On Adding $(\xi)$ to Weak Equality in Combinatory Logic
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On Adding $(\xi)$ to Weak Equality in Combinatory Logic
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| Id. |
37474634 |
| Idioma |
inglés
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| Titulo |
On Adding $(\xi)$ to Weak Equality in Combinatory Logic |
| Autor(es) |
Bunder, Martin W.
Hindley, J. Roger
Seldin, Jonathan P.
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| Localización |
http://projecteuclid.org/euclid.jsl/1183742929
J. Symbolic Logic 54, iss. 2 (1989), 590-607
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| Versión |
1.0 |
| Estado |
Final
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| Descripción |
Because the main difference between combinatory weak equality and $\lambda\beta$-equality is that the rule \begin{equation*}\tag{\xi} X = Y \vdash \lambda x.X = \lambda x.Y\end{equation*} is valid for the latter but not the former, it is easy to assume that another way of defining combinatory $\beta$-equality is to add rule $(\xi)$ to the postulates for weak equality. However, to make this true, one must choose the definition of combinatory abstraction in $(\xi)$ very carefully. If one tries to use one of the more common abstraction algorithms, the result will be an equality, $=_\xi$, that is either equivalent to $\beta\eta$-equality (and so strictly stronger than $\beta$-equality) or else strictly weaker than $\beta$-equality. This paper will study the relations $=_\xi$ for several commonly used abstraction algorithms, distinguish between them, and axiomatize them.
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| Tipo de recurso |
Text
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| Tipo de Interactividad |
Expositivo
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| Nivel de Interactividad |
muy bajo
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| Audiencia |
Estudiante
Profesor
Autor
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| Estructura |
Atomic |
| Coste |
no
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| Copyright |
sí
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Copyright 1989 Association for Symbolic Logic |
| Requerimientos técnicos |
Browser: Any
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| Fecha de contribución |
21-nov-2008 |
| Contacto |
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