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- 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 wikiPageRevisionID "601203870".
- 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 subject Category:Computational_complexity_theory.
- Computable_topology subject Category:Computational_science.
- Computable_topology subject Category:Computational_topology.
- 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=601203870.
- Computable_topology isPrimaryTopicOf Computable_topology.