Fenwick / Binary Indexed Tree for prefix sums. The classic
`i & -i` low-bit trick needs negative-aware AND, but our `land`
evaluator (iter 127, bitwise via floor/mod arithmetic) only handles
non-negative operands. Workaround: a portable lowbit helper that
finds the largest power of 2 dividing i:
let lowbit i =
let r = ref 1 in
while !r * 2 <= i && i mod (!r * 2) = 0 do
r := !r * 2
done;
!r
After building from [1;3;5;7;9;11;13;15]:
total = prefix_sum 8 = 64
update 1 by +100
after = prefix_sum 8 = 164
total + after = 228
Tests recursive update / prefix_sum chains via helper-extracted
lowbit; documents a non-obvious limit of the bitwise-emulation
layer.
168 baseline programs total.
Siamese construction for odd-order magic squares:
- place 1 at (0, n/2)
- for k = 2..n^2, move up-right with (x-1+n) mod n wrap
- if the target cell is taken, drop down one row instead
for n=5, magic constant = n*(n^2+1)/2 = 5*26/2 = 65
Returns the main-diagonal sum (65 by construction).
Tests 2D array via Array.init + Array.make, mod arithmetic with
the (x-1+n) mod n idiom for negative-safe wrap, nested begin/end
branches inside for-loop body.
166 baseline programs total.
Fibonacci via repeated-squaring matrix exponentiation:
[[1, 1], [1, 0]] ^ n = [[F(n+1), F(n)], [F(n), F(n-1)]]
Recursive O(log n) power:
let rec mpow m n =
if n = 0 then identity
else if n mod 2 = 0 then let h = mpow m (n / 2) in mul h h
else mul m (mpow m (n - 1))
Returns the .b cell after raising to the 30th power -> 832040 = F(30).
Tests record literal construction inside recursive function returns,
record field access (x.a etc), and pure integer arithmetic in the
matrix multiply.
165 baseline programs total.
Classic egg-drop puzzle DP:
dp[e][f] = 1 + min over k in [1, f] of
max(dp[e-1][k-1], dp[e][f-k])
For 2 eggs over 36 floors, the optimal worst-case is 8 trials
(closed form: triangular number bound).
Tests 2D DP with triple-nested for-loops, max-of-two via inline
if, large sentinel constant (100000000), mixed shifted indexing
(e-1) and (f-k) where both shift independently.
163 baseline programs total.
DFS topological sort — recurse on out-edges first, prepend after:
let rec dfs v =
if not visited.(v) then begin
visited.(v) <- true;
List.iter dfs adj.(v);
order := v :: !order
end
Same 6-node DAG as iter 230's Kahn's-algorithm baseline:
0 -> {1, 2}
1 -> {3}
2 -> {3, 4}
3 -> {5}
4 -> {5}
5
DFS order: [0; 2; 4; 1; 3; 5]
Horner fold: 0->0->2->24->241->2413->24135.
Complementary to topo_sort.ml (Kahn's BFS); tests recursive DFS
with no explicit stack + List.fold_left as a horner reduction.
160 baseline programs total.
LSD radix sort over base 10 digits. Per pass:
- 10 bucket-refs created via Array.init 10 (fun _ -> ref []) (each
closure call yields a distinct list cell)
- scan array, append each value to its digit's bucket
- flatten buckets back to the array in order
Input [170;45;75;90;802;24;2;66]
Output [2;24;45;66;75;90;170;802]
Sentinel: a.(0) + a.(7)*1000 = 2 + 802*1000 = 802002.
Tests array-of-refs with !buckets.(d) deref, list-mode bucket
sort within in-place array sort, unused for-loop var (`for _ =
1 to maxd`).
159 baseline programs total.
Minimum-coin DP with -1 sentinel for unreachable values:
let coin_min coins amount =
let dp = Array.make (amount + 1) (-1) in
dp.(0) <- 0;
for i = 1 to amount do
List.iter (fun c ->
if c <= i && dp.(i - c) >= 0 then begin
let cand = dp.(i - c) + 1 in
if dp.(i) < 0 || cand < dp.(i) then dp.(i) <- cand
end
) coins
done;
dp.(amount)
coin_min [1; 5; 10; 25] 67 = 6 (* 25+25+10+5+1+1 *)
Tests `if c <= i && dp.(i-c) >= 0 then` short-circuit guard;
relies on iter-242 fix so dp.(i-c) is not evaluated when c > i.
158 baseline programs total.
Recursive 4-way flood fill from every unvisited 1-cell:
let rec flood visited r c =
if r < 0 || r >= h || c < 0 || c >= w then 0
else if visited.(r).(c) || grid.(r).(c) = 0 then 0
else begin
visited.(r).(c) <- true;
1 + flood visited (r - 1) c
+ flood visited (r + 1) c
+ flood visited r (c - 1)
+ flood visited r (c + 1)
end
Grid (1s shown as #, 0s as .):
# # . # #
# . . . #
. . # . .
# # # # .
. . . # #
Largest component: {(2,2),(3,0),(3,1),(3,2),(3,3),(4,3),(4,4)} = 7.
Bounds check r >= 0 must short-circuit before visited/grid reads;
relies on the && / || fix from iter 242.
157 baseline programs total.
Standard in-place next-permutation (Narayana's algorithm):
let next_perm a =
let n = Array.length a in
let i = ref (n - 2) in
while !i >= 0 && a.(!i) >= a.(!i + 1) do i := !i - 1 done;
if !i < 0 then false
else begin
let j = ref (n - 1) in
while a.(!j) <= a.(!i) do j := !j - 1 done;
swap a.(!i) a.(!j);
reverse a (!i + 1) (n - 1);
true
end
Starting from [1;2;3;4;5], next_perm returns true 119 times then
false (when reverse-sorted). 5! - 1 = 119.
Tests guarded `while … && a.(!i) … do` loops that rely on the
iter-242 short-circuit fix.
156 baseline programs total.
Before: `:op` handler always evaluated both operands before dispatching
to ocaml-eval-op. For pure binops that's fine, but `&&` / `||` MUST
short-circuit:
if nr >= 0 && grid.(nr).(nc) = 0 then ...
When nr = -1, real OCaml never evaluates `grid.(-1)`. Our evaluator
did, and crashed with "nth: list/string and number".
Fix: special-case `&&` and `||` in :op dispatch, mirroring the same
pattern already used for `:=` and `<-`. Evaluate lhs, branch on it,
and only evaluate rhs when needed.
Latent since baseline 1 — earlier programs never triggered it because
the rhs was unconditionally safe.
bfs_grid.ml: shortest path through a 5x5 grid with walls. Standard
BFS using Queue.{push,pop,is_empty} + Array.init for the 2D distance
matrix. Path 0,0 -> ... -> 4,4 has length 8. 155 baseline programs
total.
Bug: characters not recognised by any branch of `scan!` (`?`,
`!`, `#`, `@`, `&`, `|`, `\\`, `^`, etc.) were silently consumed
via `(else (advance! 1) (scan!))`. Programs with typos would
parse to a stripped version of themselves with no warning —
`?(X).` became `(X).` and produced confusing downstream errors.
Fix: the else branch now raises a clear "unexpected character"
error with the offending char and its position.
1 new tokenize test.
Bug: dl-magic-query crashed with cryptic "rest: 1 list arg" when
the goal argument was a string, number, or arbitrary dict. The
first thing the function does is dl-rel-name + dl-adorn-goal,
both of which assume a positive-literal list shape.
Fix: explicit shape check up front. A goal must be a non-empty
list whose first element is a symbol. Otherwise raise with a
clear diagnostic. Built-in / aggregate / negation dispatch (the
fall-back to dl-query) is unchanged.
2 new magic tests cover string and bare-dict goal rejection.
Two malformed-rule paths used to slip through:
- Empty head list `{:head () :body ()}` was accepted; the rule
would never fire but the relation-name lookup later returned
nil with confusing downstream errors.
- Non-list body (`{:head (...) :body 42}`) crashed in `rest`
during safety check with a cryptic "rest: 1 list arg".
dl-add-rule! now checks head shape (non-empty list with symbol
head) and body type (list) before any safety walk. Errors are
descriptive and surface at add time rather than during the next
saturation.
2 new eval tests.
Bug: read-quoted ran to EOF silently when the closing quote was
missing. The token's value was whatever ran-to-end string had been
accumulated; the parser later saw an unexpected EOF, but the error
message blamed the wrong location ("expected `)` got eof") and
hid the real problem.
Fix: read-quoted now raises with a message that distinguishes
strings from quoted atoms, including the position where the
opening quote was lost. The escape-sequence handling and proper
closing are unaffected.
2 new tokenize tests.
Bug: `/* unclosed` was silently consumed to EOF, swallowing any
Datalog code that followed inside the (never-closing) comment.
Programs would produce empty parses with no error.
Fix: skip-block-comment! now raises when it hits EOF without
finding `*/`. Error message includes the position where the
problem was first detected. Line comments (`%`) and properly
closed block comments (`/* ... */`) are unaffected.
1 new tokenize test verifies the error path.
Bug: `n(-1).` failed to parse — the tokenizer produced op `-`
followed by number `1`, and dl-pp-parse-arg expected a term after
seeing `-` as an op (and a `(` for a compound) but found a bare
number. Users had to write `(- 0 1)` or compute via `is`.
Fix: dl-pp-parse-arg detects op `-` directly followed by a number
token (no intervening `(`) and consumes both as a single negative
number literal. Subtraction (`is(Y, -(X, 2))`) and compound
arithmetic via the operator form are unaffected — they use the
`-(` lookahead path.
2 new parser tests: negative integer literal and subtraction
compound preserved.
Real bugs surfaced by parser/safety bug-hunt round:
- `not(X) :- p(X).` parsed as a regular literal with relation
"not". The user could accidentally define a `not` relation,
silently shadowing the negation construct.
- `count(N, X, p(X)) :- ...` defined a `count` relation that
would conflict with the aggregate operator.
- `<(X, 5) :- p(X).` defined a `<` relation.
- `is(N, +(1, 2)) :- p(N).` defined an `is` relation.
- `+.` (operator alone) parsed as a 0-ary fact.
Fix: dl-add-fact! and dl-add-rule! now reject any literal whose
head's relation name is in dl-reserved-rel-names — built-in
operators (< <= > >= = != + - * /), aggregate operators
(count sum min max findall), `is`, `not`, and the arrows
(:-, ?-).
4 new eval tests cover the rejection cases.
Note: an initial "no compound args in facts" check was overly
strict — it would reject findall's list output (which derives a
fact like (all_p (a b c))). Reverted that branch; treating
findall results as opaque list values rather than function
symbols.
kernel-eval/kernel-combine dispatch on tagged values: operatives see
un-evaluated args + dynamic env; applicatives evaluate args then recurse.
No hardcoded special forms — $if/$quote tested as ordinary operatives
built on the fly. Pure-SX env representation
{:knl-tag :env :bindings DICT :parent P}, surfaced as a candidate
lib/guest/reflective/env.sx API since SX make-env is HTTP-mode only.
hk-collect-module-body previously ran a fixed import-loop at the start
and then a separate decl-loop; merged into a single hk-body-step
dispatcher that routes `import` to the imports list and everything else
to hk-parse-decl. Both call sites (initial step + post-semicolon loop)
use the dispatcher. The eval side reads imports as a list (not by AST
position) so mid-stream imports feed into hk-bind-decls! unchanged.
tests/parse-extras.sx 12 → 17: very-top, mid-stream, post-main,
two-imports-different-positions, unqualified-mid-file. Regression
sweep clean: eval 66/0, exceptions 14/0, typecheck 15/0, records 14/0,
ioref 13/0, map 26/0, set 17/0.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Iterative Levenshtein DP with rolling 1D arrays for O(min(m,n))
space. Distances:
kitten -> sitting : 3
saturday -> sunday : 3
abc -> abc : 0
"" -> abcde : 5
intention -> execution : 5
----------------------------
total : 16
Complementary to the existing levenshtein.ml which uses the
exponential recursive form (only sums tiny strings); this one is
the practical iterative variant used for real ED.
Tests the recently-fixed <- with bare `if` rhs:
curr.(j) <- (if m1 < c then m1 else c) + 1
153 baseline programs total.
Array-backed binary min-heap with explicit size tracking via ref:
let push a size x =
a.(!size) <- x; size := !size + 1; sift_up a (!size - 1)
let pop a size =
let m = a.(0) in
size := !size - 1;
a.(0) <- a.(!size);
sift_down a !size 0;
m
Push [9;4;7;1;8;3;5;2;6], pop nine times -> 1,2,3,4,5,6,7,8,9.
Fold-as-decimal: ((((((((1*10+2)*10+3)*10+4)*10+5)*10+6)*10+7)*10+8)*10+9 = 123456789.
Tests recursive sift_up + sift_down, in-place array swap,
parent/lchild/rchild index arithmetic, combined push/pop session
with refs.
152 baseline programs total.
Polynomial rolling hash mod 1000003 with base 257:
- precompute base^(m-1)
- slide window updating hash in O(1) per step
- verify hash match with O(m) memcmp to skip false positives
rolling_match "abcabcabcabcabcabc" "abc" = 6
Six non-overlapping copies of "abc" at positions 0,3,6,9,12,15.
Tests `for _ = 0 to m - 2 do … done` unused loop variable
(uses underscore wildcard pattern), Char.code arithmetic, mod
arithmetic with intermediate negative subtractions, complex nested
if/begin branching with inner break-via-flag.
151 baseline programs total.
Classic CLRS Huffman code example. ADT:
type tree = Leaf of int * char | Node of int * tree * tree
Build by repeatedly merging two lightest trees (sorted-list pq):
let rec build_tree lst = match lst with
| [t] -> t
| a :: b :: rest ->
let merged = Node (weight a + weight b, a, b) in
build_tree (insert merged rest)
weighted path length (= total Huffman bits):
leaves {(5,a) (9,b) (12,c) (13,d) (16,e) (45,f)} -> 224
Tests sum-typed ADT with mixed arities, `function` keyword
pattern matching, recursive sorted insert, depth-counting recursion.
150 baseline programs total.
Previously `a.(i) <- if c then x else y` failed with
"unexpected token keyword if" because parse-binop-rhs called
parse-prefix for the rhs, which doesn't accept if/match/let/fun.
Real OCaml allows full expressions on the rhs of <-/:=. Fix:
special-case prec-1 ops in parse-binop-rhs to call parse-expr-no-seq
instead of parse-prefix. The recursive parse-binop-rhs with
min-prec restored after picks up any further chained <- (since both
ops are right-associative with no higher-prec binops above them).
Manacher baseline updated to use bare `if` on rhs of <-,
removing the parens workaround from iter 235. 607/607 regressions
remain clean.
Manacher's algorithm: insert # separators (length 2n+1) to unify
odd/even cases, then maintain palindrome radii p[] alongside a
running (center, right) pair to skip work via mirror reflection.
Linear time.
manacher "babadaba" = 7 (* witness: "abadaba", positions 1..7 *)
Note: requires parenthesizing the if-expression on the rhs of <-:
p.(i) <- (if pm < v then pm else v)
Real OCaml parses bare `if` at <-rhs since the rhs is at expr
level; our parser places <-rhs at binop level which doesn't include
`if` / `match` / `let`. Workaround until we relax the binop
RHS grammar.
149 baseline programs total.
