www.s-cube-network.eu

S-Cube Learning Package

The Chemical Computing model and HOCL Programming

INRIA, CNR, SZTAKI

Zsolt Németh, SZTAKI

Learning Package Categorization

S-Cube

Service Infrastructure

Multi-level and self-adaptation

Supporting adaptation of

service-based applications

Learning Package Overview

The vision of chemical computing

Gamma

The γ-calculus

The Higher Order Chemical Language

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]

i:=1

*{i<n →

i:= i+1

m:=max(m, a[i])}

mxset: if tail(l)=nil

then head(l)

else max(head(l),mxset(tail(l)))

Notion of chemical computing

Solution

Data

Procedure

Notion of chemical computing

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.

Learning Package Overview

The vision of chemical computing

Gamma

The γ-calculus

The Higher Order Chemical Language

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.

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

Learning Package Overview

The vision of chemical computing

Gamma

The γ-calculus

The Higher Order Chemical Language

The -calculus

captures the chemical notion

a declarative, functional formalism

inherently concurrent, indeterministic model of computation

shows similarities to the λ-calculus

1 2

7

5

8

γx,y.x+y

The -calculus

basic data structure: multiset (chemical solution)

– passive molecules: booleans, integers, tuples, naming molecules

– active molecules: -abstraction

reaction: an active molecule captures others and transforms

execution: perform reactions until a stable (inert) chemical solution is resulted

reactions are independent concurrent and indeterministic

1 2

7

5

8

2

7 8

6

2

7 8

γx,y.x+y

γx,y.x+y

1 5

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: PC.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)

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

The -calculus

-terms are

– Commutative: M1,M2≡M2,M1

– Associative: (M1,M2),M3≡M1,(M2,M3)

– Realize Brownian motion

Reactions

– Locality: if M1→M2, then M,M1→M,M2

– Solution: if M1→M2, then <M1>→<M2>

1 2

7

5

8

γx,y.x+y

1

2 7

5

8 γx,y.x+y

1

2 7

5

8 γx,y.x+y

5 7

3 γx.x*x

6

Learning Package Overview

The vision of chemical computing

Gamma

The γ-calculus

The Higher Order Chemical Language

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>

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>

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>

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>

blue

white

red 3

6

2

5

4

1

white

blue

white

b w

r

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

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).