diff --git a/_bookdown.yml b/_bookdown.yml
index bd89fd1b..7ecbb1e8 100644
--- a/_bookdown.yml
+++ b/_bookdown.yml
@@ -40,7 +40,6 @@ rmd_files:
   - "rmarkdown-workflow.Rmd"
 
   - "appendixes.Rmd"
-  - "references.Rmd"
 
 before_chapter_script: "_common.R"
 book_filename: "r4ds-solutions"
diff --git a/appendixes.Rmd b/appendixes.Rmd
index ac0dd46c..342873c5 100644
--- a/appendixes.Rmd
+++ b/appendixes.Rmd
@@ -1,64 +1,3 @@
 # (PART) Appendixes {-}
 
-# Functions for Primary and Foreign Keys {-}
-
-The chapter [Relational data](#relational-data) describes primary key and foreign key relations.
-However, the dplyr package does not provide functions to check for these.
-
-The `any_missing()` function is a helper function that will be used later. 
-```{r}
-any_missing <- function(x) any(is.na(x))
-```
-
-The `is_primary_key()` function checks whether variables are 
-```{r}
-#' Check whether variables are a primary key
-#' 
-#' Check whether a set of variables is a primary key for a data frame.
-#' Unlike SQL databases, R data frames do not enforce a primary key 
-#' constraint. This function checks whether a set of variables uniquely
-#' identify a row.
-#'
-#' @param tbl A tbl.
-#' @param ... One or more unquoted expressions separated by commas. 
-#'   You can treat variable names like they are positions. This uses
-#'   The same semantics as [dplyr::select()].
-#' @return A logical vector of length one that is `TRUE` if the 
-#'   variables are primary key, and `FALSE` otherwise.
-is_primary_key <- function(tbl, ...) {
-  variables <- quos(...)
-  # no elements can be missing
-  has_nulls <- summarise_at(tbl, vars(UQS(variables)), any_missing)
-  if (any(as.logical(has_nulls))) {
-    return(FALSE)
-  }
-  nrow(distinct(tbl, !!!variables)) == nrow(tbl)
-}
-
-foo <- tribble(
-  ~a, ~b, ~c,
-  1, NA, 1,
-  2, 2, 1,
-  3, 3, 3
-)
-
-is_key(foo, a)
-is_key(foo, b)
-is_key(foo, c)
-
-is_key(foo, 1:3)
-```
-
-The `is_foreign_key()` function checks whether 
-```{r is_foreign_key}
-# check that columns in y are are foreign key of x
-is_foreign_key <- function(x, y, by = NULL) {
-  # check that y is a primary key
-  if (!rlang::eval_tidy(quo(is_primary_key(y, !!!by)))) {
-    return(FALSE)
-  }
-  # check that all x are found in y
-  !nrow(anti_join(x, y, by = by))
-}
-
-```
+# References {-}
diff --git a/bin/keys_example.R b/bin/keys_example.R
new file mode 100644
index 00000000..da2d39df
--- /dev/null
+++ b/bin/keys_example.R
@@ -0,0 +1,48 @@
+any_missing <- function(x) any(is.na(x))
+
+#' Check whether variables are a primary key
+#'
+#' Check whether a set of variables is a primary key for a data frame.
+#' Unlike SQL databases, R data frames do not enforce a primary key
+#' constraint. This function checks whether a set of variables uniquely
+#' identify a row.
+#'
+#' @param tbl A tbl.
+#' @param ... One or more unquoted expressions separated by commas.
+#'   You can treat variable names like they are positions. This uses
+#'   The same semantics as [dplyr::select()].
+#' @return A logical vector of length one that is `TRUE` if the
+#'   variables are primary key, and `FALSE` otherwise.
+is_primary_key <- function(tbl, ...) {
+  variables <- quos(...)
+  # no elements can be missing
+  has_nulls <- summarise_at(tbl, vars(UQS(variables)), any_missing)
+  if (any(as.logical(has_nulls))) {
+    return(FALSE)
+  }
+  nrow(distinct(tbl, !!!variables)) == nrow(tbl)
+}
+
+foo <- tribble(
+  ~a, ~b, ~c,
+  1, NA, 1,
+  2, 2, 1,
+  3, 3, 3
+)
+
+is_key(foo, a)
+is_key(foo, b)
+is_key(foo, c)
+
+is_key(foo, 1:3)
+
+# check that columns in y are are foreign key of x
+is_foreign_key <- function(x, y, by = NULL) {
+  # check that y is a primary key
+  if (!rlang::eval_tidy(quo(is_primary_key(y, !!!by)))) {
+    return(FALSE)
+  }
+  # check that all x are found in y
+  !nrow(anti_join(x, y, by = by))
+}
+
diff --git a/references.Rmd b/references.Rmd
deleted file mode 100644
index b553324e..00000000
--- a/references.Rmd
+++ /dev/null
@@ -1 +0,0 @@
-# References {-}