Programming is Math Proof: Structured Programming

Keywords:

• Dijkstra, Edge Wyber (born 1930 Rotterdam)
• Goto is harmful
• Structures: sequence, selection, iteration

Three Programming Paradigms:

1. Structured Programming (1968 Dijkstra)

• Impose discipline on direct transfer of control aka “Goto“.
• “If/ then /else, do/while” control structures are structured.

2. Object-Oriented ‘OO’ (1966 Ole Johan Dahl & Kristen Nygaard)

• Impose discipline on Indirect transfer of control (polymorphism, ‘constructor‘ function of class, it’s local variables = instance variables).

OO = Combination of Data & Function.

3. Functional Programming (1958 John McCarthy’s LISP language, based on Math “Lambda Calculus” from Alonzo Church 1936).

• Impose discipline upon assignment (side effect, immutability of data, Referential Transparency).

4. Any more ?

All Programs can be constructed from just 3 structures (Böhm and Jacopini, 1966):

Sequence / Selection / Iteration.

Dijkstra’s Math Proofs for:

1. Sequence – by simple enumeration.

• Math Technique: trace the inputs…