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The move out of compulsory education is a key transition period in adolescents' lives. The aim of the present study was to investigate physical activity and sedentary behaviour (using 'screen time' as the proxy measure) among adolescents during the transition from completing compulsory education to entering further education, training or (un)employment. A prospective population-based longitudinal design was adopted, using a large cohort of adolescents in Gloucestershire. A questionnaire was administered to participants at two time points (baseline and follow-up). At baseline, 2204 Year 11 pupils (aged 14 to 17 years) and at follow-up, 886 participants from the baseline sample (aged 15 to 17 years) completed the questionnaire. ( For all statistical analyses performed, two sets of analysis were conducted. Analysis one included the final sample of participants (n = 663) who had an associated output area (OA) code to include in statistical analyses and analysis two included the final sample of participants (n = 834) who did not have an associated OA code included in statistical analyses. Since the overall findings for each analysis were similar, only findings from analysis one are presented. For physical activity, there was a significant change in the number of participants meeting guidelines at baseline but not meeting guidelines at follow-up. For screen time status, there was no significant change between baseline and follow-up. Binary logistic regression (BLR) revealed that for gender, in comparison to males, females were 52.4% less likely to meet guidelines for physical activity at follow-up. Meanwhile, BLR revealed that there were no significant associations with screen time status at follow-up. Further BLR for the decline in physical activity through the transition, revealed that for gender, in comparison to males, females were 42.4% less likely to move from meeting guidelines at baseline to not meeting guidelines at follow-up (i.e., physical activity decline was associated with being male). The findings of the present study have demonstrated: i) a decline in physical activity through the transition; ii) the high proportion of adolescents not meeting guidelines for screen time at either baseline or follow-up; and iii) associations between gender and physical activity during this transitional period. There is a need for future research to longitudinally examine adolescents' physical activity and sedentary behaviour during this transitional period.

One reason for studying and programming in functional programming languages is that they are easy to reason about, yet there is surprisingly little work on proving the correctness of large functional programs. In this dissertation I show how to provide a system for proving the correctness of large programs written in a major functional programming language, ML. ML is split into two parts: the Core (in which the actual programs are written), and Modules (which are used to structure Core programs). The dissertation has three main themes: Due to the detail and complexity of proofs of programs, a realistic system should use a computer proof assistant, and so I first discuss how such a system can be coded in a generic proof assistant (I use Paulson's Isabelle). I give a formal proof system for proving properties of programs written in the functional part of Core ML. The Modules language is one of ML's strengths: it allows the programmer to write large programs by controlling the interactions between its parts. In the final part of the dissertation I give a method of proving correctness of ML Modules programs using the well-known data reification method. Proofs of reification using this method boil down to proofs in the system for the Core.