Compiling Interaction Nets · Outlines Compiling Interaction Nets Abubakar.Hassan at kcl.ac.uk...

Outlines

Compiling Interaction Nets

Abubakar.Hassan at kcl.ac.uk

Department of Computer ScienceKings College London

April 4, 2006

Abubakar.Hassan at kcl.ac.uk Compiling Interaction Nets

Outlines Interaction Nets Programming Language

Outline

1 Interaction Nets Programming LanguageBackgroundLanguage SyntaxForeign Language InterfaceModule System

2 Compilation of Interaction netsAbstract MachineCompilation schemes

3 Conclusions and Future work


Programming Language

Part I

Interaction Nets Programming Language



BackgroundLanguage SyntaxForeign Language InterfaceModule System

Interaction nets system

Define a set Σ of Agents

��α

?

@ �· · ·x1 xn

y = α(x1, . . . , xn)

and a set R of Rules

��α ��

β-�@

�

�

@

......

x1

xn

ym

y1

=⇒ N...

...x1

xn

ym

y1




Example

Σ = {Z, S , +}:

��Z6

��S6

��+

@@��

x = Z() y = S(a) w = +(d , e)

R =

��Z

��+

��S

��+

��+

��S6

�� @

� @

��

�

� @@

=⇒ =⇒




a = Add(x , y), a = Z =⇒ x = ya = Add(x , y), a = S(z) =⇒ x = S(b), z = Add(b, y)

Replace equals for equals:

Z = Add(x , x) =⇒S(Add(b, y)) = Add(S(b), y) =⇒

we replace the ‘=’ by ‘><’ and remove =⇒ if empty.

Z >< Add(x , x)S(Add(b, y)) >< Add(S(b), y)




Net with active pair and Reduction

��S

��Z6

��Z6

��+

@@��

� ��S

I −→ ��Z

��Z6

��+

��S6

@@��

� ��S

I −→

��Z6

��S6

��S6

After replacing equals for equals:

S(Z) = Add(z ,S(Z)) −→ Z = Add(S ,S(Z))−→ S(S(Z))




Language Syntax

We can see interaction nets as a configurationc = (Σ, 〈~t | u1 = v1, . . . un = vn〉,R)

P ::= (agent | rule)∗ netagent ::= agentName : arityrule ::= [ruleName: ] term >< term ( => net | )net ::= [netName: ] equation (, equation)∗ |equation ::= term = termterm ::= agentName(term, ..., term) | var




Example

Z:0 S:1Add:2AddZ: Z >< Add(x,x)AddS: S(Add(b,y)) >< Add(S(b),y)S(Z) = Add(b,S(Z))




Foreign Language Interface

P ::= (agent | rule)∗ netagent ::= agentName : arityrule ::= [ruleName: ] term >< term ( => net | )net ::= [netName: ] equation (, equation)∗ |equation ::= term = termterm ::= agentName{`}(term, ..., term)




Example

fact:1 num:0 ans:0num{int n} >< fact(ans{Factorial.fact(n)})fact(x) = num{8}




Module System

P ::= module { [import modName[. compName]](agent | rule)∗ net }

agent ::= [*]agentName : arityrule ::= [[*]ruleName: ] term >< term ( => net | )net ::= [[*]netName: ] equation (, equation)∗ |equation ::= term = termterm ::= [*]agentName{`}(term, ..., term)




Example

module add {import arith.Zimport arith.S*Add:2*AddZ: Z >< Add(x,x)*AddS: S(Add(b,y)) >< Add(S(b),y)S(Z) = Add(b,S(Z)) }


Compiler

Part II

Compilation of Interaction nets



Compilation schemes

A program may consist of a list of modules M1, ...Mn. Thecompilation scheme Cp compiles each module using the schemeCm. This in turn compiles each of the component

c = (Σ, 〈~t | u1 = v1, . . . un = vn〉,R)

in the module by using the appropriate scheme:

Cp = CmJM1K, ..., CmJMnK



The compilation of a module generates the following code:

CmJ(Σ, 〈~t | u1 = v1, . . . un = vn〉,R)K =

ruleName :CRJr1K...ruleName :CRJrnKnetName :CNJu1 = v1K...netName :CNJun = vnKinterface :CT JtK



Example

The code generated by compiling:module Erase{Eps:0EpsEpsRule: Eps >< EpsEpsNet: Eps = Eps}is:EpsEpsRule:loadc epsloadc 1mkAgentstore 0load 0store 1loadc epsloadc 1mkAgentstore 0load 0store 0

loadc 2load 0load 1mkRulepopEpsNet:loadc epsloadc 1mkAgentstore 0load 0store 1loadc eps

loadc 1mkAgentstore 0load 0store 0load 0load 1mkNetevalpop



Execution starts from the initial configuration:

P ` 〈0, [], [], [], []〉

The machine starts executing the instructions under the labelEpsEpsRule. After interpreting all the code in this label, weobtain the configuration:

p ` 〈16, [], [], [], [Eps,Eps]〉

The configuration obtained after executing the code in the labelEpsNet, before the instruction eval:

p ` 〈32, [], [], [Eps,Eps], [Eps,Eps]〉

The final configuration obtained after the eval instruction:

p ` 〈33, [], [0 7→ ε], [], [Eps,Eps]〉


Conclusions and Future work

Future work

We have seen for the first time a compilation scheme forInteraction nets.

extend the core language

study alternative compilation schemes

compilation for parallel hardware

optimisations

type system



Compilation Schemes

Cv JvK =

loadc vmkVarstore−i

CtJα(t1 · · · tn)K

CaJαKstore−iCaJt1Kstore−i + 1load iloadc 1load i + 1



CnJα(u1, ..., un) = β(v1, ..., vn)K =

CtJα(u1 · · · un)KCtJβ(v1 · · · vn)KmkNetevalpop

Cr Jα(t1, ..., tn) >< β(u1, ..., un)K =

CtJα(t1 · · · tn)KCtJβ(u1 · · · un)KmkRulepop



CaJαK =

loadc αloadc armkAgentstore−iloadc 0connectPortsstore−i...CaJtnK

store−i + 1load iloadc nload i + 1loadc 0connectPortsstore−i


Compiling Interaction Nets · Outlines Compiling Interaction Nets Abubakar.Hassan at kcl.ac.uk...

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