diff --git a/.gitignore b/.gitignore
index 0b209db..9d1f418 100644
--- a/.gitignore
+++ b/.gitignore
@@ -3,7 +3,7 @@
 # https://github.com/github/gitignore/blob/main/community/Golang/Go.AllowList.gitignore
 #
 # Binaries for programs and plugins
-lambda
+/lambda
 *.exe
 *.exe~
 *.dll
diff --git a/pkg/lambda/iterator.go b/pkg/lambda/iterator.go
new file mode 100644
index 0000000..76b711a
--- /dev/null
+++ b/pkg/lambda/iterator.go
@@ -0,0 +1,59 @@
+package lambda
+
+type Iterator struct {
+	trace []*Expression
+}
+
+func NewIterator(expr *Expression) *Iterator {
+	return &Iterator{
+		trace: []*Expression{expr},
+	}
+}
+
+func (i *Iterator) Current() *Expression {
+	if len(i.trace) < 1 {
+		return nil
+	}
+
+	return i.trace[len(i.trace)-1]
+}
+
+func (i *Iterator) Parent() *Expression {
+	if len(i.trace) < 2 {
+		return nil
+	}
+
+	return i.trace[len(i.trace)-2]
+}
+
+func (i *Iterator) Next() {
+	switch typed := (*i.Current()).(type) {
+	case *Abstraction:
+		i.trace = append(i.trace, &typed.body)
+	case *Application:
+		i.trace = append(i.trace, &typed.abstraction)
+	case *Variable:
+		for len(i.trace) > 1 {
+			if app, ok := (*i.Parent()).(*Application); ok {
+				if app.abstraction == *i.Current() {
+					i.Back()
+					i.trace = append(i.trace, &app.argument)
+					return
+				}
+			}
+
+			i.Back()
+		}
+
+		i.trace = []*Expression{}
+	}
+}
+
+func (i *Iterator) Back() bool {
+	if len(i.trace) == 0 {
+		return false
+	}
+
+	i.trace = i.trace[:len(i.trace)-1]
+	return true
+}