diff --git a/src/runtime/python/expr.c b/src/runtime/python/expr.c
index 82ac1f028..7d6229296 100644
--- a/src/runtime/python/expr.c
+++ b/src/runtime/python/expr.c
@@ -15,25 +15,25 @@ Expr_str(ExprObject *self)
     return str;
 }
 
-static PyObject *
-Expr_richcompare(ExprObject *e1, ExprObject *e2, int op)
-{
-    bool same = false;
-
-    // TODO
-
-    // same = true;
-// done:
-
-    if (op == Py_EQ) {
-        if (same) Py_RETURN_TRUE;  else Py_RETURN_FALSE;
-    } else if (op == Py_NE) {
-        if (same) Py_RETURN_FALSE; else Py_RETURN_TRUE;
-    } else {
-        PyErr_SetString(PyExc_TypeError, "comparison operation not supported");
-        Py_RETURN_NOTIMPLEMENTED;
-    }
-}
+// static PyObject *
+// Expr_richcompare(ExprObject *e1, ExprObject *e2, int op)
+// {
+//     bool same = false;
+//
+//     // TODO
+//
+//     // same = true;
+// // done:
+//
+//     if (op == Py_EQ) {
+//         if (same) Py_RETURN_TRUE;  else Py_RETURN_FALSE;
+//     } else if (op == Py_NE) {
+//         if (same) Py_RETURN_FALSE; else Py_RETURN_TRUE;
+//     } else {
+//         PyErr_SetString(PyExc_TypeError, "comparison operation not supported");
+//         Py_RETURN_NOTIMPLEMENTED;
+//     }
+// }
 
 static PyMethodDef Expr_methods[] = {
 //     {"unpack", (PyCFunction)Expr_unpack, METH_VARARGS,
@@ -106,7 +106,7 @@ PyTypeObject pgf_ExprType = {
     "abstract syntax tree",    /*tp_doc*/
     0,                           /*tp_traverse */
     0,                           /*tp_clear */
-    (richcmpfunc) Expr_richcompare, /*tp_richcompare */
+    0, //(richcmpfunc) Expr_richcompare, /*tp_richcompare */
     0,                           /*tp_weaklistoffset */
     0,                           /*tp_iter */
     0,                           /*tp_iternext */
@@ -125,6 +125,174 @@ PyTypeObject pgf_ExprType = {
 
 // ----------------------------------------------------------------------------
 
+static ExprFunObject *
+ExprFun_new(PyTypeObject *subtype, PyObject *args, PyObject *kwds)
+{
+    ExprFunObject* self = (ExprFunObject *)subtype->tp_alloc(subtype, 0);
+    return self;
+}
+
+static int
+ExprFun_init(ExprFunObject *self, PyObject *args, PyObject *kwds)
+{
+    PyObject* lit = NULL;
+    if (!PyArg_ParseTuple(args, "U", &lit)) {
+        return -1;
+    }
+    self->name = lit;
+    return 0;
+}
+
+static PyObject *
+ExprFun_richcompare(ExprFunObject *t1, ExprFunObject *t2, int op)
+{
+    bool same = false;
+    if (PyUnicode_Compare(t1->name, t2->name) != 0) goto done;
+
+    same = true;
+done:
+
+    if (op == Py_EQ) {
+        if (same) Py_RETURN_TRUE;  else Py_RETURN_FALSE;
+    } else if (op == Py_NE) {
+        if (same) Py_RETURN_FALSE; else Py_RETURN_TRUE;
+    } else {
+        PyErr_SetString(PyExc_TypeError, "comparison operation not supported");
+        Py_RETURN_NOTIMPLEMENTED;
+    }
+}
+
+/* static */
+PyTypeObject pgf_ExprFunType = {
+    PyVarObject_HEAD_INIT(NULL, 0)
+    //0,                         /*ob_size*/
+    "pgf.ExprFun",                /*tp_name*/
+    sizeof(ExprFunObject),        /*tp_basicsize*/
+    0,                         /*tp_itemsize*/
+    0, //(destructor)Expr_dealloc,  /*tp_dealloc*/
+    0,                         /*tp_print*/
+    0,                         /*tp_getattr*/
+    0,                         /*tp_setattr*/
+    0,                         /*tp_compare*/
+    0,                         /*tp_repr*/
+    0,                         /*tp_as_number*/
+    0,                         /*tp_as_sequence*/
+    0,                         /*tp_as_mapping*/
+    0, //(hashfunc) Expr_hash,      /*tp_hash */
+    0, //(ternaryfunc) Expr_call,   /*tp_call*/
+    0, //(reprfunc) Expr_str,      /*tp_str*/
+    0, //(getattrofunc) Expr_getattro,/*tp_getattro*/
+    0,                         /*tp_setattro*/
+    0,                         /*tp_as_buffer*/
+    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE, /*tp_flags*/
+    "function or data constructor",    /*tp_doc*/
+    0,                           /*tp_traverse */
+    0,                           /*tp_clear */
+    (richcmpfunc) ExprFun_richcompare, /*tp_richcompare */
+    0,                           /*tp_weaklistoffset */
+    0,                           /*tp_iter */
+    0,                           /*tp_iternext */
+    0, //Expr_methods,              /*tp_methods */
+    0,                         /*tp_members */
+    0, //Expr_getseters,            /*tp_getset */
+    &pgf_ExprType,             /*tp_base */
+    0,                         /*tp_dict */
+    0,                         /*tp_descr_get */
+    0,                         /*tp_descr_set */
+    0,                         /*tp_dictoffset */
+    (initproc) ExprFun_init,   /*tp_init */
+    0,                         /*tp_alloc */
+    (newfunc) ExprFun_new,     /*tp_new */
+};
+
+// ----------------------------------------------------------------------------
+
+static ExprAppObject *
+ExprApp_new(PyTypeObject *subtype, PyObject *args, PyObject *kwds)
+{
+    ExprAppObject* self = (ExprAppObject *)subtype->tp_alloc(subtype, 0);
+    return self;
+}
+
+static int
+ExprApp_init(ExprAppObject *self, PyObject *args, PyObject *kwds)
+{
+    PyObject* e1 = NULL;
+    PyObject* e2 = NULL;
+    if (!PyArg_ParseTuple(args, "O!O!", &pgf_ExprType, &e1, &pgf_ExprType, &e2)) {
+        return -1;
+    }
+
+    self->e1 = (ExprObject *)e1;
+    self->e2 = (ExprObject *)e2;
+    return 0;
+}
+
+static PyObject *
+ExprApp_richcompare(ExprAppObject *t1, ExprAppObject *t2, int op)
+{
+    bool same = false;
+
+    // TODO
+
+    same = true;
+// done:
+
+    if (op == Py_EQ) {
+        if (same) Py_RETURN_TRUE;  else Py_RETURN_FALSE;
+    } else if (op == Py_NE) {
+        if (same) Py_RETURN_FALSE; else Py_RETURN_TRUE;
+    } else {
+        PyErr_SetString(PyExc_TypeError, "comparison operation not supported");
+        Py_RETURN_NOTIMPLEMENTED;
+    }
+}
+
+/* static */
+PyTypeObject pgf_ExprAppType = {
+    PyVarObject_HEAD_INIT(NULL, 0)
+    //0,                         /*ob_size*/
+    "pgf.ExprApp",                /*tp_name*/
+    sizeof(ExprAppObject),        /*tp_basicsize*/
+    0,                         /*tp_itemsize*/
+    0, //(destructor)Expr_dealloc,  /*tp_dealloc*/
+    0,                         /*tp_print*/
+    0,                         /*tp_getattr*/
+    0,                         /*tp_setattr*/
+    0,                         /*tp_compare*/
+    0,                         /*tp_repr*/
+    0,                         /*tp_as_number*/
+    0,                         /*tp_as_sequence*/
+    0,                         /*tp_as_mapping*/
+    0, //(hashfunc) Expr_hash,      /*tp_hash */
+    0, //(ternaryfunc) Expr_call,   /*tp_call*/
+    0, //(reprfunc) Expr_str,      /*tp_str*/
+    0, //(getattrofunc) Expr_getattro,/*tp_getattro*/
+    0,                         /*tp_setattro*/
+    0,                         /*tp_as_buffer*/
+    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE, /*tp_flags*/
+    "application",    /*tp_doc*/
+    0,                           /*tp_traverse */
+    0,                           /*tp_clear */
+    (richcmpfunc) ExprApp_richcompare, /*tp_richcompare */
+    0,                           /*tp_weaklistoffset */
+    0,                           /*tp_iter */
+    0,                           /*tp_iternext */
+    0, //Expr_methods,              /*tp_methods */
+    0,                         /*tp_members */
+    0, //Expr_getseters,            /*tp_getset */
+    &pgf_ExprType,             /*tp_base */
+    0,                         /*tp_dict */
+    0,                         /*tp_descr_get */
+    0,                         /*tp_descr_set */
+    0,                         /*tp_dictoffset */
+    (initproc) ExprApp_init,   /*tp_init */
+    0,                         /*tp_alloc */
+    (newfunc) ExprApp_new,     /*tp_new */
+};
+
+// ----------------------------------------------------------------------------
+
 static ExprLitObject *
 ExprLit_new(PyTypeObject *subtype, PyObject *args, PyObject *kwds)
 {
diff --git a/src/runtime/python/expr.h b/src/runtime/python/expr.h
index 19b3fa45d..04576a0a1 100644
--- a/src/runtime/python/expr.h
+++ b/src/runtime/python/expr.h
@@ -11,7 +11,7 @@
 typedef struct {
     PyObject_HEAD
     PyObject *hypos; // PyListObject of PyTupleObject: (bind_type: int, cid: string, type: TypeObject)
-    PyObject *cat;   // PyStringObject
+    PyObject *cat;   // PyUnicodeObject
     PyObject *exprs; // PyListObject of ExprObject
 } TypeObject;
 
@@ -23,21 +23,36 @@ typedef struct {
 
 typedef struct {
     PyObject_HEAD
-    PyObject *value;
+    PyObject *name; // PyUnicodeObject
+} ExprFunObject;
+
+typedef struct {
+    PyObject_HEAD
+    ExprObject *e1; // ExprObject
+    ExprObject *e2; // ExprObject
+} ExprAppObject;
+
+typedef struct {
+    PyObject_HEAD
+    PyObject *value; // PyLongObject | PyFloatObject | PyUnicodeObject
 } ExprLitObject;
 
 typedef struct {
     PyObject_HEAD
-    PyObject *id;
+    PyObject *id; // PyLongObject
 } ExprMetaObject;
 
 typedef struct {
     PyObject_HEAD
-    PyObject *index;
+    PyObject *index; // PyLongObject
 } ExprVarObject;
 
 extern PyTypeObject pgf_ExprType;
 
+extern PyTypeObject pgf_ExprFunType;
+
+extern PyTypeObject pgf_ExprAppType;
+
 extern PyTypeObject pgf_ExprLitType;
 
 extern PyTypeObject pgf_ExprMetaType;
diff --git a/src/runtime/python/marshaller.c b/src/runtime/python/marshaller.c
index e2dab89fd..7dcb4bd63 100644
--- a/src/runtime/python/marshaller.c
+++ b/src/runtime/python/marshaller.c
@@ -7,6 +7,35 @@
 #include "./compat.h"
 #include "./expr.h"
 
+// ----------------------------------------------------------------------------
+
+PgfText *
+PyUnicode_AsPgfText(PyObject *pystr)
+{
+    if (!PyUnicode_Check(pystr)) {
+        PyErr_SetString(PyExc_TypeError, "input to PyUnicode_AsPgfText is not a string");
+        return NULL;
+    }
+    if (PyUnicode_READY(pystr) != 0) {
+        return NULL;
+    }
+
+    Py_ssize_t size;
+    const char *enc = PyUnicode_AsUTF8AndSize(pystr, &size);
+    PgfText *ptext = malloc(sizeof(PgfText)+size+1);
+    memcpy(ptext->text, enc, size+1);
+    ptext->size = size;
+    return ptext;
+}
+
+PyObject *
+PyUnicode_FromPgfText(PgfText *text)
+{
+    return PyUnicode_FromStringAndSize(text->text, text->size);
+}
+
+// ----------------------------------------------------------------------------
+
 /* The PgfUnmarshaller structure tells the runtime how to create
  * abstract syntax expressions and types in the heap of the host language.
  * In Python the expressions are normal objects.
@@ -22,8 +51,12 @@ PgfExpr eabs(PgfUnmarshaller *this, PgfBindType btype, PgfText *name, PgfExpr bo
 
 PgfExpr eapp(PgfUnmarshaller *this, PgfExpr fun, PgfExpr arg)
 {
-    PyErr_SetString(PyExc_NotImplementedError, "eapp not implemented");
-    return 0;
+    ExprAppObject *pyexpr = (ExprAppObject *)pgf_ExprAppType.tp_alloc(&pgf_ExprAppType, 0);
+    pyexpr->e1 = (ExprObject *)fun;
+    pyexpr->e2 = (ExprObject *)arg;
+    // Py_INCREF(fun);
+    // Py_INCREF(arg);
+    return (PgfExpr) pyexpr;
 }
 
 PgfExpr elit(PgfUnmarshaller *this, PgfLiteral lit)
@@ -44,8 +77,11 @@ PgfExpr emeta(PgfUnmarshaller *this, PgfMetaId meta)
 
 PgfExpr efun(PgfUnmarshaller *this, PgfText *name)
 {
-    PyErr_SetString(PyExc_NotImplementedError, "efun not implemented");
-    return 0;
+    ExprFunObject *pyexpr = (ExprFunObject *)pgf_ExprFunType.tp_alloc(&pgf_ExprFunType, 0);
+    PyObject *pyobj = PyUnicode_FromPgfText(name);
+    pyexpr->name = pyobj;
+    Py_INCREF(pyobj);
+    return (PgfExpr) pyexpr;
 }
 
 PgfExpr evar(PgfUnmarshaller *this, int index)
@@ -154,27 +190,6 @@ PgfUnmarshaller unmarshaller = { &unmarshallerVtbl };
 
 // ----------------------------------------------------------------------------
 
-PgfText *
-PyUnicode_AsPgfText(PyObject *pystr)
-{
-    if (!PyUnicode_Check(pystr)) {
-        PyErr_SetString(PyExc_TypeError, "input to PyUnicode_AsPgfText is not a string");
-        return NULL;
-    }
-    if (PyUnicode_READY(pystr) != 0) {
-        return NULL;
-    }
-
-    Py_ssize_t size;
-    const char *enc = PyUnicode_AsUTF8AndSize(pystr, &size);
-    PgfText *ptext = malloc(sizeof(PgfText)+size+1);
-    memcpy(ptext->text, enc, size+1);
-    ptext->size = size;
-    return ptext;
-}
-
-// ----------------------------------------------------------------------------
-
 object match_lit(PgfMarshaller *this, PgfUnmarshaller *u, PgfLiteral lit)
 {
     PyObject *pyobj = (PyObject *)lit;
@@ -226,13 +241,23 @@ object match_expr(PgfMarshaller *this, PgfUnmarshaller *u, PgfExpr expr)
 {
     PyObject *pyobj = (PyObject *)expr;
 
+    if (PyObject_TypeCheck(pyobj, &pgf_ExprFunType)) {
+        ExprFunObject *efun = (ExprFunObject *)expr;
+        return u->vtbl->efun(u, PyUnicode_AsPgfText(efun->name));
+    } else
+    if (PyObject_TypeCheck(pyobj, &pgf_ExprAppType)) {
+        ExprAppObject *eapp = (ExprAppObject *)expr;
+        return u->vtbl->eapp(u, (PgfExpr) eapp->e1, (PgfExpr) eapp->e2); // TODO check
+    } else
     if (PyObject_TypeCheck(pyobj, &pgf_ExprLitType)) {
         ExprLitObject *elit = (ExprLitObject *)expr;
         return this->vtbl->match_lit(this, u, (PgfLiteral) elit->value);
-    } else if (PyObject_TypeCheck(pyobj, &pgf_ExprMetaType)) {
+    } else
+    if (PyObject_TypeCheck(pyobj, &pgf_ExprMetaType)) {
         ExprMetaObject *emeta = (ExprMetaObject *)expr;
         return u->vtbl->emeta(u, (PgfMetaId) PyLong_AsLong(emeta->id));
-    } else if (PyObject_TypeCheck(pyobj, &pgf_ExprVarType)) {
+    } else
+    if (PyObject_TypeCheck(pyobj, &pgf_ExprVarType)) {
         ExprVarObject *evar = (ExprVarObject *)expr;
         return u->vtbl->evar(u, PyLong_AsLong(evar->index));
     } else {
diff --git a/src/runtime/python/marshaller.h b/src/runtime/python/marshaller.h
index bec013fe8..110334f21 100644
--- a/src/runtime/python/marshaller.h
+++ b/src/runtime/python/marshaller.h
@@ -8,6 +8,8 @@
 
 PgfText *PyUnicode_AsPgfText(PyObject *pystr);
 
+PyObject *PyUnicode_FromPgfText(PgfText *text);
+
 extern PgfUnmarshaller unmarshaller;
 
 extern PgfMarshaller marshaller;
diff --git a/src/runtime/python/pypgf.c b/src/runtime/python/pypgf.c
index 6b4bff183..335d7fc1a 100644
--- a/src/runtime/python/pypgf.c
+++ b/src/runtime/python/pypgf.c
@@ -2666,6 +2666,12 @@ MOD_INIT(pgf)
     if (PyType_Ready(&pgf_ExprType) < 0)
         return MOD_ERROR_VAL;
 
+    if (PyType_Ready(&pgf_ExprFunType) < 0)
+        return MOD_ERROR_VAL;
+
+    if (PyType_Ready(&pgf_ExprAppType) < 0)
+        return MOD_ERROR_VAL;
+
     if (PyType_Ready(&pgf_ExprLitType) < 0)
         return MOD_ERROR_VAL;
 
@@ -2703,6 +2709,12 @@ MOD_INIT(pgf)
     PyModule_AddObject(m, "Expr", (PyObject *) &pgf_ExprType);
     Py_INCREF(&pgf_ExprType);
 
+    PyModule_AddObject(m, "ExprFun", (PyObject *) &pgf_ExprFunType);
+    Py_INCREF(&pgf_ExprFunType);
+
+    PyModule_AddObject(m, "ExprApp", (PyObject *) &pgf_ExprAppType);
+    Py_INCREF(&pgf_ExprAppType);
+
     PyModule_AddObject(m, "ExprLit", (PyObject *) &pgf_ExprLitType);
     Py_INCREF(&pgf_ExprLitType);
 
diff --git a/src/runtime/python/test_suite.py b/src/runtime/python/test_suite.py
index b3fb45a59..0e47ceae4 100644
--- a/src/runtime/python/test_suite.py
+++ b/src/runtime/python/test_suite.py
@@ -216,8 +216,27 @@ def test_readExpr_lstr_str():
 
 # expressions: functions
 
-      # ,TestCase (assertEqual "show expression 1" "f x y" (showExpr [] (EApp (EApp (EFun "f") (EFun "x")) (EFun "y"))))
-      # ,TestCase (assertEqual "show expression 2" "f (g x)" (showExpr [] (EApp (EFun "f") (EApp (EFun "g") (EFun "x")))))
+def test_readExpr_efun_equality_1():
+    assert pgf.readExpr("f") == pgf.ExprFun("f")
+
+def test_readExpr_efun_equality_2():
+    assert pgf.readExpr("f x y") == pgf.ExprApp(
+        pgf.ExprApp(
+            pgf.ExprFun("f"),
+            pgf.ExprFun("x")
+        ),
+        pgf.ExprFun("y")
+    )
+
+def test_readExpr_efun_equality_3():
+    assert pgf.readExpr("f (g x)") == pgf.ExprApp(
+        pgf.ExprFun("f"),
+        pgf.ExprApp(
+            pgf.ExprFun("g"),
+            pgf.ExprFun("x")
+        )
+    )
+
       # ,TestCase (assertEqual "show expression 3" "f {g x}" (showExpr [] (EApp (EFun "f") (EImplArg (EApp (EFun "g") (EFun "x"))))))
 
 # expressions: variables