diff --git a/src/solvers/flattening/boolbv.cpp b/src/solvers/flattening/boolbv.cpp
index 96bc17c42b4..746cf4ae703 100644
--- a/src/solvers/flattening/boolbv.cpp
+++ b/src/solvers/flattening/boolbv.cpp
@@ -294,7 +294,7 @@ bvt boolbvt::convert_bitvector(const exprt &expr)
   else if(expr.id()==ID_complex_imag)
     return convert_complex_imag(to_complex_imag_expr(expr));
   else if(expr.id()==ID_lambda)
-    return convert_lambda(expr);
+    return convert_lambda(to_lambda_expr(expr));
   else if(expr.id()==ID_array_of)
     return convert_array_of(to_array_of_expr(expr));
   else if(expr.id()==ID_let)
@@ -316,28 +316,21 @@ bvt boolbvt::convert_bitvector(const exprt &expr)
   return conversion_failed(expr);
 }
 
-bvt boolbvt::convert_lambda(const exprt &expr)
+bvt boolbvt::convert_lambda(const lambda_exprt &expr)
 {
   std::size_t width=boolbv_width(expr.type());
 
   if(width==0)
     return conversion_failed(expr);
 
-  DATA_INVARIANT(
-    expr.operands().size() == 2, "lambda expression should have two operands");
-
-  if(expr.type().id()!=ID_array)
-    return conversion_failed(expr);
-
-  const exprt &array_size=
-    to_array_type(expr.type()).size();
+  const exprt &array_size = expr.type().size();
 
   const auto size = numeric_cast<mp_integer>(array_size);
 
   if(!size.has_value())
     return conversion_failed(expr);
 
-  typet counter_type=expr.op0().type();
+  typet counter_type = expr.arg().type();
 
   bvt bv;
   bv.resize(width);
@@ -346,10 +339,10 @@ bvt boolbvt::convert_lambda(const exprt &expr)
   {
     exprt counter=from_integer(i, counter_type);
 
-    exprt expr_op1(expr.op1());
-    replace_expr(expr.op0(), counter, expr_op1);
+    exprt body = expr.body();
+    replace_expr(expr.arg(), counter, body);
 
-    const bvt &tmp=convert_bv(expr_op1);
+    const bvt &tmp = convert_bv(body);
 
     INVARIANT(
       *size * tmp.size() == width,
diff --git a/src/solvers/flattening/boolbv.h b/src/solvers/flattening/boolbv.h
index b2c87f2b881..4bbb9d853e9 100644
--- a/src/solvers/flattening/boolbv.h
+++ b/src/solvers/flattening/boolbv.h
@@ -28,6 +28,7 @@ Author: Daniel Kroening, kroening@kroening.com
 
 class extractbit_exprt;
 class extractbits_exprt;
+class lambda_exprt;
 class member_exprt;
 
 class boolbvt:public arrayst
@@ -148,7 +149,7 @@ class boolbvt:public arrayst
   virtual bvt convert_complex(const complex_exprt &expr);
   virtual bvt convert_complex_real(const complex_real_exprt &expr);
   virtual bvt convert_complex_imag(const complex_imag_exprt &expr);
-  virtual bvt convert_lambda(const exprt &expr);
+  virtual bvt convert_lambda(const lambda_exprt &expr);
   virtual bvt convert_let(const let_exprt &);
   virtual bvt convert_array_of(const array_of_exprt &expr);
   virtual bvt convert_union(const union_exprt &expr);
diff --git a/src/util/simplify_expr_array.cpp b/src/util/simplify_expr_array.cpp
index 4ef9a540706..8ade73f117a 100644
--- a/src/util/simplify_expr_array.cpp
+++ b/src/util/simplify_expr_array.cpp
@@ -48,16 +48,14 @@ bool simplify_exprt::simplify_index(exprt &expr)
   {
     // simplify (lambda i: e)(x) to e[i/x]
 
-    const exprt &lambda_expr=array;
+    const lambda_exprt &lambda_expr = to_lambda_expr(array);
 
-    if(lambda_expr.operands().size()!=2)
-      return true;
-
-    if(expr.op1().type()==lambda_expr.op0().type())
+    if(expr.op1().type() == lambda_expr.arg().type())
     {
-      exprt tmp=lambda_expr.op1();
-      replace_expr(lambda_expr.op0(), expr.op1(), tmp);
+      exprt tmp = lambda_expr.body();
+      replace_expr(lambda_expr.arg(), expr.op1(), tmp);
       expr.swap(tmp);
+      simplify_rec(expr);
       return false;
     }
   }
diff --git a/src/util/std_expr.h b/src/util/std_expr.h
index 4ff695e7a34..929afb7cbd8 100644
--- a/src/util/std_expr.h
+++ b/src/util/std_expr.h
@@ -4460,4 +4460,79 @@ inline cond_exprt &to_cond_expr(exprt &expr)
   return ret;
 }
 
+/// \brief Expression to define a mapping from an argument (index) to elements.
+/// This enables constructing an array via an anonymous function.
+class lambda_exprt : public binary_exprt
+{
+public:
+  explicit lambda_exprt(symbol_exprt arg, exprt body, array_typet _type)
+    : binary_exprt(std::move(arg), ID_lambda, std::move(body), std::move(_type))
+  {
+  }
+
+  const array_typet &type() const
+  {
+    return static_cast<const array_typet &>(binary_exprt::type());
+  }
+
+  array_typet &type()
+  {
+    return static_cast<array_typet &>(binary_exprt::type());
+  }
+
+  const symbol_exprt &arg() const
+  {
+    return static_cast<const symbol_exprt &>(op0());
+  }
+
+  symbol_exprt &arg()
+  {
+    return static_cast<symbol_exprt &>(op0());
+  }
+
+  const exprt &body() const
+  {
+    return op1();
+  }
+
+  exprt &body()
+  {
+    return op1();
+  }
+};
+
+template <>
+inline bool can_cast_expr<lambda_exprt>(const exprt &base)
+{
+  return base.id() == ID_lambda;
+}
+
+inline void validate_expr(const lambda_exprt &value)
+{
+  validate_operands(value, 2, "'Lambda' must have two operands");
+}
+
+/// \brief Cast an exprt to a \ref lambda_exprt
+///
+/// \a expr must be known to be \ref lambda_exprt.
+///
+/// \param expr: Source expression
+/// \return Object of type \ref lambda_exprt
+inline const lambda_exprt &to_lambda_expr(const exprt &expr)
+{
+  PRECONDITION(expr.id() == ID_lambda);
+  const lambda_exprt &ret = static_cast<const lambda_exprt &>(expr);
+  validate_expr(ret);
+  return ret;
+}
+
+/// \copydoc to_lambda_expr(const exprt &)
+inline lambda_exprt &to_lambda_expr(exprt &expr)
+{
+  PRECONDITION(expr.id() == ID_lambda);
+  lambda_exprt &ret = static_cast<lambda_exprt &>(expr);
+  validate_expr(ret);
+  return ret;
+}
+
 #endif // CPROVER_UTIL_STD_EXPR_H