhm-out technique a a b 1 e c a a b e d Corrado Böhm Technology Programming Logics λ 25 January / 25
36 Logics Böhm-out technique a a b 1 e c a a b e d Corrado Böhm Technology Programming Logics λ 25 January / 25
37 Logics Böhm-out technique a a b 1 e c a a b e d a ROTATE(3) Corrado Böhm Technology Programming Logics λ 25 January / 25
38 Logics Böhm-out technique b e c b e d Corrado Böhm Technology Programming Logics λ 25 January / 25
39 Logics Böhm-out technique b e c b e d b SELECT(3, 2) Corrado Böhm Technology Programming Logics λ 25 January / 25
40 Logics Böhm-out technique c e d e Corrado Böhm Technology Programming Logics λ 25 January / 25
41 Logics Böhm-out technique c e d e e SELECT(3, 1) Corrado Böhm Technology Programming Logics λ 25 January / 25
42 Logics Böhm-out technique c d Corrado Böhm Technology Programming Logics λ 25 January / 25
43 Logics Böhm s theorem is constructive Corrado Böhm Technology Programming Logics λ 25 January / 25
44 Corrado Böhm with Combinators Corrado Böhm Technology Programming Logics λ 25 January / 25
45 Corrado Böhm with Combinators Corrado Böhm Technology Programming Logics λ 25courtesy Januaryof 2013 Carol Hindley 25 / 25
46 Corrado Böhm with Combinators Corrado Böhm Technology Programming Logics λ 25courtesy Januaryof 2013 Carol Hindley 25 / 25
47 Corrado Böhm with Combinators Corrado Böhm Technology Programming Logics λ 25courtesy Januaryof 2013 Carol Hindley 25 / 25
48 Corrado Bo hm with Combinators courtesy of Carol Hindley Corrado Bo hm Technology Programming Logics λ 25 January / 25
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