In　order　to　express　tree　pattern　query　in　query　plan　and　take　advantage　of　formal　method　to　analyze　its　behavioral　characteristics,　this　paper　present　a　formal　description　of　tree　pattern　query　based　on　functional　language　and　denotational　semantics.　This　description　major　focuses　on　behavior　of　a　tree　pattern　query　on　matching　against　an　eXtensible　Markup　Language　(XML)　document　tree.　First,　we　introduce　a　formal　definition　for　a　kind　of　extended　generalized　tree　pattern　(GTP++).　Then　we　present　a　functional　tree　pattern　description　language　(XTPL)　for　GTP++　and　give　its　complete　denotational　semantics　based　on　a　novel　data　structure,　named　WTree,　which　efficiently　organizes　this　typical　XML　data　query　results　and　provides　flexible　data　access　method.　In　the　end,　we　present　the　formal　semantics　of　identifying　tree　pattern　from　path　expressions.　By　using　formal　methods,　the　semantics　of　tree　pattern　query　is　consistent　and　analyzable.　As　the　core　operation　of　XML　query,　this　formal　description　can　provide　an　initial　step　for　analyzing　the　correctness　of　XML　queries,　and　improves　the　reliability　and　robustness　of　query　processing　methods.