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Functorial ML
, 1996
"... . We present an extension of the HindleyMilner type system that supports a generous class of type constructors called functors, and provide a parametrically polymorphic algorithm for their mapping, i.e. for applying a function to each datum appearing in a value of constructed type. The algorithm co ..."
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Cited by 27 (9 self)
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. We present an extension of the HindleyMilner type system that supports a generous class of type constructors called functors, and provide a parametrically polymorphic algorithm for their mapping, i.e. for applying a function to each datum appearing in a value of constructed type. The algorithm comes from shape theory, which provides a uniform method for locating data within a shape. The resulting system is ChurchRosser and strongly normalising, and supports type inference. 1 Introduction The interplay between type theory, programming language semantics and category theory is now well established. Two of the strongest examples of this interaction are the representation of function types as exponential objects in a cartesian closed category [LS86] and the description of polymorphic terms as natural transformations (e.g. [BFSS90]). For example, the operation of appending lists can be represented as a natural transformation LL)L where L: D ! D is the list functor on some category D. ...
Functorial ML
, 1998
"... We present an extension of the HindleyMilner type system that supports a generous class of type constructors called functors, and provide a parametrically polymorphic algorithm for their mapping, i.e. for applying a function to each datum appearing in a value of constructed type. The algorithm come ..."
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the relationship to polytypic programming. Capsule Review A wide class of type constructors (functions producing types from types) used in functional programming are functorial, in the sense that they can be extended to mappings from functions to functions satisfying a few simple laws. The `map' functional
FUNCTORIALITY AND RECIPROCITY
"... These are, for me, the two major issues in the theory of automorphic forms and related topics. Both appear in three guises, each of which has two forms, global and local. Thus there are, in total, six theories. The global forms arise over global fields F, of which there are three types: (1) fields o ..."
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series over finite fields; (3) the field of formal Laurent series over C. My main concern in these lectures is a description of proposed strategies — in so far as they are available — for establishing the generally accepted conjectures. For functoriality the strategy has some promise but a number
Functorial boxes in string diagrams
, 2006
"... String diagrams were introduced by Roger Penrose as a handy notation to manipulate morphisms in a monoidal category. In principle, this graphical notation should encompass the various pictorial systems introduced in prooftheory (like JeanYves Girard’s proofnets) and in concurrency theory (like Ro ..."
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Cited by 16 (3 self)
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be extended with a notion of functorial box to depict a functor separating an inside world (its source category) from an outside world (its target category). We expose two elementary applications of the notation: first, we characterize graphically when a faithful balanced monoidal functor F: C − → D
Fixing the functoriality of Khovanov homology
"... Abstract We describe a modification of Khovanov homology [13], in the spirit of BarNatan [3], which makes the theory properly functorial with respect to link cobordisms. This requires introducing ‘disorientations ’ in the category of smoothings and abstract cobordisms between them used in BarNatan ..."
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Cited by 16 (1 self)
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Abstract We describe a modification of Khovanov homology [13], in the spirit of BarNatan [3], which makes the theory properly functorial with respect to link cobordisms. This requires introducing ‘disorientations ’ in the category of smoothings and abstract cobordisms between them used in Bar
ON THE FUNCTORIALITY OF A TORIC CONSTRUCTION
, 2002
"... In [3] Borel and Serre present the construction of some manifold with corners as the compactification of the quotient of the space X of maximal compact subgroups of a semisimple Qalgebraic group G by the action of a torsion free arithmetic subgroup Γ. In particular, a ”corner” X(P) is associated ..."
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In [3] Borel and Serre present the construction of some manifold with corners as the compactification of the quotient of the space X of maximal compact subgroups of a semisimple Qalgebraic group G by the action of a torsion free arithmetic subgroup Γ. In particular, a ”corner” X(P) is associated
Functorial Semantics for Multialgebras
 Recent Trends in Algebraic Development Techniques, volume 1589 of LNCS
, 1998
"... . Multialgebras allow to model nondeterminism in an algebraic framework by interpreting operators as functions from individual arguments to sets of possible results. We propose a functorial presentation of various categories of multialgebras and partial algebras, analogous to the classical pre ..."
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Cited by 7 (4 self)
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. Multialgebras allow to model nondeterminism in an algebraic framework by interpreting operators as functions from individual arguments to sets of possible results. We propose a functorial presentation of various categories of multialgebras and partial algebras, analogous to the classical
Functorial Models for Petri Nets
, 2001
"... this paper we investigate the operational, algebraic and logical aspects of PT nets under both the CTph and the ITph, exploiting the features of the algebraic approach to establish formal relationships between different proposals. As in [21], an important feature of our comparison and unification of ..."
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Cited by 5 (4 self)
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of different approaches to Petri net semantics in both the collective and individual token philosophies is that we emphasize the functorial character of the different semantic constructions. This is important for at least two reasons. First, by defining the appropriate categories, we make explicit
Automorphic LFunctions and Functoriality
, 2002
"... This is a report on the global aspects of the LanglandsShahidi method which in conjunction with converse theorems of Cogdell and PiatetskiShapiro has recently been instrumental in establishing a significant number of new and surprising cases of Langlands Functoriality Conjecture over number fields ..."
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Cited by 4 (0 self)
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This is a report on the global aspects of the LanglandsShahidi method which in conjunction with converse theorems of Cogdell and PiatetskiShapiro has recently been instrumental in establishing a significant number of new and surprising cases of Langlands Functoriality Conjecture over number
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