Tonight my colleague Byron Cook from MSR Cambridge will be speaking at the F#unctional Londoners meetup group Byron Cook: Proving program termination with F# Wednesday, November 16, 2011, 6:30 PM The Skills Matter eXchange 116-120 Goswell Road,  London (map) In recent years we have seen great progress made in the area of  automatic source-level static analysis tools. However, most of today’s program verification tools are limited to properties that guarantee the absence of bad events (safety pr[...]

Problem The square root of 2 can be written as an infinite continued fraction. The infinite continued fraction can be written, ?2 = [1;(2)], (2) indicates that 2 repeats ad infinitum. In a similar way, ?23 = [4;(1,3,1,8)]. It turns out that the sequence of partial values of continued fractions for square roots provide the [...]

Problem Consider the fraction, n/d, where n and d are positive integers. If n < d and HCF(n,d)=1, it is called a reduced proper fraction. If we list the set of reduced proper fractions for d <= 8 in ascending order of size, we get: 1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, [...]