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letrecfor receiving multiple values. The syntactic extension is fully compatible with the existing syntax. It is the intention that single-value bindings, i.e.
(let ((var expr)) ...), and multiple-value binding can be mixed freely and conveniently.
The most simple form of the new syntax is best explained by an example:
(define (quo-rem x y) (values (quotient x y) (remainder x y))) (define (quo x y) (let ((q r (quo-rem x y))) q))The procedure
quo-remdelivers two values to its continuation. These values are received as
let-expression of the procedure
quo. In other words, the syntax of
letis extended such that several variables can be specified---and these variables receive the values delivered by the expression
(quo-rem x y).
The syntax of
let is further extended to cases in which
a rest argument receives the list of all residual values.
Again by example,
(let (((values y1 y2 . y3+) (foo x))) body)In this example,
valuesis a syntactic keyword indicating the presence of multiple values to be received, and
y3+, resp., are variables bound to the first value, the second value, and the list of the remaining values, resp., as produced by
(foo x). The syntactic keyword
valuesallows receiving all values as in
(let (((values . xs) (foo x))) body). It also allows receiving no values at all as in
(let (((values) (for-each foo list))) body).
A common application of binding multiple values is
decomposing data structures into their components.
This mechanism is illustrated in its most primitive form as follows:
uncons (defined below)
decomposes a pair
x into its car and its cdr
and delivers them as two values to its continuation.
Then an extended
let can receive these values:
(let ((car-x cdr-x (uncons x))) (foo car-x cdr-x))Of course, for pairs this method is probably neither faster nor clearer than using the procedures
cdr. However, for data structures doing substantial work upon decomposition this is different: Extracting the element of highest priority from a priority queue, while at the same time constructing the residual queue, can both be more efficient and more convenient than doing both operations independently. In fact, the
quo-remexample illustrates this point already as both quotient and remainder are probably computed by a common exact division algorithm. (And often caching is used to avoid executing this algorithm twice as often as needed.)
As the last feature of this SRFI, a mechanism is specified
to store multiple values in heap-allocated data structures.
For this purpose,
construct a list (a vector, resp.) storing all values delivered
by evaluating their argument expression.
Note that these operations cannot be procedures.
The reason for this hesitation is that multiple values are
nearly fully integrated into Scheme---but not quite.
(Unlike for example in the languages Matlab, Octave, or
the computer algebra system Magma, in which returning
multiple values from a function is the most natural thing
in the world:
q, r := quo_rem(x, y);)
However, considerable progress has been made on this point,
and I understand this SRFI as a minor contribution
"placing the last corner stone".
But first a very brief history of multiple values in Scheme,
as far as relevant for this SRFI.
R5RS specifies the procedures
call-with-values for passing any number of values
from a producer procedure to a consumer procedure.
This is the only construct in R5RS
dealing with multiple values explicitly, and it is sufficient
to implement anything that can be implemented for multiple values.
However, as John David Stone observed in SRFI 8,
the mechanism exposes explicitly how multiple values are
passed---but that is hardly ever interesting.
call-with-values is often clumsy because
the continuations are made explicit.
SRFI 8 improves on this situation
by adding the special form
(receive <formals> <expression> <body>)
for receiving several values produced by the expression
in variables specified by
using them in the body.
The major limitation of
receive is that it can only
handle a single expression, which means programs dealing with
multiple values frequently get deeply nested.
SRFI 11 provides a more versatile construct:
<variable> by an argument list
with the syntax of
let-values binding construct makes multiple
values about as convenient as it will ever get in Scheme.
Its primary shortcoming is that
incompatible with the existing syntax of
(let-values ((v x)) ...) is
to the list of all values delivered by
x (as in SRFI 11)?
x to deliver a single value to be
v (as in
Refer to the
archive of SRFI 11 for details.
let-values suffers from "parenthesis complexity",
despite Scheme programmers are tolerant to braces.
Eli Barzilay's Swindle library (for MzScheme) on
the other hand redefines let to include multiple-values and internal
procedures: The syntactic keyword
values indicates the
presence of multiple values, while additional parentheses (with the
lambda-expression as right-hand side.
This SRFI follows Eli's approach, while keeping the syntax simple (few parentheses and concepts) and adding tools for dealing more conveniently with multiple values. The aim is convenient integration of multiple values into Scheme, at full coexistence with the existing syntax (R5RS.) This is achieved by extending the syntax in two different ways (multiple left-hand sides or a syntactic keyword) and adding operations to convert between (implicitly passed) values and (first class) data structures.
Finally, I would like to mention that Oscar Waddell et al.
describe an efficient compilation method for Scheme's
letrec (Fixing Letrec)
and propose a
letrec* binding construct
to as a basis for internal
I expect their compilation method (and
and this SRFI to be fully compatible with one another,
although I have not checked this claim by way of implementation.
<binding spec> --> (<variable> <expression>)by the three new productions
<binding spec> --> ((values <variable>*) <expression>) <binding spec> --> ((values <variable>* . <variable>) <expression>) <binding spec> --> (<variable>+ <expression>)The form
(<variable>+ <expression>)is just an abbreviation for
((values <variable>+) <expression>), and it includes the original
<binding spec>of R5RS.
The first two forms are evaluated as follows: The variables are bound and
the expression is evaluated according to the enclosing construct
However, the expression may deliver any number of values to its continuation,
which stores these values into the variables specified,
possibly allocating a rest list in case of the
. <variable> form.
The number of values delivered by the expression must match the
number of values expected by the binding specification.
Otherwise an error is raised, as
This implies in particular, that each binding of a named let involves
exactly one value, because this binding can also be an argument to a
(define (uncons pair) (values (car pair) (cdr pair))) (define (uncons-2 list) (values (car list) (cadr list) (cddr list))) (define (uncons-3 list) (values (car list) (cadr list) (caddr list) (cdddr list))) (define (uncons-4 list) (values (car list) (cadr list) (caddr list) (cadddr list) (cddddr list))) (define (uncons-cons alist) (values (caar alist) (cdar alist) (cdr alist))) (define (unlist list) (apply values list)) (define (unvector vector) (apply values (vector->list vector)))These procedures decompose the standard concrete data structures (pair, list, vector) and deliver the components as values. It is an error if the argument cannot be decomposed as expected. Note that the procedures are not necessarily implemented by the definition given above.
The preferred way of decomposing a list into the first two elements
and the rest list is
(let ((x1 x2 x3+ (uncons-2 x))) body),
and similar for three or four elements and a rest.
This is not equivalent to
(let (((values x1 x2 . x3+) (unlist x))) body)
because the latter binds
x3+ to a newly allocated
Finally, the following two macros are added to the standard macros:
(values->list <expression>) (values->vector <expression>)These operation receive all values (if any) delivered by their argument expression and return a newly allocated list (vector, resp.) of these values. Note that
values->listis not the same as
list(the procedure returning the list of its arguments).
values, or simply listing the variables if there is at least one. There are several alternatives for this design, some of which were proposed during the discussion. (Refer in particular to msg00000, msg00001, and msg00002, msg00007.) The alternatives considered include:
(let ((x1 x2 expr)) body).
values, as in
(let (((values x1 x2 . x3+) expr)) body).
dot, indicating the rest list as in
(let ((x1 x2 dot x3+ expr)) body).
...indicating the rest list as in
(let ((x1 x2 x3+ ... expr)) body).
rest, indicating the rest list as in
(let ((x1 x2 (rest x3+) expr)) body).
<formals>syntax of R5RS as in
(let (((x1 x2 . x3+) expr)) body).
<formals>but with one level of parentheses removed as in
(let ((x1 x2 . x3+ expr)) body).
(let ((! expr)) body)and
(let ((xs . expr)) body).
The requirements for the design are
compatibility with the existing
concise notation for the frequent use cases,
robustness against most common mistakes, and
full flexibility of receiving values.
For the sake of compatibility,
only modifications of
<binding spec> were
The alternative, i.e. modifying the syntax of
in other ways, was not considered.
Concerning concise notation, by far the most convenient notation
is listing the variables.
As this notation also covers the existing syntax, it was adopted
as the basis of the extension to be specified.
The listing the variables notation is limited by the fact that
the preferred marker for a rest list ("
cannot follow an opening parenthesis as in
(let ((. xs expr)) body),
nor that it can be followed by two syntactic elements as in
(let ((x1 . x2+ expr)) body).
Lifting these restrictions would require major modifications
in unrelated parts of the Scheme syntax, which is not an
Another problematic aspect of the listing the variables notation
is the case of no variables at all.
While this case is not conflicting with existing syntax,
it seriously harms syntactic robustness:
(let (((run! foo))) body) and
(let ((run! foo)) body) would both be
syntactically correct and could easily be confused with one another.
For this reason, the notation of listing the variables was
restricted to one or more variables.
This leaves the problem of extending the notation in order to cover rest arguments and the "no values"-case. This can either be done ad hoc, covering the open cases, or by adding a general notation covering all cases. In view of readability and uniformity (useful when code gets processed automatically) the latter approach was chosen. This has resulted in the design specified in this SRFI.
valuesneeded in the "zero values"-case?
(let (((values) (for-each foo (bar)))) body). An alternative is allowing
(<expression>)as a binding specification. (Refer to the discussion archive starting at msg00001.)
The syntax specified in this SRFI is designed for static
detection of the most frequent types (forgotten parentheses).
For example, writing
(let ((values) (for-each foo (bar))) body)
is not a well-formed let-expression in this SRFI.
In the alternative syntax, both
(let (((for-each foo (bar)))) body)
(let ((for-each foo (bar))) body)
are syntactically correct.
The first just executes
(for-each foo (bar)),
whereas the second binds the variables
foo to the two values delivered by
Assuming the first meaning was intended,
the error will probably manifest itself at the moment
(bar) fails to deliver exactly two values.
Unless it does, in which case the error must manifest itself much
further downstream from the fact that
foo never got called.
In order to avoid this sort of expensive typos, the syntax proposed in this SRFI is more verbose than it needs to be.
letetc. in order to include multiple values. It is also desirable to extend the syntax of
letfor simplifying the definition of local procedures. (For example, as in Swindle.) However, this SRFI does not include this feature.
The reason I have chosen not restrict this SRFI to a syntax for multiple values is simplicity.
list->values, which is more symmetric with respect to its inverse operation
This symmetry ends, however, as soon as more complicated
data structures with other operations are involved.
Then it becomes apparent that the same data structure can
support different decomposition operations:
A double-ended queue (deque) for example supports splitting off
the head and splitting of the tail; and neither of these
operations should be named
un-convention covers this in a natural way.
Please also refer to the double-ended queue (deque) example in examples.scm to see how to use decomposition procedures for dealing with data structures.
As Al Petrofsky has pointed out during the discussion
msg00018) it is not sufficient to have only
unlist as this will copy the rest list.
For this reason specialized decomposition operations
for splitting off the first 1, ..., 4 elements are
provided, and a decomposition operation expecting the
first element to be a pair itself.
These appear to be the most common cases.
letrec. The definition of the actual functionality can be found here. The implementation defines macros
srfi-let/*/recetc. in terms of
r5rs-let/*/rec. Implementors may use this to redefine (or even re-implement)
let/*/recin terms of
srfi-let/*/rec, while providing implementations of
r5rs-let/*/rec. An efficient method for the latter is given in Fixing Letrec by O. Waddell et al.
For trying out the functionality, a complete implementation under
R5RS can be found here.
r5rs-let/*/rec in terms of
This may not be the most efficient implementation, because many
Scheme systems handle
let etc. specially and do not
reduce it into
The implementation found here
uses PLT's module system for exporting
under the name of
let/*/rec, while defining
r5rs-let/*/rec as a copy of the built-in
let/*/rec. This code should be efficient.
Examples using the new functionality can be found in examples.scm.
|[R5RS]||Richard Kelsey, William Clinger, and Jonathan Rees (eds.): Revised^5 Report on the Algorithmic Language Scheme of 20 February 1998. Higher-Order and Symbolic Computation, Vol. 11, No. 1, September 1998. http://schemers.org/Documents/Standards/R5RS/.|
|[SRFI 8]||John David Stone: |
|[SRFI 11]||Lars T. Hansen: Syntax for receiving multiple values. http://srfi.schemers.org/srfi-11/|
|[Swindle]||Eli Barzilay: Swindle, documentation for "base.ss" (Swindle Version 20040908.) http://www.cs.cornell.edu/eli/Swindle/base-doc.html#let|
|[Fix]||O. Waddell, D. Sarkar, R. K. Dybvig: Fixing Letrec: A Faithful Yet Efficient Implementation of Scheme's Recursive Binding Construct. To appear, 2005. http://www.cs.indiana.edu/~dyb/pubs/fixing-letrec.pdf|
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