J. Greiner, Programming with inductive and co-inductive types, Tech. Report CMU-CS-92-109, School of Computer Science, Carnegie-Mellon Univ., Pittsburgh, PA, USA (1992). Home/Search Document Details and Download
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Least and Greatest Fixed Points in Intuitionistic Natural.. - Uustalu, Vene (2002) (Correct)
....in (extensions of) 2st order simply typed lambda calculus from proofs in (extensions of) the n.d. proof system for 2nd order intuitionistic predicate logic. Parigot s work [24,25] on realizability based programming with proofs bears connection to both Leivant s and Mendler s works. Greiner [10] and Howard [13, chapter 3] considered programming in an extension of 1st order simply typed lambda calculus with axiomatized constructors of conventional style (co)inductive types with (co)iteration and data destruction (codata construction) Both had their motivation in Hagino s ....
J. Greiner, Programming with inductive and co-inductive types, Tech. Report CMU-CS-92-109, School of Computer Science, Carnegie-Mellon Univ., Pittsburgh, PA, USA (1992).
Another Iteration on Darlington's "A Synthesis of Several Sorting .. - Howard (1994) (Correct)
....extracts programs for Insertion Sort, Merge Sort, and Quick Sort as realizers of the corresponding correctness proofs, although he does not exploit the symmetry of the algorithms. Other work on iteration and coiteration includes Hagino [Hag87a, Hag87b] Mendler [Men87] Geuvers [Geu92] Greiner [Gre92], and Howard [How92, How93] all of which discuss typed languages (mostly extensions to the lambda calculus) with provisions for inductive and coinductive types and the natural operations over them. More general views of how to use such structures in programming, particularly in cases where ....
J. Greiner. Programming with inductive and co-inductive types. Technical Report CMU-CS-92109, Carnegie Mellon University, January 1992.
Inductive, Projective, and Retractive Types - Howard (1993) (Correct)
....languages containing these recursive types. The first, which we refer to as , adds only the inductive and projective types to a simply typed lambda calculus with finite products and sums. This language is essentially identical to the language MM developed independently by Greiner [Gre92]; both and MM were inspired by Hagino s work with categorical datatypes [Hag87a, Hag87b] The obvious non deterministic operational semantics for is shown to be both confluent and strongly normalizing, hence the non determinism is inessential and any of the common reduction ....
J. Greiner. Programming with inductive and co-inductive types. Technical Report CMU-CS-92-109, Carnegie Mellon University, January 1992.
Fixed Points and Extensionality in Typed Functional Programming.. - Howard (1992) (12 citations) (Correct)
....concept of F; G dialgebra and, through various computationally imposed restrictions, result in a language with a type system equivalent to that of , although with a more elegant (but less practical) notation. More recently, a language almost identical to has been studied by Greiner [19]; his primary concern is to show examples of types and programs that may be written in the language. Greiner also discusses the problem that arises when inductive and projective (which he calls co inductive) types are simulated in a language such as Girard s system F, namely that the types are no ....
J. Greiner. Programming with inductive and co-inductive types. Technical Report CMU-CS-92-109, Carnegie Mellon University, January 1992.
A Cube of Proof Systems for the Intuitionistic Predicate.. - Uustalu, Vene (1997) (2 citations) (Correct)
....in Geuvers [Geu92] We are not aware of any accounts of the calculi at the back nodes of the cube in the literature. Hagino s category theoretically motivated calculus in [Hag87] is a relative of ; A calculus with two destructors for (namely, cata and an inverse of wrap) appears in [Gre92] and [How92, chapter 3] Martin Lof published a paper about a n.d. calculus supporting iterated inductive definitions of predicates as early as in 1971 [ML71] 3.2 The embeddings There exist embeddings (i.e. injective homomorphisms) between any two n.d. calculi at adjacent nodes in the cube in ....
John Greiner. Programming with inductive and co-inductive types. Technical Report CMU-CS-92-109, School of Computer Science, Carnegie-Mellon Univ., Pittsburgh, PA, USA, January 1992.
Fixpoint Computations and Coiteration (Extended Abstract) - Howard (Correct)
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J. Greiner. Programming with inductive and co-inductive types. Technical Report CMUCS -92-109, Carnegie Mellon University, January 1992.
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