kernel: Phase 3 $vau/$lambda/wrap/unwrap + 34 tests [shapes-reflective]

User-defined operatives via $vau; applicatives via $lambda (wrap ∘ $vau).
wrap/unwrap as Kernel-level applicatives. kernel-call-operative forks
on :impl (primitive) vs :body (user) tag. kernel-base-env wires the
four combiners + operative?/applicative? predicates. Env-param sentinel
`_` / `#ignore` → :knl-ignore (skip dyn-env bind). Flat parameter list
only; destructuring later. Headline test: custom applicative + custom
operative composed from user code.

lib/kernel/eval.sx

@@ -1,8 +1,8 @@
-;; lib/kernel/eval.sx — Kernel evaluator (Phase 2 skeleton).
+;; lib/kernel/eval.sx — Kernel evaluator.
 ;;
 ;; The evaluator is `lookup-and-combine`: there are no hardcoded special
-;; forms. Even $if / $define! / $lambda will be ordinary operatives bound
-;; in the standard environment (Phase 4). This file builds the dispatch
+;; forms. Even $if / $define! / $lambda are ordinary operatives bound in
+;; the standard environment (Phase 4). This file builds the dispatch
 ;; machinery and the operative/applicative tagged-value protocol.
 ;;
 ;; Tagged values
@@ -12,24 +12,31 @@
 ;;     keyed by symbol name; parent walks up the lookup chain.
 ;;
 ;;   {:knl-tag :operative :impl FN}
-;;     A primitive operative. FN receives (args dyn-env) — args are the
+;;     Primitive operative. FN receives (args dyn-env) — args are the
 ;;     UN-evaluated argument expressions, dyn-env is the calling env.
 ;;
-;;   {:knl-tag :applicative :underlying OP}
-;;     An applicative wraps an operative. Calls evaluate args first, then
-;;     forward to the underlying operative.
+;;   {:knl-tag :operative :params P :env-param EP :body B :static-env SE}
+;;     User-defined operative (built by $vau). Same tag; dispatch in
+;;     kernel-call-operative forks on which keys are present.
 ;;
-;; User-defined ($vau) operatives are added in Phase 3 — same tag, with
-;; extra fields :params :env-param :body :static-env.
+;;   {:knl-tag :applicative :underlying OP}
+;;     An applicative wraps an operative. Calls evaluate args first,
+;;     then forward to the underlying operative.
+;;
+;; The env-param of a user operative may be the sentinel :knl-ignore,
+;; in which case the dynamic env is not bound.
 ;;
 ;; Public API
 ;;   (kernel-eval EXPR ENV)                     — primary entry
-;;   (kernel-combine COMBINER ARGS DYN-ENV)     — apply a combiner
+;;   (kernel-combine COMBINER ARGS DYN-ENV)
+;;   (kernel-call-operative OP ARGS DYN-ENV)
+;;   (kernel-bind-params! ENV PARAMS ARGS)
 ;;   (kernel-make-env) / (kernel-extend-env P)
 ;;   (kernel-env-bind! E N V) / (kernel-env-lookup E N)
 ;;   (kernel-env-has? E N) / (kernel-env? V)
 ;;   (kernel-make-primitive-operative IMPL)
-;;   (kernel-make-primitive-applicative IMPL)   — IMPL receives evaled args
+;;   (kernel-make-primitive-applicative IMPL)
+;;   (kernel-make-user-operative PARAMS EPARAM BODY STATIC-ENV)
 ;;   (kernel-wrap OP) / (kernel-unwrap APP)
 ;;   (kernel-operative? V) / (kernel-applicative? V) / (kernel-combiner? V)
 ;;
@@ -72,6 +79,10 @@
 
 (define kernel-make-primitive-operative (fn (impl) {:impl impl :knl-tag :operative}))
 
+(define
+  kernel-make-user-operative
+  (fn (params eparam body static-env) {:knl-tag :operative :static-env static-env :params params :body body :env-param eparam}))
+
 (define
   kernel-operative?
   (fn (v) (and (dict? v) (= (get v :knl-tag) :operative))))
@@ -100,8 +111,6 @@
       ((kernel-applicative? app) (get app :underlying))
       (:else (error "kernel-unwrap: argument must be an applicative")))))
 
-;; A primitive applicative: sugar for (wrap (primitive-operative …)) where
-;; the impl receives already-evaluated args.
 (define
   kernel-make-primitive-applicative
   (fn
@@ -136,7 +145,8 @@
   (fn
     (combiner args dyn-env)
     (cond
-      ((kernel-operative? combiner) ((get combiner :impl) args dyn-env))
+      ((kernel-operative? combiner)
+        (kernel-call-operative combiner args dyn-env))
       ((kernel-applicative? combiner)
         (kernel-combine
           (get combiner :underlying)
@@ -144,6 +154,44 @@
           dyn-env))
       (:else (error (str "kernel-eval: not a combiner: " combiner))))))
 
+;; Operatives may be primitive (:impl is a host fn) or user-defined
+;; (carry :params / :env-param / :body / :static-env). The dispatch
+;; fork is here so kernel-combine stays small.
+(define
+  kernel-call-operative
+  (fn
+    (op args dyn-env)
+    (cond
+      ((dict-has? op :impl) ((get op :impl) args dyn-env))
+      ((dict-has? op :body)
+        (let
+          ((local (kernel-extend-env (get op :static-env))))
+          (kernel-bind-params! local (get op :params) args)
+          (let
+            ((eparam (get op :env-param)))
+            (when
+              (not (= eparam :knl-ignore))
+              (kernel-env-bind! local eparam dyn-env)))
+          (kernel-eval (get op :body) local)))
+      (:else (error "kernel-call-operative: malformed operative")))))
+
+;; Phase 3 supports a flat parameter list only — destructuring later.
+(define
+  kernel-bind-params!
+  (fn
+    (env params args)
+    (cond
+      ((or (nil? params) (= (length params) 0))
+        (cond
+          ((or (nil? args) (= (length args) 0)) nil)
+          (:else (error "kernel-call: too many arguments"))))
+      ((or (nil? args) (= (length args) 0))
+        (error "kernel-call: too few arguments"))
+      (:else
+        (begin
+          (kernel-env-bind! env (first params) (first args))
+          (kernel-bind-params! env (rest params) (rest args)))))))
+
 (define
   kernel-eval-args
   (fn
@@ -155,7 +203,6 @@
           (kernel-eval (first args) env)
           (kernel-eval-args (rest args) env))))))
 
-;; Evaluate a sequence of forms in env, returning the value of the last.
 (define
   kernel-eval-program
   (fn

lib/kernel/runtime.sx

@@ -0,0 +1,167 @@
+;; lib/kernel/runtime.sx — the operative–applicative substrate.
+;;
+;; Builds the first user-visible operatives so Kernel programs can
+;; construct their own combiners:
+;;
+;;   $vau    — primitive operative that returns a user operative
+;;   $lambda — primitive operative; sugar for (wrap ($vau …))
+;;   wrap    — primitive applicative; wraps an operative
+;;   unwrap  — primitive applicative; extracts the underlying op
+;;
+;; In Kernel, $lambda is *defined* in terms of $vau and wrap:
+;;   ($define! $lambda
+;;     ($vau (formals . body) #ignore
+;;       (wrap (eval (list $vau formals #ignore (cons $sequence body)) env))))
+;; Phase 3 supplies it natively (single-expression body) so tests can
+;; build applicatives without a working $define!/$sequence yet. The
+;; native-then-portable migration is a Phase 4 concern.
+;;
+;; The env-param sentinel
+;; ----------------------
+;; A user operative records an `:env-param` slot. If the source said
+;; `#ignore`, the slot holds the keyword :knl-ignore and kernel-call-
+;; operative skips binding the dynamic env. The parser doesn't recognise
+;; `#ignore` yet (Phase 1 covered #t/#f only); guests must spell it
+;; `_` for now — the spelling-to-sentinel conversion lives here in
+;; knl-eparam-sentinel.
+;;
+;; Public API
+;;   (kernel-base-env)  — fresh env with $vau, $lambda, wrap, unwrap
+;;
+;; Consumes: lib/kernel/eval.sx (everything tagged kernel-*).
+
+(define
+  knl-eparam-sentinel
+  (fn
+    (sym)
+    (cond
+      ((= sym "_") :knl-ignore)
+      ((= sym "#ignore") :knl-ignore)
+      (:else sym))))
+
+;; Validate that a formals list is a plain list of symbol names.
+(define
+  knl-formals-ok?
+  (fn
+    (formals)
+    (cond
+      ((not (list? formals)) false)
+      ((= (length formals) 0) true)
+      ((string? (first formals)) (knl-formals-ok? (rest formals)))
+      (:else false))))
+
+;; ── $vau ─────────────────────────────────────────────────────────
+;; ($vau FORMALS ENV-PARAM BODY) → user operative.
+;;
+;; FORMALS    — unevaluated list of parameter symbols.
+;; ENV-PARAM  — symbol (or `_` / `#ignore`).
+;; BODY       — single expression (Phase 3 limitation; $sequence later).
+;;
+;; The returned operative closes over the env where $vau was invoked.
+
+(define
+  kernel-vau-impl
+  (fn
+    (args dyn-env)
+    (cond
+      ((not (= (length args) 3))
+        (error "$vau: expects (formals env-param body)"))
+      (:else
+        (let
+          ((formals (first args))
+            (eparam-raw (nth args 1))
+            (body (nth args 2)))
+          (cond
+            ((not (knl-formals-ok? formals))
+              (error "$vau: formals must be a list of symbols"))
+            ((not (string? eparam-raw))
+              (error "$vau: env-param must be a symbol"))
+            (:else
+              (kernel-make-user-operative
+                formals
+                (knl-eparam-sentinel eparam-raw)
+                body
+                dyn-env))))))))
+
+(define
+  kernel-vau-operative
+  (kernel-make-primitive-operative kernel-vau-impl))
+
+;; ── $lambda ──────────────────────────────────────────────────────
+;; ($lambda FORMALS BODY) → user applicative.
+;;
+;; Equivalent to (wrap ($vau FORMALS #ignore BODY)) — args are evaluated
+;; before the operative body runs, and the operative ignores the dynamic
+;; environment.
+
+(define
+  kernel-lambda-impl
+  (fn
+    (args dyn-env)
+    (cond
+      ((not (= (length args) 2))
+        (error "$lambda: expects (formals body)"))
+      (:else
+        (let
+          ((formals (first args)) (body (nth args 1)))
+          (cond
+            ((not (knl-formals-ok? formals))
+              (error "$lambda: formals must be a list of symbols"))
+            (:else
+              (kernel-wrap
+                (kernel-make-user-operative formals :knl-ignore body dyn-env)))))))))
+
+(define
+  kernel-lambda-operative
+  (kernel-make-primitive-operative kernel-lambda-impl))
+
+;; ── wrap / unwrap as Kernel applicatives ─────────────────────────
+
+(define
+  kernel-wrap-applicative
+  (kernel-make-primitive-applicative
+    (fn
+      (args)
+      (cond
+        ((not (= (length args) 1))
+          (error "wrap: expects exactly 1 argument"))
+        (:else (kernel-wrap (first args)))))))
+
+(define
+  kernel-unwrap-applicative
+  (kernel-make-primitive-applicative
+    (fn
+      (args)
+      (cond
+        ((not (= (length args) 1))
+          (error "unwrap: expects exactly 1 argument"))
+        (:else (kernel-unwrap (first args)))))))
+
+;; Convenience predicates as applicatives too — tests want them.
+(define
+  kernel-operative?-applicative
+  (kernel-make-primitive-applicative
+    (fn (args) (kernel-operative? (first args)))))
+
+(define
+  kernel-applicative?-applicative
+  (kernel-make-primitive-applicative
+    (fn (args) (kernel-applicative? (first args)))))
+
+;; ── Base environment ─────────────────────────────────────────────
+;; A fresh env with the Phase 3 combiners bound. Standard env (Phase 4)
+;; will extend this with $if, $define!, arithmetic, list ops, etc.
+
+(define
+  kernel-base-env
+  (fn
+    ()
+    (let
+      ((env (kernel-make-env)))
+      (kernel-env-bind! env "$vau" kernel-vau-operative)
+      (kernel-env-bind! env "$lambda" kernel-lambda-operative)
+      (kernel-env-bind! env "wrap" kernel-wrap-applicative)
+      (kernel-env-bind! env "unwrap" kernel-unwrap-applicative)
+      (kernel-env-bind! env "operative?" kernel-operative?-applicative)
+      (kernel-env-bind! env "applicative?" kernel-applicative?-applicative)
+      env)))

lib/kernel/tests/vau.sx

@@ -0,0 +1,289 @@
+;; lib/kernel/tests/vau.sx — exercises lib/kernel/runtime.sx.
+;;
+;; Verifies the Phase 3 promise: user-defined operatives and applicatives
+;; constructible from inside the language. Tests build a Kernel
+;; base-env, bind a few helper applicatives (+, *, list, =, $if), and
+;; run programs that construct and use custom combiners.
+
+(define kv-test-pass 0)
+(define kv-test-fail 0)
+(define kv-test-fails (list))
+
+(define
+  kv-test
+  (fn
+    (name actual expected)
+    (if
+      (= actual expected)
+      (set! kv-test-pass (+ kv-test-pass 1))
+      (begin
+        (set! kv-test-fail (+ kv-test-fail 1))
+        (append! kv-test-fails {:name name :actual actual :expected expected})))))
+
+(define kv-eval-src (fn (src env) (kernel-eval (kernel-parse src) env)))
+
+(define
+  kv-make-env
+  (fn
+    ()
+    (let
+      ((env (kernel-base-env)))
+      (kernel-env-bind!
+        env
+        "+"
+        (kernel-make-primitive-applicative
+          (fn (args) (+ (first args) (nth args 1)))))
+      (kernel-env-bind!
+        env
+        "*"
+        (kernel-make-primitive-applicative
+          (fn (args) (* (first args) (nth args 1)))))
+      (kernel-env-bind!
+        env
+        "-"
+        (kernel-make-primitive-applicative
+          (fn (args) (- (first args) (nth args 1)))))
+      (kernel-env-bind!
+        env
+        "="
+        (kernel-make-primitive-applicative
+          (fn (args) (= (first args) (nth args 1)))))
+      (kernel-env-bind!
+        env
+        "list"
+        (kernel-make-primitive-applicative (fn (args) args)))
+      (kernel-env-bind!
+        env
+        "cons"
+        (kernel-make-primitive-applicative
+          (fn (args) (cons (first args) (nth args 1)))))
+      (kernel-env-bind!
+        env
+        "$quote"
+        (kernel-make-primitive-operative (fn (args dyn-env) (first args))))
+      (kernel-env-bind!
+        env
+        "$if"
+        (kernel-make-primitive-operative
+          (fn
+            (args dyn-env)
+            (if
+              (kernel-eval (first args) dyn-env)
+              (kernel-eval (nth args 1) dyn-env)
+              (kernel-eval (nth args 2) dyn-env)))))
+      env)))
+
+;; ── $vau: builds an operative ───────────────────────────────────
+(kv-test
+  "vau: identity returns first arg unevaluated"
+  (kv-eval-src "(($vau (a) _ a) hello)" (kv-make-env))
+  "hello")
+
+(kv-test
+  "vau: returns args as raw expressions"
+  (kv-eval-src "(($vau (a b) _ (list a b)) (+ 1 2) (+ 3 4))" (kv-make-env))
+  (list (list "+" 1 2) (list "+" 3 4)))
+
+(kv-test
+  "vau: env-param is a kernel env"
+  (kernel-env? (kv-eval-src "(($vau () e e))" (kv-make-env)))
+  true)
+
+(kv-test
+  "vau: returns operative"
+  (kernel-operative? (kv-eval-src "($vau (x) _ x)" (kv-make-env)))
+  true)
+
+(kv-test
+  "vau: returns operative not applicative"
+  (kernel-applicative? (kv-eval-src "($vau (x) _ x)" (kv-make-env)))
+  false)
+
+(kv-test
+  "vau: zero-arg body"
+  (kv-eval-src "(($vau () _ 42))" (kv-make-env))
+  42)
+
+(kv-test
+  "vau: static-env closure captured"
+  (let
+    ((outer (kv-make-env)))
+    (kernel-env-bind! outer "captured" 17)
+    (let
+      ((op (kv-eval-src "($vau () _ captured)" outer))
+        (caller (kv-make-env)))
+      (kernel-env-bind! caller "captured" 99)
+      (kernel-combine op (list) caller)))
+  17)
+
+(kv-test
+  "vau: env-param exposes caller's dynamic env"
+  (let
+    ((outer (kv-make-env)))
+    (kernel-env-bind! outer "x" 1)
+    (let
+      ((op (kv-eval-src "($vau () e e)" outer)) (caller (kv-make-env)))
+      (kernel-env-bind! caller "x" 2)
+      (let
+        ((e-val (kernel-combine op (list) caller)))
+        (kernel-env-lookup e-val "x"))))
+  2)
+
+;; ── $lambda: applicatives evaluate their args ───────────────────
+(kv-test
+  "lambda: identity"
+  (kv-eval-src "(($lambda (x) x) 42)" (kv-make-env))
+  42)
+
+(kv-test
+  "lambda: addition"
+  (kv-eval-src "(($lambda (x y) (+ x y)) 3 4)" (kv-make-env))
+  7)
+
+(kv-test
+  "lambda: args are evaluated before bind"
+  (kv-eval-src "(($lambda (x) x) (+ 2 3))" (kv-make-env))
+  5)
+
+(kv-test
+  "lambda: zero args"
+  (kv-eval-src "(($lambda () 99))" (kv-make-env))
+  99)
+
+(kv-test
+  "lambda: returns applicative"
+  (kernel-applicative? (kv-eval-src "($lambda (x) x)" (kv-make-env)))
+  true)
+
+(kv-test
+  "lambda: returns applicative not operative"
+  (kernel-operative? (kv-eval-src "($lambda (x) x)" (kv-make-env)))
+  false)
+
+(kv-test
+  "lambda: higher-order"
+  (kv-eval-src "(($lambda (f) (f 10)) ($lambda (x) (+ x 1)))" (kv-make-env))
+  11)
+
+;; ── wrap / unwrap as user-callable applicatives ─────────────────
+
+(kv-test
+  "wrap: makes applicative from operative"
+  (kernel-applicative? (kv-eval-src "(wrap ($vau (x) _ x))" (kv-make-env)))
+  true)
+
+(kv-test
+  "wrap: result evaluates its arg"
+  (kv-eval-src "((wrap ($vau (x) _ x)) (+ 1 2))" (kv-make-env))
+  3)
+
+(kv-test
+  "unwrap: extracts operative from applicative"
+  (kernel-operative? (kv-eval-src "(unwrap ($lambda (x) x))" (kv-make-env)))
+  true)
+
+(kv-test
+  "wrap/unwrap roundtrip preserves identity"
+  (kv-eval-src
+    "(($lambda (op) (= op (unwrap (wrap op)))) ($vau (x) _ x))"
+    (kv-make-env))
+  true)
+
+;; ── operative? / applicative? as user-visible predicates ────────
+
+(kv-test
+  "operative? on vau result"
+  (kv-eval-src "(operative? ($vau (x) _ x))" (kv-make-env))
+  true)
+
+(kv-test
+  "operative? on lambda result"
+  (kv-eval-src "(operative? ($lambda (x) x))" (kv-make-env))
+  false)
+
+(kv-test
+  "applicative? on lambda result"
+  (kv-eval-src "(applicative? ($lambda (x) x))" (kv-make-env))
+  true)
+
+(kv-test
+  "applicative? on vau result"
+  (kv-eval-src "(applicative? ($vau (x) _ x))" (kv-make-env))
+  false)
+
+(kv-test
+  "operative? on number"
+  (kv-eval-src "(operative? 42)" (kv-make-env))
+  false)
+
+;; ── Build BOTH layers from user code ────────────────────────────
+;; The headline Phase 3 test: defining an operative on top of an
+;; applicative defined on top of a vau.
+
+(kv-test
+  "custom: applicative + operative compose"
+  (let
+    ((env (kv-make-env)))
+    (kernel-env-bind! env "square" (kv-eval-src "($lambda (x) (* x x))" env))
+    (kv-eval-src "(square 4)" env))
+  16)
+
+(kv-test "custom: operative captures argument syntax"
+  ;; ($capture x) returns the raw expression `x`, regardless of value.
+  (let ((env (kv-make-env)))
+    (kernel-env-bind! env "$capture"
+      (kv-eval-src "($vau (form) _ form)" env))
+    (kv-eval-src "($capture (+ 1 2))" env))
+  (list "+" 1 2))
+
+(kv-test "custom: applicative re-wraps an operative"
+  ;; Build a captured operative, then wrap it into an applicative that
+  ;; evaluates args before re-entry. This exercises wrap+$vau composed.
+  (let ((env (kv-make-env)))
+    (kernel-env-bind! env "id-app"
+      (kv-eval-src "(wrap ($vau (x) _ x))" env))
+    (kv-eval-src "(id-app (+ 10 20))" env))
+  30)
+
+;; ── Error cases ──────────────────────────────────────────────────
+
+(kv-test
+  "vau: rejects non-list formals"
+  (guard (e (true :raised)) (kv-eval-src "($vau x _ x)" (kv-make-env)))
+  :raised)
+
+(kv-test
+  "vau: rejects non-symbol formal"
+  (guard (e (true :raised)) (kv-eval-src "($vau (1) _ x)" (kv-make-env)))
+  :raised)
+
+(kv-test
+  "vau: rejects non-symbol env-param"
+  (guard (e (true :raised)) (kv-eval-src "($vau (x) 7 x)" (kv-make-env)))
+  :raised)
+
+(kv-test
+  "vau: too few args at call site"
+  (guard
+    (e (true :raised))
+    (kv-eval-src "(($vau (x y) _ x) 1)" (kv-make-env)))
+  :raised)
+
+(kv-test
+  "vau: too many args at call site"
+  (guard
+    (e (true :raised))
+    (kv-eval-src "(($vau (x) _ x) 1 2)" (kv-make-env)))
+  :raised)
+
+(kv-test
+  "wrap: rejects non-operative"
+  (guard (e (true :raised)) (kv-eval-src "(wrap 42)" (kv-make-env)))
+  :raised)
+
+(kv-test
+  "unwrap: rejects non-applicative"
+  (guard (e (true :raised)) (kv-eval-src "(unwrap 42)" (kv-make-env)))
+  :raised)
+
+(define kv-tests-run! (fn () {:total (+ kv-test-pass kv-test-fail) :passed kv-test-pass :failed kv-test-fail :fails kv-test-fails}))

plans/kernel-on-sx.md

@@ -68,11 +68,11 @@ The whole interesting thing: there are no special forms hardcoded in the evaluat
 - [x] Tests in `lib/kernel/tests/eval.sx`.
 
 ### Phase 3 — `$vau` / `$lambda` / `wrap` / `unwrap`
-- [ ] Operative tagged value: `{:type :operative :params :env-param :body :static-env}`.
-- [ ] Applicative tagged value wraps an operative + the "evaluate args first" contract.
-- [ ] `$vau` builds operatives; `$lambda` is `wrap` ∘ `$vau`.
-- [ ] `wrap` / `unwrap` round-trip cleanly.
-- [ ] Tests: define a custom operative, define a custom applicative on top of it.
+- [x] Operative tagged value: `{:type :operative :params :env-param :body :static-env}`.
+- [x] Applicative tagged value wraps an operative + the "evaluate args first" contract.
+- [x] `$vau` builds operatives; `$lambda` is `wrap` ∘ `$vau`.
+- [x] `wrap` / `unwrap` round-trip cleanly.
+- [x] Tests: define a custom operative, define a custom applicative on top of it.
 
 ### Phase 4 — Standard environment
 - [ ] Standard env construction: bind `$if`, `$define!`, `$lambda`, `$vau`, `wrap`, `unwrap`, `eval`, `make-environment`, `get-current-environment`, plus arithmetic and list primitives.
@@ -100,6 +100,15 @@ The whole interesting thing: there are no special forms hardcoded in the evaluat
 
 **May propose:** `lib/guest/reflective/` sub-layer — environment manipulation, evaluator-as-value, applicative/operative dispatch protocols.
 
+**Proposed `lib/guest/reflective/combiner.sx` API** (from Phase 3 chiselling — pending second consumer):
+- `(refl-make-primitive-operative IMPL)` — IMPL receives `(args dyn-env)`, args unevaluated.
+- `(refl-make-user-operative PARAMS EPARAM BODY STATIC-ENV)` — for $vau-like constructors. The EPARAM sentinel for "ignore dyn-env" is a fixed keyword (`:refl-ignore` in the proposal).
+- `(refl-wrap OP)` / `(refl-unwrap APP)` — round-trip pair.
+- `(refl-operative? V)` / `(refl-applicative? V)` / `(refl-combiner? V)`.
+- `(refl-call-combiner COMBINER ARGS DYN-ENV)` — the dispatch fork. Pairs with `refl-eval` from the evaluator kit.
+- Representation: `{:refl-tag :operative :impl FN}` or `{:refl-tag :operative :params P :env-param EP :body B :static-env SE}`; applicatives are `{:refl-tag :applicative :underlying OP}`. The dispatch decision lives in one fork: presence of `:impl` is primitive, presence of `:body` is user-defined.
+- Driving insight: every reflective Lisp must distinguish "eval my args first" from "hand me the syntax". The tag protocol is identical across Kernel, CL fexprs, vau-style Schemes, possibly Forth's IMMEDIATE words.
+
 **Proposed `lib/guest/reflective/env.sx` API** (from Phase 2 chiselling — pending second consumer per the two-consumer rule):
 - `(refl-make-env)` / `(refl-extend-env PARENT)` — fresh / chained envs, plain SX dicts so they're easy to introspect.
 - `(refl-env? V)` — predicate.
@@ -119,6 +128,7 @@ The motivation is that SX's host `make-env` family is registered only in HTTP/si
 
 ## Progress log
 
+- 2026-05-11 — Phase 3 operatives landed. `lib/kernel/runtime.sx` adds `$vau` (primitive operative that returns a user operative), `$lambda` (sugar for `wrap ∘ $vau`), `wrap` and `unwrap` (Kernel-level applicatives), plus `operative?` and `applicative?` predicates. `kernel-base-env` wires them all into a fresh env. `kernel-eval.sx` now dispatches in `kernel-call-operative` between primitive ops (carry `:impl`) and user ops (carry `:params :env-param :body :static-env`). Parameter binding is a flat list — destructuring/`&rest` deferred. Env-param sentinel: spell `_` or `#ignore` → `:knl-ignore`, which skips the dyn-env bind. 34 tests in `tests/vau.sx`, including the headline custom-operative + custom-applicative composition. chisel: shapes-reflective. Two further reflective-API candidates surfaced: (a) the operative/applicative tag protocol — `make-primitive-operative`, `make-user-operative`, `wrap`, `unwrap` are general for any Lisp-of-fexprs; (b) the call-dispatch fork (primitive vs user) is a *single decision* that every reflective evaluator hits. Both shape go into the proposed `lib/guest/reflective/combiner.sx` candidate.
 - 2026-05-10 — Phase 2 evaluator landed. `lib/kernel/eval.sx` is `lookup-and-combine`: zero hardcoded special forms. `kernel-eval EXPR ENV` dispatches on shape — literals self-evaluate, Kernel strings unwrap, symbols lookup, lists evaluate head and combine. `kernel-combine` distinguishes operatives (impl receives un-evaluated args + dynamic env) from applicatives (eval args, recurse into underlying op). `kernel-wrap`/`kernel-unwrap` round-trip cleanly. 36 tests verify literal evaluation, symbol lookup with parent-chain shadowing, tagged-value predicates, and the operative-vs-applicative contract (notably `$if` only evaluates the chosen branch, `$quote` returns its arg unevaluated). chisel: shapes-reflective. Substrate gap surfaced: SX's `make-env` / `env-bind!` family is only registered in HTTP/site mode (`http_setup_platform_constructors`), not in CLI epoch mode used for tests. So Kernel envs are modelled in pure SX as `{:knl-tag :env :bindings DICT :parent P}` — a binding-dict + parent-pointer + recursive lookup walk. This is exactly the `lib/guest/reflective/env.sx` candidate API: any reflective language needs first-class env values that can be extended, queried, and walked. Recording the shape (constructor, extend, bind!, has?, lookup) here for the eventual Phase 7 extraction.
 - 2026-05-10 — Phase 1 parser landed. `lib/kernel/parser.sx` reads R-1RK lexical syntax: numbers (int/float/exp), strings (with escapes), symbols (permissive — anything non-delimiting), booleans `#t`/`#f`, the empty list `()`, nested lists, and `;` line comments. Reader macros (`'` `,` `,@`) deferred per plan. AST: numbers/booleans/lists pass through; strings are wrapped as `{:knl-string …}` to distinguish from symbols which are bare SX strings. 54 tests in `lib/kernel/tests/parse.sx` pass via `sx_server.exe` epoch protocol. chisel: consumes-lex (uses `lex-digit?` and `lex-whitespace?` from `lib/guest/lex.sx` — pratt deliberately not consumed because Kernel is plain s-expressions, no precedence climbing).