Mogensen-Scott Encoding: Computer Science, Lambda Calculus, Anonymous Function - Brossura

 
9786133249813: Mogensen-Scott Encoding: Computer Science, Lambda Calculus, Anonymous Function

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In computer science, Scott encoding is a way to embed inductive datatypes in the lambda calculus. Mogensen-Scott encoding extends and slightly modifies this to an embedding of all terms of the untyped lambda calculus. The Scott and Church encodings coincide on enumerated datatypes such as the boolean datatype. Church encoded data and operations on them are typable in system F, but Scott encoded data and operations are not obviously typable in system F. Universal as well as recursive types appear to be required, and since strong normalization does not hold for recursively typed lambda calculus, termination of programs manipulating Scott-encoded data cannot be established by determining well-typedness of such programs.

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