Chapter 5: Join Calculus

1
Chapter 5 Join Calculus

• Programming Distributed Computing Systems A
  Foundational Approach
• Carlos Varela
• Rensselaer Polytechnic Institute

2
Reflexive CHAMandJoin Calculus

• Attempt to overcome distribution issues in
  p-calculus, yet keeping formal investigation
  results.
• Bridge gap between theory and practice, and form
  the basics for a programming language.
• Imposes locality and adds reflexion to generic
  CHAM of Boudol and Berry.
• Combines restriction, reception, and replication
  (of p-calculus) into a single (joint) receptor
  definition.

3
Reflexive Chemical Abstract Machine

• xltygt atom
• M M molecule
• e.g.
• readyltlasergt
• readyltlasergt joblt1gt
• D or J P reaction
• e.g.
• readyltprintergt jobltfilegt printerltfilegt

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Printer Example

• 0 readyltlasergt, joblt1gt, joblt2gt
• 0 readyltlasergt joblt1gt , joblt2gt
• Let D readyltprintergt jobltfilegt
  printerltfilegt
• D readyltlasergt joblt1gt, joblt2gt
• D laserlt1gt, joblt2gt

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Reflection

• def D in P molecule
• 0 def D in readyltlasergt joblt1gt joblt2gt
• D readyltlasergt joblt1gt joblt2gt

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Names, Processes, Definitions

def

• P xltvgt asynchronous polyadic message
• def D in P definition of new names
• P P parallel composition
• J xltvgt join patterns
• J J
• D J P matching join
• D D patterns to processes

def
def
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Variable Types

• Received variables (join patterns)
• rv(xltvgt) u in v
• rv(J J) rv(J) U rv(J)
• Defined variables (join patterns and definitions)
• dv(xltvgt) x
• dv(J J) dv(J) U dv(J)
• dv(J P) dv(J)
• dv(D D) dv(D) U dv(D)

def
def

def
def
def
def
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Free Variables

• (processes and definitions)
• fv(J P) dv(J) U (fv(P) rv(J))
• fv(D D) fv(D) U fv(D)
• fv(xltvgt) x U u in v
• fv(def D in P) (fv(P) U fv(D)) dv(D)
• fv(P P) fv(P) U fv(P)

def
def


def
def
def
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Operational SemanticsStructural Equivalence

• (str-join) P Q P,Q (
  heating, cooling)
• (str-and) D E D,E
• (str-def) def D in P D P
• (red) J P J J P P
• sdv instantiates port variable dv(D) to fresh
  names.
• srv substitutes transmitted names for distinct
  received variables rv(J).

sdv
sdv
srv
srv
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Examples

• def xltugt yltugt in P
• messages on local name x in P are forwarded to
  the outside as messages on y.
• def yltugt xltugt in def xltugt yltugt in P
• messages on local name x are forwarded in two
  steps on the external name x (internal x needs
  renaming).
• def x1ltugt x2ltvgt xltu,vgt in P
• performs multiplexing of messages on x whose
  parts are supplied on x1 and x2.

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Examples (continued)

• def xltvgt yltkgt kltvgt in P
• models p-calculus-like channels, as values are
  sent on x and requests for values are sent on y.
• def sltgt P sltgt Q in sltgt
• express internal non-determinism P Q
• def onceltgt yltvgt xltvgt in ylt1gt ylt2gt ylt3gt
  onceltgt
• uses the message on once as a lock for
  non-determinism xlt1gt xlt2gt xlt3gt

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Recursion Example

• def loopltgt P loopltgt in loopltgt
• replicates the process P (!P), starting a new
  copy each time the definition is used.

13
Reference Cell

• def mkcellltv0, k0gt
  in P
• P def cltg,sgt sltw1,kgt in mkcell ltw0, cgt

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Mutual Exclusion

• def sltgt P sltgt Q sltgt in sltgt
  (semaphore)
• def
  in sltgt
• (guarantees mutual exclusion)

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Dining Philosophers

• def
  in P
• P ? (phillti, ci, c(i1)mod ngt chopstickltcigt)

0 i lt n