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A language supporting polymorphism is a boon to programmers: they can express complex ideas once and reuse functions in a variety of situations. However, polymorphism is pain for compilers tasked with producing efficient code that manipulates concrete values. This paper presents a new intermediate language that allows for efficient static compilation, while still supporting flexible polymorphism. Specifically, it permits polymorphism over not only the types of values, but also the representation of values, the arity of primitive machine functions, and the evaluation order of arguments---all three of which are useful in practice. The key insight is to encode information about a value's calling convention in the kind of its type, rather than in the type itself.more » « less
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A language supporting polymorphism is a boon to programmers: they can express complex ideas once and reuse functions in a variety of situations. However, polymorphism is a pain for compilers tasked with producing efficient code that manipulates concrete values. This paper presents a new intermediate language that allows for efficient static compilation, while still supporting flexible polymorphism. Specifically, it permits polymorphism over not only the types of values, but also the representation of values, the arity of primitive machine functions, and the evaluation order of arguments---all three of which are useful in practice. The key insight is to encode information about a value's calling convention in the kind of its type, rather than in the type itself.more » « less
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Recursion and induction are mature, well-understood topics in programming. Yet their duals, co-recursion and co-induction, are still exotic and underdeveloped programming features. We aim to put them on equal footing by giving a foundation for co-recursion based on computation, analogous to the original computational foundation of recursion. At the lower level, we show how the connection between the two can be strengthened through their implementation details in an abstract machine. At the higher level, we develop a syntactic equational theory for inductive and co-inductive reasoning based on control flow. We also observe the impact of evaluation strategy: call-by-name has efficient recursion and strong co-inductive reasoning, but call-by-value has efficient co-recursion and strong inductive reasoning.more » « less
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Computer scientists are well-versed in dealing with data structures. The same cannot be said about their dual: codata. Even though codata is pervasive in category theory, universal algebra, and logic, the use of codata for programming has been mainly relegated to representing infinite objects and processes. Our goal is to demonstrate the benefits of codata as a general-purpose programming abstraction independent of any specific language: eager or lazy, statically or dynamically typed, and functional or object-oriented. While codata is not featured in many programming languages today, we show how codata can be easily adopted and implemented by offering simple inter-compilation techniques between data and codata. We believe codata is a common ground between the functional and object-oriented paradigms; ultimately, we hope to utilize the Curry-Howard isomorphism to further bridge the gap.more » « less
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