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  "body": "\n## Summary\n\nDomain theory studies special partially ordered sets, called domains, whose elements are read as pieces of partial information.\nIts basic objects are [[directed-complete partial orders|7TSXP95QN6]], the [[way-below relation|RDM7J5J9HQ]], [[Scott-continuous maps|C6GAHS1Z2P]] and the [[Scott topology|ZR8A03FV67]].\nDana Scott created it in the late 1960s to give a mathematical semantics for programming languages and for the [[lambda calculus|BD756KR8FM]].\nRecursive definitions are interpreted as [[least fixed points|DBD64TH52D]] of continuous maps.\n\n## Explanations\n\n### L1 human\n\nA program that has not finished yet has produced only part of its answer.\nDomain theory orders such partial answers by \"carries less information than\", and treats a full answer as the limit of partial ones.\nFor example, partial functions from $\\N$ to $\\N$ are ordered by extension.\nA recursive definition of a function is then the limit of the finite approximations produced by unfolding the recursion.\nThe theory sits between order theory, topology and computer science.\n",
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