fix(auth): url parse is not correct (#402)

The format method is not good for url.

Author: jokemanfire

crates/rmcp/src/transport/auth.rs

@@ -16,6 +16,8 @@ use thiserror::Error;
 use tokio::sync::{Mutex, RwLock};
 use tracing::{debug, error};
 
+const DEFAULT_EXCHANGE_URL: &str = "http://localhost";
+
 /// sse client with oauth2 authorization
 #[derive(Clone)]
 pub struct AuthClient<C> {
@@ -225,10 +227,17 @@ impl AuthorizationManager {
             // discard the path part, only keep scheme, host, port
             auth_base.set_path("");
 
+            // Helper function to create endpoint URL
+            let create_endpoint = |path: &str| -> String {
+                let mut url = auth_base.clone();
+                url.set_path(path);
+                url.to_string()
+            };
+
             Ok(AuthorizationMetadata {
-                authorization_endpoint: format!("{}/authorize", auth_base),
-                token_endpoint: format!("{}/token", auth_base),
-                registration_endpoint: format!("{}/register", auth_base),
+                authorization_endpoint: create_endpoint("authorize"),
+                token_endpoint: create_endpoint("token"),
+                registration_endpoint: create_endpoint("register"),
                 issuer: None,
                 jwks_uri: None,
                 scopes_supported: None,
@@ -686,7 +695,7 @@ impl OAuthState {
         if let OAuthState::Unauthorized(manager) = self {
             let mut manager = std::mem::replace(
                 manager,
-                AuthorizationManager::new("http://localhost").await?,
+                AuthorizationManager::new(DEFAULT_EXCHANGE_URL).await?,
             );
 
             // write credentials
@@ -716,7 +725,7 @@ impl OAuthState {
     ) -> Result<(), AuthError> {
         if let OAuthState::Unauthorized(mut manager) = std::mem::replace(
             self,
-            OAuthState::Unauthorized(AuthorizationManager::new("http://localhost").await?),
+            OAuthState::Unauthorized(AuthorizationManager::new(DEFAULT_EXCHANGE_URL).await?),
         ) {
             debug!("start discovery");
             let metadata = manager.discover_metadata().await?;
@@ -736,7 +745,7 @@ impl OAuthState {
     pub async fn complete_authorization(&mut self) -> Result<(), AuthError> {
         if let OAuthState::Session(session) = std::mem::replace(
             self,
-            OAuthState::Unauthorized(AuthorizationManager::new("http://localhost").await?),
+            OAuthState::Unauthorized(AuthorizationManager::new(DEFAULT_EXCHANGE_URL).await?),
         ) {
             *self = OAuthState::Authorized(session.auth_manager);
             Ok(())
@@ -748,7 +757,7 @@ impl OAuthState {
     pub async fn to_authorized_http_client(&mut self) -> Result<(), AuthError> {
         if let OAuthState::Authorized(manager) = std::mem::replace(
             self,
-            OAuthState::Authorized(AuthorizationManager::new("http://localhost").await?),
+            OAuthState::Authorized(AuthorizationManager::new(DEFAULT_EXCHANGE_URL).await?),
         ) {
             *self = OAuthState::AuthorizedHttpClient(AuthorizedHttpClient::new(
                 Arc::new(manager),