Abstract
Programs contain variables, and the bindings of these variables to the corresponding values are kept in a so-called ’environment’. A first-class environment is a mechanism that the environments in programs can be treated as first-class entities, which are objects that can to be passed and returned between functions and procedures. Nishizaki proposed the lambda calculus with first-class environments, called the environment lambda calculus, and has investigated its theoretical properties [6–8, 10]. The various systems of the environment lambda calculus are based on weak reduction, that is, application of a substitution to a lambda abstraction is postponed until an argument is applied to it. In this paper, we propose a simply-typed lambda calculus with strong reduction. We investigate several theoretical properties such as the subject reduction theorem.
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Nishizaki, Sy., Fujii, M. (2012). Strong Reduction for Typed Lambda Calculus with First-Class Environments. In: Liu, B., Ma, M., Chang, J. (eds) Information Computing and Applications. ICICA 2012. Lecture Notes in Computer Science, vol 7473. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34062-8_82
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DOI: https://doi.org/10.1007/978-3-642-34062-8_82
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