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.
Both take an inner predicate / comparator and walk both lists in
lockstep:
equal eq a b short-circuits on first mismatch
compare cmp a b -1 if a is a strict prefix
1 if b is
0 if both empty
otherwise first non-zero element comparison
Mirrors real OCaml's signatures.
List.equal (=) [1;2;3] [1;2;3] = true
List.equal (=) [1;2;3] [1;2;4] = false
List.compare compare [1;2;3] [1;2;4] = -1
List.compare compare [1;2] [1;2;3] = -1
List.compare compare [] [] = 0
Bool module:
equal a b = a = b
compare a b = 0 if equal, 1 if a, -1 if b (false < true)
to_string 'true' / 'false'
of_string s = s = 'true'
not_ wraps host not
to_int true=1, false=0
Option additions (take eq/cmp parameter for the inner value):
equal eq a b None=None, otherwise eq the inner values
compare cmp a b None < Some _; otherwise cmp inner
Option.equal (=) (Some 1) (Some 1) = true
Option.equal (=) (Some 1) None = false
Option.compare compare (Some 5) (Some 3) = 1
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)
Real OCaml's Seq.t is 'unit -> Cons of elt * Seq.t | Nil' — a lazy
thunk that lets you build infinite sequences. Ours is just a list,
which gives the right shape for everything in baseline programs that
don't rely on laziness (taking from infinite sequences would force
memory).
API: empty, cons, return, is_empty, iter, iteri, map, filter,
filter_map, fold_left, length, take, drop, append, to_list,
of_list, init, unfold.
unfold takes a step fn 'acc -> Option (elt * acc)' and threads
through until it returns None:
Seq.fold_left (+) 0
(Seq.unfold (fun n -> if n > 4 then None
else Some (n, n + 1))
1)
= 1 + 2 + 3 + 4 = 10
parse-fun's collect-params now detects '(IDENT, ...)' as a
tuple-pattern parameter (lookahead at peek-tok-at 1/2 distinguishes
from '(x : T)' and '()' cases that try-consume-param! already
handles). For each tuple param it:
1. parse-pattern to get the full pattern AST
2. generate a synthetic __pat_N name as the actual fun parameter
3. push (synth_name, pattern) onto tuple-binds
After parsing the body, wraps it innermost-first with one
'match __pat_N with PAT -> ...' per tuple-param. The user-visible
result is a (:fun (params...) body) where params are all simple
names but the body destructures.
Also retroactively simplifies Hashtbl.keys/values from
'fun pair -> match pair with (k, _) -> k' to plain
'fun (k, _) -> k', closing the iteration-99 workaround.
(fun (a, b) -> a + b) (3, 7) = 10
List.map (fun (a, b) -> a * b)
[(1, 2); (3, 4); (5, 6)] = [2; 12; 30]
List.map (fun (k, _) -> k)
[("a", 1); ("b", 2)] = ["a"; "b"]
(fun a (b, c) d -> a + b + c + d) 1 (2, 3) 4 = 10
Linear-congruential PRNG with mutable seed (_state ref). API:
init s seed the PRNG
self_init () default seed (1)
int bound 0 <= n < bound
bool () fair coin
float bound uniform in [0, bound)
bits () 30 bits
Stepping rule:
state := (state * 1103515245 + 12345) mod 2147483647
result := |state| mod bound
Same seed reproduces the same sequence. Real OCaml's Random uses
Lagged Fibonacci; ours is simpler but adequate for shuffles and
Monte Carlo demos in baseline programs.
Random.init 42; Random.int 100 = 48
Random.init 1; Random.int 10 = 0
Two new host primitives:
_hashtbl_remove t k -> dissoc the key from the underlying dict
_hashtbl_clear t -> reset the cell to {}
Eight new OCaml-syntax helpers in runtime.sx Hashtbl module:
bindings t = _hashtbl_to_list t
keys t = List.map (fun (k, _) -> k) (...)
values t = List.map (fun (_, v) -> v) (...)
to_seq t = bindings t
to_seq_keys / to_seq_values
remove / clear / reset
The keys/values implementations use a 'fun pair -> match pair with
(k, _) -> k' indirection because parse-fun does not currently allow
tuple patterns directly on parameters. Same restriction we worked
around in iteration 98's let-pattern desugaring.
Also: a detour attempting to add top-level 'let (a, b) = expr'
support was started but reverted — parse-decl-let in the outer
ocaml-parse-program scope does not have access to parse-pattern
(which is local to ocaml-parse). Will need a slice + re-parse trick
later.
When 'let' is followed by '(', parse-let now reads a full pattern
(via the existing parse-pattern used by match), expects '=', then
'in', and desugars to:
let PATTERN = EXPR in BODY => match EXPR with PATTERN -> BODY
This reuses the entire pattern-matching machinery, so any pattern
the match parser accepts works here too — paren-tuples, nested
tuples, cons patterns, list patterns. No 'rec' allowed for pattern
bindings (real OCaml's restriction).
let (a, b) = (1, 2) in a + b = 3
let (a, b, c) = (10, 20, 30) in a + b + c = 60
let pair = (5, 7) in
let (x, y) = pair in x * y = 35
Also retroactively cleaned up Printf's iter-97 width-pos packing
hack ('width * 1000000 + spec_pos') — it's now
'let (width, spec_pos) = parse_width_loop after_flags in ...' like
real OCaml.
The Printf walker now parses optional flags + width digits between
'%' and the spec letter:
- left-align (default is right-align)
0 zero-pad (default is space-pad; only honoured when not left-aligned)
Nd... decimal width digits (any number)
After formatting the argument into a base string with the existing
spec dispatch (%d/%i/%u/%s/%f/%c/%b/%x/%X/%o), the result is padded
to the requested width.
Workaround: width and spec_pos are returned packed as
width * 1000000 + spec_pos
because the parser does not yet support tuple destructuring in let
('let (a, b) = expr in body' fails with 'expected ident'). TODO: lift
that limitation; for now the encoding round-trips losslessly for any
practical width.
Printf.sprintf '%5d' 42 = ' 42'
Printf.sprintf '%-5d|' 42 = '42 |'
Printf.sprintf '%05d' 42 = '00042'
Printf.sprintf '%4s' 'hi' = ' hi'
Printf.sprintf 'hi=%-3d, hex=%04x' 9 15 = 'hi=9 , hex=000f'
The previous List.sort was O(n^2) insertion sort. Replaced with a
straightforward mergesort:
split lst -> alternating-take into ([odd], [even])
merge xs ys -> classic two-finger merge under cmp
sort cmp xs -> base cases [], [x]; otherwise split + recursive
sort on each half + merge
Tuple destructuring on the split result is expressed via nested
match — let-tuple-destructuring would be cleaner but works today.
This benefits sort_uniq (which calls sort first), Set.Make.add via
sort etc., and any user program using List.sort. Stable_sort is
already aliased to sort.
Three things in this commit:
1. Integer / is now truncate-toward-zero on ints, IEEE on floats. The
eval-op handler for '/' checks (number? + (= (round x) x)) on both
sides; if both integral, applies host floor/ceil based on sign;
otherwise falls through to host '/'.
2. Fixes Int.rem, which was returning 0 because (a - b * (a / b))
was using float division: 17 - 5 * 3.4 = 0.0. Now Int.rem 17 5 = 2.
3. Int module fleshed out:
max_int / min_int / zero / one / minus_one,
succ / pred / neg, add / sub / mul / div / rem,
equal, compare.
Also adds globals: max_int, min_int, abs_float, float_of_int,
int_of_float (the latter two are identity in our dynamic runtime).
17 / 5 = 3
-17 / 5 = -3 (trunc toward zero)
Int.rem 17 5 = 2
Int.compare 5 3 = 1
Eight new Array functions, all in OCaml syntax inside runtime.sx,
delegating to the corresponding List operation on the cell's
underlying list:
sort cmp a -> a := List.sort cmp !a (* mutates the cell *)
stable_sort = sort
fast_sort = sort
append a b -> ref (List.append !a !b)
sub a pos n -> ref (take n (drop pos !a))
exists p -> List.exists p !a
for_all p -> List.for_all p !a
mem x a -> List.mem x !a
Round-trip:
let a = Array.of_list [3;1;4;1;5;9;2;6] in
Array.sort compare a;
Array.to_list a = [1;1;2;3;4;5;6;9]
Array module (runtime.sx, OCaml syntax):
Backed by a 'ref of list'. make/length/get/init build the cell;
set rewrites the underlying list with one cell changed (O(n) but
works for short arrays in baseline programs). Includes
iter/iteri/map/mapi/fold_left/to_list/of_list/copy/blit/fill.
(op) operator sections (parser.sx, parse-atom):
When the token after '(' is a binop (any op with non-zero
precedence in the binop table) and the next token is ')', emit
(:fun ('a' 'b') (:op OP a b)) — i.e. (+) becomes fun a b -> a + b.
Recognises every binop including 'mod', 'land', '^', '@', '::',
etc.
Lets us write:
List.fold_left (+) 0 [1;2;3;4;5] = 15
let f = ( * ) in f 6 7 = 42
List.map ((-) 10) [1;2;3] = [9;8;7]
let a = Array.make 5 7 in
Array.set a 2 99;
Array.fold_left (+) 0 a = 127
sort_uniq:
Sort with the user comparator, then walk the sorted list dropping
any element equal to its predecessor. Output is sorted and unique.
List.sort_uniq compare [3;1;2;1;3;2;4] = [1;2;3;4]
find_map:
Walk until the user fn returns Some v; return that. If all None,
return None.
List.find_map (fun x -> if x > 5 then Some (x * 2) else None)
[1;2;3;6;7]
= Some 12
Both defined in OCaml syntax in runtime.sx — no host primitive
needed since they're pure list traversals over existing operations.
Six new String functions, all in OCaml syntax inside runtime.sx:
iter : index-walk with side-effecting f
iteri : iter with index
fold_left : thread accumulator left-to-right
fold_right: thread accumulator right-to-left
to_seq : return a char list (lazy in real OCaml; eager here)
of_seq : concat a char list back to a string
Round-trip:
String.of_seq (List.rev (String.to_seq "hello")) = "olleh"
Note: real OCaml's Seq is lazy. We return a plain list because the
existing stdlib already provides exhaustive list operations and we
don't yet have lazy sequences. If a baseline needs Seq.unfold or
similar, we'll graduate to a proper Seq module then.
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.
Tokenizer already had 'lazy' as a keyword. This commit wires it through:
parser : parse-prefix emits (:lazy EXPR), like the existing 'assert'
handler.
eval : creates a one-element cell with state ('Thunk' expr env).
host : _lazy_force flips the cell to ('Forced' v) on first call
and returns the cached value thereafter.
runtime : module Lazy = struct let force lz = _lazy_force lz end.
Memoisation confirmed by tracking a side-effect counter through two
forces of the same lazy:
let counter = ref 0 in
let lz = lazy (counter := !counter + 1; 42) in
let a = Lazy.force lz in
let b = Lazy.force lz in
(a + b) * 100 + !counter = 8401 (= 84*100 + 1)
New host primitive _hashtbl_to_list returns the entries as a list of
OCaml tuples — ('tuple' k v) form, matching the AST representation
that the pattern-match VM (:ptuple) expects. Without that exact
shape, '(k, v) :: rest' patterns fail to match.
Hashtbl.iter / Hashtbl.fold in runtime walk that list with the user
fn. This closes a long-standing gap: previously Hashtbl was opaque
once values were written (we could only find_opt one key at a time).
let t = Hashtbl.create 4 in
Hashtbl.add t "a" 1; Hashtbl.add t "b" 2; Hashtbl.add t "c" 3;
Hashtbl.fold (fun _ v acc -> acc + v) t 0 = 6
Replaces the stub sprintf in runtime.sx with a real implementation:
walk fmt char-by-char accumulating a prefix; on recognised %X return a
one-arg fn that formats the arg and recurses on the rest of fmt. The
function self-curries to the spec count — there's no separate arity
machinery, just a closure chain.
Specs: %d (int), %s (string), %f (float), %c (char/string in our model),
%b (bool), %% (literal). Unknown specs pass through.
Same expression returns a string (no specs) or a function (>=1 spec) —
OCaml proper would reject this; works fine in OCaml-on-SX's dynamic
runtime.
Also adds top-level aliases:
string_of_int = _string_of_int
string_of_float = _string_of_float
string_of_bool = if b then "true" else "false"
int_of_string = _int_of_string
Printf.sprintf "x=%d" 42 = "x=42"
Printf.sprintf "%s = %d" "answer" 42 = "answer = 42"
Printf.sprintf "%d%%" 50 = "50%"
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.
Option: join, to_result, some, none.
Result: value, iter, fold.
Bytes: length, get, of_string, to_string, concat, sub — thin alias of
String (SX has no separate immutable byte type).
Ordering fix: Bytes module placed after String so its closures capture
String in scope. Earlier draft put Bytes before String which made
String.* lookups fail with 'not a record/module' (treated as nullary
ctor).
Parser fix: at-app-start? and parse-app's loop recognise prefix !
as a deref of the next app arg. So 'List.rev !b' parses as
'(:app List.rev (:deref b))' instead of stalling at !.
Buffer module backed by a ref holding string list:
create _ = ref []
add_string b s = b := s :: !b
contents b = String.concat "" (List.rev !b)
add_char/length/clear/reset
Both written in OCaml inside lib/ocaml/runtime.sx:
module Map = struct module Make (Ord) = struct
let empty = []
let add k v m = ... (* sorted insert via Ord.compare *)
let find_opt / find / mem / remove / bindings / cardinal
end end
module Set = struct module Make (Ord) = struct
let empty = []
let mem / add / remove / elements / cardinal
end end
Sorted association list / sorted list backing — linear ops but
correct. Strong substrate-validation: Map.Make is a non-trivial
functor implemented entirely on top of the OCaml-on-SX evaluator.
os_type="SX", word_size=64, max_array_length, max_string_length,
executable_name="ocaml-on-sx", big_endian=false, unix=true,
win32=false, cygwin=false. Constants-only for now — argv/getenv_opt/
command would need host platform integration.
compare is a host builtin returning -1/0/1 (Stdlib.compare semantics)
deferred to host SX </>. List.sort is insertion-sort in OCaml: O(n²)
but works correctly. List.stable_sort = sort.
Tested: ascending int sort, descending via custom comparator (b - a),
empty list, string sort.
Backing store is a one-element list cell holding a SX dict; keys
coerced to strings via str so int/string keys work uniformly. API:
create, add, replace, find, find_opt, mem, length.
_hashtbl_create / _hashtbl_add / _hashtbl_replace / _hashtbl_find_opt /
_hashtbl_mem / _hashtbl_length primitives wired in eval.sx; OCaml-side
Hashtbl module wraps them in lib/ocaml/runtime.sx.
List: concat/flatten, init, find/find_opt, partition, mapi/iteri,
assoc/assoc_opt. Option: iter/fold/to_list. Result: get_ok/get_error/
map_error/to_option.
Fixed skip-to-boundary! in parser to track let..in / begin..end /
struct..end / for/while..done nesting via a depth counter — without
this, nested-let inside a top-level decl body trips over the
decl-boundary detector. Stdlib functions like List.init / mapi / iteri
use begin..end to make their nested-let intent explicit.
lib/ocaml/runtime.sx defines the stdlib in OCaml syntax (not SX): every
function exercises the parser, evaluator, match engine, and module
machinery built in earlier phases. Loaded once via ocaml-load-stdlib!,
cached in ocaml-stdlib-env, layered under user code via ocaml-base-env.
List: length, rev, rev_append, map, filter, fold_left/right, append,
iter, mem, for_all, exists, hd, tl, nth.
Option: map, bind, value, get, is_none, is_some.
Result: map, bind, is_ok, is_error.
Substrate validation: this stdlib is a nontrivial OCaml program — its
mere existence proves the substrate works.
