© P. H. Welch 1 Occam 2 the Rest Chapter 10
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© P. H. Welch 1
Occam 2the Rest
Chapter 10
© P. H. Welch 2
{{{ occam 2 (the rest!)
… ANSI/IEEE 754 floating-point… abbreviations… retyping… VAL OF expressions… functions… CASE process… full protocols
}}}
© P. H. Welch 3
Rigorous expression in Z
Rigorous expression in occam
“mid-level” occamS/W forT414
“low-level” occam
-code & VLSI forthe T800 FP processor
H/W forT800
ANSI/IEEE 754-1985standard for
floating-point arithmetic
© P. H. Welch 4
The TDS provides a complete set of standard library functions for
SIN, COS, EXP, ...
Accuracies of these routines in the least significant bit are provided for relevant ranges of input values.
(The T800 supports SQRT with hardware.)
(See any INMOS sales literature for T800 floating-point speeds.)
© P. H. Welch 5
Abbreviations
• Generalisation of parameters
• VAL and reference abbreviations
[8][8][10]BYTE mesh:[8][10]BYTE mid.plane IS mesh[5]:
[10]BYTE edge IS mid.plane[i]:
VAL [10]BYTE old.edge IS mid.plane[i-1]:
• Enhances semantic clarity• Code optimisations• Enables anti-aliasing laws
occam is secure – unlikeC, Pascal, F77, Ada, ...
© P. H. Welch 6
• Any changeable object has only one name available at any time<type> <id> IS <old.id>:
• <old.id> is not allowed in
• Any variable used within <old.id> cannot be altered in
Anti-Aliasing Rules
© P. H. Welch 7
Anti-Aliasing Rules
• VAL <type> <id> IS <expression>:
• <id> is a constant in
• Any variable in <expression> cannot be altered in
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PROC fred (VAL INT n, BOOL ok, CHAN OF BYTE in, out)PROC fred (VAL INT n, BOOL ok, CHAN OF BYTE in, out) ......::
SEQ ... ... fred ((2 * i) + 42, flag[i], c[i], c[i + 1])fred ((2 * i) + 42, flag[i], c[i], c[i + 1]) ... ... ...
body of fred
Parameter Passing
Anti-Aliasing enforced
invocation of fred
© P. H. Welch 9
Parameter Passing
Formally, a process instance (invocation or procedure call) is defined by an “in-lining” transformation using abbreviations:
SEQ ... ... VAL INT n IS (2 * i) + 42: BOOL ok IS flag[i]: CHAN OF BYTE in IS c[i]: CHAN OF BYTE out IS c[i + 1]: ...... ... ... ...
body of fred
Anti-Aliasing enforced
invocation of fred
© P. H. Welch 10
Anti-Aliasing Rules
• One object has only one name available at any time.
• Aliasing accidents are a common source of bugs in all other languages.
• Aliasing rules permit large VAL parameters to be passed by an address, giving both efficiency and security.
• Aliasing rules permit “reference” parameters to be passed by “address”, “copy-in/copy-out” or even “macro-substitution”. Compiler chooses most efficient without violating security.
© P. H. Welch 11
Retypings
• Similar to abbreviations.
• VAL and reference retypes:<type> <id> RETYPES <old.id>:VAL <type> <id> RETYPES <exp>:
• The types on each side of the RETYPES are different but must have the same number of bits in their representations.
• Same anti-aliasing rules as for abbreviations.
© P. H. Welch 12
a, b, c := x, y+1, z-2a, b, c := x, y+1, z-2a, b, c := x, y+1, z-2a, b, c := x, y+1, z-2
INT a.temp, b.temp, c.temp:INT a.temp, b.temp, c.temp:
SEQSEQ
PARPAR
a.temp := xa.temp := x
b.temp := y+1b.temp := y+1
c.temp := z-2c.temp := z-2
PARPAR
a := a.tempa := a.temp
b := b.tempb := b.temp
c := c.tempc := c.temp
INT a.temp, b.temp, c.temp:INT a.temp, b.temp, c.temp:
SEQSEQ
PARPAR
a.temp := xa.temp := x
b.temp := y+1b.temp := y+1
c.temp := z-2c.temp := z-2
PARPAR
a := a.tempa := a.temp
b := b.tempb := b.temp
c := c.tempc := c.temp
Parallel AssignmentParallel Assignment
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p, q := q, pp, q := q, p -- swap variables-- swap variables
• The above we can do!The above we can do!
• The below we cannot do:The below we cannot do:
i, A[i] := 4, 8i, A[i] := 4, 8 -- illegal-- illegal
• since it involves since it involves assigningassigning to to ii and and usingusing it in parallel. The it in parallel. The compiler will trap this.compiler will trap this.
• This is a This is a safesafe parallel assignment parallel assignment process. process.
Parallel AssignmentParallel Assignment
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<local declarations>
<list of expressions>
((
VALOFVALOF
RESULTRESULT))
<process>
VALOF ExpressionsVALOF Expressions
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[1000]INT x:[1000]INT x:INT total:INT total:......total := total +total := total + ((INT n:INT n: VALOFVALOF SEQSEQ n := 0n := 0 SEQ i = 0 FOR SIZE xSEQ i = 0 FOR SIZE x n := n + x[i]n := n + x[i] RESULTRESULT nn ))
VALOF ExpressionsVALOF Expressions
© P. H. Welch 16
a, b, c, := (INT x, y, z: VALOF <compute x, y, z>
RESULT x, y, z )
VALOF ExpressionsVALOF Expressions
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The The <params><params> may only be may only be VALVAL data types (no data types (no reference reference datadata or or channels).channels).
<type.list><type.list> FUNCTIONFUNCTION <id><id> ( (<params><params>))
<local declarations><local declarations>
VALOFVALOF
<process><process>
RESULTRESULT <list of expressions><list of expressions>
::
Functions are deterministic and side-effect free (i.e. theFunctions are deterministic and side-effect free (i.e. the <process><process> does not assign to global variables, input or does not assign to global variables, input or output on global channels, and has no internal output on global channels, and has no internal PARPAR or or ALTALT.).)
FunctionsFunctions
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<type.list><type.list> FUNCTIONFUNCTION <id><id> ( (<params><params>) ) IS IS
<list of expressions><list of expressions> : :
BOOLBOOL FUNCTIONFUNCTION capital ( capital (VAL BYTE chVAL BYTE ch) ) ISIS
(‘A’ <= ch) AND (ch <= ‘Z’):(‘A’ <= ch) AND (ch <= ‘Z’):
for example for example ……
Functions (short)Functions (short)
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ELSEELSE
CASE chCASE ch
''aa'', , ''ee'', , ''ii'', , ''oo'', , ''uu‘‘
''AA'', , ''EE'', , ''II'', , ''OO'', , ''UU''
''00'', , ''11'', , ''22'', , ''33'', , ''44''
''??'', , ''!!'', , ''hh'', , ''HH'', , ''****''
any process ...any process ...
optionaloptional
CASE ProcessCASE Process
© P. H. Welch 20
PROTOCOLPROTOCOL BLUE.INTBLUE.INT ISIS INT: INT:
PROTOCOLPROTOCOL STRINGSTRING ISIS INT::[]BYTE: INT::[]BYTE:
PROTOCOLPROTOCOL PACKETPACKET ISIS INT::[]REAL32: INT::[]REAL32:
PROTOCOLPROTOCOL MESSAGEMESSAGE ISIS STRINGSTRING; ; PACKETPACKET::
PROTOCOLPROTOCOL ALTERNATIVESALTERNATIVES CASECASE dogdog; INT; INT catcat; ; STRINGSTRING pigpig; ; PACKETPACKET canarycanary; ; MESSAGEMESSAGE poisonpoison::
renamingrenaming
counted arraycounted array
sequentialsequential
variantvariant
Channel PROTOCOLsChannel PROTOCOLs
© P. H. Welch 21
The previous slide uses some license. Classical occam does not allow user-defined protocols to be components of user-defined protocols. Everything must be expanded down to primitive types . We have to write:
PROTOCOLPROTOCOL MESSAGEMESSAGE ISIS INT::[]BYTE; INT::[]BYTE; -- STRING-- STRING INT::[]REAL32: INT::[]REAL32: -- PACKET-- PACKET
PROTOCOLPROTOCOL ALTERNATIVESALTERNATIVES CASECASE dogdog; INT; INT catcat; INT::[]BYTE ; INT::[]BYTE -- STRING-- STRING pigpig; INT::[]REAL32 ; INT::[]REAL32 -- PACKET-- PACKET canarycanary;; INT::[]BYTE; INT::[]BYTE; -- MESSAGE-- MESSAGE INT::[]REAL32INT::[]REAL32 poisonpoison::
Not needed Not needed in modern in modern occamoccam
© P. H. Welch 22
c QP
CHAN OF ALTERNATIVES ALTERNATIVES c:PARPAR P (P (c)) Q (Q (c))
Channel PROTOCOLsChannel PROTOCOLs
© P. H. Welch 23
PROC P (CHAN OF ALTERNATIVES out)PROC P (CHAN OF ALTERNATIVES out)
::
outP
VAL []BYTE s IS "sat on the mat":VAL []BYTE s IS "sat on the mat": VAL []REAL32 t IS [1.0, -0.4, 8.8, 9.0, 4.4, 10.2]:VAL []REAL32 t IS [1.0, -0.4, 8.8, 9.0, 4.4, 10.2]: [256]BYTE a:[256]BYTE a: [1000]REAL32 b:[1000]REAL32 b: SEQSEQ ... set up a and b... set up a and b out ! dog; 42out ! dog; 42 out ! cat; (SIZE s)::sout ! cat; (SIZE s)::s out ! pig; (SIZE t)::tout ! pig; (SIZE t)::t out ! canary; (SIZE a)::a;out ! canary; (SIZE a)::a; (SIZE b)::b(SIZE b)::b ... more stuff... more stuff out ! poisonout ! poison
Channel PROTOCOLsChannel PROTOCOLs
© P. H. Welch 24
PROC Q (CHAN OF ALTERNATIVES in)PROC Q (CHAN OF ALTERNATIVES in)
::
inQ
[256]BYTE s:[256]BYTE s: [1024]REAL32 x:[1024]REAL32 x: INT state:INT state: BOOL ok:BOOL ok:
SEQSEQ ok := TRUEok := TRUE WHILE okWHILE ok ... process input alternatives from in... process input alternatives from in
Channel PROTOCOLsChannel PROTOCOLs
© P. H. Welch 25
inQ
in ? CASEin ? CASE dog; statedog; state ... deal with this variant... deal with this variant INT size:INT size: cat; size::scat; size::s ... deal with this variant... deal with this variant INT size:INT size: pig; size::xpig; size::x ... deal with this variant... deal with this variant INT size.s, size.x:INT size.s, size.x: canary; size.s::s; size.x::xcanary; size.s::s; size.x::x ... deal with this variant... deal with this variant poisonpoison ok := FALSEok := FALSE
SEQSEQ ok := TRUEok := TRUE WHILE okWHILE ok
Channel PROTOCOLsChannel PROTOCOLs
[256]BYTE s:[256]BYTE s:[1024]REAL32 x:[1024]REAL32 x:INT state:INT state:BOOL ok:BOOL ok:
© P. H. Welch 26
PROC fair.plex([]CHAN OF INT in, CHAN OF CHAN.INT out)PROC fair.plex([]CHAN OF INT in, CHAN OF CHAN.INT out) VAL INT n IS SIZE in:VAL INT n IS SIZE in: INT favourite:INT favourite: SEQSEQ favourite := 0favourite := 0 WHILE TRUEWHILE TRUE PRI ALT i = favourite FOR nPRI ALT i = favourite FOR n VAL INT i.mod.n IS i\n:VAL INT i.mod.n IS i\n: INT x:INT x: in[i.mod.n] ? xin[i.mod.n] ? x SEQSEQ out ! i.mod.n; xout ! i.mod.n; x favourite := (i.mod.n+1)favourite := (i.mod.n+1): :
cf.plex
fair.plex(n)
.
.
.
in[]
outn fair.plex
(n)...
in[]
out
© P. H. Welch 27
Impact on Software Cycle???
RequirementSpecification
StructuralSoftwareDesign
DetailedSoftwareDesign
Code &Unit Test
SoftwareIntegration
SystemIntegration
awareness of new potential
JSD/Yourdon/Mascot/OOD(“real-world” parallelism)
Big! simpler?
Big! load balance?
Big! new problems?
Big! testing?? deadlock??
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We do NOT have to re-invent everything to take advantage of parallelism.
Traditional software engineering:
rich set of principles that are relevant to the
“real world” and are, therefore, sympathetic
to parallelism.
© P. H. Welch 29
• Need a method which allows us to capture the natural parallelism of the problem:
OODJSDMASCOTde MarcoYOURDONPROGRAPH
• Need graphical tools (pencil & paper, automated) to describe, understand, and communicate the system.
Structural Software Design
occam 2
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Advice:
Find graphics tools that are not specificallytied to a particular methodology.
Warning:
While pictures are a very powerful tool forconveying ideas, they may confine our ideas towhat can easily be drawn. (Remember flow diagrams and their influence on sequentiallogic.)
© P. H. Welch 31
We (may) need to develop more algebraic notations
that give us greater freedom of expression
(cf. WHILE - loops, recursion, ...)
Occam gives us a notation for static hierarchic
data-flow diagrams, plus object interfaces & channel
structures.
So does Ada – although more awkwardly.
Neither does the compete job.
© P. H. Welch 32
Detailed Software Design
• The occam expression is directly distributable and executable (fast!).
• The Ada expression is directly executable (slow!).
• Break into separate programs (for distribution) [Ada only!]
• Remove parallelism (for single processor execution) [Ada only!]
“prototype”
“program inversion”
© P. H. Welch 33
Reusable Software?
• industry thrives;• physically discrete with precisely defined
interfaces (pins);• well-defined protocols for using these interfaces;• are reusable;• are reused.
Hardware components:
© P. H. Welch 34
• industry practically non-existent;
• no automatic constraints on interfaces & protocols – anything is possible,
Software components:
Physically Distributed Software components:
• same constraints as for hardware components;
• precise interfaces;
• clear protocols;
• reusable.
© P. H. Welch 35
All software components
• are (models of) “real-world” objects;
• should have the same constraints as hardware;
• precise interfaces;
• clear protocols;
• should be reusable;
• are hard to express with traditional programming languages (e.g., Pascal, FORTRAN-77, ...);
• are distributable.
© P. H. Welch 36
The capabilities of a component may be enhanced by reusing the component (thereby inheriting its capabilities) in conjunction with another component to provide extra control over its use.
© P. H. Welch 37
open-db
ins ansreq
© P. H. Welch 38
open-db
ins ansreq
user-mgr
ins s.req s.ans add del
secure-db
© P. H. Welch 39
.
.
.
For "many 1" communication, pick up appropriate multiplexer component:
The "fairness" of the multiplexing is user definable.
© P. H. Welch 40
Systems Programming:-• Compilers• Support Environments• Networks e.g., OSI "layers"• Databases
Real-Time:-• Image Processing• Signal Processing• Control Systems (e.g., "fly-by-light")• AI
Numerical methods:-• Simultaneous Equations• Eigenvalues• (Large) System Modeling (e.g., weather, galactic collisions...)
© P. H. Welch 41
Customized Logic (in silicon):-• Specification• Design• Simulation• Test
Formal Methods:-• Algebraic semantics• Process proving• Process transformations
© P. H. Welch 42
CSP Discipline
• Hardware model of components is followed:
• Simple interfaces (pins, wires, channels, ports);
• Well-defined protocols;
• Component semantics determined solely by its effect on its environment through its interfacing channels ("rendezvous").
© P. H. Welch 43
CSP Discipline
• Uniform method for the description of system components;– in isolation (for presentation by the component
supplier);– within an integrated network (for the system
builder).
• Components can be specified, used, physically distributed, and reasoned about at all levels.
© P. H. Welch 44
Some Features of Occam
• SMALL language
• Oriented parallel processes
• Synchronized, unbuffered point-to-point message passing– NO shared variables– NO shared channels
• Fixed resource allocation– NO garbage collection
© P. H. Welch 45
• Transputer links implement occam channels;• Transputers do not share memory with other
Transputers;• No bus contention problems arise with large
Transputer networks;• Accessible processing power is directly proportional
to the number of processors (with no top limit!);• To access the power requires (highly) parallel
algorithms;• We need occam!
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