Complex Systems Design &DistributedCalculusandCoordination

Complex Systems Design &DistributedCalculusandCoordination Concurrency and Process Algebras: Theory and Practice - Klaim Francesco Tiezzi University of Camerino francesco.tiezzi@unicam.it A.A. 2014/2015 F. Tiezzi (Unicam) CoSyDesign & DCC 1/ 45

Outline 1 Motivations 2 Klaim syntax 3 Klaim semantics 4 An example 5 Klaim implementation F. Tiezzi (Unicam) CoSyDesign & DCC 2/ 45

Original goal Motivations Programming Global Computers: distributed software architecture models Large number of heterogeneous and autonomous components Wide area distribution, manifest to application programmers Different authorities with different administrative and security policies Components with highly dynamic behavior that must adapt to unpredictable changes over time oftheenvironment,duee.g.to lack of services node failures network reconfiguration... Mobile components must support heterogeneity and interoperability, as they may detach from a node and re-attach later on a different one Openended, loosely coupled, possibly collaborative settings F. Tiezzi (Unicam) CoSyDesign & DCC 3/ 45

Motivations Programming Global Computers Programming Languages would definitely benefit from explicit primitives for Concurrency considering parallel and non-deterministic computations Distribution computing over different (explicit) localities Mobility moving code and processes over localities and from formal semantics and associated tools for Reasoning on programs behaviour F. Tiezzi (Unicam) CoSyDesign & DCC 4/ 45

The spatial dimension Motivations Many foundational languages have been designed that features mechanisms for coordinating and monitoring the use of resources for code and process mobility for managing security All these foundational languages encompass a notion of location to reflect the idea of administrative domains to model the fact that computations at a certain location are under the control of a specific authority They focus on the spatial dimension of GC programming (which is often referred to as network awareness) F. Tiezzi (Unicam) CoSyDesign & DCC 5/ 45

Motivations Card game F. Tiezzi (Unicam) CoSyDesign & DCC 6 / 45

Motivations Klaim design goal Developing a simple programming language and associated tools for network aware and mobile applications with a tractable semantic theory that permits programs verification Our Starting Points (1980... ) Process Algebras CCS, CSP,... Calculi and languages for Mobility Pi-calculus, Obliq, Ambients,... Tuple-based Interaction Models Linda Modal and Temporal Logics HML, CTL, ACTL, µ-calculus,... F. Tiezzi (Unicam) CoSyDesign & DCC 7/ 45

Klaim: mainingredients Motivations Kernel Language for Agent Interaction and Mobility a formalism for concurrent, distributed and mobile systems Linda communication model Asynchronous communication Shared tuple spaces Pattern Matching Explicit use of localities Multiple distributed tuple spaces Code and process mobility Process Calculus flavored Small set of basic operators Clean operational semantics F. Tiezzi (Unicam) CoSyDesign & DCC 8/ 45

Motivations Tuples and Pattern Matching Tuples: ( foo, 10 + 5, true) Actual Fields (i.e. expressions) Templates: (!s, 15,!b) Actual Fields Formal Fields (i.e. variables) Pattern Matching: Formal fields match any field of the same type Actual fields match if identical F. Tiezzi (Unicam) CoSyDesign & DCC 9/ 45

Motivations Linda communication model Tuple Space F. Tiezzi (Unicam) CoSyDesign & DCC 10 / 45

Motivations Linda communication model out(t) Tuple Space F. Tiezzi (Unicam) CoSyDesign & DCC 10 / 45

Motivations Linda communication model out(t) Tuple Space eval(t) F. Tiezzi (Unicam) CoSyDesign & DCC 10 / 45

Motivations Linda communication model out(t) in(t ) Tuple Space eval(t) F. Tiezzi (Unicam) CoSyDesign & DCC 10 / 45

Motivations Linda communication model out(t) in(t ) Tuple Space eval(t) read(t ) F. Tiezzi (Unicam) CoSyDesign & DCC 10 / 45

From Linda to Klaim Motivations Localities to model distribution Physical localities (network addresses), i.e. names Logical localities (aliases for addresses), i.e. variables Adistinctvariableself indicates the node a process is on Local and remote operations to read/withdraw/write tuples, spawn processes, create nodes Allocation environments to associate physical to logical localities Logical localities are local aliases for network addresses Programmers may not know the exact network topology Process Calculi operators to specify behaviours Action prefix Parallel composition Name creation / scope delimitation F. Tiezzi (Unicam) CoSyDesign & DCC 11 / 45

Klaim Motivations Klaim consists of three layers: nets, processes, and actions Nets specify the overall structure of a system, including where processes and tuple spaces are located how nodes are interconnected Processes are the actors in this system and execute by performing actions F. Tiezzi (Unicam) CoSyDesign & DCC 12 / 45

Klaim Nodes Motivations Locality name (address) Allocation environment Processes Tuple Space F. Tiezzi (Unicam) CoSyDesign & DCC 13 / 45

Klaim Nodes Motivations Locality name (address) Allocation environment Processes Tuple Space s F. Tiezzi (Unicam) CoSyDesign & DCC 13 / 45

Klaim Nodes Motivations Locality name (address) Allocation environment Processes Tuple Space s ρ F. Tiezzi (Unicam) CoSyDesign & DCC 13 / 45

Klaim Nodes Motivations Locality name (address) Allocation environment Processes Tuple Space s ρ Q F. Tiezzi (Unicam) CoSyDesign & DCC 13 / 45

Klaim Nodes Motivations Locality name (address) Allocation environment Processes Tuple Space s ρ Q eval(p)@s F. Tiezzi (Unicam) CoSyDesign & DCC 13 / 45

Klaim Nodes Motivations Locality name (address) Allocation environment Processes Tuple Space s ρ P Q eval(p)@s F. Tiezzi (Unicam) CoSyDesign & DCC 13 / 45

Klaim Nodes Motivations Locality name (address) Allocation environment Processes Tuple Space s ρ P Q t 1 eval(p)@s F. Tiezzi (Unicam) CoSyDesign & DCC 13 / 45

Klaim Nodes Motivations Locality name (address) Allocation environment Processes Tuple Space s ρ P Q t 1 eval(p)@s out(t)@s F. Tiezzi (Unicam) CoSyDesign & DCC 13 / 45

Motivations Klaim Nodes Locality name (address) Allocation environment Processes Tuple Space s P ρ Q t 1 t 2 eval(p)@s out(t)@s F. Tiezzi (Unicam) CoSyDesign & DCC 13 / 45

Motivations Klaim Nodes Locality name (address) Allocation environment Processes Tuple Space s P ρ Q t 1 t 2 eval(p)@s out(t)@s in(t )@s F. Tiezzi (Unicam) CoSyDesign & DCC 13 / 45

Klaim Nodes Motivations Locality name (address) Allocation environment Processes Tuple Space s ρ P Q t 2 read(t )@s eval(p)@s out(t)@s in(t )@s F. Tiezzi (Unicam) CoSyDesign & DCC 13 / 45

Klaim Nodes Motivations Locality name (address) Allocation environment Processes Tuple Space s ρ newloc(s ) P Q t 2 read(t )@s eval(p)@s out(t)@s in(t )@s F. Tiezzi (Unicam) CoSyDesign & DCC 13 / 45

Klaim Nets Motivations s 2 l s 1, l s 3 out(t)@l t3 s 3 s 1 self s 3 t 1 t 2 in(t )@self F. Tiezzi (Unicam) CoSyDesign & DCC 14 / 45

Klaim: Syntax(1) Klaim syntax Locality names: s, s,... Locality variables: self, l, l,... l will stand for a locality name or a locality variable F. Tiezzi (Unicam) CoSyDesign & DCC 15 / 45

Klaim: Syntax(1) Klaim syntax Locality names: s, s,... Locality variables: self, l, l,... l will stand for a locality name or a locality variable Tuples: Templates: t ::= e l P t1, t 2 T ::= e l P! x! l! X T1, T 2 Actions: a ::= in(t )@l read(t )@l out(t)@l eval(p)@l newloc(s) exchanging data, spawning new processes, creating new nodes F. Tiezzi (Unicam) CoSyDesign & DCC 15 / 45

Klaim: Syntax(2) Klaim syntax Nets are plain collections of interconnected nodes Nodes have a unique address, an allocation environment and host components N ::= 0 s :: ρ C N 1 N 2 (νs)n Components are evaluated tuples or running processes C ::= t P C 1 C 2 Processes are built up from the inert process via action prefixing, parallel composition and process invocation (and definition) P ::= a.p P 1 P 2 A( p) (A( f ) P) F. Tiezzi (Unicam) CoSyDesign & DCC 16 / 45

Klaim: Syntax Klaim syntax Nets: Components: Processes: Actions: N ::= 0 s :: ρ C N 1 N 2 (νs)n P ::= C ::= t P C 1 C 2 a.p P 1 P 2 A( p) (A( f ) P) a ::= in(t )@l read(t )@l out(t)@l eval(p)@l newloc(s) Tuples: t ::= e l P t1, t 2 Templates: T ::= e l P! x! l! X T1, T 2 F. Tiezzi (Unicam) CoSyDesign & DCC 17 / 45

Binders Klaim semantics Prefix in(...,!x,!l,!x,...)@l.p binds x, l, X in P (read acts similarly) Prefix newloc(s).p binds s in P Restriction (νs)n binds s in N F. Tiezzi (Unicam) CoSyDesign & DCC 18 / 45

Klaim semantics Klaim: StructuralCongruence Monoid laws for, i.e. N 0 N, N 1 N 2 N 2 N 1, (N 1 N 2 ) N 3 N 1 (N 2 N 3 ) (Alpha) N N if N = α N (RCom) (νs 1 )(νs 2 )N (νs 2 )(νs 1 )N (Ext) N 1 (νs)n 2 (νs)(n 1 N 2 ) if s fl(n 1 ) (Abs) s :: ρ C s :: ρ (C ) (Clone) s :: ρ C 1 C 2 s :: ρ C 1 s :: ρ C 2 (PDef) s :: ρ A( p) s :: ρ P[ p/ f ] if A( f ) P F. Tiezzi (Unicam) CoSyDesign & DCC 19 / 45

Klaim semantics Klaim: Operational Semantics (1) Producing data: ρ(l) =s E[[ t ]] ρ = t s :: ρ out(t)@l.p s :: ρ s :: ρ P s :: ρ t where the local environment ρ is used to determine the location s that is the target of the action function E[[ t ]]ρ replaces the free locality variables occurring in t according to the local environment ρ yielding t static binding discipline Remark: Free variables act as aliases that have to be replaced by network addresses F. Tiezzi (Unicam) CoSyDesign & DCC 20 / 45

Klaim semantics Klaim: Operational Semantics (2) Consuming data: ρ(l) =s match(e[[ T ]] ρ, t) =σ s :: ρ in(t )@l.p s :: ρ t s :: ρ Pσ s :: ρ where: function match(t, t) checkscompliance of E[[ T ]] ρ and t and associates values (i.e. basic values, names and processes) to variables bound by the template atuplematchesagainstatemplateiftheyhavethesamenumberof fields, and corresponding fields match σ is a substitution of names and processes for the free variables in T F. Tiezzi (Unicam) CoSyDesign & DCC 21 / 45

Matching Function Klaim semantics match(!x, v) =[v/x] match(v, v) =ϵ match(!l, s) =[s/l] match(s, s) =ϵ match(!x, P) =[P/X ] match(t 1, t 1 )=σ 1 match(t 2, t 2 )=σ 2 match((t 1, T 2 ), (t 1, t 2 )) = σ 1 σ 2 F. Tiezzi (Unicam) CoSyDesign & DCC 22 / 45

Klaim semantics Klaim: Operational Semantics (3) Accessing data: ρ(l) =s match(e[[ T ]] ρ, t) =σ s :: ρ read(t )@l.p s :: ρ t s :: ρ Pσ s :: ρ t read is similar to in, buttheaccessedtupleisleftinthetuplespace F. Tiezzi (Unicam) CoSyDesign & DCC 23 / 45

Klaim semantics Klaim: Operational Semantics (4) Spawning new processes: ρ(l) =s s :: ρ eval(q)@l.p s :: ρ s :: ρ P s :: ρ Q No interpretation of eval s argument is performed: free variables in Q will be translated according to the remote allocation environment dynamic binding discipline F. Tiezzi (Unicam) CoSyDesign & DCC 24 / 45

Dynamic Scoping Klaim semantics s 2 l s 1, l s 3 eval(out(t)@self)@l s 3 self s 3 F. Tiezzi (Unicam) CoSyDesign & DCC 25 / 45

Dynamic Scoping Klaim semantics s 2 l s 1, l s 3 eval(out(t)@self)@l s 3 self s 3 out(t)@self F. Tiezzi (Unicam) CoSyDesign & DCC 25 / 45

Dynamic Scoping Klaim semantics s 2 l s 1, l s 3 eval(out(t)@self)@l s 3 self s 3 out(t)@self t F. Tiezzi (Unicam) CoSyDesign & DCC 25 / 45

Static Scoping Klaim semantics s 2 l s 1, l s 3 out(out(t)@self)@l s 3 self s 3 F. Tiezzi (Unicam) CoSyDesign & DCC 26 / 45

Static Scoping Klaim semantics s 2 l s 1, l s 3 out(out(t)@self)@l s 3 self s 3 out(t)@s 2 F. Tiezzi (Unicam) CoSyDesign & DCC 26 / 45

Static Scoping Klaim semantics s 2 l s 1, l s 3 out(out(t)@self)@l t s 3 self s 3 out(t)@s 2 F. Tiezzi (Unicam) CoSyDesign & DCC 26 / 45

Klaim semantics Klaim: Operational Semantics (5) Creating new nodes: s :: ρ newloc(s ).P (νs )(s :: ρ P s :: ρ[s /self] ) with s codom(ρ) where the environment of the creator is used to build up the environment for the new node F. Tiezzi (Unicam) CoSyDesign & DCC 27 / 45

Klaim semantics Klaim: Operational Semantics (7) Rules summary: ρ(l) =s E[[ t ]] ρ = t s :: ρ out(t)@l.p s :: ρ s :: ρ P s :: ρ t ρ(l) =s s :: ρ eval(q)@l.p s :: ρ s :: ρ P s :: ρ Q ρ(l) =s match(e[[ T ]] ρ, t) =σ s :: ρ in(t )@l.p s :: ρ t s :: ρ Pσ s :: ρ ρ(l) =s match(e[[ T ]] ρ, t) =σ s :: ρ read(t )@l.p s :: ρ t s :: ρ Pσ s :: ρ t s :: ρ newloc(s ).P (νs )(s :: ρ P s :: ρ[s /self] ) with s codom(ρ) F. Tiezzi (Unicam) CoSyDesign & DCC 28 / 45

Klaim semantics Klaim: Operational Semantics (6) Remaining rules: N 1 N 1 N 1 N 2 N 1 N 2 N N (νs)n (νs)n N M M N N N F. Tiezzi (Unicam) CoSyDesign & DCC 29 / 45

An example Leader Election (assumptions) n participants distributed on the nodes of a network must elect a leader Each participant is univocally identified by an id The leader will be the participant with the smaller id The topology of the network is a ring: every node is directly connected to two other nodes (prev and next) n nodes with addresses s 0,...,s n 1 The allocation environment ρ i of node s i,inadditiontothestandard mapping self s i,mapsthelogicallocalitynext to s i+1 mod n At the outset, each process retrieves an id from the node rg that acts as a random generator The ids arealldifferent F. Tiezzi (Unicam) CoSyDesign & DCC 30 / 45

An example Leader Election: algorithm Once a participant has assigned an id, it spawns the mobile process checker to the next node This process travels along the ring to determine if the source node has to be the leader checker carries the id of the source node, retrieves the id of the node where it is running (stored in x) and compares the two ids If id < x, thecurrentlyhostingnodeisnottheleader: the process moves to the next node and restarts If id > x, thesourcenodeisnottheleader:theprocesscrossesthe rest of the ring to come back to the source node and insert this information in the local tuple space Otherwise, i.e. id = x, theprocessisbackonthesourcenode(thusno node with a smaller id has been found in the ring) and inserts the information that this is the leader in the local tuple space F. Tiezzi (Unicam) CoSyDesign & DCC 31 / 45

An example Leader Election: specification P in( ID,! id)@rg. out( ID, id)@self. eval(checker(id))@next. checker(myid) read( ID,! x)@self. if myid < x then eval(checker(myid))@next. else if myid > x then eval(notifier(myid))@next. else out( LEADER )@self. notifier(myid) read( ID,! x)@self. if x = myid then out( FOLLOWER )@self. else eval(notifier(myid))@next. F. Tiezzi (Unicam) CoSyDesign & DCC 32 / 45

(Mild) Extensions An example By exploiting pattern matching and parallel composition, the conditional construct can be rendered as if bcond then P else Q out( EVALUATE, bcond)@self. (in( EVALUATE, true)@self.p in( EVALUATE, false)@self.q) since only one of the two parallel processes can proceed F. Tiezzi (Unicam) CoSyDesign & DCC 33 / 45

An example Leader Election: specification s 0 :: [self s0,next s 1 ] P s 1 :: [self s1,next s 2 ] P s 2 :: [self s2,next s 0 ] P rg :: [self rg] ID, 7 ID, 4 ID, 5 F. Tiezzi (Unicam) CoSyDesign & DCC 34 / 45

The overall system s 0 next s 1 P An example rg ρ ID, 5 ID, 7 ID, 4 s 1 next s 2 s 2 next s 0 P P F. Tiezzi (Unicam) CoSyDesign & DCC 35 / 45

A computation s 0 next s 1 in( ID,!id)@rg.... An example rg ρ ID, 5 ID, 7 ID, 4 s 1 next s 2 s 2 next s 0 in( ID,!id)@rg.... in( ID,!id)@rg.... F. Tiezzi (Unicam) CoSyDesign & DCC 36 / 45

A computation s 0 next s 1 in( ID,!id)@rg.... An example rg ρ ID, 5 ID, 7 s 1 next s 2 s 2 next s 0 out( ID, 4)@self.... in( ID,!id)@rg.... F. Tiezzi (Unicam) CoSyDesign & DCC 36 / 45

A computation s 0 next s 1 in( ID,!id)@rg.... An example rg ρ ID, 5 ID, 7 s 1 next s 2 s 2 next s 0 eval(checker(4)) @next. ID, 4 in( ID,!id)@rg.... F. Tiezzi (Unicam) CoSyDesign & DCC 36 / 45

An example A computation s 0 next s 1 rg ρ ID, 7 in( ID,!id)@rg.... ID, 5 s 1 next s 2 s 2 next s 0 ID, 4 in( ID,!id)@rg.... checker(4) F. Tiezzi (Unicam) CoSyDesign & DCC 36 / 45

An example A computation s 0 next s 1 rg ρ ID, 7 in( ID,!id)@rg.... ID, 5 s 1 next s 2 s 2 next s 0 ID, 4 in( ID,!id)@rg.... checker(4) F. Tiezzi (Unicam) CoSyDesign & DCC 37 / 45

A computation s 0 next s 1 An example rg ρ in( ID,!id)@rg.... ID, 5 s 1 next s 2 s 2 next s 0 ID, 4 out( ID, 7)@self.... checker(4) F. Tiezzi (Unicam) CoSyDesign & DCC 37 / 45

A computation s 0 next s 1 An example rg ρ in( ID,!id)@rg.... ID, 5 s 1 next s 2 s 2 next s 0 ID, 4 eval(checker(7)) ID, 7 @next. checker(4) F. Tiezzi (Unicam) CoSyDesign & DCC 37 / 45

A computation s 0 next s 1 An example rg ρ in( ID,!id)@rg.... checker(7) ID, 5 s 1 next s 2 s 2 next s 0 ID, 4 ID, 7 checker(4) F. Tiezzi (Unicam) CoSyDesign & DCC 37 / 45

A computation s 0 next s 1 An example rg ρ in( ID,!id)@rg.... checker(7) ID, 5 s 1 next s 2 s 2 next s 0 ID, 4 ID, 7 checker(4) F. Tiezzi (Unicam) CoSyDesign & DCC 38 / 45

A computation s 0 next s 1 An example rg ρ out( ID, 5)@self.... checker(7) s 1 next s 2 s 2 next s 0 ID, 4 ID, 7 checker(4) F. Tiezzi (Unicam) CoSyDesign & DCC 38 / 45

A computation s 0 next s 1 An example rg ρ eval(checker(5)) @next. ID, 5 checker(7) s 1 next s 2 s 2 next s 0 ID, 4 ID, 7 checker(4) F. Tiezzi (Unicam) CoSyDesign & DCC 38 / 45

A computation s 0 next s 1 An example rg ρ ID, 5 checker(7) s 1 s 2 next s 2 next s 0 checker(5) ID, 4 ID, 7 checker(4) F. Tiezzi (Unicam) CoSyDesign & DCC 38 / 45

A computation s 0 next s 1 An example rg ρ ID, 5 checker(7) s 1 s 2 next s 2 next s 0 checker(5) ID, 4 ID, 7 checker(4) F. Tiezzi (Unicam) CoSyDesign & DCC 39 / 45

A computation s 0 next s 1 An example rg ρ ID, 5 checker(7) s 1 next s 2 s 2 next s 0 checker(5) ID, 4 ID, 7 checker(4) F. Tiezzi (Unicam) CoSyDesign & DCC 39 / 45

A computation s 0 next s 1 An example rg ρ ID, 5 checker(7) s 1 next s 2 s 2 next s 0 notifier(5) ID, 4 ID, 7 checker(4) F. Tiezzi (Unicam) CoSyDesign & DCC 39 / 45

A computation s 0 next s 1 An example rg ρ notifier(5) checker(7) ID, 5 s 1 next s 2 s 2 next s 0 ID, 4 ID, 7 checker(4) F. Tiezzi (Unicam) CoSyDesign & DCC 39 / 45

An example A computation s 0 next s 1 checker(7) FOLLOWER ID, 5 rg ρ s 1 next s 2 s 2 next s 0 ID, 4 ID, 7 checker(4) F. Tiezzi (Unicam) CoSyDesign & DCC 39 / 45

An example A computation s 0 next s 1 checker(7) FOLLOWER ID, 5 rg ρ s 1 next s 2 s 2 next s 0 ID, 4 ID, 7 checker(4) F. Tiezzi (Unicam) CoSyDesign & DCC 40 / 45

An example A computation s 0 next s 1 checker(4) checker(7) FOLLOWER ID, 5 rg ρ s 1 next s 2 s 2 next s 0 ID, 4 ID, 7 F. Tiezzi (Unicam) CoSyDesign & DCC 40 / 45

An example s 1 next s 2 s 2 next s 0 A computation s 0 next s 1 checker(7) FOLLOWER ID, 5 rg ρ checker(4) ID, 4 ID, 7 F. Tiezzi (Unicam) CoSyDesign & DCC 40 / 45

A computation s 0 next s 1 An example FOLLOWER ID, 5 rg ρ checker(7) s 1 next s 2 s 2 next s 0 LEADER ID, 4 ID, 7 F. Tiezzi (Unicam) CoSyDesign & DCC 40 / 45

A computation s 0 next s 1 An example FOLLOWER ID, 5 rg ρ checker(7) s 1 next s 2 s 2 next s 0 LEADER ID, 4 ID, 7 F. Tiezzi (Unicam) CoSyDesign & DCC 41 / 45

A computation s 0 next s 1 An example FOLLOWER ID, 5 rg ρ notifier(7) s 1 next s 2 s 2 next s 0 LEADER ID, 4 ID, 7 F. Tiezzi (Unicam) CoSyDesign & DCC 41 / 45

A computation s 0 next s 1 An example FOLLOWER ID, 5 rg ρ s 1 next s 2 s 2 next s 0 LEADER ID, 4 ID, 7 notifier(7) F. Tiezzi (Unicam) CoSyDesign & DCC 41 / 45

A computation s 0 next s 1 An example FOLLOWER ID, 5 rg ρ s 1 next s 2 s 2 next s 0 LEADER FOLLOWER ID, 4 ID, 7 F. Tiezzi (Unicam) CoSyDesign & DCC 41 / 45

A computation s 0 next s 1 An example FOLLOWER ID, 5 rg ρ s 1 next s 2 s 2 next s 0 LEADER FOLLOWER ID, 4 ID, 7 F. Tiezzi (Unicam) CoSyDesign & DCC 42 / 45

Klaim implementation Implementation X-Klaim (extended Klaim) A fully-fledged programming language including the Klaim operations and a high-level syntax: Variable declarations Assignments Conditionals, iteration,... Time-outs Klava (Klaim in Java) AJavapackageimplementing Klaim operations and concepts Communications among processes and nodes Code mobility F. Tiezzi (Unicam) CoSyDesign & DCC 43 / 45

Klaim implementation Klaim Programming Framework X-Klaim program xklaim compiler klava package Java program Java compiler Java virtual machine F. Tiezzi (Unicam) CoSyDesign & DCC 44 / 45

Klaim implementation KLAIM website: http://music.dsi.unifi.it/klaim.html F. Tiezzi (Unicam) CoSyDesign & DCC 45 / 45