zip walks both lists in lockstep, truncating at the shorter. unzip
uses tuple-pattern destructuring on the recursive result.
let pairs = zip [1;2;3;4] [10;20;30;40] in
let (xs, ys) = unzip pairs in
List.fold_left (+) 0 xs * List.fold_left (+) 0 ys
= 10 * 100
= 1000
Exercises:
- tuple-cons patterns in match scrutinee: 'match (xs, ys) with'
- tuple constructor in return value: '(a :: la, b :: lb)'
- the iter-98 let-tuple destructuring: 'let (la, lb) = unzip rest'
53 baseline programs total.
Recursive 4-arm match on (a, b) tuples threading a carry:
match (a, b) with
| ([], []) -> if carry = 0 then [] else [carry]
| (x :: xs, []) -> (s mod 10) :: aux xs [] (s / 10) where s = x + carry
| ([], y :: ys) -> ...
| (x :: xs, y :: ys) -> ... where s = x + y + carry
Little-endian digit lists. Three tests:
[9;9;9] + [1] = [0;0;0;1] (=1000, digit sum 1)
[5;6;7] + [8;9;1] = [3;6;9] (=963, digit sum 18)
[9;9;9;9;9;9;9;9] + [1] length 9 (carry propagates 8x)
Sum = 1 + 18 + 9 = 28.
Exercises tuple-pattern match on nested list-cons with the integer
arithmetic and carry-threading idiom typical of multi-precision
implementations.
52 baseline programs total.
Recursive ADT with three constructors (Num/Add/Mul). simp does
bottom-up rewrite using algebraic identities:
x + 0 -> x
0 + x -> x
x * 0 -> 0
0 * x -> 0
x * 1 -> x
1 * x -> x
constant folding for Num + Num and Num * Num
Uses tuple pattern in nested match: 'match (simp a, simp b) with'.
Add (Mul (Num 3, Num 5), Add (Num 0, Mul (Num 1, Num 7)))
-> simp -> Add (Num 15, Num 7)
-> eval -> 22
51 baseline programs total.
Triple-nested for loop with row-major indexing:
for i = 0 to n - 1 do
for j = 0 to n - 1 do
for k = 0 to n - 1 do
c.(i * n + j) <- c.(i * n + j) + a.(i * n + k) * b.(k * n + j)
done
done
done
For 3x3 matrices A=[[1..9]] and B=[[9..1]], the resulting C has sum
621. Tests deeply nested for loops on Array, Array.make + arr.(i) +
arr.(i) <- v + Array.fold_left.
50 baseline programs total — milestone.
Iterative binary search on a sorted int array:
let bsearch arr target =
let n = Array.length arr in
let lo = ref 0 and hi = ref (n - 1) in
let found = ref (-1) in
while !lo <= !hi && !found = -1 do
let mid = (!lo + !hi) / 2 in
if arr.(mid) = target then found := mid
else if arr.(mid) < target then lo := mid + 1
else hi := mid - 1
done;
!found
For [1;3;5;7;9;11;13;15;17;19;21]:
bsearch a 13 = 6
bsearch a 5 = 2
bsearch a 100 = -1
sum = 7
Exercises Array.of_list + arr.(i) + multi-let 'let lo = ... and
hi = ...' + while + multi-arm if/else if/else.
49 baseline programs total.
Two-pointer palindrome check:
let is_palindrome s =
let n = String.length s in
let rec check i j =
if i >= j then true
else if s.[i] <> s.[j] then false
else check (i + 1) (j - 1)
in
check 0 (n - 1)
Tests on six strings:
racecar = true
hello = false
abba = true
'' = true (vacuously, i >= j on entry)
'a' = true
'ab' = false
Sum = 4.
Uses s.[i] <> s.[j] (string-get + structural inequality), recursive
2-arg pointer advancement, and a multi-clause if/else if/else for
the three cases.
48 baseline programs total.
Bottom-up dynamic programming. dp[i] = minimum coins to make
amount i.
let dp = Array.make (target + 1) (target + 1) in (* sentinel *)
dp.(0) <- 0;
for i = 1 to target do
List.iter (fun c ->
if c <= i && dp.(i - c) + 1 < dp.(i) then
dp.(i) <- dp.(i - c) + 1
) coins
done
Sentinel 'target + 1' means impossible — any real solution uses at
most 'target' coins.
coin_change [1; 5; 10; 25] 67 = 6 (= 25+25+10+5+1+1)
Exercises Array.make + arr.(i) + arr.(i) <- v + nested
for/List.iter + guard 'c <= i'.
47 baseline programs total.
Kadane's algorithm in O(n):
let max_subarray xs =
let max_so_far = ref min_int in
let cur = ref 0 in
List.iter (fun x ->
cur := max x (!cur + x);
max_so_far := max !max_so_far !cur
) xs;
!max_so_far
For [-2;1;-3;4;-1;2;1;-5;4] the optimal subarray is [4;-1;2;1] = 6.
Exercises min_int (iter 94), max as global, ref / ! / :=, and
List.iter with two side-effecting steps in one closure body.
46 baseline programs total.
next_row prepends 1, walks adjacent pairs (x, y) emitting x+y,
appends a final 1:
let rec next_row prev =
let rec aux a =
match a with
| [_] -> [1]
| x :: y :: rest -> (x + y) :: aux (y :: rest)
| [] -> []
in
1 :: aux prev
row n iterates next_row n times starting from [1] using a ref +
'for _ = 1 to n do r := next_row !r done'.
row 10 = [1;10;45;120;210;252;210;120;45;10;1]
List.nth (row 10) 5 = 252 = C(10, 5)
Exercises three-arm match including [_] singleton wildcard, x :: y
:: rest binding, and the for-loop with wildcard counter. 45 baseline
programs total.
Run-length encoding via tail-recursive 4-arg accumulator:
let rle xs =
let rec aux xs cur n acc =
match xs with
| [] -> List.rev ((cur, n) :: acc)
| h :: t ->
if h = cur then aux t cur (n + 1) acc
else aux t h 1 ((cur, n) :: acc)
in
match xs with
| [] -> []
| h :: t -> aux t h 1 []
rle [1;1;1;2;2;3;3;3;3;1;1] = [(1,3);(2,2);(3,4);(1,2)]
sum of counts = 11 (matches input length)
The sum-of-counts test verifies that the encoding preserves total
length — drops or duplicates would diverge.
44 baseline programs total.
Defines a recursive str_contains that walks the haystack with
String.sub to find a needle substring. Real OCaml's String.contains
only accepts a single char, so this baseline implements its own
substring search to stay portable.
let rec str_contains s sub i =
if i + sl > nl then false
else if String.sub s i sl = sub then true
else str_contains s sub (i + 1)
count_matching splits text on newlines, folds with the predicate.
'the quick brown fox\nfox runs fast\nthe dog\nfoxes are clever'
needle = 'fox'
matches = 3 (lines 1, 2, 4 — 'foxes' contains 'fox')
43 baseline programs total.
The binop precedence table already had land/lor/lxor/lsl/lsr/asr
(iter 0 setup) but eval-op fell through to 'unknown operator' for
all of them. SX doesn't expose host bitwise primitives, so each is
implemented in eval.sx via arithmetic on the host:
land/lor/lxor: mask & shift loop, accumulating 1<<k digits
lsl k: repeated * 2 k times
lsr k: repeated floor (/ 2) k times
asr: aliased to lsr (no sign extension at our bit width)
bits.ml baseline: popcount via 'while m > 0 do if m land 1 = 1 then
... ; m := m lsr 1 done'. Sum of popcount(1023, 5, 1024, 0xff) = 10
+ 2 + 1 + 8 = 21.
5 land 3 = 1
5 lor 3 = 7
5 lxor 3 = 6
1 lsl 8 = 256
256 lsr 4 = 16
41 baseline programs total.
Classic Ackermann function:
let rec ack m n =
if m = 0 then n + 1
else if n = 0 then ack (m - 1) 1
else ack (m - 1) (ack m (n - 1))
ack(3, 4) = 125, expanding to ~6700 evaluator frames — a useful
stress test of the call stack and control transfer. Real OCaml
evaluates this in milliseconds; ours takes ~2 minutes on a
contended host but completes correctly.
40 baseline programs total.
Stack-based RPN evaluator:
let eval_rpn tokens =
let stack = Stack.create () in
List.iter (fun tok ->
if tok is operator then
let b = Stack.pop stack in
let a = Stack.pop stack in
Stack.push (apply tok a b) stack
else
Stack.push (int_of_string tok) stack
) tokens;
Stack.pop stack
For tokens [3 4 + 2 * 5 -]:
3 4 + -> 7
7 2 * -> 14
14 5 - -> 9
Exercises Stack.create / push / pop, mixed branch on string
equality, multi-arm if/else if for operator dispatch, int_of_string
for token parsing.
39 baseline programs total.
Newton's method for square root:
let sqrt_newton x =
let g = ref 1.0 in
for _ = 1 to 20 do
g := (!g +. x /. !g) /. 2.0
done;
!g
20 iterations is more than enough to converge for x=2 — result is
~1.414213562. Multiplied by 1000 and int_of_float'd: 1414.
First baseline exercising:
- for _ = 1 to N do ... done (wildcard loop variable)
- pure float arithmetic with +. /.
- the int_of_float truncate-toward-zero fix from iter 117
38 baseline programs total.
Classic doubly-recursive solution returning the move count:
hanoi n from to via =
if n = 0 then 0
else hanoi (n-1) from via to + 1 + hanoi (n-1) via to from
For n = 10, returns 2^10 - 1 = 1023.
Exercises 4-arg recursion, conditional base case, and tail-position
addition. Uses 'to_' instead of 'to' for the destination param to
avoid collision with the 'to' keyword in for-loops — the OCaml
conventional workaround.
37 baseline programs total.
validate_int returns Left msg on empty / non-digit, Right
(int_of_string s) on a digit-only string. process folds inputs with a
tuple accumulator (errs, sum), branching on the result.
['12'; 'abc'; '5'; ''; '100'; 'x']
-> 3 errors (abc, '', x), valid sum = 12+5+100 = 117
-> errs * 100 + sum = 417
Exercises:
- Either constructors used bare (Left/Right without 'Either.'
qualification)
- char range comparison: c >= '0' && c <= '9'
- tuple-pattern destructuring on let-binding (iter 98)
- recursive helper defined inside if-else
- List.fold_left with tuple accumulator
36 baseline programs total.
First baseline using Map.Make on a string-keyed map:
module StringOrd = struct
type t = string
let compare = String.compare
end
module SMap = Map.Make (StringOrd)
let count_words text =
let words = String.split_on_char ' ' text in
List.fold_left (fun m w ->
let n = match SMap.find_opt w m with
| Some n -> n
| None -> 0
in
SMap.add w (n + 1) m
) SMap.empty words
For 'the quick brown fox jumps over the lazy dog' ('the' appears
twice), SMap.cardinal -> 8.
Complements bag.ml (Hashtbl-based) and unique_set.ml (Set.Make)
with a sorted Map view of the same kind of counting problem. 35
baseline programs total.
Defines a JSON-like algebraic data type:
type json =
| JNull
| JBool of bool
| JInt of int
| JStr of string
| JList of json list
Recursively serialises to a string via match-on-constructor, then
measures the length:
JList [JInt 1; JBool true; JNull; JStr 'hi'; JList [JInt 2; JInt 3]]
-> '[1,true,null,"hi",[2,3]]' length 24
Exercises:
- five-constructor ADT (one nullary, three single-arg, one list-arg)
- recursive match
- String.concat ',' (List.map to_string xs)
- string-cat with embedded escaped quotes
34 baseline programs total.
In-place Fisher-Yates shuffle using:
Random.init 42 deterministic seed
let a = Array.of_list xs
for i = n - 1 downto 1 do reverse iteration
let j = Random.int (i + 1)
let tmp = a.(i) in
a.(i) <- a.(j);
a.(j) <- tmp
done
Sum is invariant under permutation, so the test value (55 for
[1..10] = 1+2+...+10) verifies the shuffle is a valid permutation
regardless of which permutation the seed yields.
Exercises Random.init / Random.int + Array.of_list / to_list /
length / arr.(i) / arr.(i) <- v + downto loop + multi-statement
sequencing within for-body.
33 baseline programs total.
pi_leibniz.ml: Leibniz formula for pi.
pi/4 = 1 - 1/3 + 1/5 - 1/7 + ...
pi ~= 4 * sum_{k=0}^{n-1} (-1)^k / (2k+1)
For n=1000, pi ~= 3.140593. Multiply by 100 and int_of_float -> 314.
Side-quest: int_of_float was wrongly defined as identity in
iteration 94. Fixed to:
let int_of_float f =
if f < 0.0 then _float_ceil f else _float_floor f
(truncate toward zero, mirroring real OCaml's int_of_float). The
identity definition was a stub from when integer/float dispatch was
not yet split — now they're separate, the stub is wrong.
Float.to_int still uses floor since OCaml's docs say the result is
unspecified for nan / out-of-range; close enough for our scope.
32 baseline programs total.
bag.ml: split a sentence on spaces, count each word in a Hashtbl,
return the maximum count via Hashtbl.fold.
count_words 'the quick brown fox jumps over the lazy dog the fox'
-> Hashtbl with 'the' = 3 as the max
-> 3
Exercises String.split_on_char + Hashtbl.find_opt/replace +
Hashtbl.fold (k v acc -> ...). Together with frequency.ml from
iter 84 we now have two Hashtbl-counting baselines exercising
slightly different idioms. 29 baseline programs total.
String additions:
equal a b = a = b
compare a b = -1 / 0 / 1 via host < / >
cat a b = a ^ b
empty = '' (constant)
Defines:
type frac = { num : int; den : int }
let rec gcd a b = if b = 0 then a else gcd b (a mod b)
let make n d = (* canonicalise: gcd-reduce and
force den > 0 *)
let add x y = make (x.num * y.den + y.num * x.den) (x.den * y.den)
let mul x y = make (x.num * y.num) (x.den * y.den)
Test:
let r = add (make 1 2) (make 1 3) in (* 5/6 *)
let s = mul (make 2 3) (make 3 4) in (* 1/2 *)
let t = add r s in (* 5/6 + 1/2 = 4/3 *)
t.num + t.den (* = 7 *)
Exercises records, recursive gcd, mod, abs, integer division (the
truncate-toward-zero semantics from iter 94 are essential here —
make would diverge from real OCaml's behaviour with float division).
28 baseline programs total.
First baseline that exercises the functor pipeline end to end:
module IntOrd = struct
type t = int
let compare a b = a - b
end
module IntSet = Set.Make (IntOrd)
let unique_count xs =
let s = List.fold_left (fun s x -> IntSet.add x s) IntSet.empty xs in
IntSet.cardinal s
Counts unique elements in [3;1;4;1;5;9;2;6;5;3;5;8;9;7;9]:
{1,2,3,4,5,6,7,8,9} -> 9
The input has 15 elements with 9 unique values. The 'type t = int'
declaration in IntOrd is required by real OCaml; OCaml-on-SX is
dynamic and would accept it without, but we include it for source
fidelity. 27 baseline programs total.
User-implemented mergesort that exercises features added across the
last few iterations:
let rec split lst = match lst with
| x :: y :: rest ->
let (a, b) = split rest in (* iter 98 let-tuple destruct *)
(x :: a, y :: b)
| ...
let rec merge xs ys = match xs with
| x :: xs' ->
match ys with (* nested match-in-match *)
| y :: ys' -> ...
...
List.fold_left (+) 0 (sort [...]) (* iter 89 (op) section *)
Sum of [3;1;4;1;5;9;2;6;5;3;5] = 44 regardless of order, so the
result is also a smoke test of the implementation correctness — if
merge_sort drops or duplicates an element the sum diverges. 26
baseline programs total.
Five '+++++.' groups, cumulative accumulator 5+10+15+20+25 = 75.
This is a brainfuck *subset* — only > < + - . (no [ ] looping). That's
intentional: the goal is to stress imperative idioms that the recently
added Array module + array indexing syntax + s.[i] make ergonomic, all
in one program.
Exercises:
Array.make 256 0
arr.(!ptr)
arr.(!ptr) <- arr.(!ptr) + 1
prog.[!pc]
ref / ! / :=
while + nested if/else if/else if for op dispatch
25 baseline programs total.
Counts primes <= 50, expected 15.
Stresses the recently-added Array module + the new array-indexing
syntax together with nested control flow:
let sieve = Array.make (n + 1) true in
sieve.(0) <- false;
sieve.(1) <- false;
for i = 2 to n do
if sieve.(i) then begin
let j = ref (i * i) in
while !j <= n do
sieve.(!j) <- false;
j := !j + i
done
end
done;
...
Exercises: Array.make, arr.(i), arr.(i) <- v, nested for/while,
begin..end blocks, ref/!/:=, integer arithmetic. 24 baseline
programs total.
Inline CSV-like text:
a,1,extra
b,2,extra
c,3,extra
d,4,extra
Two-stage String.split_on_char: first on '\n' for rows, then on ','
for fields per row. List.fold_left accumulates int_of_string of the
second field across rows. Result = 1+2+3+4 = 10.
Exercises char escapes inside string literals ('\n'), nested
String.split_on_char, List.fold_left with a non-trivial closure body,
and int_of_string. 23 baseline programs total.
frequency.ml exercises the recently-added Hashtbl.iter / fold +
Hashtbl.find_opt + s.[i] indexing + for-loop together: build a
char-count table for 'abracadabra' then take the max via
Hashtbl.fold. Expected = 5 (a x 5). Total 25 baseline programs.
Format module added as a thin alias of Printf — sprintf, printf, and
asprintf all delegate to Printf.sprintf. The dynamic runtime doesn't
distinguish boxes/breaks, so format strings work the same as in
Printf and most Format-using OCaml programs now compile.
Recursive Levenshtein edit distance with no memoization (the test
strings are short enough for the exponential-without-memo version to
fit in <2 minutes on contended hosts). Sums distances for five short
pairs:
('abc','abx') + ('ab','ba') + ('abc','axyc') + ('','abcd') + ('ab','')
= 1 + 2 + 2 + 4 + 2 = 11
Exercises:
* curried four-arg recursion
* s.[i] equality test (char comparison)
* min nested twice for the three-way recurrence
* mixed empty-string base cases
Side-quests required to land caesar.ml:
1. Top-level 'let r = expr in body' is now an expression decl, not a
broken decl-let. ocaml-parse-program's dispatch now checks
has-matching-in? at every top-level let; if matched, slices via
skip-let-rhs-boundary (which already opens depth on a leading let
with matching in) and ocaml-parse on the slice, wrapping as :expr.
2. runtime.sx: added String.make / String.init / String.map. Used by
caesar.ml's encode = String.init n (fun i -> shift_char s.[i] k).
3. baseline run.sh per-program timeout 240->480s (system load on the
shared host frequently exceeds 240s for large baselines).
caesar.ml exercises:
* the new top-level let-in expression dispatch
* s.[i] string indexing
* Char.code / Char.chr round-trip math
* String.init with a closure that captures k
Test value: Char.code r.[0] + Char.code r.[4] after ROT13(ROT13('hello')) = 104 + 111 = 215.
Side-quest emerged from adding roman.ml baseline (Roman numeral greedy
encoding): top-level 'let () = expr' was unsupported because
ocaml-parse-program's parse-decl-let consumed an ident strictly. Now
parse-decl-let recognises a leading '()' as a unit binding and
synthesises a __unit_NN name (matching how parse-let already handles
inner-let unit patterns).
roman.ml exercises:
* tuple list literal [(int * string); ...]
* recursive pattern match on tuple-cons
* String.length + List.fold_left
* the new top-level let () support (sanity in a comment, even though
the program ends with a bare expression for the test harness)
Bumped lib/ocaml/test.sh server timeout 180->360s — the recent surge in
test count plus a CPU-contended host was crowding out the sole epoch
reaching the deeper smarts.
Graph BFS using Queue + Hashtbl visited-set + List.assoc_opt + List.iter.
Returns 6 for a graph where A reaches B/C/D/E/F. Demonstrates 4 stdlib
modules (Queue, Hashtbl, List) cooperating in a real algorithm.
Parser: in parse-decl-type, dispatch on the post-= token:
'|' or Ctor -> sum type
'{' -> record type
otherwise -> type alias (skip to boundary)
AST (:type-alias NAME PARAMS) with body discarded. Runtime no-op since
SX has no nominal types.
poly_stack.ml baseline exercises:
module type ELEMENT = sig type t val show : t -> string end
module IntElem = struct type t = int let show x = ... end
module Make (E : ELEMENT) = struct ... use E.show ... end
module IntStack = Make(IntElem)
Demonstrates the substrate handles signature decls + abstract types +
functor parameter with sig constraint.
Group anagrams by canonical (sorted-chars) key using Hashtbl +
List.sort. Demonstrates char-by-char traversal via String.get + for-loop +
ref accumulator + Hashtbl as a multi-valued counter.
Untyped lambda calculus interpreter inside OCaml-on-SX:
type term = Var | Abs of string * term | App | Num of int
type value = VNum of int | VClos of string * term * env
let rec eval env t = match t with ...
(\x.\y.x) 7 99 = 7. The substrate handles two ADTs, recursive eval,
closure-based env, and pattern matching all written as a single
self-contained OCaml program — strong validation.
Memoized fibonacci using Hashtbl.find_opt + Hashtbl.add.
fib(25) = 75025. Demonstrates mutable Hashtbl through the OCaml
stdlib API in real recursive code.
4-queens via recursive backtracking + List.fold_left. Returns 2 (the
two solutions of 4-queens). Per-program timeout in run.sh bumped to
240s — the tree-walking interpreter is slow on heavy recursion but
correct.
The substrate handles full backtracking + safe-check recursion +
list-driven candidate enumeration end-to-end.
Counter-style record with two mutable fields. Validates the new
r.f <- v field mutation end-to-end through type decl + record literal
+ field access + field assignment + sequence operator.
type counter = { mutable count : int; mutable last : int }
let bump c = c.count <- c.count + 1 ; c.last <- c.count
After 5 bumps: count=5, last=5, sum=10.
Polymorphic binary search tree with insert + in-order traversal.
Exercises parametric ADT (type 'a tree = Leaf | Node of 'a * 'a tree
* 'a tree), recursive match, List.append, List.fold_left.
Classic fizzbuzz using ref-cell accumulator, for-loop, mod, if/elseif
chain, String.concat, Int.to_string. Output verified via String.length
of the comma-joined result for n=15: 57.
Recursive-descent calculator parses '(1 + 2) * 3 + 4' = 13. Two parser
bugs fixed:
1. parse-let now handles inline 'let rec a () = ... and b () = ... in
body' via new (:let-rec-mut BINDINGS BODY) and (:let-mut BINDINGS
BODY) AST shapes; eval handles both.
2. has-matching-in? lookahead no longer stops at 'and' — 'and' is
internal to let-rec, not a decl boundary. Without this fix, the
inner 'let rec a () = ... and b () = ...' inside a let-decl rhs
would have been treated as the start of a new top-level decl.
Baseline exercises mutually-recursive functions, while-loops, ref-cell
imperative parsing, and ADT-based AST construction.
Uses Map.Make(StrOrd) + List.fold_left to count word frequencies;
exercises the full functor pipeline with a real-world idiom:
let inc_count m word =
match StrMap.find_opt word m with
| None -> StrMap.add word 1 m
| Some n -> StrMap.add word (n + 1) m
let count words = List.fold_left inc_count StrMap.empty words
10/10 baseline programs pass.
A tiny arithmetic-expression evaluator using:
type expr = Lit of int | Add of expr*expr | Mul of expr*expr | Neg of expr
let rec eval e = match e with | Lit n -> n | Add (a,b) -> ...
Exercises type-decl + multi-arg ctor + recursive match end-to-end.
Per-program timeout in run.sh bumped to 120s.
lib/ocaml/baseline/{factorial,list_ops,option_match,module_use,sum_squares}.ml
exercised through ocaml-run-program (file-read F). lib/ocaml/baseline/
run.sh runs them and compares against expected.json — all 5 pass.
To make module_use.ml (with nested let-in) parse, parser's
skip-let-rhs-boundary! now uses has-matching-in? lookahead: a let at
depth 0 in a let-decl rhs opens a nested block IFF a matching in
exists before any decl-keyword. Without that in, the let is a new
top-level decl (preserves test 274 'let x = 1 let y = 2').
This is the first piece of Phase 5.1 'vendor a slice of OCaml
testsuite' — handcrafted fixtures for now, real testsuite TBD.
