P.T. Johnstone and R. Par'e, editors. Indexed Categories and their Applications, volume 661 of Lecture Notes In Mathematics. Springer-Verlag, 1978. Home/Search Document Not in Database Summary Related Articles Check |
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Programming Metalogics with a Fixpoint Type - Crole (1992) (9 citations) (Correct)
....we are done. Case (mono ) implies (mono) The rule (mono ) yields Gamma j 2(Val(M) x:x = M) Now apply (2e) to this along with the hypothesis of (mono) 2 75 76 Categorical Semantics of the FIX Logic 5. 1 FIX Hyperdoctrines For background on hyperdoctrines and indexed categories see [JP78], See83] and [Pit89] Definition 5.1.1 A FIX hyperdoctrine is specified by a FIX category C (referred to as the base category) together with a C indexed poset, C: C Poset ; where if f : A B is a morphism in the base category C we denote the corresponding pullback function by f : C(B) ....
P.T. Johnstone and R. Par'e, editors. Indexed Categories and their Applications, volume 661 of Lecture Notes In Mathematics. Springer-Verlag, 1978.
Computational Lambda-Calculus and Monads - Moggi (1989) (272 citations) (Correct)
....most natural way to model computations (and datatypes) for more complex languages is simply by monads (and adjunctions) in a suitable 2 category. Following this general principle we can give two explanations for t, one based on enriched categories (see [4] and the other on indexed categories (see [3]) The rst explanation takes as fundamental a commutative monoidal structure on C, which models the tensor product of linear logic (see [6, 14] If C is a monoidal closed category, in particular a ccc, then it can be enriched over itself by taking C(A; B) to be the object B A . The equations ....
P.T. Johnstone and R. Pare, editors. Indexed Categories and their Applications, volume 661 of Lecture Notes in Mathematics. Springer Verlag, 1978.
Notions of Computation and Monads - Moggi (1989) (83 citations) (Correct)
....Id C : T and : T 2 : T are C enriched natural transformations, where Id C , T and T 2 are enriched in the obvious way (see Remark 1.4 in [Koc72] There is another purely categorical characterisation of strong monads, suggested to us by G. Plotkin, in terms of C indexed categories (see [JP78]) Both characterisations are instances of a general methodological principle for studying programming languages (or logics) categorically (see [Mog89b] when studying a complex language the 2 category Cat of small categories, functors and natural transformations may not be adequate; however, one ....
P.T. Johnstone and R. Pare, editors. Indexed Categories and their Applications, volume 661 of Lecture Notes in Mathematics. Springer Verlag, 1978.
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