🐐 First order functions

README.md

@@ -244,6 +244,28 @@ Calling a function is done with the `INVOCA` keyword.
 > CXXI
 ```
 
+## First-class functions
+Functions are first-class values in CENTVRION. They can be assigned to variables, passed as arguments, returned from functions, and stored in arrays or dicts.
+
+Anonymous functions are created with the `FVNCTIO` keyword:
+
+![FVNCTIO](snippets/fvnctio.png)
+
+```
+> XIV
+```
+
+`INVOCA` accepts any expression as the callee, not just a name:
+
+![INVOCA expressions](snippets/invoca_expr.png)
+```
+> VI
+> VI
+> XVI
+```
+
+Note: CENTVRION does **not** have closures. When a function is called, it receives a copy of the *caller's* scope, not the scope where it was defined. Variables from a function's definition site are only available if they also exist in the caller's scope at call time.
+
 ## Built-ins
 ### DICE
 `DICE(value, ...)`

centvrion/ast_nodes.py

@@ -144,6 +144,8 @@ def make_string(val, magnvm=False, svbnvlla=False) -> str:
       for k, v in val.value().items()
     )
     return "{" + inner + "}"
+  elif isinstance(val, ValFunc):
+    return "FVNCTIO"
   else:
     raise CentvrionError(f"Cannot display {val!r}")
 
@@ -577,6 +579,31 @@ class Defini(Node):
     return vtable, ValNul()
 
 
+class Fvnctio(Node):
+  def __init__(self, parameters: list[ID], statements: list[Node]) -> None:
+    self.parameters = parameters
+    self.statements = statements
+
+  def __eq__(self, other):
+    return (type(self) == type(other)
+      and self.parameters == other.parameters
+      and self.statements == other.statements)
+
+  def __repr__(self) -> str:
+    parameter_string = f"parameters([{rep_join(self.parameters)}])"
+    statements_string = f"statements([{rep_join(self.statements)}])"
+    fvn_string = rep_join([parameter_string, statements_string])
+    return f"Fvnctio({fvn_string})"
+
+  def print(self):
+    params = ", ".join(p.print() for p in self.parameters)
+    body = "\n".join(s.print() for s in self.statements)
+    return f"FVNCTIO ({params}) VT {{\n{body}\n}}"
+
+  def _eval(self, vtable):
+    return vtable, ValFunc(self.parameters, self.statements)
+
+
 class Redi(Node):
   def __init__(self, values: list[Node]) -> None:
     self.values = values
@@ -954,32 +981,36 @@ class PerStatement(Node):
 
 
 class Invoca(Node):
-  def __init__(self, name, parameters) -> None:
-    self.name = name
+  def __init__(self, callee, parameters) -> None:
+    self.callee = callee
     self.parameters = parameters
 
   def __eq__(self, other):
-    return type(self) == type(other) and self.name == other.name and self.parameters == other.parameters
+    return (type(self) == type(other)
+      and self.callee == other.callee
+      and self.parameters == other.parameters)
 
   def __repr__(self) -> str:
     parameters_string = f"parameters([{rep_join(self.parameters)}])"
-    invoca_string = rep_join([self.name, parameters_string])
+    invoca_string = rep_join([self.callee, parameters_string])
     return f"Invoca({invoca_string})"
 
   def print(self):
     args = ", ".join(p.print() for p in self.parameters)
-    return f"INVOCA {self.name.print()} ({args})"
+    return f"INVOCA {self.callee.print()} ({args})"
 
   def _eval(self, vtable):
     params = [p.eval(vtable)[1] for p in self.parameters]
-    if self.name.name not in vtable:
-      raise CentvrionError(f"Undefined function: {self.name.name}")
-    func = vtable[self.name.name]
+    vtable, func = self.callee.eval(vtable)
     if not isinstance(func, ValFunc):
-      raise CentvrionError(f"{self.name.name} is not a function")
+      callee_desc = (self.callee.name
+        if isinstance(self.callee, ID) else "expression")
+      raise CentvrionError(f"{callee_desc} is not a function")
     if len(params) != len(func.params):
+      callee_desc = (self.callee.name
+        if isinstance(self.callee, ID) else "FVNCTIO")
       raise CentvrionError(
-        f"{self.name.name} expects {len(func.params)} argument(s), got {len(params)}"
+        f"{callee_desc} expects {len(func.params)} argument(s), got {len(params)}"
       )
     func_vtable = vtable.copy()
     for i, param in enumerate(func.params):

centvrion/compiler/context.py

@@ -7,6 +7,10 @@ class EmitContext:
     self.functions = {}
     # source-level name / alias → c_func_name; populated by emitter pre-pass
     self.func_resolve = {}
+    # id(Fvnctio_node) → c_func_name; populated by lambda lifting pass
+    self.lambda_names = {}
+    # [(c_name, Fvnctio_node), ...]; populated by lambda lifting pass
+    self.lambdas = []
 
   def fresh_tmp(self):
     name = f"_t{self._tmp_counter}"

centvrion/compiler/emit_expr.py

@@ -3,7 +3,7 @@ from centvrion.ast_nodes import (
   String, InterpolatedString, Numeral, Fractio, Bool, Nullus, ID,
   BinOp, UnaryMinus, UnaryNot,
   ArrayIndex, DataArray, DataRangeArray, DataDict,
-  BuiltIn, Invoca,
+  BuiltIn, Invoca, Fvnctio,
   num_to_int, frac_to_fraction,
 )
 
@@ -162,6 +162,9 @@ def emit_expr(node, ctx):
   if isinstance(node, Invoca):
     return _emit_invoca(node, ctx)
 
+  if isinstance(node, Fvnctio):
+    return _emit_fvnctio(node, ctx)
+
   raise NotImplementedError(type(node).__name__)
 
 
@@ -261,7 +264,8 @@ def _emit_builtin(node, ctx):
 def _emit_invoca(node, ctx):
   """
   Emits a user-defined function call.
-  Requires ctx.functions[name] = [param_names] populated by the emitter pre-pass.
+  Supports both static resolution (ID callee with known function) and
+  dynamic dispatch (arbitrary expression callee via CENT_FUNC values).
   """
   lines = []
   param_vars = []
@@ -270,21 +274,59 @@ def _emit_invoca(node, ctx):
     lines.extend(p_lines)
     param_vars.append(p_var)
 
-  func_name = node.name.name
-  c_func_name = ctx.func_resolve.get(func_name)
-  if c_func_name is None:
-    raise CentvrionError(f"Undefined function: {func_name}")
+  # Try static resolution for simple ID callees
+  if isinstance(node.callee, ID):
+    c_func_name = ctx.func_resolve.get(node.callee.name)
+    if c_func_name is not None:
+      call_scope_var = ctx.fresh_tmp() + "_sc"
+      lines.append(f"CentScope {call_scope_var} = cent_scope_copy(&_scope);")
+      param_names = ctx.functions[c_func_name]
+      if len(param_vars) != len(param_names):
+        raise CentvrionError(
+          f"Function '{node.callee.name}' expects {len(param_names)} argument(s), "
+          f"got {len(param_vars)}"
+        )
+      for i, pname in enumerate(param_names):
+        lines.append(f'cent_scope_set(&{call_scope_var}, "{pname}", {param_vars[i]});')
+      tmp = ctx.fresh_tmp()
+      lines.append(f"CentValue {tmp} = {c_func_name}({call_scope_var});")
+      return lines, tmp
+
+  # Dynamic dispatch: evaluate callee, call via function pointer
+  callee_lines, callee_var = emit_expr(node.callee, ctx)
+  lines.extend(callee_lines)
+  lines.append(f'if ({callee_var}.type != CENT_FUNC) cent_type_error("cannot call non-function");')
   call_scope_var = ctx.fresh_tmp() + "_sc"
   lines.append(f"CentScope {call_scope_var} = cent_scope_copy(&_scope);")
-
-  param_names = ctx.functions[c_func_name]
-  if len(param_vars) != len(param_names):
-    raise CentvrionError(
-      f"Function '{func_name}' expects {len(param_names)} argument(s), got {len(param_vars)}"
+  nargs = len(param_vars)
+  lines.append(
+    f"if ({callee_var}.fnval.param_count != {nargs}) "
+    f'cent_runtime_error("wrong number of arguments");'
+  )
+  for i, pv in enumerate(param_vars):
+    lines.append(
+      f'cent_scope_set(&{call_scope_var}, '
+      f'{callee_var}.fnval.param_names[{i}], {pv});'
     )
-  for i, pname in enumerate(param_names):
-    lines.append(f'cent_scope_set(&{call_scope_var}, "{pname}", {param_vars[i]});')
-
   tmp = ctx.fresh_tmp()
-  lines.append(f"CentValue {tmp} = {c_func_name}({call_scope_var});")
+  lines.append(f"CentValue {tmp} = {callee_var}.fnval.fn({call_scope_var});")
+  return lines, tmp
+
+
+def _emit_fvnctio(node, ctx):
+  """Emit a FVNCTIO lambda expression as a CENT_FUNC value."""
+  c_name = ctx.lambda_names[id(node)]
+  param_names = ctx.functions[c_name]
+  tmp = ctx.fresh_tmp()
+  lines = []
+  # Build static param name array
+  params_arr = ctx.fresh_tmp() + "_pn"
+  lines.append(
+    f"static const char *{params_arr}[] = {{"
+    + ", ".join(f'"{p}"' for p in param_names)
+    + "};"
+  )
+  lines.append(
+    f"CentValue {tmp} = cent_func_val({c_name}, {params_arr}, {len(param_names)});"
+  )
   return lines, tmp

centvrion/compiler/emit_stmt.py

@@ -11,9 +11,6 @@ def emit_stmt(node, ctx):
   Returns lines — list of C statements.
   """
   if isinstance(node, Designa):
-    # Function alias: resolved at compile time, no runtime code needed
-    if isinstance(node.value, ID) and node.value.name in ctx.func_resolve:
-      return []
     val_lines, val_var = emit_expr(node.value, ctx)
     return val_lines + [f'cent_scope_set(&_scope, "{node.id.name}", {val_var});']
 
@@ -87,7 +84,20 @@ def emit_stmt(node, ctx):
     return lines
 
   if isinstance(node, Defini):
-    # Function definitions are hoisted by emitter.py; no-op here.
+    # Top-level definitions are handled by emitter.py (hoisted + scope-set).
+    # Nested definitions (inside another function) need runtime scope-set.
+    if ctx.current_function is not None:
+      name = node.name.name
+      c_name = ctx.func_resolve[name]
+      param_names = ctx.functions[c_name]
+      pn_var = ctx.fresh_tmp() + "_pn"
+      return [
+        f"static const char *{pn_var}[] = {{"
+        + ", ".join(f'"{p}"' for p in param_names)
+        + "};",
+        f'cent_scope_set(&_scope, "{name}", '
+        f"cent_func_val({c_name}, {pn_var}, {len(param_names)}));",
+      ]
     return []
 
   if isinstance(node, Redi):

centvrion/compiler/emitter.py

@@ -1,11 +1,32 @@
 import os
-from centvrion.ast_nodes import Defini, Designa, ID
+from centvrion.ast_nodes import Defini, Designa, Fvnctio, ID, Node
 from centvrion.compiler.context import EmitContext
 from centvrion.compiler.emit_stmt import emit_stmt, _emit_body
 
 _RUNTIME_DIR = os.path.join(os.path.dirname(__file__), "runtime")
 
 
+def _collect_lambdas(node, ctx, counter):
+  """Walk AST recursively, find all Fvnctio nodes, assign C names."""
+  if isinstance(node, Fvnctio):
+    c_name = f"_cent_lambda_{counter[0]}"
+    counter[0] += 1
+    ctx.lambda_names[id(node)] = c_name
+    ctx.functions[c_name] = [p.name for p in node.parameters]
+    ctx.lambdas.append((c_name, node))
+  for attr in vars(node).values():
+    if isinstance(attr, Node):
+      _collect_lambdas(attr, ctx, counter)
+    elif isinstance(attr, list):
+      for item in attr:
+        if isinstance(item, Node):
+          _collect_lambdas(item, ctx, counter)
+        elif isinstance(item, tuple):
+          for elem in item:
+            if isinstance(elem, Node):
+              _collect_lambdas(elem, ctx, counter)
+
+
 def compile_program(program):
   """Return a complete C source string for the given Program AST node."""
   ctx = EmitContext()
@@ -26,10 +47,11 @@ def compile_program(program):
       ctx.functions[c_name] = [p.name for p in stmt.parameters]
       ctx.func_resolve[name] = c_name
       func_definitions.append((c_name, stmt))
-    elif isinstance(stmt, Designa) and isinstance(stmt.value, ID):
-      rhs = stmt.value.name
-      if rhs in ctx.func_resolve:
-        ctx.func_resolve[stmt.id.name] = ctx.func_resolve[rhs]
+
+  # Lambda lifting: find all Fvnctio nodes in the entire AST
+  counter = [0]
+  for stmt in program.statements:
+    _collect_lambdas(stmt, ctx, counter)
 
   lines = []
 
@@ -39,13 +61,13 @@ def compile_program(program):
     "",
   ]
 
-  # Forward declarations
+  # Forward declarations (named functions + lambdas)
   for c_name in ctx.functions:
     lines.append(f"CentValue {c_name}(CentScope _scope);")
   if ctx.functions:
     lines.append("")
 
-  # Hoisted function definitions
+  # Hoisted named function definitions
   for c_name, stmt in func_definitions:
     ctx.current_function = c_name
     lines.append(f"CentValue {c_name}(CentScope _scope) {{")
@@ -55,6 +77,16 @@ def compile_program(program):
     lines += ["_func_return:", "  return _return_val;", "}", ""]
     ctx.current_function = None
 
+  # Hoisted lambda definitions
+  for c_name, fvnctio_node in ctx.lambdas:
+    ctx.current_function = c_name
+    lines.append(f"CentValue {c_name}(CentScope _scope) {{")
+    lines.append("  CentValue _return_val = cent_null();")
+    for l in _emit_body(fvnctio_node.statements, ctx):
+      lines.append(f"  {l}")
+    lines += ["_func_return:", "  return _return_val;", "}", ""]
+    ctx.current_function = None
+
   # main()
   lines.append("int main(void) {")
   lines.append("  cent_init();")
@@ -62,8 +94,25 @@ def compile_program(program):
     lines.append("  cent_magnvm = 1;")
   lines.append("  CentScope _scope = {0};")
   lines.append("  CentValue _return_val = cent_null();")
+
+  # Build a map from id(Defini_node) → c_name for scope registration
+  defini_c_names = {id(stmt): c_name for c_name, stmt in func_definitions}
+
   for stmt in program.statements:
     if isinstance(stmt, Defini):
+      name = stmt.name.name
+      c_name = defini_c_names[id(stmt)]
+      param_names = ctx.functions[c_name]
+      pn_var = f"_pn_{c_name}"
+      lines.append(
+        f"  static const char *{pn_var}[] = {{"
+        + ", ".join(f'"{p}"' for p in param_names)
+        + "};"
+      )
+      lines.append(
+        f'  cent_scope_set(&_scope, "{name}", '
+        f"cent_func_val({c_name}, {pn_var}, {len(param_names)}));"
+      )
       continue
     for l in emit_stmt(stmt, ctx):
       lines.append(f"  {l}")

centvrion/compiler/runtime/cent_runtime.c

@@ -290,6 +290,10 @@ static int write_val(CentValue v, char *buf, int bufsz) {
       return total;
     }
 
+    case CENT_FUNC:
+      if (buf && bufsz > 7) { memcpy(buf, "FVNCTIO", 7); buf[7] = '\0'; }
+      return 7;
+
     case CENT_DICT: {
       /* "{key VT val, key VT val}" */
       int total = 2;  /* '{' + '}' */
@@ -454,6 +458,7 @@ CentValue cent_eq(CentValue a, CentValue b) {
   switch (a.type) {
     case CENT_STR:  return cent_bool(strcmp(a.sval, b.sval) == 0);
     case CENT_BOOL: return cent_bool(a.bval == b.bval);
+    case CENT_FUNC: return cent_bool(a.fnval.fn == b.fnval.fn);
     case CENT_NULL: return cent_bool(1);
     default:
       cent_type_error("'EST' not supported for this type");

centvrion/compiler/runtime/cent_runtime.h

@@ -15,12 +15,23 @@ typedef enum {
   CENT_LIST,
   CENT_FRAC,
   CENT_DICT,
+  CENT_FUNC,
   CENT_NULL
 } CentType;
 
 typedef struct CentValue CentValue;
 typedef struct CentList  CentList;
 typedef struct CentDict  CentDict;
+struct CentScope;  /* forward declaration */
+
+/* First-class function value */
+typedef CentValue (*CentFuncPtr)(struct CentScope);
+
+typedef struct {
+  CentFuncPtr   fn;
+  const char  **param_names;
+  int           param_count;
+} CentFuncInfo;
 
 /* Duodecimal fraction: num/den stored as exact integers */
 typedef struct {
@@ -48,14 +59,15 @@ struct CentValue {
     char    *sval;  /* CENT_STR  */
     int      bval;  /* CENT_BOOL */
     CentList lval;  /* CENT_LIST */
-    CentFrac fval;  /* CENT_FRAC */
-    CentDict dval;  /* CENT_DICT */
+    CentFrac fval;      /* CENT_FRAC */
+    CentDict dval;      /* CENT_DICT */
+    CentFuncInfo fnval; /* CENT_FUNC */
   };
 };
 
 /* Scope: flat name→value array.  Stack-allocated by the caller;
    cent_scope_set uses cent_arena when it needs to grow. */
-typedef struct {
+typedef struct CentScope {
   const char **names;
   CentValue   *vals;
   int          len;
@@ -111,6 +123,14 @@ static inline CentValue cent_list(CentValue *items, int len, int cap) {
   r.lval.cap   = cap;
   return r;
 }
+static inline CentValue cent_func_val(CentFuncPtr fn, const char **param_names, int param_count) {
+  CentValue r;
+  r.type = CENT_FUNC;
+  r.fnval.fn = fn;
+  r.fnval.param_names = param_names;
+  r.fnval.param_count = param_count;
+  return r;
+}
 static inline CentValue cent_dict_val(CentValue *keys, CentValue *vals, int len, int cap) {
   CentValue r;
   r.type = CENT_DICT;

centvrion/lexer.py

@@ -18,6 +18,7 @@ keyword_tokens = [("KEYWORD_"+i, i) for i in [
   "ET",
   "FACE",
   "FALSITAS",
+  "FVNCTIO",
   "INVOCA",
   "IN",
   "MINVE",

centvrion/parser.py

@@ -287,10 +287,14 @@ class Parser():
     def unary_not(tokens):
       return ast_nodes.UnaryNot(tokens[1])
 
-    @self.pg.production('expression : KEYWORD_INVOCA id expressions')
+    @self.pg.production('expression : KEYWORD_INVOCA expression expressions')
     def invoca(tokens):
       return ast_nodes.Invoca(tokens[1], tokens[2])
 
+    @self.pg.production('expression : KEYWORD_FVNCTIO ids KEYWORD_VT SYMBOL_LCURL statements SYMBOL_RCURL')
+    def fvnctio(tokens):
+      return ast_nodes.Fvnctio(tokens[1], tokens[4])
+
     @self.pg.production('expression : SYMBOL_LPARENS expression SYMBOL_RPARENS')
     def parens(tokens):
       return tokens[1]

language/main.tex

@@ -55,7 +55,8 @@
         \languageline{expression}{\texttt{(} \textit{expression} \texttt{)}} \\
         \languageline{expression}{\textbf{id}} \\
         \languageline{expression}{\textbf{builtin} \texttt{(} \textit{optional-expressions} \texttt{)}} \\
-        \languageline{expression}{\texttt{INVOCA} \textbf{id} \texttt{(} \textit{optional-expressions} \texttt{)}} \\
+        \languageline{expression}{\texttt{INVOCA} \textit{expression} \texttt{(} \textit{optional-expressions} \texttt{)}} \\
+        \languageline{expression}{\texttt{FVNCTIO} \texttt{(} \textit{optional-ids} \texttt{)} \texttt{VT} \textit{scope}} \\
         \languageline{expression}{\textit{literal}} \\
         \languageline{expression}{\textit{expression} \texttt{[} \textit{expression} \texttt{]}} \\
         \languageline{expression}{\textit{expression} \textbf{binop} \textit{expression}} \\

snippets/fvnctio.cent

@@ -0,0 +1,9 @@
+DEFINI apply (f, x) VT {
+    REDI (INVOCA f (x))
+}
+
+DESIGNA dbl VT FVNCTIO (n) VT {
+    REDI (n * II)
+}
+
+DICE(INVOCA apply (dbl, VII))

snippets/invoca_expr.cent

@@ -0,0 +1,11 @@
+// Immediately invoked
+DICE(INVOCA FVNCTIO (x) VT { REDI (x + I) } (V))
+
+// From an array
+DESIGNA fns VT [FVNCTIO (x) VT { REDI (x + I) }]
+DICE(INVOCA fns[I] (V))
+
+// Passing a named function as an argument
+DEFINI apply (f, x) VT { REDI (INVOCA f (x)) }
+DEFINI sqr (x) VT { REDI (x * x) }
+DICE(INVOCA apply (sqr, IV))

snippets/syntaxes/centvrion.sublime-syntax

@@ -78,7 +78,7 @@ contexts:
       scope: support.class.module.centvrion
 
   keywords:
-    - match: '\b(AETERNVM|ALVID|AVGE|AVT|CONTINVA|DEFINI|DESIGNA|DISPAR|DONICVM|DVM|ERVMPE|EST|ET|FACE|INVOCA|IN|MINVE|MINVS|NON|PER|PLVS|REDI|RELIQVVM|SI|TABVLA|TVNC|VSQVE|VT|CVM)\b'
+    - match: '\b(AETERNVM|ALVID|AVGE|AVT|CONTINVA|DEFINI|DESIGNA|DISPAR|DONICVM|DVM|ERVMPE|EST|ET|FACE|FVNCTIO|INVOCA|IN|MINVE|MINVS|NON|PER|PLVS|REDI|RELIQVVM|SI|TABVLA|TVNC|VSQVE|VT|CVM)\b'
       scope: keyword.control.centvrion
 
   operators:

tests.py

@@ -12,9 +12,9 @@ from fractions import Fraction
 from centvrion.ast_nodes import (
   ArrayIndex, Bool, BinOp, BuiltIn, DataArray, DataDict, DataRangeArray,
   Defini, Continva, Designa, DesignaDestructure, DesignaIndex, DumStatement,
-  Erumpe, ExpressionStatement, ID, InterpolatedString, Invoca, ModuleCall,
-  Nullus, Numeral, PerStatement, Program, Redi, SiStatement, String,
-  UnaryMinus, UnaryNot, Fractio, frac_to_fraction, fraction_to_frac,
+  Erumpe, ExpressionStatement, Fvnctio, ID, InterpolatedString, Invoca,
+  ModuleCall, Nullus, Numeral, PerStatement, Program, Redi, SiStatement,
+  String, UnaryMinus, UnaryNot, Fractio, frac_to_fraction, fraction_to_frac,
   num_to_int, int_to_num, make_string,
 )
 from centvrion.compiler.emitter import compile_program
@@ -2047,5 +2047,157 @@ class TestDictDisplay(unittest.TestCase):
     run_test(self, source, nodes, value, output)
 
 
+# --- First-class functions / FVNCTIO ---
+
+fvnctio_tests = [
+  # Lambda assigned to variable, then called
+  (
+    "DESIGNA f VT FVNCTIO (x) VT { REDI (x + I) }\nINVOCA f (V)",
+    Program([], [
+      Designa(ID("f"), Fvnctio([ID("x")], [Redi([BinOp(ID("x"), Numeral("I"), "SYMBOL_PLUS")])])),
+      ExpressionStatement(Invoca(ID("f"), [Numeral("V")])),
+    ]),
+    ValInt(6),
+  ),
+  # IIFE: immediately invoked lambda
+  (
+    "INVOCA FVNCTIO (x) VT { REDI (x * II) } (III)",
+    Program([], [
+      ExpressionStatement(Invoca(
+        Fvnctio([ID("x")], [Redi([BinOp(ID("x"), Numeral("II"), "SYMBOL_TIMES")])]),
+        [Numeral("III")],
+      )),
+    ]),
+    ValInt(6),
+  ),
+  # Zero-arg lambda
+  (
+    "INVOCA FVNCTIO () VT { REDI (XLII) } ()",
+    Program([], [
+      ExpressionStatement(Invoca(
+        Fvnctio([], [Redi([Numeral("XLII")])]),
+        [],
+      )),
+    ]),
+    ValInt(42),
+  ),
+  # Function passed as argument
+  (
+    "DEFINI apply (f, x) VT { REDI (INVOCA f (x)) }\n"
+    "DESIGNA dbl VT FVNCTIO (n) VT { REDI (n * II) }\n"
+    "INVOCA apply (dbl, V)",
+    Program([], [
+      Defini(ID("apply"), [ID("f"), ID("x")], [
+        Redi([Invoca(ID("f"), [ID("x")])])
+      ]),
+      Designa(ID("dbl"), Fvnctio([ID("n")], [
+        Redi([BinOp(ID("n"), Numeral("II"), "SYMBOL_TIMES")])
+      ])),
+      ExpressionStatement(Invoca(ID("apply"), [ID("dbl"), Numeral("V")])),
+    ]),
+    ValInt(10),
+  ),
+  # Lambda uses caller-scope variable (copy-caller semantics)
+  (
+    "DESIGNA n VT III\n"
+    "DESIGNA f VT FVNCTIO (x) VT { REDI (x + n) }\n"
+    "INVOCA f (V)",
+    Program([], [
+      Designa(ID("n"), Numeral("III")),
+      Designa(ID("f"), Fvnctio([ID("x")], [
+        Redi([BinOp(ID("x"), ID("n"), "SYMBOL_PLUS")])
+      ])),
+      ExpressionStatement(Invoca(ID("f"), [Numeral("V")])),
+    ]),
+    ValInt(8),
+  ),
+  # Named function passed as value
+  (
+    "DEFINI sqr (x) VT { REDI (x * x) }\n"
+    "DESIGNA f VT sqr\n"
+    "INVOCA f (IV)",
+    Program([], [
+      Defini(ID("sqr"), [ID("x")], [Redi([BinOp(ID("x"), ID("x"), "SYMBOL_TIMES")])]),
+      Designa(ID("f"), ID("sqr")),
+      ExpressionStatement(Invoca(ID("f"), [Numeral("IV")])),
+    ]),
+    ValInt(16),
+  ),
+  # Nested lambdas
+  (
+    "INVOCA FVNCTIO (x) VT { REDI (INVOCA FVNCTIO (y) VT { REDI (y + I) } (x)) } (V)",
+    Program([], [
+      ExpressionStatement(Invoca(
+        Fvnctio([ID("x")], [
+          Redi([Invoca(
+            Fvnctio([ID("y")], [Redi([BinOp(ID("y"), Numeral("I"), "SYMBOL_PLUS")])]),
+            [ID("x")],
+          )])
+        ]),
+        [Numeral("V")],
+      )),
+    ]),
+    ValInt(6),
+  ),
+  # DICE on a function value
+  (
+    "DESIGNA f VT FVNCTIO (x) VT { REDI (x) }\nDICE(f)",
+    Program([], [
+      Designa(ID("f"), Fvnctio([ID("x")], [Redi([ID("x")])])),
+      ExpressionStatement(BuiltIn("DICE", [ID("f")])),
+    ]),
+    ValStr("FVNCTIO"),
+    "FVNCTIO\n",
+  ),
+  # Lambda stored in array, called via index
+  (
+    "DESIGNA fns VT [FVNCTIO (x) VT { REDI (x + I) }, FVNCTIO (x) VT { REDI (x * II) }]\n"
+    "INVOCA fns[I] (V)",
+    Program([], [
+      Designa(ID("fns"), DataArray([
+        Fvnctio([ID("x")], [Redi([BinOp(ID("x"), Numeral("I"), "SYMBOL_PLUS")])]),
+        Fvnctio([ID("x")], [Redi([BinOp(ID("x"), Numeral("II"), "SYMBOL_TIMES")])]),
+      ])),
+      ExpressionStatement(Invoca(
+        ArrayIndex(ID("fns"), Numeral("I")),
+        [Numeral("V")],
+      )),
+    ]),
+    ValInt(6),
+  ),
+  # Lambda stored in dict, called via key
+  (
+    'DESIGNA d VT TABVLA {"add" VT FVNCTIO (x) VT { REDI (x + I) }}\n'
+    'INVOCA d["add"] (V)',
+    Program([], [
+      Designa(ID("d"), DataDict([
+        (String("add"), Fvnctio([ID("x")], [Redi([BinOp(ID("x"), Numeral("I"), "SYMBOL_PLUS")])])),
+      ])),
+      ExpressionStatement(Invoca(
+        ArrayIndex(ID("d"), String("add")),
+        [Numeral("V")],
+      )),
+    ]),
+    ValInt(6),
+  ),
+  # Multi-param lambda
+  (
+    "DESIGNA add VT FVNCTIO (a, b) VT { REDI (a + b) }\nINVOCA add (III, IV)",
+    Program([], [
+      Designa(ID("add"), Fvnctio([ID("a"), ID("b")], [
+        Redi([BinOp(ID("a"), ID("b"), "SYMBOL_PLUS")])
+      ])),
+      ExpressionStatement(Invoca(ID("add"), [Numeral("III"), Numeral("IV")])),
+    ]),
+    ValInt(7),
+  ),
+]
+
+class TestFvnctio(unittest.TestCase):
+  @parameterized.expand(fvnctio_tests)
+  def test_fvnctio(self, source, nodes, value, output=""):
+    run_test(self, source, nodes, value, output)
+
+
 if __name__ == "__main__":
   unittest.main()

vscode-extension/syntaxes/cent.tmLanguage.json

@@ -45,7 +45,7 @@
 			"patterns": [
 				{
 					"name": "keyword.control.cent",
-					"match": "\\b(AETERNVM|ALVID|AVT|CONTINVA|CVM|DEFINI|DESIGNA|DONICVM|DVM|ERVMPE|ET|FACE|IN|INVOCA|NON|PER|REDI|SI|TVNC|VSQVE|VT)\\b"
+					"match": "\\b(AETERNVM|ALVID|AVT|CONTINVA|CVM|DEFINI|DESIGNA|DONICVM|DVM|ERVMPE|ET|FACE|FVNCTIO|IN|INVOCA|NON|PER|REDI|SI|TVNC|VSQVE|VT)\\b"
 				},
 				{
 					"name": "keyword.operator.comparison.cent",