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- W28925417 abstract "Programming languages which are capable of interpreting themselves have been fascinating computer scientists. Indeed, if this is possible then a ‘strange loop’ (in the sense of Hofstadter, 1979) is involved. Nevertheless, the phenomenon is a direct consequence of the existence of universal languages. Indeed, if all computable functions can be captured by a language, then so can the particular job of interpreting the code of a program of that language. Self-interpretation will be shown here to be possible in lambda calculus. The set of λ-terms , notation Λ, is defined by the following abstract syntax where is the set {v, v′, v″, v′″,…} of variables . Arbitrary variables are usually denoted by x, y,z,… and λ -terms by M,N,L,…. A redex is a λ -term of the form that is, the result of substituting N for (the free occurrences of) x in M. Stylistically, it can be said that λ -terms represent functional programs including their input. A reduction machine executes such terms by trying to reduce them to normal form; that is, redexes are continuously replaced by their contracta until hopefully no more redexes are present. If such a normal form can be reached, then this is the output of the functional program; otherwise, the program diverges." @default.
- W28925417 created "2016-06-24" @default.
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- W28925417 date "1991-04-01" @default.
- W28925417 modified "2023-10-17" @default.
- W28925417 title "Theoretical Pearls: <i>Self-interpretation in lambda calculus</i>" @default.
- W28925417 cites W1964062928 @default.
- W28925417 doi "https://doi.org/10.1017/s0956796800020062" @default.
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