Scott continuity
E755390
Scott continuity is a concept in domain theory describing functions between partially ordered sets that preserve directed suprema and are monotone, fundamental in the mathematical foundations of denotational semantics.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
concept in domain theory
ⓘ
mathematical concept ⓘ property of functions ⓘ |
| appliesTo |
functions between dcpos
ⓘ
functions between partially ordered sets ⓘ functions between posets ⓘ |
| characterizedBy |
monotonicity
ⓘ
preservation of directed suprema ⓘ preservation of least upper bounds of directed sets ⓘ |
| context |
lattice-theoretic semantics
ⓘ
order-theoretic models of computation ⓘ |
| definedOn |
directed complete partial orders
ⓘ
partially ordered sets ⓘ |
| ensures |
least fixed point of a function exists on a cpo
ⓘ
limits of increasing chains are preserved ⓘ |
| field |
denotational semantics
ⓘ
domain theory ⓘ order theory ⓘ theoretical computer science ⓘ |
| formalizedAs | continuity with respect to the Scott topology ⓘ |
| generalizationOf | topological continuity with respect to Scott topology ⓘ |
| hasApplication |
construction of semantic domains
ⓘ
modeling non-terminating computations ⓘ modeling partial information ⓘ |
| hasProperty | monotone ⓘ |
| hasRole |
ensuring existence of least fixed points
ⓘ
supporting compositional semantics ⓘ |
| implies |
monotonicity of the function
ⓘ
preservation of all existing directed joins ⓘ |
| namedAfter | Dana Scott NERFINISHED ⓘ |
| relatedTo |
Scott topology
NERFINISHED
ⓘ
complete partial order ⓘ continuous function in topology ⓘ continuous lattices ⓘ dcpo ⓘ monotone function ⓘ |
| requires |
monotonicity
ⓘ
preservation of suprema of directed subsets ⓘ |
| typicalCodomain |
complete partial order
ⓘ
directed complete partial order ⓘ |
| typicalDomain |
complete partial order
ⓘ
directed complete partial order ⓘ |
| usedIn |
denotational semantics of programming languages
ⓘ
fixed-point theory in domain theory ⓘ semantics of higher-order functions ⓘ semantics of recursive definitions ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.