1. S-Cube Learning Package
The Chemical Computing model and HOCL
Programming
INRIA, CNR, SZTAKI
Zsolt Németh, SZTAKI
www.s-cube-network.eu

2. Learning Package Categorization
S-Cube
Service Infrastructure
Multi-level and self-adaptation
Supporting adaptation of
service-based applications

3. Learning Package Overview
 The vision of chemical computing
 Gamma
 The γ-calculus
 The Higher Order Chemical Language

4. Problem statement and motivation
 Most algorithms are sequential even if the problem solving is
inherently parallel
 Many algorithms are expressed in a cumbersome way
 Declarative vs. imperative style of programming
 Clear mathematical model for defining semantics
mxset: m:=a[1] mxset: if tail(l)=nil
i:=1 then head(l)
*{i<n → else max(head(l),mxset(tail(l)))
i:= i+1
m:=max(m, a[i])}

5. Notion of chemical computing
Solution
Procedure
Data

6. Notion of chemical computing

7. Why chemical
 Concise problem description
 Locality
– decisions on actual and timely conditions
– decisions on partial information
 Self-evolving, autonomic, adaptive behaviour
 Inherently parallel and concurrent
 Highly dynamic
 Coordinating problems
– large number of entities
– changing conditions
 Beware! This model is not computational chemistry!
 A large class of problems in SOA require unconventional approaches
– service composition, service coordination, service adaptation, workflow, etc.

8. Learning Package Overview
 The vision of chemical computing
 Gamma
 The γ-calculus
 The Higher Order Chemical Language

9. GAMMA
 GAMMA (General Abstract Model for Multiset Manipulation)
 multiset M
 R(x1, x2,…xn) guard
 A(x1, x2,…xn) action
 (Ri, Ai) reaction
 replace (x1, x2,…xn) in M
if R(x1, x2,…xn)
by A(x1, x2,…xn)
 a large set of problems expressed in a concise way
– prime search, sorting, string processing, geometric problems, graph
algorithms, process control, etc.

10. GAMMA
 The first language to capture the notion of chemical
programming
 Now of merely historic value
 Based on the idea of GAMMA
– the γ-calculus
- different of GAMMA
- higher order
- reaction rules = active molecules, part of the solution
- active molecules vanish in reactions
– Higher Order Chemical Language
- a language based on the γ-calculus

11. Learning Package Overview
 The vision of chemical computing
 Gamma
 The γ-calculus
 The Higher Order Chemical Language

12. The -calculus
 captures the chemical notion
 a declarative, functional formalism
 inherently concurrent, indeterministic model
of computation
 shows similarities to the λ-calculus
2
1 5
γx,y.x+y
8 7

13. The -calculus
2
1
 basic data structure: multiset (chemical 5
solution) γx,y.x+y
8 7
– passive molecules: booleans, integers, tuples,
naming molecules
– active molecules: -abstraction 2
 reaction: an active molecule captures others 1 5
and transforms γx,y.x+y
8 7
 execution: perform reactions until a stable
(inert) chemical solution is resulted
2
 reactions are independent concurrent and
indeterministic 6
8 7

14. Active molecules: -abstraction
 P.M
– P is a pattern that selects elements for the reaction (head)
– M is the action (body)
– capture x and replace by its square: x . x*x
 Conditional reactions: PC.M
– C is a condition; the reaction takes place if C is true
– capture x and if positive, replace by its square root: x x>0 . sqr(x)

15. Active molecules: -abstraction
 Atomic capture:  x1,x2,…xn.M
– a single reaction may capture multiple molecules
– capture x,y and replace them by their sum: x,y . x+y
 Reaction: active molecules capture other molecules
– formal parameters are substituted in the body
– notion of free and bound variables
– x.M, N → M[x:=N]
– x,y . x+y, 2, 3 → 2+3
– 2, x,y . x+y, 3 → 2+3
– 3, 2, x,y . x+y → 2+3
– x,y . x.x+y, 2, 3 → x.x+2
– x,y . x.x+y, 2, 3 → x.x+3

16. The -calculus
2
1 5
 -terms are γx,y.x+y
– Commutative: M1,M2≡M2,M1 8 7
– Associative: (M1,M2),M3≡M1,(M2,M3)
– Realize Brownian motion
γx,y.x+y
8
 Reactions
1
– Locality: if M1→M2, then M,M1→M,M2 5
7
– Solution: if M1→M2, then <M1>→<M2> 2
γx,y.x+y
8
γx.x*x
3
1
5
5 7
7 2
6

17. Learning Package Overview
 The vision of chemical computing
 Gamma
 The γ-calculus
 The Higher Order Chemical Language

18. A chemical language: HOCL
• Higher Order Chemical Language (HOCL)
• Higher order: active molecules (procedures)
– capture other active molecules
– produce other active molecules
• Multiset rewriting
• Program: solution of atoms
• < A1, A2, …An>

19. HOCL
• replace P by M if C in <>
– P: pattern, captured molecules
– M: action, produced molecules
– C: condition
 max = replace x,y by x if x ≥ y in
<1, 2, 3, 4, 5, 6, 7, 8, 9, max>
 primes = replace x,y by y if x div y in
<1, 2, 3, 4, 5, 6, 7, 8, 9, primes>

20. HOCL execution
 max = replace x,y by x if x ≥ y in
<1, 2, 3, 4, 5, 6, 7, 8, 9, max>
 <1, 2, 3, 4, 5, 6, 7, 8, 9, max>
 <1, 3, 4, 5, 6, 7, 8, 9, max>
 <1, 3, 4, 5, 6, 8, 9, max>
 <1, 4, 5, 6, 8, 9, max>
 <4, 5, 6, 8, 9, max>
 <4, 6, 8, 9, max>
 <6, 8, 9, max>
 <8, 9, max>
 <9, max>

21. The Dutch flag example
let r = replace <i,red>,<j,white> by <i,white>,<j,red> if i>j in
let w = replace <i,white>,<j, blue> by <i, blue>,<j,white> if i>j in
let b = replace <i,red>,<j,blue> by <i,blue>,<j,red> if i>j in
<<1,blue>,<2,white>,<3,white>,<4,red>,<5,blue>,<6,white>,r,w,b>
2
5 blue
white 6
1
r white
blue
white
3 4 b
w red

22. References
Jean-Pierre Banatre and Daniel LeMetayer. Programming by multiset transformation. Commun. ACM,
36(1):98–111, 1993.
Jean-Pierre Banatre, Pascal Fradet, and Yann Radenac. Generalized multisets for chemical programming.
Math. Struct. in Comp. Science, 16:557–580, 2006.
Jean-Pierre Banatre, Pascal Fradet, and Yann Radenac. Programming self-organizing systems with the
higher-order chemical language. International Journal of Unconventional Computing, 3(3):161–177, 2007

23. Acknowledgements
The research leading to these results has
received funding from the European
Community’s Seventh Framework
Programme [FP7/2007-2013] under grant
agreement 215483 (S-Cube).