; very inefficient but correct reverse
let reverse = \lst. lst (\h sofar. append sofar (singleton h)) empty in ; or
; 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))
+ ; 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
+ ; most elegant
+ ; revappend [a;b;c] [x;y] ~~> [c;b;a;x;y]
+ let revappend = \lst. lst (\hd sofar. \lst. sofar (make_list hd lst)) I in
+ let rev = \lst. revappend lst empty in
; 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
; now you can search for primes, do encryption :-)
- let gcd = Y (\gcd m n. iszero n m (gcd n (mod m n))) in
- let lcm = \m n. or (iszero m) (iszero n) 0 (mul (div m (gcd m n)) n) in
+ let gcd = Y (\gcd m n. iszero n m (gcd n (mod m n))) in ; or
+ let gcd = \m n. iszero m n (Y (\gcd m n. iszero n m (lt n m (gcd (sub m n) n) (gcd m (sub n m)))) m n) in
+ let lcm = \m n. or (iszero m) (iszero n) 0 (mul (div m (gcd m n)) n) in
; length for version 1 lists