X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=lambda_library.mdwn;h=6441d3b9d65e626fcd0fe8ca883bd68a6ec4644c;hp=289b28438916da6ca8a35ff9d23b34e772e43177;hb=1859a8c4b42139e3a557ec44dd8edd1e1acb71f9;hpb=9cb038c46ca337f654266aa75769bb304ed3cafb diff --git a/lambda_library.mdwn b/lambda_library.mdwn index 289b2843..6441d3b9 100644 --- a/lambda_library.mdwn +++ b/lambda_library.mdwn @@ -27,8 +27,8 @@ and all sorts of other places. Others of them are our own handiwork. ; pairs let make_pair = \x y f. f x y in - let get_1st = \x y. x in ; aka true - let get_2nd = \x y. y in ; aka false + let get_fst = \x y. x in ; aka true + let get_snd = \x y. y in ; aka false ; triples let make_triple = \x y z f. f x y z in @@ -50,7 +50,7 @@ and all sorts of other places. Others of them are our own handiwork. let isempty = \lst. lst (\h sofar. false) true in let head = \lst. lst (\h sofar. h) junk in let tail_empty = empty in - let tail = \lst. (\shift. lst shift (make_pair empty tail_empty) get_2nd) + let tail = \lst. (\shift. lst shift (make_pair empty tail_empty) get_snd) ; where shift is (\h p. p (\t y. make_pair (make_list h t) t)) in let length = \lst. lst (\h sofar. succ sofar) 0 in @@ -65,7 +65,7 @@ and all sorts of other places. Others of them are our own handiwork. ; more efficient reverse builds a left-fold instead ; (make_left_list a (make_left_list b (make_left_list c empty)) ~~> \f z. f c (f b (f a z)) let reverse = (\make_left_list lst. lst make_left_list empty) (\h t f z. t f (f h z)) in - ; zip [a;b;c] [x; y; z] ~~> [(a,x);(b,y);(c,z)] + ; zip [a;b;c] [x;y;z] ~~> [(a,x);(b,y);(c,z)] let zip = \left right. (\base build. reverse left build base (\x y. reverse x)) ; where base is (make_pair empty (map (\h u. u h) right)) @@ -82,10 +82,10 @@ and all sorts of other places. Others of them are our own handiwork. let empty = make_pair true junk in let make_list = \h t. make_pair false (make_pair h t) in - let isempty = \lst. lst get_1st in - let head = \lst. isempty lst err (lst get_2nd get_1st) in + let isempty = \lst. lst get_fst in + let head = \lst. isempty lst err (lst get_snd get_fst) in let tail_empty = empty in - let tail = \lst. isempty lst tail_empty (lst get_2nd get_2nd) in + let tail = \lst. isempty lst tail_empty (lst get_snd get_snd) in ; more math with Church numerals @@ -104,7 +104,7 @@ and all sorts of other places. Others of them are our own handiwork. ; three strategies for predecessor let pred_zero = zero in - let pred = (\shift n. n shift (make_pair zero pred_zero) get_2nd) + let pred = (\shift n. n shift (make_pair zero pred_zero) get_snd) ; where shift is (\p. p (\x y. make_pair (succ x) x)) in ; or ; from Oleg; observe that for any Church numeral n: n I ~~> I @@ -127,15 +127,15 @@ and all sorts of other places. Others of them are our own handiwork. ; more efficient comparisons, Oleg's gt provided some simplifications - let leq = (\base build consume. \m n. n consume (m build base) get_1st) + let leq = (\base build consume. \m n. n consume (m build base) get_fst) ; where base is (make_pair true junk) ; and build is (\p. make_pair false p) ; and consume is - (\p. p get_1st p (p get_2nd)) in + (\p. p get_fst p (p get_snd)) in let lt = \m n. not (leq n m) in - let eq = (\base build consume. \m n. n consume (m build base) get_1st) + let eq = (\base build consume. \m n. n consume (m build base) get_fst) ; 2nd element of a pair will now be of the form (K sthg) or I ; we supply the pair being consumed itself as an argument ; getting back either sthg or the pair we just consumed @@ -144,7 +144,7 @@ and all sorts of other places. Others of them are our own handiwork. ; and build is (\p. make_pair false (K p)) ; and consume is - (\p. p get_2nd p) in + (\p. p get_snd p) in ; -n is a fixedpoint of \x. add (add n x) x @@ -161,13 +161,13 @@ and all sorts of other places. Others of them are our own handiwork. (make_triple (succ cur) false (succ sofar)) ; continue )) in ; or - let sub = (\base build consume. \m n. n consume (m build base) get_1st) + let sub = (\base build consume. \m n. n consume (m build base) get_fst) ; where base is (make_pair zero I) ; see second defn of eq for explanation of 2nd element ; and build is (\p. p (\x y. make_pair (succ x) (K p))) ; and consume is - (\p. p get_2nd p) in + (\p. p get_snd p) in let min = \m n. sub m (sub m n) in @@ -208,8 +208,8 @@ and all sorts of other places. Others of them are our own handiwork. ; and mtail is (\dhead d. d (\dz mz df mf drest sel. drest dhead (sel (df dz) (mf mz)))) in - let div = \n d. divmod n d get_1st in - let mod = \n d. divmod n d get_2nd in + let div = \n d. divmod n d get_fst in + let mod = \n d. divmod n d get_snd in ; sqrt n is a fixedpoint of \x. div (div (add n (mul x x)) 2) x @@ -259,13 +259,13 @@ and all sorts of other places. Others of them are our own handiwork. + + +