Renaming lambda in Common Lisp

In Common Lisp LAMBDA is two different things: a macro and a symbol which can be used in a LAMBDA expression.

The LAMBDA expression:

(function (lambda (x) (foo x)))

shorter written as

#'(lambda (x) (foo x))

An applied lambda expression is also valid:

((lambda (x) (+ x x)) 4)

Above both forms are part of the core syntax of Common Lisp.

Late in the definition of Common Lisp a macro called LAMBDA has been added. Confusingly enough, but with good intentions. ;-) It is documented as Macro LAMBDA.

(lambda (x) (+ x x))

expands into

(function (lambda (x) (+ x x))

It makes Common Lisp code look slightly more like Scheme code and then it is not necessary to write

(mapcar #'(lambda (x) (+ x x)) some-list)

With the LAMBDA macro we can write

(mapcar (lambda (x) (+ x x)) some-list)

Your example fails because

((my-lambda (x) (* x x)) 2)

is not valid Common Lisp syntax.

Common Lisp expects either

• a data object
• a variable
• a function call in the form (function args...)
• a function call in the form ((lambda (arglist ...) body) args...)
• a macro form like (macro-name forms...)
• a special form using one of the built-in special operators like FUNCTION, LET, ... defined in the list of special operators in Common Lisp

As you can see a syntax of

((macro-name forms...) forms...)

is not a part of Common Lisp.

It is possible to read the character λ as LAMBDA:

(defun λ-reader (stream char)
  (declare (ignore char stream))
  'LAMBDA)

(set-macro-character #\λ #'λ-reader)

Example:

CL-USER 1 > ((λ (x) (* x x)) 3)
9

CL-USER 2 > '(λ (x) (* x x))
(LAMBDA (X) (* X X))

You might also think of LAMBDA as an operator which, given a term and a list of free variables, returns a function. This p.o.v. takes LAMBDA out of the family of basic functions and elementary macros -- at least as far as the interpreter is concerned.