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␈↓ ↓H␈↓␈↓βS␈↓∧ Artificial Intelligence Laboratory, STANFORD UNIVERSITY, Stanford, California 94305

␈↓ ↓H␈↓∧Telephone 415 497-4430␈↓ 
≤May 28, 1977 




␈↓ ↓H␈↓Dr. Patrick Hayes
␈↓ ↓H␈↓Department of Computer Science
␈↓ ↓H␈↓University of Essex
␈↓ ↓H␈↓P.O. Box 23
␈↓ ↓H␈↓Wivenhoe Park
␈↓ ↓H␈↓Colchester
␈↓ ↓H␈↓England CO4 3SQ

␈↓ ↓H␈↓Dear Pat:

␈↓ ↓H␈↓        Enclosed␈α
are␈α
≡ve␈α
papers,␈α
none␈α
of␈α
which␈α∞is␈α
what␈α
your␈α
sources␈α
rumor,␈α
but␈α
I␈α
would␈α∞be␈α
glad
␈↓ ↓H␈↓about␈α∞your␈α∂comments␈α∞on␈α∂them.␈α∞ I␈α∞have␈α∂just␈α∞read␈α∂Kowalski's␈α∞paper,␈α∞which␈α∂he␈α∞recently␈α∂sent␈α∞me,
␈↓ ↓H␈↓about␈α
predicate␈α
calculus␈α
as␈α∞a␈α
programming␈α
language.␈α
 Clearly␈α
it␈α∞can␈α
be␈α
used␈α
as␈α∞a␈α
programming
␈↓ ↓H␈↓language,␈α∞but␈α∞I␈α∞am␈α∞not␈α∞convinced␈α∞that␈α∂it␈α∞is␈α∞an␈α∞especially␈α∞useful␈α∞programming␈α∞language.␈α∂ I␈α∞also
␈↓ ↓H␈↓don't␈α
understand␈α
the␈α
relations␈α
between␈α
Kowalski's␈α
formalism␈α
and␈α
the␈α
one␈α
described␈α
in␈α
my␈α
␈↓↓First
␈↓ ↓H␈↓↓Order␈α
Representations␈α
of␈α
Recursive␈α
Programs␈↓.␈α∞ I␈α
must␈α
explicitly␈α
include␈α
an␈α
unde≡ned␈α∞element␈α
in
␈↓ ↓H␈↓the␈αdomain,␈αand␈αhe␈αdoesn't.␈α On␈αthe␈αother␈αhand,␈αI␈αcan␈αprove␈αthings␈αabout␈αpartial␈αfunctions␈αwith
␈↓ ↓H␈↓the␈α∪aid␈α∪of␈α∪my␈α∪schema.␈α∪ Nevertheless,␈α∪the␈α∪must␈α∪be␈α∪some␈α∪kind␈α∪of␈α∪translation.␈α∪ Besides␈α∪these
␈↓ ↓H␈↓formalisms,␈α
we␈αalso␈α
need␈α
one␈αin␈α
which␈αprograms␈α
are␈α
objects,␈αand␈α
I␈αhave␈α
some␈α
incomplete␈αdrafts
␈↓ ↓H␈↓on this subject based on a notion of ␈↓↓extensional form␈↓.

␈↓ ↓H␈↓        These␈αdrafts␈α
may␈αbe␈α
shown␈αto␈α
whomever␈αyou␈α
like,␈αbut␈α
anyone␈αwho␈α
contemplates␈αreferring
␈↓ ↓H␈↓to␈αthem␈αin␈αprint␈α-␈αpositively␈αor␈αnegatively␈α-␈αshould␈αconsult␈αme␈α≡rst,␈αbecause␈αtheir␈αprinted␈αversions
␈↓ ↓H␈↓may be di≥erent.


␈↓ ↓H␈↓Best regards,



␈↓ ↓H␈↓John McCarthy
␈↓ ↓H␈↓Director
␈↓ ↓H␈↓Professor of Computer Science