Fix server routing matching URIs with prefixes (#1484)

We are incorrectly matching URIs to the spec when the URI has a prefix
that is not in the spec.

This is because when generating the regex describing the spec, we're not
using the `^` anchor to match from the beginning of the text.

Fixes #1483.

rust-runtime/aws-smithy-http-server/src/routing/request_spec.rs

@@ -98,7 +98,7 @@ impl From<&PathSpec> for Regex {
     fn from(uri_path_spec: &PathSpec) -> Self {
         let sep = "/";
         let re = if uri_path_spec.0.is_empty() {
-            String::from("/")
+            String::from(sep)
         } else {
             uri_path_spec
                 .0
@@ -113,7 +113,7 @@ impl From<&PathSpec> for Regex {
                 .fold(String::new(), |a, b| a + sep + b)
         };
 
-        Regex::new(&format!("{}$", re)).unwrap()
+        Regex::new(&format!("^{}$", re)).expect("invalid `Regex` from `PathSpec`; please file a bug report under https://github.com/awslabs/smithy-rs/issues")
     }
 }
 
@@ -250,15 +250,15 @@ mod tests {
     #[test]
     fn path_spec_into_regex() {
         let cases = vec![
-            (PathSpec(vec![]), "/$"),
-            (PathSpec(vec![PathSegment::Literal(String::from("a"))]), "/a$"),
+            (PathSpec(vec![]), "^/$"),
+            (PathSpec(vec![PathSegment::Literal(String::from("a"))]), "^/a$"),
             (
                 PathSpec(vec![PathSegment::Literal(String::from("a")), PathSegment::Label]),
-                "/a/[^/]*$",
+                "^/a/[^/]*$",
             ),
             (
                 PathSpec(vec![PathSegment::Literal(String::from("a")), PathSegment::Greedy]),
-                "/a/.*$",
+                "^/a/.*$",
             ),
             (
                 PathSpec(vec![
@@ -266,7 +266,7 @@ mod tests {
                     PathSegment::Greedy,
                     PathSegment::Literal(String::from("suffix")),
                 ]),
-                "/a/.*/suffix$",
+                "^/a/.*/suffix$",
             ),
         ];
 
@@ -276,6 +276,34 @@ mod tests {
         }
     }
 
+    #[test]
+    fn paths_must_match_spec_from_the_beginning_literal() {
+        let spec = RequestSpec::from_parts(
+            Method::GET,
+            vec![PathSegment::Literal(String::from("path"))],
+            Vec::new(),
+        );
+
+        let misses = vec![(Method::GET, "/beta/path"), (Method::GET, "/multiple/stages/in/path")];
+        for (method, uri) in &misses {
+            assert_eq!(Match::No, spec.matches(&req(method, uri, None)));
+        }
+    }
+
+    #[test]
+    fn paths_must_match_spec_from_the_beginning_label() {
+        let spec = RequestSpec::from_parts(Method::GET, vec![PathSegment::Label], Vec::new());
+
+        let misses = vec![
+            (Method::GET, "/prefix/label"),
+            (Method::GET, "/label/suffix"),
+            (Method::GET, "/prefix/label/suffix"),
+        ];
+        for (method, uri) in &misses {
+            assert_eq!(Match::No, spec.matches(&req(method, uri, None)));
+        }
+    }
+
     #[test]
     fn greedy_labels_match_greedily() {
         let spec = RequestSpec::from_parts(