Issue: FUNCTION-COMPOSITION (Version 1)

[Kent M Pitman <KMP@STONY-BROOK.SCRC.Symbolics.COM>]

Issue:        FUNCTION-COMPOSITION
References:   None
Category:     ADDITION
Edit history: 21-Jun-88, Version 1 by Pitman
Status:	      For Internal Discussion

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):

  Add the following 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 OR of the
    given functions 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:

  This can contribute to syntactic conciseness, and may sometimes
  even make things easier for a compiler to recognize and compile
  efficiently.

  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.

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.

Cost of Non-Adoption:

  (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 supports the inclusion of these primitives.