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# Arithmetic with measures on dynamically typed object oriented languages

Presentation at OOSPLA 2005

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### Arithmetic with measures on dynamically typed object oriented languages

1. 1. Arithmetic with Measures on Dynamically Typed OO Languages Hernán Wilkinson* Mercap Development Manager Tacuarí 202, 7mo Piso C1071AAF, Buenos Aires, Argentina 54-11-4878-1118 (ext. 120) h.wilkinson@mercapsoftware.com Máximo Prieto** Lifia – Facultad de Informática Universidad Nacional de La Plata cc11, 1900, La Plata, Argentina +54 221 422-8252 (ext. 215) maximo.prieto@lifia.info.unlp.edu.ar Luciano Romeo Mercap Software Architect Tacuarí 202, 7mo Piso C1071AAF, Buenos Aires, Argentina 54-11-4878-1118 l.romeo@mercapsoftware.com * Also Universidad de Buenos Aires, UBA, Argentina ** Also Universidad Nacional de la Patagonia Austral, Unidad Académica Caleta Olivia (UNPA-UACO)
2. 2. Presentation of the Problem  Common mistakes in Financial Software  Adding amounts of different currencies  Applying interest rates with different time units  Confusing Nominal and Residual quantities  Mars Climate Orbiter  Confused English and Metric Units  Star Wars laser-beam experiment  Confused Miles with Feet
3. 3. Why?  We are NOT used to creating the right ABSTRACTIONS  We are accustomed to using “primitive objects”  Java/.Net still lacks a Fraction class!  Java/.Net do not have a “DayOfMonth” class!  Therefore, we have:  Duplicated Code all over  Maintenance Problems  Communication and Design Problems
4. 4. Motivating Example  Simple Interest Investment Formula finalCapital:=initialCapital+(initialCapital*interestRate*investmentTime)  Algorithm to invest 100 dollars just with Numbers:  Interest Rate: 10% per Year  Investment Time: 6 Months initialCapital := 100. interestRate := 0.1. investmentTime := 6. finalCapital:=initialCapital+(initialCapital*interestRate*investmentTime) = 100 +( 100 * 0.1 * 6 ) = 160  Is it right?
5. 5. Motivating Example  Investing 100 dollars just with Measures:  Interest Rate: 10% per Year  Investment Time: 6 Months initialCapital := 100 dollars. interestRate := 0.1 / 1 year. investmentTime := 6 months. finalCapital:=initialCapital+(initialCapital*interestRate*investmentTime) = 100 dollars +( 100 dollars *0.1 / 1 year* 6 months ) = 105 dollars We got a Measure!!! Not only a Number!!!
6. 6. What have we done?  We created new abstractions!  Our System has objects to represent 100 dollars, just like in real life  There are objects to represent 1 year and 6 months, JLIRL  We let those abstractions fulfill their responsibilities  We enriched our “Programming Language” with new “words”
7. 7. Why do we need to do it?  Numbers are too generic  2 ¿What does it mean?  Units give numbers a particular meaning  2 dollars, 2 months, 2 miles  Operations with numbers are context free  2 + 3 = 5  Operations with measures are context aware  3 days + 1 week = 10 days  2 dollars + 3 euros = ?... It depends
8. 8. What do we want?  Do arithmetic on Measures like in physics  The Measures to take care of unit  Simplification  Validation  Conversion  We want to relieve the programmer from those responsibilities
9. 9. How did we do it?  Definition by National Institute of Standards and Technology (NIST)  “The value of a measure is its magnitude expressed as the product of a number and a unit, and the number multiplying the unit is the numerical value of the quantity expressed in that unit.”  We already have numbers…  We need Units and we need to make them collaborate with numbers to have Measures  So …
10. 10. Units
11. 11. Measures
12. 12. Behavior  Arithmetic operations  1 year + 6 months  18 months  5 days + 3 weeks  26 days  3 miles * 4  12 miles  Comparison  3 miles < 1 kilometer  false  Conversion  1 day convertTo: hour  24 hours
13. 13. Dynamically Typed Languages  Since  Variables are not statically typed then…  We did not need to create a common interface or superclass  We could reuse exactly the same code for existing arithmetic expressions  Smalltalk is designed for supporting unexpected behavior so…  We did not change the Number implementation  Therefore  We did not change a single line of code  We just added new functionality
14. 14. Other Languages  Java:  + is not a message, it is hardcoded in the VM, numbers are not objects  It is statically typed  .Net:  operator + (Integer operand)  Statically typed  Can not be changed
15. 15. Compound Units
16. 16. Measure Bags
17. 17. Singularities of the Measure Domain  Equality  24 hours = 24 hours  true  24 hours = 1 day  true  Immutability  Just like numbers  Zero  0 miles = 0 miles  0 miles = 0 feet  0 miles = 0 dollars ?  But, by definition: 0 A = 0 B   0 miles = 0 dollars = 0 kelvin = 0
18. 18. Financial Measures  Interest Rate:  0.1 / 1 year – We can do it better!!  (InterestRate yearlyOf: 10 %) value  0.1 / 1 year  Price:  10 dollars/2 apples – We can do it better!!  (Price of: 2 apples is: 10 dollars) value  10 dollars/2 apples  Abstraction for Valuations!
19. 19. Conclusions  Generic Measure Model that:  Add vocabulary from the Problem Domain  Supports Arithmetic Operations  Encapsulates Unit Conversion  A Better Programming Language  We believe this model should be part of any programming environment
20. 20. Future Work  To reify the measure dimensions (distance, force, etc.)  Named composed units  Joule equivalent to m2 *Kg*s-2  Pascal equivalent to m-1 *Kg*s-2  To have units understand some messages to facilitate the creation of exponential units  meter pow: 2 to represent square meter.  To restrict the amount of some measures to be valid
21. 21. Questions