Giuseppe_Peano (1858-1932) is one of the most important contributor to mathematics formalization. He is the designer of a small (and beautiful) calculus model. Based on this model (Peano_axioms), he formally defined the set of natural integers. We'll use this calculus model to implement a set of small processes: the “Peano Machine”.

Why this one ? Because it perfectly simulates real world usage of business processes, on a really simple-to-understand example:

• Atomic Peano's operations represent atomic web services operations provided by the SOA
• Complex Peano's operations represent business-driven processes implemented over the SOA

The initial machine is composed by 3 atomic operations, and 2 complex ones. Operations are called complex since they use other operations.

• Atomic Operations:
  • zero?: tests if its parameter is equal to zero
  • next: computes the positive integer located after its parameter
  • prev: computes the positive integer located before its parameter
• Complex Operations:
  • sum: performs the integer addiction of two positive numbers
  • mult: performs the integer product of two positive numbers

• Formal description:

• Atomic Machine: atomic.adore
  • isZero.png, next.png, prev.png
• Complex Machine: complex.adore
  • sum.png, mult.png

• Swap enhancement
  • Rationale: to optimize the execution time by swapping the received parameter when b > a.
  • Implementation: swap.adore, swap.png
• Cache mechanism
  • Rationale: to store intermediate results instead or re-computing it.
  • Implementation: cache.adore, cache.png

• Detailed results are available here