X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment_3_evaluator.mdwn;h=eb3c18b6d52457d4f4402e53e0c9b06e2d34a4d4;hp=d30e150fb5e9fd1f9c65581e14a104070ab1d05b;hb=2a61846bbb48e29385fc7639a47c76f82d70bb18;hpb=5c196ebafcd1dcf0a786c2c7b5347983fef85120

diff --git a/assignment_3_evaluator.mdwn b/assignment_3_evaluator.mdwn
index d30e150f..eb3c18b6 100644
--- a/assignment_3_evaluator.mdwn
+++ b/assignment_3_evaluator.mdwn
@@ -1,27 +1,63 @@
 Here are the definitions pre-loaded for working on assignment 3:
 
 <textarea id="INPUT" style="border: 2px solid black; color: black; font-family: monospace; height: 3in; overflow: auto; padding: 0.5em; width: 100%;">
+; booleans
 let true = \x y. x in
 let false = \x y. y in
 let and = \l r. l (r true false) false in
-let makePair = \f s g. g f s in
-let fst = true in
-let snd = false in
-let nil = makePair true meh in
-let isNil = \x. x fst in
-let makeList = \h t. makePair false (makePair h t) in
-let head = \l. isNil l err (l snd fst) in
-let tail = \l. isNil l err (l snd snd) in
-let mylist = makeList 1 (makeList 2 (makeList 3 nil)) in
-let Y = \f. (\h. f (h h)) (\h. f (h h)) in
-let isZero = \n. n (\x. false) true in
+let or = \l r. l true r in
+let make_pair = \f s g. g f s in
+let get_fst = true in
+let get_snd = false in
+let empty = make_pair true junk in
+let isempty = \x. x get_fst in
+let make_list = \h t. make_pair false (make_pair h t) in
+let head = \l. isempty l err (l get_snd get_fst) in
+let tail = \l. isempty l err (l get_snd get_snd) in
+;
+; a list of numbers to experiment on
+let mylist = make_list 1 (make_list 2 (make_list 3 empty)) in
+;
+; church numerals
+let iszero = \n. n (\x. false) true in
 let succ = \n s z. s (n s z) in
-let mult = \m n s. m (n s) in
-let length = Y (\length l. isNil l 0 (succ (length (tail l)))) in
-let pred = \n. isZero n 0 (length (tail (n (\p. makeList meh p) nil))) in
-let leq = \m n. isZero(n pred m) in
+let mul = \m n s. m (n s) in
+let pred = (\shift n. n shift (make_pair 0 0) get_snd) (\p. p (\x y. make_pair (succ x) x))  in
+let leq = \m n. iszero(n pred m) in
 let eq = \m n. and (leq m n)(leq n m) in
-
+;
+; a fixed-point combinator for defining recursive functions
+let Y = \f. (\h. f (h h)) (\h. f (h h)) in
+;
+let length = Y (\length l. isempty l 0 (succ (length (tail l)))) in
+;
+; synonyms
+let makePair = make_pair in
+let fst = get_fst in
+let snd = get_snd in
+let nil = empty in
+let isNil = isempty in
+let makeList = make_list in
+let isZero = iszero in
+let mult = mul in
+;
+let t1 = (make_list 1 empty) in
+let t2 = (make_list 2 empty) in
+let t3 = (make_list 3 empty) in
+let t12 = (make_list t1 (make_list t2 empty)) in
+let t23 = (make_list t2 (make_list t3 empty)) in
+let ta = (make_list t1 t23) in
+let tb = (make_list t12 t3) in
+let tc = (make_list t1 (make_list t23 empty)) in
+;
+;sum-leaves t1 ~~> 1
+;sum-leaves t2 ~~> 2
+;sum-leaves t3 ~~> 3
+;sum-leaves t12 ~~> 3
+;sum-leaves t23 ~~> 5
+;sum-leaves ta ~~> 6
+;sum-leaves tb ~~> 6
+;
 length (tail mylist)
 </textarea>
 <input id="PARSE" value="Normalize" type="button">