R.F.C. Walters, Datatypes in distributive categories, Bull. Australian Math. Soc. 40 (1989) 79--82. 43  Home/Search Document Not in Database Summary Related Articles Check |
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Towards Merging Recursion and Comonads - Pardo (2000) (3 citations) (Correct)
....following equations hold: F 1 ffi F A;X = 1 (7) F ff A;X;Y ffi F A;X ThetaY = F A ThetaX;X ffi ( F A;X Theta id Y ) ffi ff FA;X;Y (8) Polynomial functors turn out to be strong under the additional assumption that category C is distributive. A category C is said to be distributive [34, 8] if it possesses both finite products and coproducts and binary products distribute over coproducts. This means that, for any objects A, B and C, the canonical map [inl Theta id C ; inr Theta id C ] A Theta C B Theta C (A B) Theta C is an isomorphism whose inverse is the natural ....
R.F.C. Walters. Data Types in Distributive Categories. Bull. Austral. Math. Soc., 40:79--82, 1989. 19
Tail Recursion Through Universal Invariants - Jay (1993) (1 citation) (Correct)
....the previous list concepts. Much remains to be done. Future papers will address: general recursion in an abstract setting; lazy datatypes, and; matrices. The explication of general datatypes in the distributive setting is also of ongoing interest; see, for example, the work of Cockett [7] Walters [37, 17] and Kelly [20] 2 Loops 2.1 Fixpoints and Invariants Let C be any category. A loop f on an object C in C is an endomorphism f : C C. A loop morphism from f to g : D D is a morphism h : C D such that h ffi f = g ffi h oe oe C D ae ae f g h These form a category C c of loop ....
....cartesian category if these are all isomorphisms. Then the inverses, labelled d A;B;C : A Theta(B C) A ThetaB) A ThetaC) are also natural. While the name of this law has remained stable the concept distributive category has often included additional structures and assumptions. Walters [37] required countably infinite coproducts while Cockett [5] required all finite limits and stability of coproducts under pullback. In [13] distributive categories were tentatively dubbed polynomial categories. The terminology here agrees with that of Lawvere [27] and should become standard (see [6] ....
R.F.C. Walters, Datatypes in distributive categories, Bull. Australian Math. Soc. 40 (1989) 79--82.
On Impartiality - Benson (Correct)
....are empty. Here is a procedure: Do forever f If nonempty ( top ) Then enqueue ( output , dequeue ( top ) If nonempty ( bottom ) Then enqueue ( output , dequeue ( bottom ) g. When the procedure looks at an input queue, it is either empty or else a daton is available for dequeuing. Following [Wal89, Wal91], we may consider the dequeuing operation to give a distinguished value when the queue is empty. In dataflow terminology, this distinguished value is sometimes called a hiaton. The collection of all datons is now a pointed set, A 1, with the distinguished nature of the hiaton made explicit. The ....
R. F. C. Walters, Datatypes in Distributive Categories, Bull. Austral. Math. Soc., 40(1989), 79--82.
Tail Recursion Through Universal Invariants - Barry Jay Lfcs (1993) (1 citation) (Correct)
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R.F.C. Walters, Datatypes in distributive categories, Bull. Australian Math. Soc. 40 (1989) 79--82. 43
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