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[lambda.git]
/
assignment1.mdwn
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b/assignment1.mdwn
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assignment1.mdwn
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assignment1.mdwn
@@
-1,4
+1,5
@@
-**Reduction**
+Reduction
+---------
Find "normal forms" for the following (that is, reduce them as far as it's possible to reduce
them):
Find "normal forms" for the following (that is, reduce them as far as it's possible to reduce
them):
@@
-12,7
+13,8
@@
them):
7. (\x (x x x)) (\x (x x x))
7. (\x (x x x)) (\x (x x x))
-**Booleans**
+Booleans
+--------
Recall our definitions of true and false.
Recall our definitions of true and false.
@@
-24,21
+26,29
@@
In Racket, these can be defined like this:
(define true (lambda (t) (lambda (f) t)))
(define false (lambda (t) (lambda (f) f)))
(define true (lambda (t) (lambda (f) t)))
(define false (lambda (t) (lambda (f) f)))
-(8). Define a "neg" operator that negates "true" and "false".
-Expected behavior: (((neg true) 10) 20) evaluates to 20,
-(((neg false) 10) 20) evaluates to 10.
+8. [8] Define a "neg" operator that negates "true" and "false".
+Expected behavior:
-(9). Define an "and" operator.
+ (((neg true) 10) 20)
-10. Define an "xor" operator. (If you haven't seen this term before, here's a truth table:
+evaluates to 20, and
+
+ (((neg false) 10) 20)
+
+evaluates to 10.
+
+9. [9] Define an "and" operator.
+
+10. [10] Define an "xor" operator. (If you haven't seen this term before, here's a truth table:
true xor true = false
true xor false = true
false xor true = true
false xor false = false
true xor true = false
true xor false = true
false xor true = true
false xor false = false
+
)
)
-11. Inspired by our definition of boolean values, propose a data structure
+
*
11. Inspired by our definition of boolean values, propose a data structure
capable of representing one of the two values "black" or "white". If we have
one of those values, call it a black-or-white-value, we should be able to
write:
capable of representing one of the two values "black" or "white". If we have
one of those values, call it a black-or-white-value, we should be able to
write: