Lambda Calculus CONS Pair implementation with Lisp

问题

I'm trying to implement a Church Pair Lambda Calc. style with CLisp.

According with Wikipedia:

pair ≡ λx.λy.λz.z x y

So far, this is my code:

 (defvar PAIR
         #'(lambda(x)
                 #'(lambda(y)
                         #'(lambda(z)
                                 (funcall (funcall z x) y)))) )

These are my FIRST and SECOND Functions:

(defvar FIRST
        #'(lambda(p)
                (funcall(p TRUE)))
)

(defvar SECOND
        #'(lambda(p)
                (funcall(p FALSE)))
)

This 2 functions convert from Int to ChurchNumber

(defun church2int(numchurch)
    (funcall (funcall numchurch #'(lambda (x) (+ x 1))) 0)
)

(defun int2church(n)
    (cond
        ((= n 0) #'(lambda(f) #'(lambda(x)x)))
        (t #'(lambda(f) #'(lambda(x) (funcall f
            (funcall(funcall(int2church (- n 1))f)x))))))

)

So, what I do is:

(setq six (int2church 6))
(setq four (int2church 4))

And then:

(setq P (funcall (funcall PAIR six) four))

And the I've got:

#<FUNCTION :LAMBDA (Y) (FUNCALL (FUNCALL F X) Y)>

So if I do this:

(funcall #'FIRST P)

I've got the this error:

*** - FIRST: #<FUNCTION :LAMBDA (Y) (FUNCALL (FUNCALL F X) Y)> is not a list

I can't see what I am doing wrong. Any help would be appreciated.

Thanks

回答1:

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来源：https://stackoverflow.com/questions/13537622/lambda-calculus-cons-pair-implementation-with-lisp

标签

lisp

lambda-calculus