"unspecified" and SET!

[Dorai Sitaram <titan!dorai@rice.edu>]

The recent discussion of "unspecified" values reveals that Scheme is
not as syntactically uniform as it is claimed to be. Some Scheme
syntactic forms return meaningful values, others don't: the former are
"expressions" and the latter "commands". "Commands" are usually used
to represent side-effects, e.g., assignment in the form of set!.  In
an expression-oriented language, a "command" is awkwardly "expressed"
by an expression returning an arbitrary "unspecified" value.

Perhaps, SET! is not the ideal side-effecting construct for an
expression-oriented language. Felleisen and Friedman [1] propose a
side-effecting construct called a SIGMA-capability. This looks just
like a LAMBDA-expression, but whereas LAMBDA introduces new bound
variables, SIGMA modifies the binding of existing lexical variables.
In other words, on applying a SIGMA-capability to arguments, the
variables corresponding to the SIGMA-parameters are side-effected.

Problems about "unspecified" return values disappear. The application
of a SIGMA-capability side-effects the SIGMA-parameters and returns
the result of evaluating the SIGMA-body (the parallel being the
application of a LAMBDA-expression). In addition, SIGMA gives a very
natural method for parallel assignment, since the arguments to a
SIGMA-capability are all evaluated before the application performs the
side-effects.

We can retrieve the old SET! from SIGMA as follows:
	(set! x a) == ((sigma (x) <what-now>) a)
where <what-now> is the "unspecified" value of your choice. Thus,
there is no dependence on a system-chosen unspecified value.

Even better, we need not fall back on a command with its necessarily
arbitrary choice of unspecified return value. We can define a
_generalized_ SET! in terms of SIGMA that is more along the lines of
LET in terms of LAMBDA:
	(set! ([x a] ...) e ...) == ((sigma (x ...) e ...) a ...)

The upshot of all this is that while we have side-effects, we still
have a syntactically uniform language.

--dorai

[1] Felleisen & Friedman, A calculus for assigments ..., POPL 1987,
314 - 325.

ps: In terms of SET!, SIGMA's effect is as follows:
	(sigma (x ...) e ...) == (lambda (x^ ...) (set! x x^) ... e ...)
where x^ ... are new variables, used only to show what's going on. A
native implementation of SIGMA is simply got by mimicking LAMBDA,
except for the following: where LAMBDA has extend-environment, SIGMA
has update-environment.
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