swarm-0.1.0.0: example/list.sw
/*******************************************************************/
/* LIST ENCODING IN INT */
/* */
/* This file defines functions that allow storing arbitrary list */
/* of values in one integer. It is possible because an integer can */
/* have unlimited length and can be split into chunks of smaller */
/* integers. See Haskell docs for Integer (used by swarm for int). */
/* */
/* For examples of usage see the unit tests in testLIST function. */
/* */
/*******************************************************************/
// Definitions:
// - MAIN: nil (Haskell []), cons (Haskell (:)), head, tail
// - BONUS: headTail, index, for, for_each, for_each_i
// - ARITH: len, mod, shiftL, shiftR, shiftLH, shiftRH
// - HELPERS: consP, getLenPart, setLenPart, to1numA, getLenA
// - TESTS: assert, testLIST, testLIST_BIG, testLIST_ALL
/*******************************************************************/
/* TYPE */
/*******************************************************************/
// Type of list of ints - the inner ints can themselves be lists,
// so *any* type can be encoded inside.
//
// It is the callers responsibility to make sure a program using this
// "type" is type safe. Notably 2 == [0] != [] == 0 but [] !! x == 0.
//
// TODO: once #153 is resolved, add types to definitions
//
// type listI = int
/*******************************************************************/
/* LAYOUT */
/*******************************************************************/
// The length of a number is kept in the header and split into 7bit
// chunks each prefixed by 1bit that marks if the byte is last in
// the header (0=YES).
/* EXAMPLE - [short_x,long_y] - concretly e.g. [42, 2^(2^7)]
0 < len short_x < 2^7
2^7 < len long_y < 2^14
cons short_x $ cons long_y $ nil
vvvvvvvvvvvv vvvvvvvvvvvvvvvvvvvvvvvvv vvv
0|len x|x | 1|len y%2^7|0|len y/2^7|y | 0
^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
head tail
*/
/*******************************************************************/
/* ARITH PRIMITIVES */
/*******************************************************************/
// bitlength of a number (shifting by one)
def naive_len : int -> int = \i.
if (i == 0) {0} {1 + naive_len (i/2)}
end
// modulus function (%)
def mod : int -> int -> int = \i.\m.
i - m * (i / m)
end
// f X Y = Y * 2^(-X)
def shiftL : int -> int -> int = \s.\i.
i / 2^s
end
// f X Y = Y * 2^(X)
def shiftR : int -> int -> int = \s.\i.
i * 2^s
end
// shift by (8bit) bytes
def shiftLH : int -> int -> int = \s. shiftL (s*8) end
def shiftRH : int -> int -> int = \s. shiftR (s*8) end
// bitlength of a number (shifting by 64)
def len : int -> int = \i.
let next = i / 2^64 in
if (next == 0) {naive_len i} {64 + len next}
end
/*******************************************************************/
/* helper functions */
/*******************************************************************/
def getLenPart : int -> int = \i. mod (i/2) (2^7) end
def setLenPart : int -> int = \i. 2 * (mod i (2^7)) end
// Split length into 7-bit parts and prefix all but last with 1
def to1numA : int -> int * int = \i.
let nextPart = shiftL 7 i in
if (nextPart == 0)
{ ((2 * i), 1) } /* last part */
{ let p = to1numA nextPart in
( 1 /* header isEnd bit */ + setLenPart i + shiftRH 1 (fst p)
, 1 + snd p
)
}
end
// Get bitlength of the first number in the list
// and also the list starting at the number itself
//
// getLenA : listI -> int * int
def getLenA = \xs.
let isEnd = 0 == mod xs 2 in
let l = getLenPart xs in
let nextPart = shiftLH 1 xs in
if isEnd
{ (l, nextPart) }
{ let p = getLenA nextPart in
(l + shiftR 7 (fst p), snd p)
}
end
/*******************************************************************/
/* LIST FUNCTIONS */
/*******************************************************************/
// headTail : listI -> {int} * {listI}
def headTail = \xs.
let sign = mod xs 2 in
let ns = xs / 2 in
let p = getLenA ns in
( { let x = mod (snd p) $ 2 ^ fst p in
if (sign == 0) {x} {-x}
}
, { shiftL (fst p) (snd p) }
)
end
// head : listI -> int
def head : int -> int = \xs.
force $ fst $ headTail xs
end
// tail : listI -> listI
def tail = \xs.
force $ snd $ headTail xs
end
// nil : listI
def nil = 0 end
// Add non-negative number to beggining of list (cons adds the sign)
// consP : nat -> listI -> int
def consP = \x.\xs.
if (x == 0)
{ 2 /* header says one bit length */ + shiftR (8+1) xs}
{ let l = len x in
let pl = to1numA l in
(fst pl + shiftRH (snd pl) (x + shiftR l xs))
}
end
// Add integer to the beggining of the list
// consP : int -> listI -> listI
def cons = \x.\xs.
if (x >= 0)
{ 2 * consP x xs }
{ 1 + 2 * consP (-x) xs }
end
/*******************************************************************/
/* MORE LIST FUNCTIONS */
/*******************************************************************/
// index : int -> listI -> int
def index = \i.\xs.
if (i <= 0)
{head xs}
{index (i-1) (tail xs)}
end
def for : int -> int -> (int -> cmd a) -> cmd unit = \s.\e.\act.
if (s == e) {}
{act s; for (s+1) e act}
end
// for_each_i : int -> listI int -> (int * int -> cmd a) -> cmd unit
def for_each_i = \i.\xs.\act.
if (xs == nil) {}
{ let ht = headTail xs
in act i (force $ fst ht); for_each_i (i+1) (force $ snd ht) act
}
end
// for_each : listI int -> (int -> cmd a) -> cmd unit
def for_each = \xs.\act.
for_each_i 0 xs (\i. act)
end
/*******************************************************************/
/* UNIT TESTS */
/*******************************************************************/
// TODO: show values when #248 is implemented
def assert = \b.\m.
if b {} {log "FAIL:"; fail m}
end
def testLIST =
log "STARTING TESTS OF LIST:";
log "check [0]";
let l0 = cons 0 nil in
assert (l0 == 4) "[0] ~ 4";
assert (head l0 == 0) "head [0] == 0";
assert (tail l0 == nil) "tail [0] == []";
log "check [1]";
let l1 = cons 1 nil in
assert (l1 == 516) "[1] ~ 516";
assert (head l1 == 1) "head [1] == 1";
assert (tail l1 == nil) "tail [1] == []";
log "check [-1]";
let ln1 = cons (-1) nil in
assert (ln1 == 517) "[-1] ~ 517";
assert (head ln1 == -1) "head [-1] == -1";
assert (tail ln1 == nil) "tail [-1] == []";
log "check [42]";
let l42 = cons 42 nil in
assert (l42 == 21528) "[42] ~ 21528";
assert (head l42 == 42) "head [42] == 42";
assert (tail l42 == nil) "tail [42] == []";
log "check [499672]";
let l499672 = cons 499672 nil in
assert (l499672 == 255832140) "[499672] ~ 255832140";
assert (head l499672 == 499672) "head [499672] == 499672";
assert (tail l499672 == nil) "tail [499672] == []";
log "check [1,0]";
let l1_0 = cons 1 l0 in
assert (l1_0 == 4612) "[1,0] ~ 4612";
assert (head l1_0 == 1) "head [1,0] == 1";
assert (tail l1_0 == l0) "tail [1,0] == [0]";
log "check [11,1,0]";
let l11_1_0 = cons 11 l1_0 in
assert (head l11_1_0 == 11) "head [11,1,0] == 11";
assert (tail l11_1_0 == l1_0) "tail [11,1,0] == [1,0]";
log "check [0..9]";
let l0__9 = cons 0 $ cons 1 $ cons 2 $ cons 3 $ cons 4 $ cons 5 $ cons 6 $ cons 7 $ cons 8 $ cons 9 nil in
assert (head l0__9 == 0) "head [0..9] == 0";
log "check indices";
assert (index 0 l0__9 == 0) "[0..9] !! 0 == 0";
assert (index 9 l0__9 == 9) "[0..9] !! 9 == 9";
// TODO: log the number of iteration once #248 is implemented
log "check for";
for 0 9 (\i.
assert (index i l0__9 == i) "[0..9] - every index I has value I"
);
log "check for_each";
for_each l0__9 (\x.
assert (x < 10) "[0..9] - every value X < 10"
);
log "check for_each_i";
for_each_i 0 l0__9 (\i.\x.
assert (i == x) "[0..9] - I == X for every value X at index I"
);
log "OK - ALL TEST PASSED\a"
end
// This tests uses VERY LONG lists of size up to 2097332 bits.
// TIP: increase the game speed (ticks/s) when you run this test.
def testLIST_BIG =
log "STARTING TESTS OF BIG LISTS:";
log "check [2^(2^7)] aka [big]";
let big = 2^2^7 in
assert (len big == 129) "len (2^2^7) == 2^7+1";
assert (to1numA 129 == (515,2)) "to1numA: 129 == 1000_0001 --> 515 == [0000 001 0] [0000 001 1]";
assert (getLenA 515 == (129,nil)) "getLenA: 515 --> 129";
let ibig = 2 * (shiftR 16 big + 515) in
let lbig = cons big nil in
assert (lbig == ibig) "[big] ~ 2 * ((big * 2^(2*8)) + 515)";
assert (head lbig == big) "head [big] == big";
assert (tail lbig == nil) "tail [big] == []";
log "check [2^(2^21)] aka [bigger]";
let bigger = 2^(2^21) in
let lbigger = cons bigger nil in
assert (head lbigger == bigger) "head [bigger] == bigger";
assert (tail lbigger == nil) "tail [bigger] == []";
log "check [2^(2^21),2^(2^7)] aka [bigger,big]";
let lbiggest = cons bigger lbig in
assert (head lbiggest == bigger) "head [bigger,big] == bigger";
assert (tail lbiggest == lbig) "tail [bigger,big] == [big]";
log "OK - ALL TEST PASSED";
end
def testLIST_ALL =
testLIST;
testLIST_BIG;
end