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- W2045773183 abstract "Hagino (1987) develops CPL , a categorical programming language based on dialgebras which include algebras, coalgebras, products, sums and exponentials. We give an introduction to dialgebras and CPL . Working from the well-known correspondence between cartesian closed categories (CCCs) and λ-calculi (Lambek, 1980; Curien, 1986), we study the relationship between CPL and F 1 , Church's simply typed λ-calculus. We show that the reduction rules of CPL correspond to β-reduction in first-order contexts. Iteration over inductive types may be added to F 1 , obtaining F i 1 (Pierce et al., 1989). We show how to represent F i 1 inductive types in CPL . Thus Ackermann's function is in CPL . We argue that all natural number functions N → N provably total in first-order arithmetic can be expressed in CPL ." @default.
- W2045773183 created "2016-06-24" @default.
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- W2045773183 date "1993-04-01" @default.
- W2045773183 modified "2023-10-18" @default.
- W2045773183 title "Comparing Hagino's categorical programming language and typed lambda-calculi" @default.
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- W2045773183 doi "https://doi.org/10.1016/0304-3975(93)90186-w" @default.
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