## Beta-Reduction As Unification (1996)

Citations: | 13 - 9 self |

### BibTeX

@MISC{Kfoury96beta-reductionas,

author = {A.J. Kfoury},

title = {Beta-Reduction As Unification},

year = {1996}

}

### Years of Citing Articles

### OpenURL

### Abstract

this report, we use a lean version of the usual system of intersection types, whichwe call . Hence, UP is also an appropriate unification problem to characterize typability of -terms in . Quite apart from the new light it sheds on fi-reduction, such an analysis turns out to have several other benefits

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Citation Context ...section types. Nevertheless, what is interesting is that there are several very different approaches to prove what is essentially the same result. For some of these approaches, we refer the reader to =-=[13, 15, 18, 21, 22, 23]-=- as well as to some of the references cited therein. Yet another approach is based on the results of [10] after appropriate adjustments (mostly required by the fact thatsis an associative binary const... |

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Citation Context ... type scheme to an occurrence of an E- or T-variable is always the same, for all occurrences of this variable. (A similar property defines the so-called "stratified terms" in second-order un=-=ification [16, 19]-=-.) None of these 4 conditions is implied by the others. This is clear for conditions 3 and 4. The next example shows the independence of conditions 1 and 2. Example 6. Let oe j FF 0 ff F 0 ff 0 ! fi. ... |

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Citation Context ...in the usual way to / : T (TVar) ! T by induction on T (TVar): 3 "Expansions" in this paper are unrelated to "expansions" as defined in various articles by researchers at the Unive=-=rsity of Turin, see [6] and [7, Definit-=-ion 2.10] and some of the references cited therein. 8 A. J. KFOURY 1. /(oe ! �� ) = /(oe) ! /(�� ). 2. /(oes�� ) = /(oe)s/(�� ). Note the basis of the preceding induction is a function... |

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Citation Context ...for Turing machines [12]. After the initial proof for the undecidabilty of 2U, by a reduction from the diophantine problem (or Hilbert's tenth problem) [8], alternative simpler proofs were discovered =-=[3, 14, 20]-=-. The relationship between 2U and SU has been an open problem for several years. A new, hopefully simpler, proof for the undecidability of SU will be a welcome addition to the literature. Open Problem... |

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Citation Context ...section types. Nevertheless, what is interesting is that there are several very different approaches to prove what is essentially the same result. For some of these approaches, we refer the reader to =-=[13, 15, 18, 21, 22, 23]-=- as well as to some of the references cited therein. Yet another approach is based on the results of [10] after appropriate adjustments (mostly required by the fact thatsis an associative binary const... |

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