# Issue: FUNCTION-COMPOSITION (Version 2)

• To: CL-Cleanup@SAIL.Stanford.EDU
• Subject: Issue: FUNCTION-COMPOSITION (Version 2)
• From: Kent M Pitman <KMP@STONY-BROOK.SCRC.Symbolics.COM>
• Date: Wed, 5 Oct 88 14:00 EDT

```An updated copy to reflect discussion since the first draft:
- Corrected typo in description of COMPLEMENT (notice by Fahlman).
- Rewrote the rationale to reflect the e-mail discussion.
- Added endorsements in the Discussion section.

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Issue:          FUNCTION-COMPOSITION
References:     None
Edit history:   21-Jun-88, Version 1 by Pitman
05-Oct-88, Version 2 by Pitman
Status:	        For Internal Discussion
Related-Issues: TEST-NOT-IF-NOT

Problem Description:

A number of useful functions on functions are conspicuously
absent from Common Lisp's basic set. Among them are functions
which return constant T, constant NIL, and functions which
combine functions in common, interesting ways.

Proposal (FUNCTION-COMPOSITION:NEW-FUNCTIONS):

COMPOSE &REST functions				[Function]

Returns a function whose value is the same as the composition
of the given functions. eg, (FUNCALL (COMPOSE #'F #'G #'H) A B C)
is the same as (F (G (H A B C))). Also, for example, #'CAADR may
be described as (COMPOSE #'CAR #'CAR #'CDR).

CONJOIN &REST functions				[Function]

Returns a function whose value is the same as the AND of the
given functions applied to the same arguments.

DISJOIN &REST functions				[Function]

Returns a function whose value is the same as the OR of the
given functions applied to the same arguments.

COMPLEMENT function					[Function]

Returns a function whose value is the same as the NOT of the
given function applied to the same arguments.

ALWAYS value						[Function]

Returns a function whose value is always VALUE.

Examples:

(MAPCAR #'(LAMBDA (X) (DECLARE (IGNORE X)) T) '(3 A 4.3))
==
(MAPCAR (ALWAYS T) '(3 A 4.3))
=> (T T T)

(MAPCAR #'(LAMBDA (X) (AND (NUMBERP X) (ZEROP X))) '(3 A 0.0))
==
(MAPCAR (CONJOIN #'NUMBERP #'ZEROP) '(3 A 0.0))
=> (NIL NIL T)

(FIND-IF #'(LAMBDA (X) (AND (INTEGERP X) (SYMBOLP X))) '(3.0 A 4))
==
(FIND-IF (DISJOIN #'INTEGERP #'SYMBOLP) '(3.0 A 4))
=> A

(FUNCALL #'(LAMBDA (&REST X) (REVERSE (APPLY #'LIST* X))) 3 4 5 '(6 7))
==
(FUNCALL (COMPOSE #'REVERSE #'LIST*) 3 4 5 '(6 7))
=> (7 6 5 4 3)

(FIND-IF-NOT #'ZEROP '(0 0 3))
==
(FIND-IF (COMPLEMENT #'ZEROP) '(0 0 3))
=> 3

Rationale:

The presence of these functions will contribute to syntactic
conciseness in some cases, and more importantly will permit
a programming style which is currently discouraged by most
Common Lisp implementations.

It is technically possible to define this functionality portably,
the really important part of this proposal is that native compiler
support is needed to really do them justice. Portable implementations
are not likely to be efficient enough for serious use.

Placing these functions in the core language not only permits
but encourages a very useful set of compiler optimizations that
would otherwise be difficult to obtain.

In principle, a proposal to flush the :TEST-NOT keywords and the
-IF-NOT functions could even be entertained if the COMPLEMENT
function were added. [See issue TEST-NOT-IF-NOT.]

Current Practice:

No Common Lisp implementations provide these primitives, but they do
exist in the T language.

Cost to Implementors:

A straightforward implementation is simple to cook up. The definitions
given here would suffice. Typically some additional work might be
desirable to make these open code in interesting ways.

(DEFUN COMPOSE (&REST FUNCTIONS)
(COND ((NOT FUNCTIONS)
(ERROR "COMPOSE requires at least one function."))
((NOT (REST FUNCTIONS))
(FIRST FUNCTIONS))
(T
(LET ((REVERSED-FUNCTIONS (REVERSE FUNCTIONS)))
(LET ((LAST-FUNCTION   (FIRST REVERSED-FUNCTIONS))
(OTHER-FUNCTIONS (REST  REVERSED-FUNCTIONS)))
#'(LAMBDA (&REST ARGUMENTS)
(DO ((O OTHER-FUNCTIONS (CDR O))
(VAL (APPLY LAST-FUNCTION ARGUMENTS)
(FUNCALL (CAR O) VAL)))
((NULL O) VAL))))))))

(DEFUN CONJOIN (&REST FUNCTIONS)
#'(LAMBDA (&REST ARGUMENTS)
(DO ((F FUNCTIONS (CDR F))
(VAL T (AND VAL (APPLY (CAR F) ARGUMENTS))))
((OR (NULL VAL) (NULL F)) VAL))))

(DEFUN DISJOIN (&REST FUNCTIONS)
#'(LAMBDA (&REST ARGUMENTS)
(DO ((F FUNCTIONS (CDR F))
(VAL NIL (OR VAL (APPLY (CAR F) ARGUMENTS))))
((OR VAL (NULL F)) VAL))))

(DEFUN COMPLEMENT (FUNCTION)
#'(LAMBDA (&REST ARGUMENTS)
(NOT (APPLY FUNCTION ARGUMENTS))))

(DEFUN ALWAYS (VALUE)
#'(LAMBDA (&REST ARGUMENTS)
(DECLARE (IGNORE ARGUMENTS))
VALUE))

Cost to Users:

None. This change is upward compatible.

(COMPLEMENT BENEFITS)

Benefits:

Some code would be more clear.
Some compilers might be able to produce better code.

Takes a step toward being able to flush the -IF-NOT functions
and the :TEST-NOT keywords, both of which are high on the list
of what people are referring to when they say Common Lisp is
bloated by too much garbage.

Aesthetics:

In situations where these could be used straightforwardly, the
alternatives are far less perspicuous.

Discussion:

Pitman and van Roggen support the proposal.

Jim McDonald (JLM@Lucid.COM) seemed supportive of this proposal
and even suggested adding more elaborate operators such as
PERMUTE and COMMUTE. eg, (COMMUTE #'CONS) would be like what
Maclisp called XCONS.

Masinter wavered on this issue, but currently seems to support it.

Fahlman thinks this slightly gratuitous but is not opposed to
it if others think it is a good idea.

```