lab10: impl

lab10/lambdaCalc.lhs

@@ -59,9 +59,9 @@ Why does this work?  Here are a couple of tests to consider.
 
 Define the 'nott' and 'orr' operators below without using andd.
 
-> nott = error "TBD"
+> nott = \b -> b fls tru
 
-> orr = error "TBD"
+> orr = \b -> \c -> b tru c
 
 Here are some test cases:
 
@@ -134,7 +134,7 @@ Write the definition for 'nil' below.  (If you are unsure of what the
 definition should be, try walking through the derivation of
 "isEmpty (pair 1 2)".
 
-> nil = error "TBD"
+> nil = \x -> tru
 
 Now we can create some sample lists.  (Note that we are using Haskell numbers
 just for easy of testing, though they are not part of the lambda calculus.)
@@ -229,7 +229,9 @@ Alternately, we could define plus with our scc function:
 
 Define multiplication in a similar manner:
 
-> multiply = error "TBD"
+> multiply = \m -> \n -> m (plus n) zero
+
+> test3times2 = transChurchNums $ multiply three two
 
 
 For ease of use, you may use the following function to convert a Haskell integer
@@ -253,6 +255,11 @@ Haskell will not accept the above combinator.
 Evaluate this function by hand yourself.
 After one step, what do you get?
 
+function: (\x -> x x)
+argument: (\x -> x x)
+substitute x with (\x -> x x) in x x = (\x -> x x) (\x -> x x)
+it evaluates to the same function, basically an infinite loop I think?
+
 
 The omega function is not terribly useful, though it is interesting.
 We can cause a lambda calculus program to go into an infinite loop.
@@ -286,3 +293,25 @@ factorial = fix g
 
 To understand how this works, write out the evaluation steps for `factorial 3`.
 
+-> factorial 3 = (fix g) 3
+-> g (fix g) 3 = test (isZero (prd 3)) one (multiply 3 (g (prd 3)))
+-> test (isZero (2)) one (multiply 3 (g (2)))
+takes the false branch until g (1) then takes the true branch because isZero (prd 1) = true
+
+> main :: IO ()
+> main = do
+>   print $ testTru ++ " : expected true"
+>   print $ testFls ++ " : expected false"
+>   print $ testAnd1 ++ " : expected true"
+>   print $ testAnd2 ++ " : expected false"
+>   print $ testOps1 ++ " : expected true"
+>   print $ testOps2 ++ " : expected false"
+>   print $ testPairFst ++ " : expected true"
+>   print $ testPairSnd ++ " : expected false"
+>   print $ show testListHead ++ " : expected 0"
+>   print $ show testListHeadTail ++ " : expected 1"
+>   print $ testNotEmpty ++ " : expected false"
+>   print $ testEmpty ++ " : expected true"
+>   print $ show test3plus2 ++ " : expected 5"
+>   print $ show test3times2 ++ " : expected 6"
+