An Introduction to Functional Programming Through Lambda Calculus

- 204 -(op (car (cdr l)))(e2 (trans (car (cdr (cdr l))))))(list op e1 e2))))For example:(trans ’(1 + 2)) ->(+ 1 2)(trans ’(3 * (4 * 5))) ->(* 3 (* 4 5))(trans ’((6 * 7) + (8 - 9))) ->(+ (* 6 7) (- 8 9))Note that quoted symbols for infix operators have been moved into the function positions in the resultant forms.Now, we can evaluate the translated expression, as a LISP form, using eval:(defun calc (l)(eval (trans l)))For example:(calc ’((6 * 7) + (8 - 9))) ->41The treatment of free variables in quoted forms depends on the scope rules. For dynamic scope systems, quoted freevariables are associated with the corresponding bound variable when the quoted form is evaluated. Thus, withdynamic scope, quoting can move free variables into different evaluation scopes.In COMMON LISP, with lexical scope, quoted free variables are not associated with bound variables in the definingscope as might be expected. Instead, they are evaluated as if there were no bound variables defined apart from thenames from global definitions.10.18. λ calculus in LISPWe can use function and funcall for rather clumsy applicative order pure λ calculus. For example, we can tryout some of the λ functions we met in chapter 2. First of all, we can apply the identity function:to itself:#’(lambda (x) x)(funcall #’(lambda (x) x) #’(lambda (x) x))Note that some LISP implementations will not print out the resultant function and others will print a system sepecificrepresentation.Let us now use definitions:(defun identity (x) x) ->identity(funcall #’identity #’identity)