Dynamically creating objects and
sequencing operations
Cliff Jones
University of Newcastle
2005-06-06
WG2.3 Niagara 2005-06-06
1
On the expectation of a WG2.3 topic
• in the tradition of 2.3, this is something I’m
trying to sort out for myself
• but …
•  apparently it is now expected to work up
from the (legacy) code 
WG2.3 Niagara 2005-06-06
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POOL example
class stack
var …
method push(i: item) …
method pop() : item …
body
%% initialize
do %% forever
if … then answer(push)
else answer(pop, push)
fi
od
WG2.3 Niagara 2005-06-06
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OO-like structuring in specifications
• I’d like to look at two issues
– how to sequence “operations”
– how to “create objects”
• first some background
WG2.3 Niagara 2005-06-06
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A dichotomy
• state based specification techniques
– VDM, Z, B, agent-B
– good for big systems; understand from data
• one can “see” (or design) a system from Σ
• process algebras
– CSP, CCS, -calculus
– states as process indices (but another notion below)
– good for intricate sequencing (e.g. deadlocks)
WG2.3 Niagara 2005-06-06
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My interest:
(specification and) development
• can be done in, say, CSP
– CCS etc goes more for bi-simulation
• but it has always felt more natural to
–
–
–
–
get an abstract state-based spec
reify data
decompose operations
and next: “splitting atoms”
• cf. CBJ’s Prato talk
WG2.3 Niagara 2005-06-06
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Modularising state based specs
• VDM
–
–
–
–
initially none
“operation quotation”
VVSL (as in CDIS)
VDM++ (as in VDM ToolSet)
• Z
– everything is a schema
– no pre-conditions!
• B
– machines/operations
WG2.3 Niagara 2005-06-06
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Sequencing operations
• VDM
– all, always available
– pre-conditions are to be respected
• one proves this!
– but there is a procedural language as well!
• B
– originally “operations” (pre P then S end)
• “action systems”/ Event-B
– “when conditions” define firing
WG2.3 Niagara 2005-06-06
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OO is a GoodThing (in design)
• sometimes as essence of system
– come back to how modelled?
• sometimes as an implementation idea
– CBJ used several times as “reification”
• modularisation (better than many specification languages)
• control of interference
– local instance variables
– unique references create “islands” of computation
– shared references when interference necessary
• option to control sequencing
WG2.3 Niagara 2005-06-06
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Look at combining processes/states
• done in Ada
– by Abrial!!
• POOL
• 
– dropped (after MIW’s observation)
WG2.3 Niagara 2005-06-06
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So, two ways of sequencing
• process descriptions
– in the style of POOL
• guards
– “when” in Event-B
– possible to “hack” at this level – abstract PC
• I’d like to view them as refinements
– in either direction
– would combinations be useful?
• … but I want to achieve even more …
WG2.3 Niagara 2005-06-06
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obl
• language itself
– typed references
– recognise “unique” references
– no inheritance (yet)
• see as design notation (cf. VDM sequential)
– use with implemented OOLs (e.g. Eiffel)
• semantics (as basis of “meta” proofs)
• SOS
• map to -calculus
WG2.3 Niagara 2005-06-06
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obl
Sort class
vars v: nat  nil; l: unique ref(Sort)  nil
insert(x: nat) method
return;
if is-nil(v) then (v  x; l  new Sort)
elif v  x then l.insert(x)
else (l.insert(v); v  x)
fi
test(x: nat) method: Bool
if is-nil(l)  x  v then return false
elif x = v then return true
else delegate l.test(x)
fi
.
.
.
end Sort
WG2.3 Niagara 2005-06-06
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Mapping (i)
[[Q]] = !IQ
IQ = qu.BQ
thus
[[new Q]] = q(u). …
WG2.3 Niagara 2005-06-06
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Mapping (ii)
IQ =
\New{\widetilde{s}\widetilde{a}}
(v\sb{nil} | l\sb{nil} |
\outp{q}{u}. B\sb{Q})
WG2.3 Niagara 2005-06-06
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We have
• a nice mapping  to -calculus
• new C maps to a reference to replication
– strictly, a communication with a name inside a
replicator which cause a new instance to exist
• we can therefore have dynamic creation of
objects/machines/…
WG2.3 Niagara 2005-06-06
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Contrast …
• Michael Butler’s paper
– tokens  Cust  {0..sx} in the “specification”
– a strange (twin) SOS
• cbj’s SOS of COOL
– map Oid to ObjInfo
• is a semantic object
• the SOS rules create this mapping
• so my semantics of POOL
– would look rather different from Michael’s
– might have a “program counter” into process
expression!!
WG2.3 Niagara 2005-06-06
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Technical issue(s)
• failure(s)
– in two senses
• internal choice (vs. external)
– divergence(s)
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Implementation questions
• CSP handshake is non-trivial
• Event-B’s “when” clause looks less
efficient than CARH’s “monitors”
– assuming …
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So, sequencing operations
VDM + OO + -calculus
(held together by reification)
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