Macro pattern not matching - macros

Full source
So I have a macro for making objects, and it is used like:
(define ob
(class (a 10) (b 20)
(set-a! (lambda (x) (set! a x)))
(set-b! (lambda (x) (set! b x)))
(foo (lambda (x)
(* (+ a b) (- a b))))))
(ob 'a) -> 10
(ob 'b) -> 20
(ob 'set-a! 50)
(ob 'a) -> 50
(ob 'foo) -> 2100
I added another pattern for having public and private members,
(define ob
(class private
(a 10) (b 20)
public
(get-a (lambda (x) a))
(set-a! (lambda (x) (set! a x)))))
and that works, but for some reason, it wont match this pattern:
(define ob2
(class private
(a 10) (b 20) (c '())
public
(get-a (lambda (x) a))
(get-b (lambda (x) b))
(set-a! (lambda (x) (set! a x)))
(set-b! (lambda (x) (set! b x)))
(push-c! (lambda (x)
(set! c (cons x c))))
(pop-c! (lambda (x)
(if (not (eq? c '()))
(set! c (cdr c))
(error "stack empty!"))))))
The error message for trying to use ob2 is in the source

As far as I understand, the first example should not work either, and, in fact, I could not get it to work. I don't think you can use two ellipses on the same level. Therefore, it would be easier to define something like
(define-syntax class
(syntax-rules (public private)
((class (public (?var ?val) ...) (private (?var1 ?val1) ...))
(list (list ?var ?val) ... (list ?var1 ?val1) ...))))
However, if you have to do it all on the same syntactic level, you could do so by applying the macro recursively, along the following lines:
(define-syntax testclass
(syntax-rules (public private)
((testclass public (var val) . rest)
(testclass ((var val)) public . rest))
((testclass ((var val) ...) public (var1 val1) . rest)
(testclass ((var val) ... (var1 val1)) public . rest))
((testclass lst public private . rest)
(list (quote lst) (quote rest)))))
In order to make this more robust, you will have to add rules for empty public and private expressions.

Related

Mapping within macro without extra parentheses?

Say I have a macro like this:
(define-syntax (choose stx)
(define data (syntax->datum stx))
(define args (cadr data))
(define body (cddr data))
(define output
`(apply (case (car ,args)
,(map (lambda (choice)
`((,(car choice)) ,(cadr choice)))
body)
(else (displayln "error")))
(cdr ,args)))
(println output)
#'(void))
If I use this on something like this (there could be more options):
(choose args
("run" runsomething)
("del" delsomethingelse))
It transforms it to
(apply
(case (car args)
((("run") runsomething)
(("del") delsomethingelse))
(else (displayln "error")))
(cdr args))
Which is not valid code, because the map gave it extra parentheses. Instead I want it to give me this:
(apply
(case (car args)
(("run") runsomething)
(("del") delsomethingelse)
(else (displayln "error")))
(cdr args))
How could I do something like this?
Use unquote-splicing (aka ,#) to get rid of the list surrounding map.
Example:
(define xs '(a b c))
`(1 2 ,xs 3 4) ; => '(1 2 (a b c) 3 4)
`(1 2 ,#xs 3 4) ; => '(1 2 a b c 3 4)
However I notice that you use syntax->datum on the input stx
of the syntax transformer. That removes lexical information, which
could end up causing problems. It recommend using either syntax-case
or syntax-parse, which use pattern matching to pick out the elements
of the input syntax and templates to generate the output.
(define-syntax (choose stx)
(syntax-case stx ()
[(_choose args
(datum fun-expr)
...)
#'(apply (case (car args)
[(datum) fun-expr]
...)
(cdr args))]))
(define (run-it . xs) (list 'ran-it xs))
(define (del-it . xs) (list 'delt-it xs))
(choose (list "run" 1 2 3)
("run" run-it)
("del" del-it))
Output: '(ran-it (1 2 3))

Any good way to declare unused variables in destructuring-bind?

I can't figure, is there any way to put something like _ in erlang, for "unused value" in destructuring-bind?
For example there we have something like that:
(destructuring-bind ((_SNIPPET
(_TITLE . title)
(_DESCRIPTION . description)
_RESOURCE-ID (_VIDEO-ID . video-id)))) entry
(declare (ignore
_SNIPPET _TITLE _DESCRIPTION _RESOURCE-ID _VIDEO-ID))
(list video-id title description)))
It'll be great not to put specific variable for every unused value, and write something like that:
(destructuring-bind ((_
(_ . title)
(_ . description)
(_ (_ . video-id)))) entry
(list video-id title description)))
Is there any way to get such behavior with standart destructuring-bind or any other standart macros? Or I have to use some ML-like pattern matching library, and if so - which one?
It's not possible with DESTRUCTURING-BIND (you can't use a variable more than once, some compiler will complain). You can enumerate the variables, _1, _2, ... But then you have to ignore each of them.
LOOP can do it:
CL-USER 23 > (loop for ((a b nil c) nil d) in '(((1 2 3 4) 5 6)
((1 2 3 4) 5 6))
collect (list a b c d))
((1 2 4 6) (1 2 4 6))
NIL is used as the wildcard variable.
You can reuse the LOOP macro:
(defmacro match-bind (pattern object &body body)
`(loop with ,pattern = ,object
while nil
finally (return (progn ,#body))))
CL-USER 37 > (match-bind ((a b nil c) nil d)
'((1 2 3 4) 5 6)
(list a b c d))
(1 2 4 6)
You can use some LET-MATCH from some library. For example: https://github.com/schani/clickr/blob/master/let-match.lisp
There are probably more fancy versions.
There's nothing built into the language for this. Rainer Joswig's answer points out that loop can do some destructuring, but it doesn't do nearly as much. In an earlier version of this answer, I suggested traversing the destructuring lambda list and collecting a list of all the symbols that begin with _ and adding a declaration to the form to ignore those variables. A safer version replaces each one with a fresh variable (so that there are no repeated variables), and ignores them all. Thus something like
(destructuring-bind (_a (_b c)) object
c)
would expand into
(destructuring-bind (#:g1 (#:g2 c)) object
(declare (ignore #:g1 #:g2))
c)
This approach will work OK if you're only using the "data-directed" described in 3.4.4.1.1 Data-directed Destructuring by Lambda Lists. However, if you're using "lambda-list-directed" approach described in 3.4.4.1.2 Lambda-list-directed Destructuring by Lambda Lists, where you can use lambda-list keywords like &optional, &key, etc., then things are much more complicated, because you shouldn't replace variables in some parts of those. For instance, if you have
&optional (_x '_default-x)
then it might be OK to replace _x with something, but not _default-x, because the latter isn't a pattern. But, in Lisp, code is data, so we can still write a macro that maps over the destructuring-lambda-list and replaces only in locations that are patterns. Here's somewhat hairy code that does just that. This takes a function and a destructuring lambda list, and calls the function for each pattern variable in the lambda list, along with the type of the argument (whole, required, optional, etc.).
(defun map-dll (fn list)
(let ((result '())
(orig list)
(keywords '(&allow-other-keys &aux &body
&key &optional &rest &whole)))
(labels ((save (x)
(push x result))
(handle (type parameter)
(etypecase parameter
(list (map-dll fn parameter))
(symbol (funcall fn type parameter)))))
(macrolet ((parse-keyword ((&rest symbols) &body body)
`(progn
(when (and (not (atom list))
(member (first list) ',symbols))
(save (pop list))
,#body)))
(doparameters ((var) &body body)
`(do () ((or (atom list) (member (first list) keywords)))
(save (let ((,var (pop list)))
,#body)))))
(parse-keyword (&whole)
(save (handle :whole (pop list))))
(doparameters (required)
(handle :required required))
(parse-keyword (&optional)
(doparameters (opt)
(if (symbolp opt)
(handle :optional opt)
(list* (handle :optional (first opt)) (rest opt)))))
(when (and (atom list) (not (null list))) ; turn (... . REST)
(setq list (list '&rest list))) ; into (... &rest REST)
(parse-keyword (&rest &body)
(save (handle :rest (pop list))))
(parse-keyword (&key)
(doparameters (key)
(if (symbolp key)
(handle :key key)
(destructuring-bind (keyspec . more) key
(if (symbolp keyspec)
(list* (handle :key keyspec) more)
(destructuring-bind (keyword var) keyspec
(list* (list keyword (handle :key var)) more)))))))
(parse-keyword (&allow-other-keys))
(parse-keyword (&aux)
(doparameters (aux) aux))
(unless (null list)
(error "Bad destructuring lambda list: ~A." orig))
(nreverse result)))))
Using this, it's pretty easy to write a destructuring-bind* that replaces each pattern variable beginning with _ with a fresh variable that will be ignored in the body.
(defmacro destructuring-bind* (lambda-list object &body body)
(let* ((ignores '())
(lambda-list (map-dll (lambda (type var)
(declare (ignore type))
(if (and (> (length (symbol-name var)) 0)
(char= #\_ (char (symbol-name var) 0)))
(let ((var (gensym)))
(push var ignores)
var)
var))
lambda-list)))
`(destructuring-bind ,lambda-list ,object
(declare (ignore ,#(nreverse ignores)))
,#body)))
Now we should look at the expansions it produces:
(macroexpand-1
'(destructuring-bind* (&whole (a _ . b)
c _ d
&optional e (f '_f)
&key g _h
&aux (_i '_j))
object
(list a b c d e f g)))
;=>
(DESTRUCTURING-BIND
(&WHOLE (A #:G1041 &REST B) C #:G1042 D
&OPTIONAL E (F '_F)
&KEY G #:G1043
&AUX (_I '_J))
OBJECT
(DECLARE (IGNORE #:G1041 #:G1042 #:G1043))
(LIST A B C D E F G))
We haven't replaced anywhere we shouldn't (init forms, aux variables, etc.), but we've taken care of the places that we should. We can see this work in your example too:
(macroexpand-1
'(destructuring-bind* ((_ (_ . title)
(_ . description)
_
(_ . video-id)))
entry
(list video-id title description)))
;=>
(DESTRUCTURING-BIND ((#:G1044 (#:G1045 &REST TITLE)
(#:G1046 &REST DESCRIPTION)
#:G1047
(#:G1048 &REST VIDEO-ID)))
ENTRY
(DECLARE (IGNORE #:G1044 #:G1045 #:G1046 #:G1047 #:G1048))
(LIST VIDEO-ID TITLE DESCRIPTION))

Mysterious Racket error: define: unbound identifier; also, no #%app syntax transformer is bound in: define

This program produces an error:
define: unbound identifier;
also, no #%app syntax transformer is bound in: define
When pasted into the REPL (to be exact, the last line: (displayln (eval-clause clause state))), it works. When run in definition window, it fails. I don't know why.
#lang racket
(define *state* '((a false) (b true) (c true) (d false)))
(define *clause* '(a (not b) c))
(define (eval-clause clause state)
(for ([x state])
(eval `(define ,(first x) ,(second x))))
(eval (cons 'or (map eval clause))))
(displayln (eval-clause *clause* *state*))
This too:
(define (eval-clause clause state)
(eval `(let ,state ,(cons 'or clause))))
produces
let: unbound identifier;
also, no #%app syntax transformer is bound in: let
This was my attempt to translate the following Common Lisp program: Common Lisp wins here?
; (C) 2013 KIM Taegyoon
; 3-SAT problem
; https://groups.google.com/forum/#!topic/lisp-korea/sVajS0LEfoA
(defvar *state* '((a nil) (b t) (c t) (d nil)))
(defvar *clause* '(a (not b) c))
(defun eval-clause (clause state)
(dolist (x state)
(set (car x) (nth 1 x)))
(some #'identity (mapcar #'eval clause)))
(print (eval-clause *clause* *state*))
And in Paren:
(set *state* (quote ((a false) (b false) (c true) (d false))))
(set *clause* (quote (a (! b) c)))
(defn eval-clause (clause state)
(for i 0 (dec (length state)) 1
(set x (nth i state))
(eval (list set (nth 0 x) (nth 1 x))))
(eval (cons || clause)))
(eval-clause *clause* *state*)
eval is tricky in Racket. As per Racket Guide, 15.1.2, you need to hook into the current namespace as follows
(define-namespace-anchor anc)
(define ns (namespace-anchor->namespace anc))
and then add ns to every call to eval:
(define (eval-clause clause state)
(for ([x state])
(eval `(define ,(first x) ,(second x)) ns))
(eval (cons 'or (map (curryr eval ns) clause)) ns))
Note that this is not necessary in the REPL, as explained in the document referenced above.
However, it's probably a better idea to create a specific namespace for your definitions so that they don't get mixed up with your own module's definitions:
(define my-eval
(let ((ns (make-base-namespace)))
(lambda (expr) (eval expr ns))))
(define *state* '((a #f) (b #t) (c #t) (d #f)))
(define *clause* '(a (not b) c))
(define (eval-clause clause state)
(for ([x state])
(my-eval `(define ,(first x) ,(second x))))
(my-eval (cons 'or (map my-eval clause))))
(displayln (eval-clause *clause* *state*))
or, if you want to continue using true and false from racket/bool, define my-eval as follows;
(define my-eval
(let ((ns (make-base-namespace)))
(parameterize ((current-namespace ns))
(namespace-require 'racket/bool))
(lambda (expr) (eval expr ns))))
I would write the Common Lisp version slightly simpler:
(defun eval-clause (clause state)
(loop for (var value) in state
do (set var value))
(some #'eval clause))
The LOOP form is more descriptive (since we can get rid of CAR and NTH) and EVAL can be directly used in the SOME function.

How to set local function definition using function (or closure) objects?

The problem with flet is that the functions bound therein must be defined inline. In other words, there's no way to do this:
(new-flet ((a (lambda (f x)
(funcall f (* x 2))))
(b (function-generator)))
(a #'b 10))
I considered defining such a macro myself, but the problem is that flet seems to be the only way to set local function values. symbol-function always gets the global definition only, and function can't be used with setf. Anyone have an idea how this can be done fairly cleanly, if at all?
You can easily build a trampoline
(defun function-generator (x)
(lambda (y) (* x y)))
(let ((fg (function-generator 42)))
(flet ((a (f x) (funcall f (* x 2)))
(b (x) (funcall fg x)))
(a #'b 10)))
A macro implementation of new-flet with this approach is
(defmacro new-flet (bindings &body body)
(let ((let-bindings (list))
(flet-bindings (list))
(args (gensym)))
(dolist (binding bindings)
(let ((name (gensym)))
(push `(,name ,(second binding))
let-bindings)
(push `(,(first binding) (&rest ,args)
(apply ,name ,args))
flet-bindings)))
`(let ,(nreverse let-bindings)
(flet ,(nreverse flet-bindings)
,#body))))
that expands in your example case as
(macroexpand-1 '(new-flet ((a (lambda (f x) (funcall f (* x 2))))
(b (function-generator)))
(a #'b 10)))
==> (LET ((#:G605 (LAMBDA (F X)
(FUNCALL F (* X 2))))
(#:G606 (FUNCTION-GENERATOR)))
(FLET ((A (&REST #:G604)
(APPLY #:G605 #:G604))
(B (&REST #:G604)
(APPLY #:G606 #:G604)))
(A #'B 10)))
Is
(let* ((a (lambda (f x) (funcall f (* x 2))))
(b (function-generator)))
(funcall a b 10))
a fairly clean solution to your problem?
How about binding the variables with let, so that they're setfable, and then using an flet as the body of the let so that they're funcallable and (function …)-able, too. E.g., where I've given a silly little function instead of (generate-function):
(let ((a (lambda (f x)
(funcall f (* x 2))))
(b (lambda (&rest args)
(print (list* 'print-from-b args)))))
(flet ((a (&rest args)
(apply a args))
(b (&rest args)
(apply b args)))
(a #'b 10)))
We can wrap this up in a macro relatively easily:
(defmacro let/flet (bindings &body body)
(let ((args (gensym (string '#:args-))))
`(let ,bindings
(flet ,(loop :for (name nil) :in bindings
:collect `(,name (&rest ,args) (apply ,name ,args)))
,#body))))
Now
(let/flet ((a (lambda (f x)
(funcall f (* x 2))))
(b (lambda (&rest args)
(print (list* 'print-from-b args)))))
(a #'b 10))
expands into the first block of code. Note that you can also use (a b 10) in the body as well, since the binding of b is the same as the value of #'b. You can use setf on the variable as well:
(let/flet ((a (lambda (x)
(print (list 'from-a x)))))
(a 23)
(setf a (lambda (x)
(print (list 'from-new-a x x))))
(a 23))
prints
(FROM-A 23)
(FROM-NEW-A 23 23)
If anyone's interested in a labels equivalent, here it is:
(defmacro my-labels ((&rest definitions) &rest body)
(let ((gensyms (loop for d in definitions collect (gensym)))
(names (loop for d in definitions collect (car d)))
(fdefs (loop for f in definitions collect (cadr f)))
(args (gensym)))
`(let (,#(loop for g in gensyms collect (list g)))
(labels (,#(loop for g in gensyms for n in names
collect `(,n (&rest ,args) (apply ,g ,args))))
,#(loop for g in gensyms for f in fdefs
collect `(setf ,g ,f))
,#body))))
This is sort of like Scheme's letrec.

CLISP Lambda Calculus Div Implementation

I'm trying to implement a Division function with clisp Lambda Calc. style
I read from this site that lambda expression of a division is:
Y (λgqab. LT a b (PAIR q a) (g (SUCC q) (SUB a b) b)) 0
These are TRUE and FALSE
(defvar TRUE #'(lambda(x)#'(lambda(y)x)))
(defvar FALSE #'(lambda(x)#'(lambda(y)y)))
These are conversion functions between Int and Church numbers
(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))))))
)
This is my IF-THEN-ELSE Implementation
(defvar IF-THEN-ELSE
#'(lambda(c)
#'(lambda(x)
#'(lambda(y)
#'(lambda(acc1)
#'(lambda (acc2)
(funcall (funcall (funcall (funcall c x) y) acc1) acc2))))))
)
And this is my div implementation
(defvar division
#'(lambda (g)
#'(lambda (q)
#'(lambda (a)
#'(lambda (b)
(funcall (funcall (funcall (funcall (funcall IF-THEN-ELSE LT) a) b)
(funcall (funcall PAIR q)a))
(funcall (funcall g (funcall succ q)) (funcall (funcall sub a)b))
)))))
)
PAIR, SUCC and SUB functions work fine. I set my church numbers up like this
(set six (int2church 6))
(set two (int2church 2))
Then I do:
(setq D (funcall (funcall division six) two))
And I've got:
#<FUNCTION :LAMBDA (A)
#'(LAMBDA (B)
(FUNCALL (FUNCALL (FUNCALL (FUNCALL (FUNCALL IF-THEN-ELSE LT) A) B) (FUNCALL (FUNCALL PAR Q) A))
(FUNCALL (FUNCALL G (FUNCALL SUCC Q)) (FUNCALL (FUNCALL SUB A) B))))>
For what I understand, this function return a Church Pair. If I try to get the first element
with a function FRST (FRST works ok) like this:
(funcall frst D)
I've got
#<FUNCTION :LAMBDA (B)
(FUNCALL (FUNCALL (FUNCALL (FUNCALL (FUNCALL IF-THEN-ELSE LT) A) B) (FUNCALL (FUNCALL PAR Q) A))
(FUNCALL (FUNCALL G (FUNCALL SUCC Q)) (FUNCALL (FUNCALL SUB A) B)))>
If I try to get the int value with Church2int (Church2int works OK) like this:
(church2int (funcall frst D))
I've got
*** - +:
#<FUNCTION :LAMBDA (N)
#'(LAMBDA (F)
#'(LAMBDA (X)
(FUNCALL (FUNCALL (FUNCALL N #'(LAMBDA (G) #'(LAMBDA (H) (FUNCALL H (FUNCALL G F))))) #'(LAMBDA (U) X)) (LAMBDA (U) U))))>
is not a number
Where I expect to get 3
I think the problem is in DIVISION function, after the IF-THEN-ELSE, I tried to change it a little bit (I thought it was a nested parenthesis problem) but I got lots of errors.
Any help would be appreciated
Thanks
There are several problems with your definition.
DIVISION does not use the Y combinator, but the original definition does.
This is important, because the DIVISION function expects a copy of itself in the g
parameter.
However, even if you added the Y invocation, your code would still not work
but go into an infinite loop instead. That's because Common Lisp, like most of today's languages, is a call-by-value language. All arguments are evaluated before a function is called. This means that you cannot define conditional functions as elegantly as the traditional lambda calculus semantics would allow.
Here's one way of doing church number division in Common Lisp. I've taken the liberty of introducing some syntax to make this a bit more readable.
;;;; -*- coding: utf-8 -*-
;;;; --- preamble, define lambda calculus language
(cl:in-package #:cl-user)
(defpackage #:lambda-calc
;; note: not using common-lisp package
(:use)
(:export #:λ #:call #:define))
;; (lambda-calc:λ (x y) body)
;; ==> (cl:lambda (x) (cl:lambda (y) body))
(defmacro lambda-calc:λ ((arg &rest more-args) body-expr)
(labels ((rec (args)
(if (null args)
body-expr
`(lambda (,(car args))
(declare (ignorable ,(car args)))
,(rec (cdr args))))))
(rec (cons arg more-args))))
;; (lambda-calc:call f a b)
;; ==> (cl:funcall (cl:funcall f a) b)
(defmacro lambda-calc:call (func &rest args)
(labels ((rec (args)
(if (null args)
func
`(funcall ,(rec (cdr args)) ,(car args)))))
(rec (reverse args))))
;; Defines top-level lexical variables
(defmacro lambda-calc:define (name value)
(let ((vname (gensym (princ-to-string name))))
`(progn
(defparameter ,vname nil)
(define-symbol-macro ,name ,vname)
(setf ,name
(flet ((,vname () ,value))
(,vname))))))
;; Syntax: {f a b}
;; ==> (lambda-calc:call f a b)
;; ==> (cl:funcall (cl:funcall f a) b)
(eval-when (:compile-toplevel :load-toplevel :execute)
(set-macro-character #\{
(lambda (stream char)
(declare (ignore char))
`(lambda-calc:call
,#(read-delimited-list #\} stream t))))
(set-macro-character #\} (get-macro-character #\))))
;;;; --- end of preamble, fun starts here
(in-package #:lambda-calc)
;; booleans
(define TRUE
(λ (x y) x))
(define FALSE
(λ (x y) y))
(define NOT
(λ (bool) {bool FALSE TRUE}))
;; numbers
(define ZERO
(λ (f x) x))
(define SUCC
(λ (n f x) {f {n f x}}))
(define PLUS
(λ (m n) {m SUCC n}))
(define PRED
(λ (n f x)
{n (λ (g h) {h {g f}})
(λ (u) x)
(λ (u) u)}))
(define SUB
(λ (m n) {n PRED m}))
(define ISZERO
(λ (n) {n (λ (x) FALSE) TRUE}))
(define <=
(λ (m n) {ISZERO {SUB m n}}))
(define <
(λ (m n) {NOT {<= n m}}))
(define ONE {SUCC ZERO})
(define TWO {SUCC ONE})
(define THREE {SUCC TWO})
(define FOUR {SUCC THREE})
(define FIVE {SUCC FOUR})
(define SIX {SUCC FIVE})
(define SEVEN {SUCC SIX})
(define EIGHT {SUCC SEVEN})
(define NINE {SUCC EIGHT})
(define TEN {SUCC NINE})
;; combinators
(define Y
(λ (f)
{(λ (rec arg) {f {rec rec} arg})
(λ (rec arg) {f {rec rec} arg})}))
(define IF
(λ (condition if-true if-false)
{{condition if-true if-false} condition}))
;; pairs
(define PAIR
(λ (x y select) {select x y}))
(define FIRST
(λ (pair) {pair TRUE}))
(define SECOND
(λ (pair) {pair FALSE}))
;; conversion from/to lisp integers
(cl:defun int-to-church (number)
(cl:if (cl:zerop number)
zero
{succ (int-to-church (cl:1- number))}))
(cl:defun church-to-int (church-number)
{church-number #'cl:1+ 0})
;; what we're all here for
(define DIVISION
{Y (λ (recurse q a b)
{IF {< a b}
(λ (c) {PAIR q a})
(λ (c) {recurse {SUCC q} {SUB a b} b})})
ZERO})
If you put this into a file, you can do:
[1]> (load "lambdacalc.lisp")
;; Loading file lambdacalc.lisp ...
;; Loaded file lambdacalc.lisp
T
[2]> (in-package :lambda-calc)
#<PACKAGE LAMBDA-CALC>
LAMBDA-CALC[3]> (church-to-int {FIRST {DIVISION TEN FIVE}})
2
LAMBDA-CALC[4]> (church-to-int {SECOND {DIVISION TEN FIVE}})
0
LAMBDA-CALC[5]> (church-to-int {FIRST {DIVISION TEN FOUR}})
2
LAMBDA-CALC[6]> (church-to-int {SECOND {DIVISION TEN FOUR}})
2