diff --git a/lib/prolog/runtime.sx b/lib/prolog/runtime.sx
index 623d91d9..8175426d 100644
--- a/lib/prolog/runtime.sx
+++ b/lib/prolog/runtime.sx
@@ -322,12 +322,71 @@
             trail
             cut-box
             k))
+        ((and (pl-compound? g) (= (pl-fun g) "->") (= (len (pl-args g)) 2))
+          (pl-solve-if-then-else!
+            db
+            (first (pl-args g))
+            (nth (pl-args g) 1)
+            (list "atom" "fail")
+            trail
+            cut-box
+            k))
         ((and (pl-compound? g) (= (pl-fun g) "call") (= (len (pl-args g)) 1))
           (let
             ((call-cb {:cut false}))
             (pl-solve! db (first (pl-args g)) trail call-cb k)))
         (true (pl-solve-user! db g trail cut-box k))))))
 
+(define
+  pl-solve-or!
+  (fn
+    (db a b trail cut-box k)
+    (cond
+      ((and (pl-compound? a) (= (pl-fun a) "->") (= (len (pl-args a)) 2))
+        (pl-solve-if-then-else!
+          db
+          (first (pl-args a))
+          (nth (pl-args a) 1)
+          b
+          trail
+          cut-box
+          k))
+      (true
+        (let
+          ((mark (pl-trail-mark trail)))
+          (let
+            ((r (pl-solve! db a trail cut-box k)))
+            (cond
+              (r true)
+              ((dict-get cut-box :cut) false)
+              (true
+                (begin
+                  (pl-trail-undo-to! trail mark)
+                  (pl-solve! db b trail cut-box k))))))))))
+
+(define
+  pl-solve-if-then-else!
+  (fn
+    (db cond-goal then-goal else-goal trail cut-box k)
+    (let
+      ((mark (pl-trail-mark trail)))
+      (let
+        ((local-cb {:cut false}))
+        (let
+          ((found {:val false}))
+          (pl-solve!
+            db
+            cond-goal
+            trail
+            local-cb
+            (fn () (begin (dict-set! found :val true) true)))
+          (cond
+            ((dict-get found :val) (pl-solve! db then-goal trail cut-box k))
+            (true
+              (begin
+                (pl-trail-undo-to! trail mark)
+                (pl-solve! db else-goal trail cut-box k)))))))))
+
 (define
   pl-solve-not-eq!
   (fn
@@ -340,22 +399,6 @@
           (pl-trail-undo-to! trail mark)
           (cond (unified false) (true (k))))))))
 
-(define
-  pl-solve-or!
-  (fn
-    (db a b trail cut-box k)
-    (let
-      ((mark (pl-trail-mark trail)))
-      (let
-        ((r (pl-solve! db a trail cut-box k)))
-        (cond
-          (r true)
-          ((dict-get cut-box :cut) false)
-          (true
-            (begin
-              (pl-trail-undo-to! trail mark)
-              (pl-solve! db b trail cut-box k))))))))
-
 (define
   pl-solve-eq!
   (fn
diff --git a/lib/prolog/tests/solve.sx b/lib/prolog/tests/solve.sx
index aacaefbd..a64ce5f2 100644
--- a/lib/prolog/tests/solve.sx
+++ b/lib/prolog/tests/solve.sx
@@ -337,4 +337,88 @@
     (pl-mk-trail))
   true)
 
+(define pl-s-db-ite (pl-mk-db))
+
+(pl-db-load! pl-s-db-ite (pl-parse "p(1). p(2). q(yes). q(no)."))
+
+(pl-s-test!
+  "if-then-else: cond true → then runs"
+  (pl-solve-once!
+    pl-s-db-ite
+    (pl-s-goal ";(->(true, =(X, ok)), =(X, fallback))" {})
+    (pl-mk-trail))
+  true)
+
+(define pl-s-env-ite1 {})
+
+(pl-solve-once!
+  pl-s-db-ite
+  (pl-s-goal ";(->(true, =(X, ok)), =(X, fallback))" pl-s-env-ite1)
+  (pl-mk-trail))
+
+(pl-s-test!
+  "if-then-else: cond true binds via then"
+  (pl-atom-name (pl-walk-deep (dict-get pl-s-env-ite1 "X")))
+  "ok")
+
+(pl-s-test!
+  "if-then-else: cond false → else"
+  (pl-solve-once!
+    pl-s-db-ite
+    (pl-s-goal ";(->(fail, =(X, ok)), =(X, fallback))" {})
+    (pl-mk-trail))
+  true)
+
+(define pl-s-env-ite2 {})
+
+(pl-solve-once!
+  pl-s-db-ite
+  (pl-s-goal ";(->(fail, =(X, ok)), =(X, fallback))" pl-s-env-ite2)
+  (pl-mk-trail))
+
+(pl-s-test!
+  "if-then-else: cond false binds via else"
+  (pl-atom-name (pl-walk-deep (dict-get pl-s-env-ite2 "X")))
+  "fallback")
+
+(pl-s-test!
+  "if-then-else: cond commits to first solution (count = 1)"
+  (pl-solve-count!
+    pl-s-db-ite
+    (pl-s-goal ";(->(p(X), =(Y, found)), =(Y, none))" {})
+    (pl-mk-trail))
+  1)
+
+(pl-s-test!
+  "if-then-else: then can backtrack"
+  (pl-solve-count!
+    pl-s-db-ite
+    (pl-s-goal ";(->(true, p(X)), =(X, none))" {})
+    (pl-mk-trail))
+  2)
+
+(pl-s-test!
+  "if-then-else: else can backtrack"
+  (pl-solve-count!
+    pl-s-db-ite
+    (pl-s-goal ";(->(fail, =(X, ignored)), p(X))" {})
+    (pl-mk-trail))
+  2)
+
+(pl-s-test!
+  "standalone -> with true cond succeeds"
+  (pl-solve-once!
+    pl-s-db-ite
+    (pl-s-goal "->(true, =(X, hi))" {})
+    (pl-mk-trail))
+  true)
+
+(pl-s-test!
+  "standalone -> with false cond fails"
+  (pl-solve-once!
+    pl-s-db-ite
+    (pl-s-goal "->(fail, =(X, hi))" {})
+    (pl-mk-trail))
+  false)
+
 (define pl-solve-tests-run! (fn () {:failed pl-s-test-fail :passed pl-s-test-pass :total pl-s-test-count :failures pl-s-test-failures}))
diff --git a/plans/prolog-on-sx.md b/plans/prolog-on-sx.md
index f08507de..7239bed6 100644
--- a/plans/prolog-on-sx.md
+++ b/plans/prolog-on-sx.md
@@ -53,7 +53,7 @@ Representation choices (finalise in phase 1, document here):
 - [x] Clause DB: `"functor/arity" → list-of-clauses`, loader inserts — `pl-mk-db` / `pl-db-add!` / `pl-db-load!` / `pl-db-lookup` / `pl-db-lookup-goal`, 14 tests in `tests/clausedb.sx`
 - [x] Solver: DFS with choice points backed by delimited continuations (`lib/callcc.sx`). On goal entry, capture; per matching clause, unify head + recurse body; on failure, undo trail, try next — first cut: trail-based undo + CPS k (no shift/reset yet, per briefing gotcha). Built-ins so far: `true/0`, `fail/0`, `=/2`, `,/2`. Refactor to delimited conts later.
 - [x] Cut (`!`): cut barrier at current choice-point frame; collapse all up to barrier — two-cut-box scheme: each `pl-solve-user!` creates a fresh inner-cut-box (set by `!` in this predicate's body) AND snapshots the outer-cut-box state on entry. After body fails, abandon clause alternatives if (a) inner was set or (b) outer transitioned false→true during this call. Lets post-cut goals backtrack normally while blocking pre-cut alternatives. 6 cut tests cover bare cut, clause-commit, choice-commit, cut+fail, post-cut backtracking, nested-cut isolation.
-- [ ] Built-ins: `=/2`, `\\=/2`, `true/0`, `fail/0`, `!/0`, `,/2`, `;/2`, `->/2` inside `;`, `call/1`, `write/1`, `nl/0` — done so far: `=/2`, `true/0`, `fail/0`, `!/0`, `,/2`, `\\=/2`, `;/2`, `call/1`. Pending: `->/2` inside `;`, `write/1`, `nl/0`. Note: cut-transparency via `;` not testable yet without operator support — `;(,(a,!), b)` parser-rejects because `,` is body-operator-only.
+- [ ] Built-ins: `=/2`, `\\=/2`, `true/0`, `fail/0`, `!/0`, `,/2`, `;/2`, `->/2` inside `;`, `call/1`, `write/1`, `nl/0` — done so far: `=/2`, `true/0`, `fail/0`, `!/0`, `,/2`, `\\=/2`, `;/2`, `call/1`, `->/2` (both inside `;` and standalone). Pending: `write/1`, `nl/0`. Note: cut-transparency via `;` not testable yet without operator support — `;(,(a,!), b)` parser-rejects because `,` is body-operator-only.
 - [ ] Arithmetic `is/2` with `+ - * / mod abs`
 - [ ] Classic programs in `lib/prolog/tests/programs/`:
   - [ ] `append.pl` — list append (with backtracking)
@@ -88,6 +88,7 @@ Representation choices (finalise in phase 1, document here):
 
 _Newest first. Agent appends on every commit._
 
+- 2026-04-25 — `->/2` if-then-else landed (both `;(->(C,T), E)` and standalone `->(C, T)` ≡ `(C -> T ; fail)`). `pl-solve-or!` now special-cases `->` in left arg → `pl-solve-if-then-else!`. Cond runs in a fresh local cut-box (ISO opacity for cut inside cond). Then-branch can backtrack, else-branch can backtrack, but cond commits to first solution. 9 new tests covering both forms, both branches, binding visibility, cond-commit, then-backtrack, else-backtrack. Total 130 (+9).
 - 2026-04-25 — Built-ins `\=/2`, `;/2`, `call/1` landed. `pl-solve-not-eq!` (try unify, always undo, succeed iff unify failed). `pl-solve-or!` (try left, on failure check cut and only try right if not cut). `call/1` opens a fresh inner cut-box (ISO opacity: cut inside `call(G)` commits G, not caller). 11 new tests in `tests/solve.sx` cover atoms+vars for `\=`, both branches + count for `;`, and `call/1` against atoms / compounds / bound goal vars. Total 121 (+11). Box not yet ticked — `->/2`, `write/1`, `nl/0` still pending.
 - 2026-04-25 — Cut (`!/0`) landed. `pl-cut?` predicate; solver functions all take a `cut-box`; `pl-solve-user!` creates a fresh inner-cut-box and snapshots `outer-was-cut`; `pl-try-clauses!` abandons alternatives when inner.cut OR (outer.cut transitioned false→true during this call). 6 new cut tests in `tests/solve.sx` covering bare cut, clause-commit, choice-commit, cut+fail blocks alt clauses, post-cut goal backtracks freely, inner cut isolation. Total 110 (+6).
 - 2026-04-25 — Phase 3 DFS solver landed (CPS, trail-based backtracking; delimited conts deferred). `pl-solve!` + `pl-solve-eq!` + `pl-solve-user!` + `pl-try-clauses!` + `pl-solve-once!` + `pl-solve-count!` in runtime.sx. Built-ins: `true/0`, `fail/0`, `=/2`, `,/2`. New `tests/solve.sx` 18/18 green covers atomic goals, =, conjunction, fact lookup, multi-solution count, recursive ancestor rule, trail-undo verification. Bug fix: `pl-instantiate` had no `("clause" h b)` case → vars in rule head/body were never instantiated, so rule resolution silently failed against runtime-var goals. Added clause case to recurse with shared var-env. Total 104 (+18).