From: Chris Barker Date: Mon, 4 Oct 2010 00:35:46 +0000 (-0400) Subject: edits X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=4cea4f69242f3a229292186c8fa652942f31f8b8;hp=-c edits --- 4cea4f69242f3a229292186c8fa652942f31f8b8 diff --combined assignment_3_evaluator.mdwn index eb3c18b6,c910064a..28693f43 --- a/assignment_3_evaluator.mdwn +++ b/assignment_3_evaluator.mdwn @@@ -5,24 -5,23 +5,25 @@@ Here are the definitions pre-loaded fo let true = \x y. x in let false = \x y. y in let and = \l r. l (r true false) false 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 ++; + 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 + 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 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 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 ; @@@ -32,34 -31,18 +33,35 @@@ let Y = \f. (\h. f (h h)) (\h. f (h h) 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 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 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) + do eta-reductions too