High%20Order%20Chemistry%20Model%20of%20Computation

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High Order Chemistry Model of Computation Student
Wilfredo Molina AdvisorDr. Lin July 17, 2009
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What is it?

• The Chemical Reaction Models describe computation
  as chemical reactions.
• Data, or the solution, are represented as a
  multiset.
• Reaction rules are given to combine molecules
  in a solution and produce new ones. This takes
  place until the solution becomes inert, or no
  more elements can be combined.

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Syntax

• The following is the BNF syntax of the high order
  chemistry model of computation
• M 12...'a''b'... constants
• ?(P)C.M ?-abstraction
• M1, M2 multiset
• ltMgt solution

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Gamma Calculus

• The multiset constructor , is associative and
  commutative (AC rule).
• Solutions encapsulate molecules.
• Molecules can move within solutions but not
  across solutions.
• ?-abstractions are elements of multisets, just
  like other elements. They can be applied to other
  elements if a match to pattern P is found and
  condition C evaluates to true.
• ?(P)C.M

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GammaMax

• GammaMax is a program that finds the greatest
  molecule in a solution.
• The following is its ?-abstraction
• ?(xS,yS)xgty.xS
• And it is read as replace x,y by x if xgty

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GammaMax Example
Chemical program that finds the greatest molecule
in a solution?(xS,yS)xgty.xS
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23
2
12
18
10
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GammaSum

• GammaSum is a program that adds the values of all
  the molecules in a solution to find their total
  sum.
• The following is its ?-abstraction
• ?(xS,yS)true.(xy)S
• And it is read as replace x,y by xy in any
  case

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GammaSum Example
Chemical program that adds all the molecules in a
solution?(xS,yS)true.(xy)S
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6
16
4
3
10
41
37
13
21
8
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Parser

• Here I'll put some snapshots of the parser
  analyzing an incorrect and a correct syntax.