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Finally Tagless, Partially Evaluated  Tagless Staged Interpreters for Simpler Typed Languages
"... We have built the first family of tagless interpretations for a higherorder typed object language in a typed metalanguage (Haskell or ML) that require no dependent types, generalized algebraic data types, or postprocessing to eliminate tags. The statically typepreserving interpretations include an ..."
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We have built the first family of tagless interpretations for a higherorder typed object language in a typed metalanguage (Haskell or ML) that require no dependent types, generalized algebraic data types, or postprocessing to eliminate tags. The statically typepreserving interpretations include an evaluator, a compiler (or staged evaluator), a partial evaluator, and callbyname and callbyvalue CPS transformers. Our main idea is to encode HOAS using cogen functions rather than data constructors. In other words, we represent object terms not in an initial algebra but using the coalgebraic structure of the λcalculus. Our representation also simulates inductive maps from types to types, which are required for typed partial evaluation and CPS transformations. Our encoding of an object term abstracts over the various ways to interpret it, yet statically assures that the interpreters never get stuck. To achieve selfinterpretation and show Jonesoptimality, we relate this exemplar of higherrank and higherkind polymorphism to plugging a term into a context of letpolymorphic bindings.
From Settheoretic Coinduction to Coalgebraic Coinduction: some results, some problems
, 1999
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Coalgebraic Coinduction in (Hyper)settheoretic Categories
, 2000
"... This paper is a contribution to the foundations of coinductive types and coiterative functions, in (Hyper)settheoretical Categories, in terms of coalgebras. We consider atoms as first class citizens. First of all, we give a sharpening, in the way of cardinality, of Aczel's Special Final Coalg ..."
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This paper is a contribution to the foundations of coinductive types and coiterative functions, in (Hyper)settheoretical Categories, in terms of coalgebras. We consider atoms as first class citizens. First of all, we give a sharpening, in the way of cardinality, of Aczel's Special Final Coalgebra Theorem, which allows for good estimates of the cardinality of the final coalgebra. To these end, we introduce the notion of Y uniform functor, which subsumes Aczel's original notion. We give also an nary version of it, and we show that the resulting class of functors is closed under many interesting operations used in Final Semantics. We define also canonical wellfounded versions of the final coalgebras of functors uniform on maps. This leads to a reduction of coiteration to ordinal induction, giving a possible answer to a question raised by Moss and Danner. Finally, we introduce a generalization of the notion of Fbisimulation inspired by Aczel's notion of precongruence, and we show t...