Kahn Networks at the Dawn of Functional Programming

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Kahn Networks at the Dawn of Functional
Programming

• David MacQueen
• University of Chicago

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Kahn Networks
The Semantics of a Simple Language for Parallel
Programming
IFIP 1974
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At work in Versailles
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Example A Process
Process f(integer in U,V integer out U)
Begin integer I logical B B true
Repeat Begin I if B then
wait(U) else wait(V) print(I)
send I on W B B
End End
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A Program
Begin Integer channel X, Y, Z, T1, T2
Process f(integer in U,V integer out U)
Begin ... End Process g(integer in U integer
out V,W) Begin ... End Process h(integer
in U integer out V integer INIT) Begin ...
End f(Y,Z,X) par g(X,T1,T2) par h(T1,Y,0) par
h(T2,Z,1) End
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The Network
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Background, Sources

• Parallel programming for OS
• Balzers ISPL, Brinch Hansen, Lauer, OS 360 (not
  yet Unix!)
• Scott Domains, denotational semantics
• Proof techniques for recursive programs
• Scott, deBakker, Manna, Vuillemin, Milner, ...

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Semantics
Represent channel histories as streams Represent
processes as stream functions Streams (over data
D) D?, the CPO of finite and infinite
sequences under prefix ordering Primitive stream
operations A(ppend) F(irst) R(est)
cons () hd tl
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Processes as Functions
f(U,V) hd(U) hd(V) f(tl(U),tl(V)) g1(U)
hd(U) g1(tl(tl(U))) g2(U) hd(tl(U))
g2(tl(tl(U))) h(U,x) x U
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Network as Recursive Eqns
X f(Y,Z) Y h(T1,0) Z h(T2,1) T1 g1(X) T2
g2(X)
X f(h(g1(X),0), h(g2(X),1))
X 0 1 f(g1(X),g2(X))
X 0 1 X
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Network semantics
channels gt streams processes gt
continuous functions on streams networks gt
systems of recursive stream equations network
behavior gt least fixed point of network
equations
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Lazy Functional Programming!
Although IFIP74 says little about scheduling or
evaluation strategy, the fixed point semantics
with reified streams implies lazy
evaluation. The functional form of network
programs may well be the first pure, lazy
functional language.
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Observations on IFIP74

• Semantics and proof as major desiderata in design
• Advantages of a pure model we see the essential
  merit as the eradication of the notion of state
  of a complex system.
• Language is deterministic. Adding nondeterminism
  through a select primitive is suggested but not
  developed.

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Implementation and Experimentation
Coroutines and Networks of Parallel
Processes Kahn and MacQueen IFIP 77
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POP-2 Implementation

• Early 1976, I investigate coroutines in POP-2
  using state-saving, a rudimentary control
  operator related to first-class continuations
  (later this is superseded by real coroutines,
  called processes.)
• Gilles and I discuss using this to implement his
  stream processing language, and I do so.
• result is a version of the imperative process
  language embedded in POP-2 and using POP-2 syntax.

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Explorations

• Sieve of Eratosthenes
• Hamming problem
• Power series
• Sorting algorithms
• Infinite precision real numbers
• Discrete Fourier transform

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Language evolution
Language evolves toward the functional form.
start doco OUTPUTF(20,X) where channels X,Y,Z
are QCONS(1,MERGE(TIMES(2,X),Y)),
QCONS(3,MERGE(TIMES(3,Y),Z)),
QCONS(5,TIMES(5,Z)) closeco
let rec X 1MERGE(TIMES(2,X),Y) and Y
3MERGE(TIMES(3,Y),Z) and Z 5TIMES(5,Z)
in X
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IFIP 77 Connections
Conway coroutines, 1963 Milner processes, 1973
(virtual streams) Landin functional streams 1965
(virtual streams) McIlroy coroutines, sieve
example, 1968 POP-2 generator functions and
dynamic lists, 1968 McIlroy Unix pipe,
1970 Lucid, Ashcroft Wadge, July 1975 (Arc et
Senans) Concrete Domains Kahn Plotkin 1975
... Lazy evaluation in LISP, Henderson Morris,
Jan 1976 Lazy evaluation in LISP, Friedman
Wise, July 1976
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Impact and Influence

• Many variations have been studied
• Languages and language features have been
  inspired (e.g. reactive languages)
• Hundreds of citations in literature
• Streams have become a standard tool
• Commonplace in lazy functional programming and
  strict as well

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