SE424: Worksheet 1- Semantic Algebras

  1. Given the algebras of natural numbers and truth values (from lecture notes), simplify the following expressions, showing all steps in your simplification.


  1. Complete the definition of the algebra for the payroll domain (page 3 of section 3 lecture notes) by defining these operations:

Use the completed algebra to define a payroll stating that:

  1. Use the algebra of dynamic array (with curried operators) and the algebra of payroll records to derive an algebra describing databases of payroll records. A database indexes employees by identity numbers. Operations should include ones for :
  1. Given the Domain Unit (lectures notes page 2 section 3) define an algebra for finite lists D* where Unit represents list of length zero, D represents a list of one element, DxD represents a list of length zero, D represents a list of one element and operations cons: D x D* ® D*, hd: D* ® D, tl: D* ® D*, null: D* ® Tr are defined.