@TechReport{Kahl-Carette-Ji-2006b,
  author = 	 {Wolfram Kahl and Jacques Carette and Xiaoheng Ji},
  title = 	 {Bimonadic Semantics for Basic Pattern Matching Calculi},
  institution =  {Software Quality Research Laboratory, McMaster Univ.},
  year = 	 2006,
  type = 	 {SQRL Report},
  number = 	 33,
  pages =        32,
  note = {long version of \cite{Kahl-Carette-Ji-2006a}, available from
          \textsf{\url{http://sqrl.mcmaster.ca/sqrl_reports.html}}},
  month = 	 JUN,
  abstract = { The pattern matching calculi
      introduced by the first author
      are a refinement of the $\lambda$-calculus
      that integrates mechanisms appropriate for
      fine-grained modelling of non-strict pattern matching.
      
      While related work in the literature
      only uses a single monad, typically \textsf{Maybe},
      for matchings,
      we present an axiomatic approach
      to semantics of these pattern matching calculi using two monads,
      one for expressions and one for matchings.
      
      Although these two monads only need to be relatively lightly coupled,
      this semantics implies soundness of all core $\PMC$ rules,
      and is a useful tool for
      exploration of the design space for pattern matching calculi.
      
      Using lifting and \textsf{Maybe} monads,
      we obtain standard Haskell semantics,
      and by adding another level of \textsf{Maybe} to both,
      we obtain a denotational semantics
      of the ``matching failure as exceptions'' approach
      of Erwig and Peyton Jones.
      Using list-like monads opens up
      interesting extensions in the direction of functional-logic programming.
      
      A short version of this report appears as \cite{Kahl-Carette-Ji-2006a}.}
}

@InProceedings{Kahl-Carette-Ji-2006a,
  author = 	 {Wolfram Kahl and Jacques Carette and Xiaoheng Ji},
  title = 	 {Bimonadic Semantics for Basic Pattern Matching Calculi},
  crossref =  {MPC2006},
  pages = 	 {253--273}
}

@Proceedings{MPC2006,
  title = {Mathematics of Program Construction, {MPC 2006, Kuressaare, Estonia}},
  booktitle = {Mathematics of Program Construction, {MPC 2006}},
  editor = {Tarmo Uustalu},
  year = 2006,
  publisher = Springer,
  series = LNCS,
  volume = {4014},
  URL = {http://link.springer.de/link/service/series/0558/tocs/t4014.htm}
}