Some lambda calculi with categorical sums and products. Dougherty, D. J.\ 1993.
Some lambda calculi with categorical sums and products [pdf]Paper  abstract   bibtex   
We consider the simply typed $łambda$-calculus with primitive recursion operators and types corresponding to categorical products and coproducts. The standard equations corresponding to extensionality and to surjectivity of pairing and its dual are oriented as expansion rules. Strong normalization and ground (base-type) confluence is proved for the full calculus; full confluence is proved for the calculus omitting the rule for strong sums. In the latter case, fixed-point constructors may be added while retaining confluence.
@conference{ c_rta93,
  author = {Daniel J.\ Dougherty},
  title = {Some lambda calculi with categorical sums and
                  products},
  pages = {137--151},
  isbn = {3-540-56868-9},
  editor = {Claude Kirchner},
  booktitle = {Proc.\ 5th International Conference on
                  Rewriting Techniques and Applications ({RTA})},
  series = {Lecture Notes in Computer Science},
  volume = {690},
  publisher = {Springer-Verlag},
  address = {Berlin},
  year = {1993},
  abstract = { We consider the simply typed
                  $łambda$-calculus with primitive recursion
                  operators and types corresponding to
                  categorical products and coproducts. The
                  standard equations corresponding to
                  extensionality and to surjectivity of pairing
                  and its dual are oriented as expansion
                  rules. Strong normalization and ground
                  (base-type) confluence is proved for the full
                  calculus; full confluence is proved for the
                  calculus omitting the rule for strong sums. In
                  the latter case, fixed-point constructors may
                  be added while retaining confluence. },
  url = {rta93.pdf}
}
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