UriTemplate.match() misparses {;var} when following literal begins with '=' #3852

Initial Checks

• I confirm that I'm using the newest release of my line (the latest 2.x, or the latest 1.x if I'm still on v1)
• I confirm that I searched for my issue in https://github.com/modelcontextprotocol/python-sdk/issues before opening this issue

Release line

2.x (current stable)

Description

UriTemplate.match() breaks match(expand(variables)) == variables when a {;var} path-style parameter expression (ifemp = True, RFC 6570 §3.2.7) is immediately followed by a literal that begins with "=" (for example "{;a}=end{+rest}" or "/api{;mode}=fast{/id}").

In src/mcp/shared/uri_template.py (_scan_prefix), the atom.ifemp check runs:

if uri.startswith(nxt.text, pos):
    result[var.name] = ""
    continue
if pos < limit and uri[pos] == "=":
    pos += 1

Checking uri.startswith(nxt.text, pos) unconditionally before uri[pos] == "=" handles the empty-value case (a == "" -> ";a=end/x"), except when a equals the stem of nxt.text (a == "end" -> expand() emits ";a=end=end/x"). At pos right after ";a", uri[pos:] is "=end=end/x", which also starts with nxt.text ("=end"). _scan_prefix prematurely treats a as "" and leaves the second "=end" to be absorbed by a downstream greedy variable {+rest} (or fails suffix matching when no greedy variable follows).

Example Code

from mcp.shared.uri_template import UriTemplate

tpl = UriTemplate.parse("{;a}=end{+rest}")
variables = {"a": "end", "rest": "/x"}

expanded = tpl.expand(variables)
matched = tpl.match(expanded)

print("expanded:", expanded)  # ';a=end=end/x'
print("matched :", matched)   # {'a': '', 'rest': '=end/x'}  (expected {'a': 'end', 'rest': '/x'})
assert matched == variables

Python & MCP Python SDK

• mcp: 2.3.0 (also verified on main 77001c96f9 in src/mcp/shared/uri_template.py)
• Python: 3.12.0