Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Computable_topology> ?p ?o }
Showing triples 1 to 83 of
83
with 100 triples per page.
- Computable_topology abstract "Computable topology is a discipline in mathematics that studies the topological and algebraic structure of computation. Computable topology includes algorithmic topology and therefore encompasses computer science. It is not to be confused with computational topology, which is equivalent to the topology of λ-calculus. Within computer science computational forms can be reduced to λ-calculus's functional based mathematics. As shown by Alan Turing and Alonzo Church, the λ-calculus is strong enough to describe all mechanically computable functions (see Church–Turing thesis). Lambda-calculus is then a foundational mathematics easily made into a principal programming language from which other languages can be built. For this reason when considering the topology of computation it is suitable to focus on the topology of λ-calculus. Functional programming, e.g. type free lambda calculus, originated as a theoretical foundation of mathematics. The premise relies on functional computability, where objects and functions are of the same type. The topology of λ-calculus is the Scott topology, and when restricted to continuous functions the type free λ-calculus amounts to a topological space reliant on the tree topology. Both the Scott and Tree topologies exhibit continuity with respect to the binary operators of application ( f applied to a = fa ) and abstraction ((λx.t(x))a = t(a)) with a modular equivalence relation based on a congruency. The algebraic structure of computation may also be considered as equivalent to the algebraic structure of λ-calculus, meaning the λ-algebra. The λ-algebra is found to be an extension of the combinatory algebra, with an element introduced to accommodate abstraction.A primary concern of algorithmic topology, as its name suggests, is to develop efficient algorithms for solving topological problems, or using topological methods to solve algorithmic problems from other fields.".
- Computable_topology wikiPageID "36075414".
- Computable_topology wikiPageLength "21709".
- Computable_topology wikiPageOutDegree "62".
- Computable_topology wikiPageRevisionID "607163443".
- Computable_topology wikiPageWikiLink Alan_Turing.
- Computable_topology wikiPageWikiLink Algebraic_extension.
- Computable_topology wikiPageWikiLink Algorithm.
- Computable_topology wikiPageWikiLink Alonzo_Church.
- Computable_topology wikiPageWikiLink Beta_normal_form.
- Computable_topology wikiPageWikiLink Binary_operation.
- Computable_topology wikiPageWikiLink Binary_operators.
- Computable_topology wikiPageWikiLink Böhm_tree.
- Computable_topology wikiPageWikiLink Böhm_trees.
- Computable_topology wikiPageWikiLink Cardinality.
- Computable_topology wikiPageWikiLink Category:Computational_complexity_theory.
- Computable_topology wikiPageWikiLink Category:Computational_science.
- Computable_topology wikiPageWikiLink Category:Computational_topology.
- Computable_topology wikiPageWikiLink Church–Turing_thesis.
- Computable_topology wikiPageWikiLink Combinatory_algebra.
- Computable_topology wikiPageWikiLink Combinatory_logic.
- Computable_topology wikiPageWikiLink Complete_lattice.
- Computable_topology wikiPageWikiLink Complete_partial_order.
- Computable_topology wikiPageWikiLink Computation.
- Computable_topology wikiPageWikiLink Computational_topology.
- Computable_topology wikiPageWikiLink Computer_science.
- Computable_topology wikiPageWikiLink Congruence_relation.
- Computable_topology wikiPageWikiLink Continuous_function.
- Computable_topology wikiPageWikiLink Continuous_map.
- Computable_topology wikiPageWikiLink Dana_Scott.
- Computable_topology wikiPageWikiLink Data_type.
- Computable_topology wikiPageWikiLink Effective_method.
- Computable_topology wikiPageWikiLink Embedding.
- Computable_topology wikiPageWikiLink Equivalence_relation.
- Computable_topology wikiPageWikiLink Fixed-point_combinator.
- Computable_topology wikiPageWikiLink Foundation_of_mathematics.
- Computable_topology wikiPageWikiLink Foundations_of_mathematics.
- Computable_topology wikiPageWikiLink Functional_programming.
- Computable_topology wikiPageWikiLink Group_theory.
- Computable_topology wikiPageWikiLink Infimum_and_supremum.
- Computable_topology wikiPageWikiLink Kolmogorov_space.
- Computable_topology wikiPageWikiLink Lambda_calculus.
- Computable_topology wikiPageWikiLink Lambda_term.
- Computable_topology wikiPageWikiLink Network_topology.
- Computable_topology wikiPageWikiLink Normal_form.
- Computable_topology wikiPageWikiLink Partially_ordered_set.
- Computable_topology wikiPageWikiLink Pointwise_convergence.
- Computable_topology wikiPageWikiLink Product_topology.
- Computable_topology wikiPageWikiLink Recursion.
- Computable_topology wikiPageWikiLink Scott_continuity.
- Computable_topology wikiPageWikiLink Scott_continuous.
- Computable_topology wikiPageWikiLink Supremum.
- Computable_topology wikiPageWikiLink Topological_space.
- Computable_topology wikiPageWikiLink Topology.
- Computable_topology wikiPageWikiLink Tree_topology.
- Computable_topology wikiPageWikiLink Turing_machine.
- Computable_topology wikiPageWikiLink Turnstile_(symbol).
- Computable_topology wikiPageWikiLink Upper_set.
- Computable_topology wikiPageWikiLink Λ-calculus.
- Computable_topology wikiPageWikiLink Wikipedia:MOS.
- Computable_topology wikiPageWikiLink Wikipedia:MOSMATH.
- Computable_topology wikiPageWikiLinkText "Computable topology".
- Computable_topology wikiPageWikiLinkText "computable topology".
- Computable_topology date "December 2013".
- Computable_topology hasPhotoCollection Computable_topology.
- Computable_topology reason "Lots of issues of punctuation and capitalization and conventions of WP:MOS and WP:MOSMATH need to be looked at.".
- Computable_topology wikiPageUsesTemplate Template:Cleanup.
- Computable_topology wikiPageUsesTemplate Template:Disambiguation_needed.
- Computable_topology wikiPageUsesTemplate Template:Reflist.
- Computable_topology subject Category:Computational_complexity_theory.
- Computable_topology subject Category:Computational_science.
- Computable_topology subject Category:Computational_topology.
- Computable_topology hypernym Discipline.
- Computable_topology type Area.
- Computable_topology type Sport.
- Computable_topology type Area.
- Computable_topology comment "Computable topology is a discipline in mathematics that studies the topological and algebraic structure of computation. Computable topology includes algorithmic topology and therefore encompasses computer science. It is not to be confused with computational topology, which is equivalent to the topology of λ-calculus. Within computer science computational forms can be reduced to λ-calculus's functional based mathematics.".
- Computable_topology label "Computable topology".
- Computable_topology sameAs m.0j_760m.
- Computable_topology sameAs Q5157268.
- Computable_topology sameAs Q5157268.
- Computable_topology wasDerivedFrom Computable_topology?oldid=607163443.
- Computable_topology isPrimaryTopicOf Computable_topology.