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Mathematical logic

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Connections with computer science
==Connections with computer science==
{{Main|Logic in computer science}}
The study of [[computability theory (computer science)|computability theory in computer science]] is closely related to the study of computability in mathematical logic. There is a difference of emphasis, however. [[Computer science|Computer scientists]] often focus on concrete programming languages and [[feasible computability]], while researchers in mathematical logic often focus on computability as a theoretical concept and on noncomputability.
The theory of [[Program semantics|semantics of programming languages]] is related to [[model theory]], as is [[program verification]] (in particular, [[model checking]]). The [[Curry–Howard isomorphism]] between proofs and programs relates to [[proof theory]], especially [[intuitionistic logic]]. Formal calculi such as the [[lambda calculus]] and [[combinatory logic]] are now studied as idealized [[programming languages]].