diff --git a/spec/compose_spec.lua b/spec/compose_spec.lua
new file mode 100644
index 0000000..0eeb337
--- /dev/null
+++ b/spec/compose_spec.lua
@@ -0,0 +1,85 @@
+local errors = require("jsonata.errors")
+local E = require("jsonata.evaluator")
+
+describe("M5d: M.is_function + T2006", function()
+  it("M.is_function recognizes lambdas and builtins, rejects data", function()
+    assert.is_true(E.is_function({ _jsonata_lambda = true }))
+    assert.is_true(E.is_function({ _jsonata_function = true }))
+    assert.is_falsy(E.is_function(5))
+    assert.is_falsy(E.is_function("x"))
+    assert.is_falsy(E.is_function({ a = 1 }))
+    assert.is_falsy(E.is_function(nil))
+  end)
+
+  it("defines the T2006 template", function()
+    local ok, e = pcall(errors.raise, "T2006", { value = 3 })
+    assert.is_false(ok)
+    assert.are.equal("T2006", e.code)
+    assert.is_not_nil(e.message:find("function application", 1, true))
+  end)
+end)
+
+describe("M5d: ~> function composition", function()
+  local jsonata = require("jsonata")
+  local function run(src, input)
+    return jsonata.compile(src):evaluate(input)
+  end
+  local function code(src, input)
+    local ok, err = pcall(run, src, input)
+    assert.is_false(ok)
+    return err.code
+  end
+
+  it("composes two builtins, applied via ~>", function()
+    assert.are.equal(225, run("($square := function($x){$x*$x}; $i := $sum ~> $square; [1..5] ~> $i())"))
+  end)
+
+  it("composes and is directly callable, left-to-right order", function()
+    assert.are.equal("HELLO WORLD", run("($ut := $trim ~> $uppercase; $ut('   Hello    World   '))"))
+  end)
+
+  it("composes partially-applied functions (partial composition)", function()
+    assert.are.equal(55, run("($square := function($x){$x*$x}; $ss := $map(?, $square) ~> $sum; [1..5] ~> $ss())"))
+  end)
+
+  it("re-composes (three-way, left-associative)", function()
+    assert.are.equal(13, run("($inc := function($x){$x+1}; $dbl := function($x){$x*2}; $f := $inc ~> $dbl ~> $inc; $f(5))"))
+  end)
+
+  it("raises T2006 when the right side is not a function", function()
+    assert.are.equal("T2006", code("42 ~> 'hello'"))
+    assert.are.equal("T2006", code("($f := $sum; $f ~> 3)"))
+  end)
+
+  it("does not break the apply form (non-function lhs unchanged)", function()
+    assert.are.equal("5", run("5 ~> $string"))
+    assert.are.equal(6, run("[1,2,3] ~> $sum"))
+    assert.are.equal("HI", run("'hi' ~> $uppercase"))
+  end)
+end)
+
+describe("M5d: ~> with a partial-application RHS", function()
+  local jsonata = require("jsonata")
+  local function run(src, input)
+    return jsonata.compile(src):evaluate(input)
+  end
+
+  it("composes two partials (case009 — both sides are functions)", function()
+    assert.are.equal("example", run('($domain := $substringAfter(?,"@") ~> $substringBefore(?,"."); $domain("john@example.com"))'))
+  end)
+
+  it("composes partials inline applied to a value", function()
+    assert.are.equal("example", run('"john@example.com" ~> $substringAfter(?, "@") ~> $substringBefore(?, ".")'))
+  end)
+
+  it("applies a partial RHS to a data lhs (fills the placeholder with lhs)", function()
+    assert.are.equal(25, run("5 ~> $power(?, 2)")) -- 5^2
+    assert.are.equal(32, run("5 ~> $power(2, ?)")) -- 2^5
+  end)
+
+  it("leaves the no-placeholder apply-with-args form unchanged", function()
+    assert.are.equal("hello", run('"hello world" ~> $substring(0, 5)'))
+    assert.are.equal("5", run("5 ~> $string"))
+    assert.are.equal(6, run("[1,2,3] ~> $sum"))
+  end)
+end)
diff --git a/spec/jsonata-suite/baseline.lua b/spec/jsonata-suite/baseline.lua
index d99abbd..490934e 100644
--- a/spec/jsonata-suite/baseline.lua
+++ b/spec/jsonata-suite/baseline.lua
@@ -234,13 +234,19 @@ return {
   ["function-applications/case002"] = true,
   ["function-applications/case003"] = true,
   ["function-applications/case004"] = true,
+  ["function-applications/case005"] = true,
   ["function-applications/case006"] = true,
   ["function-applications/case007"] = true,
   ["function-applications/case008"] = true,
+  ["function-applications/case009"] = true,
   ["function-applications/case010"] = true,
   ["function-applications/case011"] = true,
+  ["function-applications/case012"] = true,
   ["function-applications/case013"] = true,
   ["function-applications/case014"] = true,
+  ["function-applications/case015"] = true,
+  ["function-applications/case016"] = true,
+  ["function-applications/case017"] = true,
   ["function-applications/case019"] = true,
   ["function-applications/case020"] = true,
   ["function-assert/case000"] = true,
diff --git a/src/jsonata/errors.lua b/src/jsonata/errors.lua
index e51ded1..27aecdc 100644
--- a/src/jsonata/errors.lua
+++ b/src/jsonata/errors.lua
@@ -18,6 +18,7 @@ local MESSAGES = {
   T1003 = "Key in object structure must evaluate to a string; got: {{value}}",
   T1006 = "Attempted to invoke a non-function",
   T2001 = "The left side of an operator must evaluate to a number",
+  T2006 = "The right side of the function application operator ~> must be a function",
   T2002 = "The right side of an operator must evaluate to a number",
   T2003 = "The left side of the range operator (..) must evaluate to an integer",
   T2004 = "The right side of the range operator (..) must evaluate to an integer",
diff --git a/src/jsonata/evaluator.lua b/src/jsonata/evaluator.lua
index 6a19155..0aabf96 100644
--- a/src/jsonata/evaluator.lua
+++ b/src/jsonata/evaluator.lua
@@ -5,6 +5,17 @@ local sort = require("jsonata.sort")
 
 local M = {}
 
+-- The function-composition meta-lambda (jsonata chainAST): parsed once, evaluated
+-- per-compose so the inner lambda closes over the specific $f/$g. Lazy-required to
+-- avoid an evaluator->parser load edge at module init.
+local chain_ast
+local function get_chain_ast()
+  if not chain_ast then
+    chain_ast = require("jsonata.parser").parse("function($f, $g){ function($x){ $g($f($x)) } }")
+  end
+  return chain_ast
+end
+
 local evaluate -- forward declaration
 
 local function as_number(x, code)
@@ -776,14 +787,36 @@ local function _evaluate(node, input, env)
     local lhs = evaluate(node.lhs, input, env)
     local rhs = node.rhs
     if rhs.type == "function" then
-      local proc = evaluate(rhs.procedure, input, env)
-      local args = { lhs }
+      local partial = false
       for _, a in ipairs(rhs.arguments) do
-        args[#args + 1] = evaluate(a, input, env)
+        if a.type == "placeholder" then
+          partial = true
+          break
+        end
       end
-      return M.apply(proc, args, input, env)
+      -- A bare invocation (no placeholders) is the apply-with-args form:
+      -- lhs ~> $f(a, b)  =>  $f(lhs, a, b). When the rhs carries a `?`
+      -- placeholder it is a partial application; fall through and evaluate it
+      -- as a function value to compose with (or apply to) the lhs below.
+      if not partial then
+        local proc = evaluate(rhs.procedure, input, env)
+        local args = { lhs }
+        for _, a in ipairs(rhs.arguments) do
+          args[#args + 1] = evaluate(a, input, env)
+        end
+        return M.apply(proc, args, input, env)
+      end
+    end
+    local proc = evaluate(rhs, input, env)
+    if not M.is_function(proc) then
+      errors.raise("T2006", { value = proc, position = node.position })
+    end
+    if M.is_function(lhs) then
+      -- compose: $f ~> $g  =>  λ($x){ $g($f($x)) }  (f first, then g)
+      local chain = evaluate(get_chain_ast(), input, env)
+      return M.apply(chain, { lhs, proc }, input, env)
     end
-    return M.apply(evaluate(rhs, input, env), { lhs }, input, env)
+    return M.apply(proc, { lhs }, input, env)
   elseif t == "transform" then
     return {
       _jsonata_function = true,
@@ -893,6 +926,11 @@ evaluate = function(node, input, env)
   return result
 end
 
+-- True iff `x` is a callable JSONata value (a lambda closure or a builtin).
+function M.is_function(x)
+  return type(x) == "table" and (x._jsonata_lambda or x._jsonata_function)
+end
+
 -- Apply a procedure (lambda closure or builtin) to a list of evaluated args.
 function M.apply(proc, args, context, env)
   if type(proc) == "table" and proc._jsonata_lambda then
@@ -945,7 +983,7 @@ end
 
 -- Partial application: $f(?, x) -> a new function that fills the holes when applied.
 function M.partial(proc, argnodes, input, env)
-  if not (type(proc) == "table" and (proc._jsonata_lambda or proc._jsonata_function)) then
+  if not M.is_function(proc) then
     errors.raise("T1006", { value = proc })
   end
   local bound = {}