Serializable CEK state: cek-freeze and cek-thaw

Freeze a CEK state to pure s-expressions. Thaw it back to a live
state and resume with cek-run. Full round-trip through SX text works:
freeze → sx-serialize → sx-parse → thaw → resume → same result.

- cek-freeze: serialize control/env/kont/value to SX dicts
- cek-thaw: reconstruct live state from frozen SX
- Native functions serialize as (primitive "name"), looked up on resume
- Lambdas serialize as (lambda (params) body)
- Environments serialize as flat dicts of visible bindings
- Continuation frames serialize as typed dicts

Enables: localStorage persistence, content-addressed computation,
cross-machine migration, time-travel debugging.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

shared/static/scripts/sx-browser.js

@@ -14,7 +14,7 @@
   // =========================================================================
 
   var NIL = Object.freeze({ _nil: true, toString: function() { return "nil"; } });
-  var SX_VERSION = "2026-03-14T20:39:57Z";
+  var SX_VERSION = "2026-03-14T22:10:44Z";
 
   function isNil(x) { return x === NIL || x === null || x === undefined; }
   function isSxTruthy(x) { return x !== false && !isNil(x); }
@@ -5283,6 +5283,74 @@ PRIMITIVES["eval-expr-cek"] = evalExprCek;
   var trampolineCek = function(val) { return (isSxTruthy(isThunk(val)) ? evalExprCek(thunkExpr(val), thunkEnv(val)) : val); };
 PRIMITIVES["trampoline-cek"] = trampolineCek;
 
+  // primitive-name
+  var primitiveName = function(f) { return (isSxTruthy(isLambda(f)) ? lambdaName(f) : (function() {
+  var result = NIL;
+  var names = ["+", "-", "*", "/", "=", "<", ">", "<=", ">=", "not", "and", "or", "str", "len", "first", "rest", "nth", "list", "cons", "append", "map", "filter", "reduce", "for-each", "some", "every?", "get", "keys", "dict", "dict?", "has-key?", "assoc", "empty?", "nil?", "number?", "string?", "list?", "type-of", "identity", "inc", "dec", "mod", "join", "split", "slice", "contains?", "starts-with?", "upper", "lower", "trim", "replace", "format"];
+  { var _c = names; for (var _i = 0; _i < _c.length; _i++) { var name = _c[_i]; if (isSxTruthy((isSxTruthy(isNil(result)) && isSxTruthy(isPrimitive(name)) && isIdentical(f, getPrimitive(name))))) {
+  result = name;
+} } }
+  return result;
+})()); };
+PRIMITIVES["primitive-name"] = primitiveName;
+
+  // cek-serialize-value
+  var cekSerializeValue = function(val) { return (isSxTruthy(isNil(val)) ? NIL : (isSxTruthy(isNumber(val)) ? val : (isSxTruthy(isString(val)) ? val : (isSxTruthy((typeOf(val) == "boolean")) ? val : (isSxTruthy((typeOf(val) == "symbol")) ? val : (isSxTruthy((typeOf(val) == "keyword")) ? val : (isSxTruthy(isList(val)) ? map(cekSerializeValue, val) : (isSxTruthy(isLambda(val)) ? [makeSymbol("lambda"), lambdaParams(val), lambdaBody(val)] : (isSxTruthy(isCallable(val)) ? [makeSymbol("primitive"), sxOr(primitiveName(val), "?")] : (isSxTruthy(isDict(val)) ? cekSerializeEnv(val) : (String(val)))))))))))); };
+PRIMITIVES["cek-serialize-value"] = cekSerializeValue;
+
+  // cek-serialize-env
+  var cekSerializeEnv = function(env) { return (function() {
+  var result = {};
+  var ks = keys(env);
+  { var _c = ks; for (var _i = 0; _i < _c.length; _i++) { var k = _c[_i]; result[k] = cekSerializeValue(get(env, k)); } }
+  return result;
+})(); };
+PRIMITIVES["cek-serialize-env"] = cekSerializeEnv;
+
+  // cek-serialize-frame
+  var cekSerializeFrame = function(frame) { return (function() {
+  var result = {};
+  var ks = keys(frame);
+  { var _c = ks; for (var _i = 0; _i < _c.length; _i++) { var k = _c[_i]; (function() {
+  var v = get(frame, k);
+  return dictSet(result, k, (isSxTruthy((k == "type")) ? v : (isSxTruthy((k == "tag")) ? v : (isSxTruthy((k == "f")) ? cekSerializeValue(v) : (isSxTruthy((k == "env")) ? cekSerializeEnv(v) : (isSxTruthy((k == "evaled")) ? map(cekSerializeValue, v) : (isSxTruthy((k == "remaining")) ? v : (isSxTruthy((k == "results")) ? map(cekSerializeValue, v) : (isSxTruthy((k == "raw-args")) ? v : (isSxTruthy((k == "current-item")) ? cekSerializeValue(v) : (isSxTruthy((k == "name")) ? v : (isSxTruthy((k == "update-fn")) ? cekSerializeValue(v) : (isSxTruthy((k == "first-render")) ? v : cekSerializeValue(v))))))))))))));
+})(); } }
+  return result;
+})(); };
+PRIMITIVES["cek-serialize-frame"] = cekSerializeFrame;
+
+  // cek-freeze
+  var cekFreeze = function(state) { return {["phase"]: get(state, "phase"), ["control"]: get(state, "control"), ["value"]: cekSerializeValue(get(state, "value")), ["env"]: cekSerializeEnv(get(state, "env")), ["kont"]: map(cekSerializeFrame, get(state, "kont"))}; };
+PRIMITIVES["cek-freeze"] = cekFreeze;
+
+  // cek-thaw-value
+  var cekThawValue = function(val) { return (isSxTruthy(isNil(val)) ? NIL : (isSxTruthy(isNumber(val)) ? val : (isSxTruthy(isString(val)) ? val : (isSxTruthy((typeOf(val) == "boolean")) ? val : (isSxTruthy((typeOf(val) == "symbol")) ? val : (isSxTruthy((typeOf(val) == "keyword")) ? val : (isSxTruthy((isSxTruthy(isList(val)) && isSxTruthy(!isSxTruthy(isEmpty(val))) && isSxTruthy((typeOf(first(val)) == "symbol")) && (symbolName(first(val)) == "primitive"))) ? getPrimitive(nth(val, 1)) : (isSxTruthy((isSxTruthy(isList(val)) && isSxTruthy(!isSxTruthy(isEmpty(val))) && isSxTruthy((typeOf(first(val)) == "symbol")) && (symbolName(first(val)) == "lambda"))) ? makeLambda(nth(val, 1), nth(val, 2), {}) : (isSxTruthy(isList(val)) ? map(cekThawValue, val) : (isSxTruthy(isDict(val)) ? cekThawEnv(val) : val)))))))))); };
+PRIMITIVES["cek-thaw-value"] = cekThawValue;
+
+  // cek-thaw-env
+  var cekThawEnv = function(frozenEnv) { return (function() {
+  var result = makeEnv();
+  { var _c = keys(frozenEnv); for (var _i = 0; _i < _c.length; _i++) { var k = _c[_i]; envSet(result, k, cekThawValue(get(frozenEnv, k))); } }
+  return result;
+})(); };
+PRIMITIVES["cek-thaw-env"] = cekThawEnv;
+
+  // cek-thaw-frame
+  var cekThawFrame = function(frozenFrame) { return (function() {
+  var result = {};
+  var ks = keys(frozenFrame);
+  { var _c = ks; for (var _i = 0; _i < _c.length; _i++) { var k = _c[_i]; (function() {
+  var v = get(frozenFrame, k);
+  return dictSet(result, k, (isSxTruthy((k == "type")) ? v : (isSxTruthy((k == "tag")) ? v : (isSxTruthy((k == "f")) ? cekThawValue(v) : (isSxTruthy((k == "env")) ? cekThawEnv(v) : (isSxTruthy((k == "evaled")) ? map(cekThawValue, v) : (isSxTruthy((k == "remaining")) ? v : (isSxTruthy((k == "results")) ? map(cekThawValue, v) : (isSxTruthy((k == "raw-args")) ? v : (isSxTruthy((k == "current-item")) ? cekThawValue(v) : (isSxTruthy((k == "name")) ? v : (isSxTruthy((k == "update-fn")) ? cekThawValue(v) : (isSxTruthy((k == "first-render")) ? v : cekThawValue(v))))))))))))));
+})(); } }
+  return result;
+})(); };
+PRIMITIVES["cek-thaw-frame"] = cekThawFrame;
+
+  // cek-thaw
+  var cekThaw = function(frozen) { return {["phase"]: get(frozen, "phase"), ["control"]: get(frozen, "control"), ["value"]: cekThawValue(get(frozen, "value")), ["env"]: cekThawEnv(get(frozen, "env")), ["kont"]: map(cekThawFrame, get(frozen, "kont"))}; };
+PRIMITIVES["cek-thaw"] = cekThaw;
+
 
   // === Transpiled from signals (reactive signal runtime) ===
 

shared/sx/ref/cek.sx

@@ -1032,3 +1032,165 @@
     (if (thunk? val)
       (eval-expr-cek (thunk-expr val) (thunk-env val))
       val)))
+
+
+;; --------------------------------------------------------------------------
+;; 13. CEK state serialization — freeze and resume computation
+;; --------------------------------------------------------------------------
+;;
+;; Serialize a CEK state to an s-expression. The result can be:
+;;   - Printed as text (sx-serialize)
+;;   - Stored, transmitted, content-addressed
+;;   - Parsed back (sx-parse) and resumed (cek-run)
+;;
+;; Native functions serialize as (primitive "name") — looked up on resume.
+;; Lambdas serialize as (lambda (params) body closure-env).
+;; Environments serialize as dicts of their visible bindings.
+
+(define primitive-name :effects []
+  (fn (f)
+    ;; For lambdas, use lambda-name. For native callables, check common names.
+    (if (lambda? f)
+      (lambda-name f)
+      ;; Native function — try common primitive names
+      (let ((result nil)
+            (names (list "+" "-" "*" "/" "=" "<" ">" "<=" ">=" "not" "and" "or"
+                         "str" "len" "first" "rest" "nth" "list" "cons" "append"
+                         "map" "filter" "reduce" "for-each" "some" "every?"
+                         "get" "keys" "dict" "dict?" "has-key?" "assoc"
+                         "empty?" "nil?" "number?" "string?" "list?"
+                         "type-of" "identity" "inc" "dec" "mod"
+                         "join" "split" "slice" "contains?" "starts-with?"
+                         "upper" "lower" "trim" "replace" "format")))
+        (for-each (fn (name)
+          (when (and (nil? result) (primitive? name) (identical? f (get-primitive name)))
+            (set! result name)))
+          names)
+        result))))
+
+(define cek-serialize-value :effects []
+  (fn (val)
+    (cond
+      (nil? val)       nil
+      (number? val)    val
+      (string? val)    val
+      (= (type-of val) "boolean")   val
+      (= (type-of val) "symbol")    val
+      (= (type-of val) "keyword")   val
+      (list? val)      (map cek-serialize-value val)
+      (lambda? val)    (list (make-symbol "lambda")
+                             (lambda-params val)
+                             (lambda-body val))
+      (callable? val)  (list (make-symbol "primitive")
+                             (or (primitive-name val) "?"))
+      (dict? val)      (cek-serialize-env val)
+      :else            (str val))))
+
+(define cek-serialize-env :effects []
+  (fn (env)
+    (let ((result (dict))
+          (ks (keys env)))
+      (for-each (fn (k)
+        (dict-set! result k (cek-serialize-value (get env k))))
+        ks)
+      result)))
+
+(define cek-serialize-frame :effects []
+  (fn (frame)
+    (let ((result (dict))
+          (ks (keys frame)))
+      (for-each (fn (k)
+        (let ((v (get frame k)))
+          (dict-set! result k
+            (cond
+              (= k "type")       v
+              (= k "tag")        v
+              (= k "f")          (cek-serialize-value v)
+              (= k "env")        (cek-serialize-env v)
+              (= k "evaled")     (map cek-serialize-value v)
+              (= k "remaining")  v  ;; unevaluated exprs stay as-is
+              (= k "results")    (map cek-serialize-value v)
+              (= k "raw-args")   v
+              (= k "current-item") (cek-serialize-value v)
+              (= k "name")       v
+              (= k "update-fn")  (cek-serialize-value v)
+              (= k "first-render") v
+              :else              (cek-serialize-value v)))))
+        ks)
+      result)))
+
+(define cek-freeze :effects []
+  (fn (state)
+    (dict
+      "phase"   (get state "phase")
+      "control" (get state "control")
+      "value"   (cek-serialize-value (get state "value"))
+      "env"     (cek-serialize-env (get state "env"))
+      "kont"    (map cek-serialize-frame (get state "kont")))))
+
+;; Deserialize: reconstruct a runnable CEK state from frozen SX.
+;; Native functions are looked up by name in the current PRIMITIVES.
+
+(define cek-thaw-value :effects []
+  (fn (val)
+    (cond
+      (nil? val)    nil
+      (number? val) val
+      (string? val) val
+      (= (type-of val) "boolean") val
+      (= (type-of val) "symbol") val
+      (= (type-of val) "keyword") val
+      ;; (primitive "name") → look up native function
+      (and (list? val) (not (empty? val))
+           (= (type-of (first val)) "symbol")
+           (= (symbol-name (first val)) "primitive"))
+        (get-primitive (nth val 1))
+      ;; (lambda (params) body) → reconstruct Lambda
+      (and (list? val) (not (empty? val))
+           (= (type-of (first val)) "symbol")
+           (= (symbol-name (first val)) "lambda"))
+        (make-lambda (nth val 1) (nth val 2) (dict))
+      (list? val)  (map cek-thaw-value val)
+      (dict? val)  (cek-thaw-env val)
+      :else        val)))
+
+(define cek-thaw-env :effects []
+  (fn (frozen-env)
+    (let ((result (make-env)))
+      (for-each (fn (k)
+        (env-set! result k (cek-thaw-value (get frozen-env k))))
+        (keys frozen-env))
+      result)))
+
+(define cek-thaw-frame :effects []
+  (fn (frozen-frame)
+    (let ((result (dict))
+          (ks (keys frozen-frame)))
+      (for-each (fn (k)
+        (let ((v (get frozen-frame k)))
+          (dict-set! result k
+            (cond
+              (= k "type")       v
+              (= k "tag")        v
+              (= k "f")          (cek-thaw-value v)
+              (= k "env")        (cek-thaw-env v)
+              (= k "evaled")     (map cek-thaw-value v)
+              (= k "remaining")  v
+              (= k "results")    (map cek-thaw-value v)
+              (= k "raw-args")   v
+              (= k "current-item") (cek-thaw-value v)
+              (= k "name")       v
+              (= k "update-fn")  (cek-thaw-value v)
+              (= k "first-render") v
+              :else              (cek-thaw-value v)))))
+        ks)
+      result)))
+
+(define cek-thaw :effects []
+  (fn (frozen)
+    (dict
+      "phase"   (get frozen "phase")
+      "control" (get frozen "control")
+      "value"   (cek-thaw-value (get frozen "value"))
+      "env"     (cek-thaw-env (get frozen "env"))
+      "kont"    (map cek-thaw-frame (get frozen "kont")))))

shared/sx/ref/sx_ref.py

@@ -4586,6 +4586,110 @@ def trampoline_cek(val):
     else:
         return val
 
+# primitive-name
+def primitive_name(f):
+    _cells = {}
+    if sx_truthy(is_lambda(f)):
+        return lambda_name(f)
+    else:
+        _cells['result'] = NIL
+        names = ['+', '-', '*', '/', '=', '<', '>', '<=', '>=', 'not', 'and', 'or', 'str', 'len', 'first', 'rest', 'nth', 'list', 'cons', 'append', 'map', 'filter', 'reduce', 'for-each', 'some', 'every?', 'get', 'keys', 'dict', 'dict?', 'has-key?', 'assoc', 'empty?', 'nil?', 'number?', 'string?', 'list?', 'type-of', 'identity', 'inc', 'dec', 'mod', 'join', 'split', 'slice', 'contains?', 'starts-with?', 'upper', 'lower', 'trim', 'replace', 'format']
+        for name in names:
+            if sx_truthy((is_nil(_cells['result']) if not sx_truthy(is_nil(_cells['result'])) else (is_primitive(name) if not sx_truthy(is_primitive(name)) else is_identical(f, get_primitive(name))))):
+                _cells['result'] = name
+        return _cells['result']
+
+# cek-serialize-value
+def cek_serialize_value(val):
+    if sx_truthy(is_nil(val)):
+        return NIL
+    elif sx_truthy(number_p(val)):
+        return val
+    elif sx_truthy(string_p(val)):
+        return val
+    elif sx_truthy((type_of(val) == 'boolean')):
+        return val
+    elif sx_truthy((type_of(val) == 'symbol')):
+        return val
+    elif sx_truthy((type_of(val) == 'keyword')):
+        return val
+    elif sx_truthy(list_p(val)):
+        return map(cek_serialize_value, val)
+    elif sx_truthy(is_lambda(val)):
+        return [make_symbol('lambda'), lambda_params(val), lambda_body(val)]
+    elif sx_truthy(is_callable(val)):
+        return [make_symbol('primitive'), (primitive_name(val) if sx_truthy(primitive_name(val)) else '?')]
+    elif sx_truthy(dict_p(val)):
+        return cek_serialize_env(val)
+    else:
+        return sx_str(val)
+
+# cek-serialize-env
+def cek_serialize_env(env):
+    result = {}
+    ks = keys(env)
+    for k in ks:
+        result[k] = cek_serialize_value(get(env, k))
+    return result
+
+# cek-serialize-frame
+def cek_serialize_frame(frame):
+    result = {}
+    ks = keys(frame)
+    for k in ks:
+        v = get(frame, k)
+        result[k] = (v if sx_truthy((k == 'type')) else (v if sx_truthy((k == 'tag')) else (cek_serialize_value(v) if sx_truthy((k == 'f')) else (cek_serialize_env(v) if sx_truthy((k == 'env')) else (map(cek_serialize_value, v) if sx_truthy((k == 'evaled')) else (v if sx_truthy((k == 'remaining')) else (map(cek_serialize_value, v) if sx_truthy((k == 'results')) else (v if sx_truthy((k == 'raw-args')) else (cek_serialize_value(v) if sx_truthy((k == 'current-item')) else (v if sx_truthy((k == 'name')) else (cek_serialize_value(v) if sx_truthy((k == 'update-fn')) else (v if sx_truthy((k == 'first-render')) else cek_serialize_value(v)))))))))))))
+    return result
+
+# cek-freeze
+def cek_freeze(state):
+    return {'phase': get(state, 'phase'), 'control': get(state, 'control'), 'value': cek_serialize_value(get(state, 'value')), 'env': cek_serialize_env(get(state, 'env')), 'kont': map(cek_serialize_frame, get(state, 'kont'))}
+
+# cek-thaw-value
+def cek_thaw_value(val):
+    if sx_truthy(is_nil(val)):
+        return NIL
+    elif sx_truthy(number_p(val)):
+        return val
+    elif sx_truthy(string_p(val)):
+        return val
+    elif sx_truthy((type_of(val) == 'boolean')):
+        return val
+    elif sx_truthy((type_of(val) == 'symbol')):
+        return val
+    elif sx_truthy((type_of(val) == 'keyword')):
+        return val
+    elif sx_truthy((list_p(val) if not sx_truthy(list_p(val)) else ((not sx_truthy(empty_p(val))) if not sx_truthy((not sx_truthy(empty_p(val)))) else ((type_of(first(val)) == 'symbol') if not sx_truthy((type_of(first(val)) == 'symbol')) else (symbol_name(first(val)) == 'primitive'))))):
+        return get_primitive(nth(val, 1))
+    elif sx_truthy((list_p(val) if not sx_truthy(list_p(val)) else ((not sx_truthy(empty_p(val))) if not sx_truthy((not sx_truthy(empty_p(val)))) else ((type_of(first(val)) == 'symbol') if not sx_truthy((type_of(first(val)) == 'symbol')) else (symbol_name(first(val)) == 'lambda'))))):
+        return make_lambda(nth(val, 1), nth(val, 2), {})
+    elif sx_truthy(list_p(val)):
+        return map(cek_thaw_value, val)
+    elif sx_truthy(dict_p(val)):
+        return cek_thaw_env(val)
+    else:
+        return val
+
+# cek-thaw-env
+def cek_thaw_env(frozen_env):
+    result = make_env()
+    for k in keys(frozen_env):
+        result[k] = cek_thaw_value(get(frozen_env, k))
+    return result
+
+# cek-thaw-frame
+def cek_thaw_frame(frozen_frame):
+    result = {}
+    ks = keys(frozen_frame)
+    for k in ks:
+        v = get(frozen_frame, k)
+        result[k] = (v if sx_truthy((k == 'type')) else (v if sx_truthy((k == 'tag')) else (cek_thaw_value(v) if sx_truthy((k == 'f')) else (cek_thaw_env(v) if sx_truthy((k == 'env')) else (map(cek_thaw_value, v) if sx_truthy((k == 'evaled')) else (v if sx_truthy((k == 'remaining')) else (map(cek_thaw_value, v) if sx_truthy((k == 'results')) else (v if sx_truthy((k == 'raw-args')) else (cek_thaw_value(v) if sx_truthy((k == 'current-item')) else (v if sx_truthy((k == 'name')) else (cek_thaw_value(v) if sx_truthy((k == 'update-fn')) else (v if sx_truthy((k == 'first-render')) else cek_thaw_value(v)))))))))))))
+    return result
+
+# cek-thaw
+def cek_thaw(frozen):
+    return {'phase': get(frozen, 'phase'), 'control': get(frozen, 'control'), 'value': cek_thaw_value(get(frozen, 'value')), 'env': cek_thaw_env(get(frozen, 'env')), 'kont': map(cek_thaw_frame, get(frozen, 'kont'))}
+
 
 # === Transpiled from signals (reactive signal runtime) ===