notes on relation algebra

From : Graham , Between Functions and Relations in Calculating Programs

Calculational approach to programming ( derive program from specification):

• fold/unfold of Burstall and Darlingto
• imperative refinement calculus of Back Morgan , Morris 
• functional Squiggol of Bird and Meertens
• relational Ruby of Jones and Sheeran
• categorical approach of Bird and De Moor   
• From Dynamic Programming to greedy algorithm
• Oege . Categories, Relations and Dynamic Programming

History of Binary Relation Theory:

• Peirce 1870
• Schroder 1895
• Tarski 1941 .On the calculus of relations 

Relational calulus as Programming Language

• Ruby , Jones and Sheeran
• Bird and de Moor 
• Backhouse el.  A relational theory of datatypes
• MacLennan RPL 
• D. M. Cattrall . The Design and Implementation of a Relational Programming System. Phd
• Veloso. Partial relations for program derivation.

Developement of Squiggol

• Boom Hierarchy: tree , lists, bags, sets
• Malcom : recursive types , F-algebra, catamorphic. Algebraic Data Types and Program Transformation. PhD.
• Gibbons 29
• Meijer 50. types are cpo. unify finite and infinite objects , deriving compiler from denotational semantics. 
• Fokkinga 27. extend F-algebra to constructors with laws. Law and Order in Algorithmics. PhD.
  

Relational Algebra as specification 

• Berghammer [7]. specify types and programs
• Desharnais [21]. specify types by relational formulae
• Haeberer [67]. extend RA to first order logic
• Fredy [28]. Barr[6], Carboni [16]Categorical treatment

Unfinished.