The paradigm of type-based termination is explored for functional programming with recursive data types. The article introduces ${\Lambda}_{\mu}^{+}$, a lambda-calculus with recursion, inductive types, subtyping and bounded quantification. Decorated type variables representing approximations of inductive types are used to track the size of function arguments and return values. The system is shown to be type safe and strongly normalizing. The main novelty is a bidirectional type checking algorithm whose soundness is established formally.

Keywords: type-based termination, sized types, inductive types, course-of-value recursion, bidirectional type checking, strong normalization

@article{ITA_2004__38_4_277_0, author = {Abel, Andreas}, title = {Termination checking with types}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {277--319}, publisher = {EDP-Sciences}, volume = {38}, number = {4}, year = {2004}, doi = {10.1051/ita:2004015}, mrnumber = {2098193}, zbl = {1089.68028}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ita:2004015/} }

TY - JOUR AU - Abel, Andreas TI - Termination checking with types JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2004 SP - 277 EP - 319 VL - 38 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita:2004015/ DO - 10.1051/ita:2004015 LA - en ID - ITA_2004__38_4_277_0 ER -

%0 Journal Article %A Abel, Andreas %T Termination checking with types %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2004 %P 277-319 %V 38 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita:2004015/ %R 10.1051/ita:2004015 %G en %F ITA_2004__38_4_277_0

Abel, Andreas. Termination checking with types. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 38 (2004) no. 4, pp. 277-319. doi : 10.1051/ita:2004015. http://www.numdam.org/articles/10.1051/ita:2004015/

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