ocaml: phase 5.1 calc.ml baseline (11/11 pass) + inline let-rec-and parser fix

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.

lib/ocaml/baseline/calc.ml

@@ -0,0 +1,76 @@
+(* Baseline: recursive-descent calculator for "+", "*", parens, ints. *)
+type expr =
+  | Lit of int
+  | Add of expr * expr
+  | Mul of expr * expr
+;;
+
+let parse_input src =
+  let pos = ref 0 in
+  let peek () = if !pos < String.length src then String.get src !pos else "" in
+  let advance () = pos := !pos + 1 in
+  let skip_ws () =
+    while !pos < String.length src && peek () = " " do advance () done
+  in
+
+  let rec parse_atom () =
+    skip_ws () ;
+    if peek () = "(" then begin
+      advance () ;
+      let e = parse_expr () in
+      skip_ws () ;
+      advance () ; (* consume ')' *)
+      e
+    end
+    else
+      let start = !pos in
+      let rec digits () =
+        if !pos < String.length src then
+          let c = peek () in
+          if c >= "0" && c <= "9" then begin advance () ; digits () end
+          else ()
+      in
+      digits () ;
+      let n = Int.of_string (String.sub src start (!pos - start)) in
+      Lit n
+
+  and parse_term () =
+    skip_ws () ;
+    let lhs = ref (parse_atom ()) in
+    let rec loop () =
+      skip_ws () ;
+      if peek () = "*" then begin
+        advance () ;
+        lhs := Mul (!lhs, parse_atom ()) ;
+        loop ()
+      end
+    in
+    loop () ;
+    !lhs
+
+  and parse_expr () =
+    skip_ws () ;
+    let lhs = ref (parse_term ()) in
+    let rec loop () =
+      skip_ws () ;
+      if peek () = "+" then begin
+        advance () ;
+        lhs := Add (!lhs, parse_term ()) ;
+        loop ()
+      end
+    in
+    loop () ;
+    !lhs
+  in
+  parse_expr ()
+;;
+
+let rec eval e =
+  match e with
+  | Lit n -> n
+  | Add (a, b) -> eval a + eval b
+  | Mul (a, b) -> eval a * eval b
+;;
+
+(* (1 + 2) * 3 + 4 = 9 + 4 = 13 *)
+eval (parse_input "(1 + 2) * 3 + 4")

lib/ocaml/baseline/expected.json

@@ -1,4 +1,5 @@
 {
+  "calc.ml": 13,
   "closures.ml": 315,
   "exception_handle.ml": 4,
   "expr_eval.ml": 16,

lib/ocaml/eval.sx

@@ -619,6 +619,57 @@
                         (ocaml-eval rhs env)
                         (ocaml-make-curried params rhs env))))
               (ocaml-eval body (ocaml-env-extend env name rhs-val)))))
+        ((= tag "let-mut")
+          ;; (:let-mut BINDINGS BODY) — non-rec multi-binding let-in.
+          ;; Each rhs evaluated in the parent env, then names bound
+          ;; sequentially before evaluating BODY.
+          (let ((bindings (nth ast 1)) (body (nth ast 2)) (env-cur env))
+            (begin
+              (define one
+                (fn (b)
+                  (let ((nm (nth b 0)) (ps (nth b 1)) (rh (nth b 2)))
+                    (let ((v (if (= (len ps) 0)
+                                 (ocaml-eval rh env-cur)
+                                 (ocaml-make-curried ps rh env-cur))))
+                      (set! env-cur (ocaml-env-extend env-cur nm v))))))
+              (define loop
+                (fn (xs)
+                  (when (not (= xs (list)))
+                    (begin (one (first xs)) (loop (rest xs))))))
+              (loop bindings)
+              (ocaml-eval body env-cur))))
+        ((= tag "let-rec-mut")
+          ;; (:let-rec-mut BINDINGS BODY) — mutually-recursive let-in.
+          (let ((bindings (nth ast 1)) (body (nth ast 2))
+                (env2 env) (cells (list)))
+            (begin
+              (define alloc
+                (fn (xs)
+                  (when (not (= xs (list)))
+                    (let ((b (first xs)))
+                      (let ((c (list nil)) (nm (nth b 0)))
+                        (begin
+                          (append! cells c)
+                          (set! env2 (ocaml-env-extend env2 nm
+                                       (fn (a) ((nth c 0) a))))
+                          (alloc (rest xs))))))))
+              (alloc bindings)
+              (let ((idx 0))
+                (begin
+                  (define fill
+                    (fn (xs)
+                      (when (not (= xs (list)))
+                        (let ((b (first xs)))
+                          (let ((nm (nth b 0)) (ps (nth b 1)) (rh (nth b 2)))
+                            (let ((v (if (= (len ps) 0)
+                                         (ocaml-eval rh env2)
+                                         (ocaml-make-curried ps rh env2))))
+                              (begin
+                                (set-nth! (nth cells idx) 0 v)
+                                (set! idx (+ idx 1))
+                                (fill (rest xs)))))))))
+                  (fill bindings)
+                  (ocaml-eval body env2))))))
         ((= tag "let-rec")
           ;; Tie the knot via a mutable cell when rhs is function-typed.
           ;; The placeholder closure dereferences the cell on each call.

lib/ocaml/parser.sx

@@ -666,36 +666,43 @@
                 (let ((body (parse-expr))) (list :fun params body))))))
         (define
           parse-let
-          (fn
-            ()
-            (let
-              ((reccy false))
+          (fn ()
+            (let ((reccy false) (bindings (list)))
               (begin
-                (when
-                  (at-kw? "rec")
+                (when (at-kw? "rec")
                   (begin (advance-tok!) (set! reccy true)))
-                (let
-                  ((name (ocaml-tok-value (consume! "ident" nil)))
-                    (params (list)))
-                  (begin
-                    (define
-                      collect-params
-                      (fn ()
-                        (let ((nm (try-consume-param!)))
-                          (when (not (= nm nil))
-                            (begin (append! params nm) (collect-params))))))
-                    (collect-params)
-                    (consume! "op" "=")
-                    (let
-                      ((rhs (parse-expr)))
+                (define parse-one!
+                  (fn ()
+                    (let ((nm (ocaml-tok-value (consume! "ident" nil)))
+                          (ps (list)))
                       (begin
-                        (consume! "keyword" "in")
-                        (let
-                          ((body (parse-expr)))
-                          (if
-                            reccy
-                            (list :let-rec name params rhs body)
-                            (list :let name params rhs body)))))))))))
+                        (define collect-params
+                          (fn ()
+                            (let ((p (try-consume-param!)))
+                              (when (not (= p nil))
+                                (begin (append! ps p) (collect-params))))))
+                        (collect-params)
+                        (consume! "op" "=")
+                        (let ((rhs (parse-expr)))
+                          (append! bindings (list nm ps rhs)))))))
+                (parse-one!)
+                (define more
+                  (fn ()
+                    (when (at-kw? "and")
+                      (begin (advance-tok!) (parse-one!) (more)))))
+                (more)
+                (consume! "keyword" "in")
+                (let ((body (parse-expr)))
+                  (cond
+                    ((= (len bindings) 1)
+                      (let ((b (first bindings)))
+                        (if reccy
+                            (list :let-rec (nth b 0) (nth b 1) (nth b 2) body)
+                            (list :let     (nth b 0) (nth b 1) (nth b 2) body))))
+                    (else
+                      (if reccy
+                          (list :let-rec-mut bindings body)
+                          (list :let-mut     bindings body)))))))))
         (define
           parse-if
           (fn
@@ -975,7 +982,6 @@
                                 ((and (= tt "keyword") (= tv "exception")) (set! done true))
                                 ((and (= tt "keyword") (= tv "open")) (set! done true))
                                 ((and (= tt "keyword") (= tv "include")) (set! done true))
-                                ((and (= tt "keyword") (= tv "and")) (set! done true))
                                 ((and (= tt "keyword") (= tv "let"))
                                   (begin (set! d (+ d 1)) (set! p (+ p 1)) (scan)))
                                 ((and (= tt "keyword") (= tv "in"))

plans/ocaml-on-sx.md

@@ -394,6 +394,14 @@ _Newest first._
   recognise `!` as the prefix-deref of an application argument, so
   `String.concat "" (List.rev !b)` parses as `(... (deref b))`. Buffer
   uses a ref holding a string list; contents reverses and concats.
+- 2026-05-08 Phase 5.1+1+2 — calc.ml baseline (11/11 pass) — a
+  recursive-descent calculator parsing `(1 + 2) * 3 + 4` to 13. Two
+  parser bugs fixed along the way: parse-let now handles inline
+  `let rec ... and ... in body` via new `:let-rec-mut` / `:let-mut`
+  AST shapes (eval supports both); `has-matching-in?` no longer stops
+  at `and` (which is internal to a let-rec, not a decl boundary). The
+  baseline exercises mutually-recursive functions, while-loops, and
+  ref-cell-driven imperative parsing.
 - 2026-05-08 Phase 5.1 — word_count.ml baseline (10/10 pass). Uses
   Map.Make(StrOrd) + List.fold_left to count word frequencies; tests
   the full functor pipeline with a real OCaml idiom.