Church numerals: Difference between revisions
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=={{header|Common Lisp}}== |
=={{header|Common Lisp}}== |
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In many solutions to this task, Church numerals are given a [[Currying|Curried]] form. In Common Lisp, that looks like this: |
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<pre>(lambda (f) (lambda (x) ...))</pre> |
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However, they can also be given an uncurried, 2-argument form: |
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<pre>(lambda (f x) ...)</pre> |
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Common Lisp has separate namespaces for variable and function names. When a variable, <code>f</code>, has a function as its value, the usual function-calling syntax, <code>(f ...)</code> can't be used to call the function; instead you have to write |
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<pre>(funcall f ...)</pre> |
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(<code>Funcall</code> is also needed when the function is the value of a more complex expression, rather than just a variable.) |
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<pre> |
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(n g v) ; uncurried, 1 namespace |
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((n g) v) ; curried, 1 namespace |
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(funcall n g v) ; uncurried, 2 namespaces |
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(funcall (funcall n g) v) ; curried, 2 namespaces |
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</pre> |
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===Uncurried Church numerals=== |
===Uncurried Church numerals=== |
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{{trans|Acornsoft Lisp}} |
{{trans|Acornsoft Lisp}} |
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In this section, Church numerals are uncurried, 2-argument functions. |
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<syntaxhighlight lang="lisp"> |
<syntaxhighlight lang="lisp"> |
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(funcall n (lambda (product) (times m product)) one)) |
(funcall n (lambda (product) (times m product)) one)) |
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(defun church (i) |
(defun church (i) ; int -> Church |
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(if (zerop i) zero (succ (church (1- i))))) |
(if (zerop i) zero (succ (church (1- i))))) |
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(defun unchurch (n) |
(defun unchurch (n) ; Church -> int |
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(funcall n #'1+ 0)) |
(funcall n #'1+ 0)) |
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<syntaxhighlight lang="lisp"> |
<syntaxhighlight lang="lisp"> |
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(defvar zero (lambda (f) (lambda (x) x))) |
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(defvar one (lambda (f) (lambda (x) (funcall f x)))) |
(defvar one (lambda (f) (lambda (x) (funcall f x)))) |
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(lambda (x) (funcall f (funcall g x)))) |
(lambda (x) (funcall f (funcall g x)))) |
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(defun church (i) |
(defun church (i) ; int -> Church |
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(if (zerop i) zero (succ (church (1- i))))) |
(if (zerop i) zero (succ (church (1- i))))) |
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(defun unchurch (n) |
(defun unchurch (n) ; Church -> int |
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(funcall (funcall n #'1+) 0)) |
(funcall (funcall n #'1+) 0)) |
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</syntaxhighlight> |
</syntaxhighlight> |
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(defun minus (m n) |
(defun minus (m n) |
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(funcall n #'pred m)) |
(funcall n #'pred m)) |
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</syntaxhighlight> |
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<syntaxhighlight lang="lisp"> |
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(defmacro church-if (test then else) |
(defmacro church-if (test then else) |
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`(funcall ,test (lambda () ,then) (lambda () ,else))) |
`(funcall ,test (lambda () ,then) (lambda () ,else))) |
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(defun unbool (b) |
(defun unbool (b) |
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(church-if b t nil)) |
(church-if b t nil)) |
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</syntaxhighlight> |
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<syntaxhighlight lang="lisp"> |
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(defun is-zero (n) |
(defun is-zero (n) |
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(funcall n (lambda (x) false) true)) |
(funcall n (lambda (x) false) true)) |
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===Further, curried=== |
===Further, curried=== |
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Again, the remaining definitions, the calls to <code>show</code>, and the resulting output are the same as in uncurried version above. |
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<syntaxhighlight lang="lisp"> |
<syntaxhighlight lang="lisp"> |
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