Monographs in Computer Science

0 What can we learn from a cake?.- 0.0 Introduction.- 0.1 What can we learn from a cake?.- 1 Preliminary notions, notations, and terminology.- 1.0 Introduction.- 1.1 The shapes of our calculations.- 1.2 Laws and so on.- 1.3 On avoiding parentheses.- 1.4 On carrying out calculations.- 1.5 Three new arithmetic operators.- 1.6 The problem with the three dots.- 1.7 What are the natural numbers?.- 1.8 A bit about function application.- 1.9 What next?.- 2 Predicates A - Boolean operators.- 2.0 Introduction.- 2.1 The equivalence.- 2.2 The disjunction.- 2.3 Intermezzo on some interesting formulae.- 2.4 The conjunction.- 2.5 The implication.- 2.6 The consequence.- 2.7 The negation.- 2.8 The discrepancy.- 2.9 Summary of binding powers.- 2.10 Final comments.- 2.11 Exercises.- 3 Predicates B - Quantified expressions.- 3.0 How to write quantified expressions.- 3.1 Laws for quantified expressions.- 3.2 Universal quantification.- 3.3 Existential quantification.- 3.4 Some arithmetic quantifications.- 3.5 Other quantified expressions.- 3.6 Additional exercises.- 4 Specifications.- 4.0 Introduction.- 4.1 Assigning meaning to our predicates.- 4.2 Towards writing specifications.- 4.3 Examples of specifications.- 4.4 Intermezzo on the array.- 4.5 More examples of specifications.- 4.6 Intermezzo on ascending functions.- 4.7 Even more examples of specifications.- 4.8 Other notations for functional specifications.- 4.9 Comments on specifications.- 5 The shapes of programs.- 5.0 Introduction.- 5.1 The shapes of programs.- 5.2 When is a program correct?.- 5.3 A bit about wp.S.- 5.4 Defining wp.S for all programs S.- 5.4.0 The skip and the abort.- 5.4.1 The composition.- 5.4.2 The assignment.- 5.4.3 The alternation.- 5.4.4 The repetition.- 6 Intermezzo on calculations.- 7 Developing loopless programs.- 7.0 Introduction.- 7.1 Calculating expressions in assignments.- 7.2 Developing IFs.- 8 Developing loops - an introduction.- 9 Loops A - On deleting a conjunct.- 9.0 Introduction.- 9.1 An example - Integer-division.- 9.2 An example - The linear search (and its billions of uses).- 9.3 An example - 3-tuple sort (and avoiding avoidable case-analyses).- 9.4 An example - Integer-division improved (and postponing design decisions).- 10 Loops B - On replacing constants by fresh variables.- 10.0 Introduction.- 10.1 An example - Evaluating a polynomial.- 10.2 An example - The minimum value.- 10.3 An example - Determining the multiple.- 10.4 An example - A table of cubes.- 10.5 An example - The maximum section sum.- 10.6 An example - The binary search (and its numerous applications).- 10.7 An example - Rearranging an array.- 10.8 An example - The bounded linear search.- 11 Mainly on recursion.- 11.0 Introduction.- 11.1 The general solution.- 11.2 An example - The sum of digits.- 11.3 An example - Exponentiation.- 11.4 Introducing four new types.- 11.5 An example - Reversing a sequence (and the importance of good notation).- 11.6 An example - The post-order of a binary tree.- 11.7 An example - The depth of a binary tree.- 11.8 Exercises.- 12 Back to scratch.- 12.0 Introduction.- 12.1 An example - Evaluating a polynomial (and the discovery of nice specifications).- 12.2 An example - Greatest common divisors (and the discovery of useful properties).- 12.3 An example - All shortest paths (and the specification as logical firewall).- 12.4 A final example - Shiloach's algorithm.- 12.5 Additional exercises.- 13 Where to go from here.- 13.0 On what we have learned.- 13.1 Where to go from here.- 13.2 Be a little discriminating.- 13.3 Inspirations and acknowledgements.- 13.4 Selected references.- 13.5 If you find a nice example....