ocaml: phase 5.1 kmp.ml baseline (5 occurrences of "abab" in haystack)

Knuth-Morris-Pratt linear-time string search:
  - kmp_table builds failure function in O(|pattern|)
  - kmp_search scans text once in O(|text|), counting matches
  - After a hit, k := t.(n-1) so overlapping matches still count

  kmp_search "abababcabababcababcc" "abab" = 5

Hits at positions 0, 2, 7, 9, 14 (overlapping at 0/2 and 7/9).

Tests: nested while-inside-for, char inequality (.<>), pat.[i]
string indexing, Array.make 0, combined string + array indexing.

140 baseline programs total.

plans/ocaml-on-sx.md

@@ -407,6 +407,13 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-10 Phase 5.1 — kmp.ml baseline (KMP string search, count
+  occurrences of "abab" in "abababcabababcababcc" = 5). Two-phase
+  classic: build failure table in O(m), then linear scan in O(n).
+  After a full match, set k := t.(n-1) so overlapping matches still
+  count (so "abab" hits at positions 0, 2, 7, 9, 14). Tests nested
+  while-inside-for, char comparison via `pat.[i]`, Array.make 0,
+  combined string + array indexing. 140 baseline programs total.
 - 2026-05-10 Phase 5.1 — union_find.ml baseline (disjoint-set union
   on n=10 with 6 unions → 4 components). Path-compressing find:
   recursively walks parent links, splices subtree onto root in place.