diff --git a/src/util.rs b/src/util.rs
index 81553b5a..92f1810b 100644
--- a/src/util.rs
+++ b/src/util.rs
@@ -1,4 +1,7 @@
-use crate::run::Rewrites;
+use crate::{
+  ast::{Net, Tree},
+  run::Rewrites,
+};
 use std::time::Duration;
 
 /// Creates a variable uniquely identified by `id`.
@@ -15,6 +18,7 @@ pub(crate) fn create_var(mut id: usize) -> String {
 }
 
 /// Inverse function of [`create_var`].
+///
 /// Returns None when the provided string is not an output of
 /// `create_var`.
 pub fn var_to_num(s: &str) -> Option<usize> {
@@ -151,44 +155,64 @@ macro_rules! deref {
   };
 }
 
-impl crate::ast::Net {
-  /// Transforms the net `x & ...` into `y & x ~ (arg y) & ...`
-  pub fn with_argument(&mut self, arg: crate::ast::Tree) {
-    use crate::ast::Tree;
-    let mut fresh = 0usize;
-    fn ensure_no_conflicts(tree: &Tree, fresh: &mut usize) {
-      match tree {
-        Tree::Ctr { lft, rgt, .. } | Tree::Op2 { lft, rgt, .. } | Tree::Mat { sel: lft, ret: rgt } => {
-          ensure_no_conflicts(lft, fresh);
-          ensure_no_conflicts(rgt, fresh);
-        }
-        Tree::Op1 { rgt, .. } => {
-          ensure_no_conflicts(rgt, fresh);
-        }
-        Tree::Var { nam } => {
-          if let Some(var_num) = var_to_num(nam) {
-            *fresh = (*fresh).max(var_num);
-          }
+pub(crate) use deref;
+
+impl Tree {
+  /// Increases `fresh` until `create_var(*fresh)` does not conflict
+  /// with a [`Tree::Var`]  in `tree`
+  ///
+  /// This function can be called multiple times with many trees to
+  /// ensure that `fresh` does not conflict with any of them.
+  pub(crate) fn ensure_no_conflicts(&self, fresh: &mut usize) {
+    match self {
+      Tree::Var { nam } => {
+        if let Some(var_num) = var_to_num(nam) {
+          *fresh = (*fresh).max(var_num);
         }
-        _ => (),
       }
+      // Recurse on children
+      Tree::Ctr { lft, rgt, .. } | Tree::Op2 { lft, rgt, .. } | Tree::Mat { sel: lft, ret: rgt } => {
+        lft.ensure_no_conflicts(fresh);
+        rgt.ensure_no_conflicts(fresh);
+      }
+      Tree::Op1 { rgt, .. } => {
+        rgt.ensure_no_conflicts(fresh);
+      }
+      Tree::Era => (),
+      Tree::Num { .. } => (),
+      Tree::Ref { .. } => (),
     }
-    ensure_no_conflicts(&self.root, &mut fresh);
-    for (l, r) in &self.rdex {
-      ensure_no_conflicts(l, &mut fresh);
-      ensure_no_conflicts(r, &mut fresh);
+  }
+}
+
+impl Net {
+  pub(crate) fn ensure_no_conflicts(&self, fresh: &mut usize) {
+    self.root.ensure_no_conflicts(fresh);
+    for (a, b) in &self.rdex {
+      a.ensure_no_conflicts(fresh);
+      b.ensure_no_conflicts(fresh);
     }
+  }
+  /// Transforms the net `x & ...` into `y & x ~ (arg y) & ...`
+  ///
+  /// The result is equivalent a λ-calculus application. Thus,
+  /// if the net is a λ-calculus term, then this function will
+  /// apply an argument to it.
+  #[allow(dead_code)] // used in tests
+  pub(crate) fn with_argument(&mut self, arg: Tree) {
+    let mut fresh = 0usize;
+    self.ensure_no_conflicts(&mut fresh);
+    arg.ensure_no_conflicts(&mut fresh);
+
     let fresh_str = create_var(fresh + 1);
 
     let fun = core::mem::take(&mut self.root);
-    let oth = Tree::Ctr { lab: 0, lft: Box::new(arg), rgt: Box::new(Tree::Var { nam: fresh_str.clone() }) };
+    let app = Tree::Ctr { lab: 0, lft: Box::new(arg), rgt: Box::new(Tree::Var { nam: fresh_str.clone() }) };
     self.root = Tree::Var { nam: fresh_str };
-    self.rdex.push((fun, oth));
+    self.rdex.push((fun, app));
   }
 }
 
-pub(crate) use deref;
-
 pub fn show_rewrites(rwts: &Rewrites) -> String {
   format!(
     "{}{}{}{}{}{}",
diff --git a/tests/api.rs b/tests/api.rs
new file mode 100644
index 00000000..53c5fefc
--- /dev/null
+++ b/tests/api.rs
@@ -0,0 +1,59 @@
+//! Tests for front-facing APIs and interfaces
+
+use hvmc::{
+  ast::{Book, Net, Tree},
+  host::Host,
+};
+use insta::assert_display_snapshot;
+
+#[test]
+fn test_with_argument() {
+  use hvmc::run;
+  fn eval_with_args(fun: &str, args: &[&str]) -> Net {
+    let area = run::Net::<run::Strict>::init_heap(1 << 10);
+
+    let mut fun: Net = fun.parse().unwrap();
+    for arg in args {
+      let arg: Tree = arg.parse().unwrap();
+      fun.with_argument(arg)
+    }
+    // TODO: When feature/sc-472/argument-passing, use encode_net instead.
+    let mut book = Book::default();
+    book.nets.insert("main".into(), fun);
+    let host = Host::new(&book);
+
+    let mut rnet = run::Net::<run::Strict>::new(&area);
+    rnet.boot(&host.defs["main"]);
+    rnet.normal();
+    let got_result = host.readback(&rnet);
+    got_result
+  }
+  assert_display_snapshot!(
+    eval_with_args("(a a)", &vec!["(a a)"]),
+    @"(a a)"
+  );
+  assert_display_snapshot!(
+    eval_with_args("b & (a b) ~ a", &vec!["(a a)"]),
+    @"a"
+  );
+  assert_display_snapshot!(
+    eval_with_args("(z0 z0)", &vec!["(z1 z1)"]),
+    @"(a a)"
+  );
+  assert_display_snapshot!(
+    eval_with_args("(* #1)", &vec!["(a a)"]),
+    @"#1"
+  );
+  assert_display_snapshot!(
+    eval_with_args("(<+ a b> (a b))", &vec!["#1", "#2"]),
+    @"#3"
+  );
+  assert_display_snapshot!(
+    eval_with_args("(<* a b> (a b))", &vec!["#2", "#3"]),
+    @"#6"
+  );
+  assert_display_snapshot!(
+    eval_with_args("(<* a b> (a b))", &vec!["#2"]),
+    @"(<2* a> a)"
+  );
+}
diff --git a/tests/lists.rs b/tests/lists.rs
index f68269e6..523ba5a4 100644
--- a/tests/lists.rs
+++ b/tests/lists.rs
@@ -7,10 +7,10 @@ fn list_got(index: u32) -> Book {
   let code = load_file("list_put_got.hvmc");
   let mut book = parse_core(&code);
   println!("{:#?}", book.keys().collect::<Vec<_>>());
-  let mut def = book.get_mut("GenGotIndex").unwrap();
-  core_apply(&mut def, hvmc::ast::Tree::Ref { nam: format!("S{index}") });
-  let mut def = book.get_mut("main").unwrap();
-  core_apply(&mut def, hvmc::ast::Tree::Ref { nam: format!("GenGotIndex") });
+  let def = book.get_mut("GenGotIndex").unwrap();
+  def.with_argument(hvmc::ast::Tree::Ref { nam: format!("S{index}") });
+  let def = book.get_mut("main").unwrap();
+  def.with_argument(hvmc::ast::Tree::Ref { nam: format!("GenGotIndex") });
   book
 }
 
diff --git a/tests/loaders/mod.rs b/tests/loaders/mod.rs
index 4094e9be..afbff8ca 100644
--- a/tests/loaders/mod.rs
+++ b/tests/loaders/mod.rs
@@ -8,14 +8,6 @@ pub fn load_file(file: &str) -> String {
   fs::read_to_string(path).unwrap()
 }
 
-pub fn core_apply(net: &mut Net, arg: Tree) {
-  let fun = core::mem::take(&mut net.root);
-  let var = format!("$_TEST_APP{:p}", net);
-  let oth = Tree::Ctr { lab: 0, lft: Box::new(arg), rgt: Box::new(Tree::Var { nam: var.clone() }) };
-  net.root = Tree::Var { nam: var };
-  net.rdex.push((fun, oth));
-}
-
 // Parses code and generate Book from hvm-core syntax
 pub fn parse_core(code: &str) -> Book {
   code.parse().unwrap()