A valid rule of beta-conversion for the logic of partial functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F17%3A86098994" target="_blank" >RIV/61989100:27240/17:86098994 - isvavai.cz</a>
Result on the web
<a href="http://www.klemens.sav.sk/fiusav/organon/?q=en/valid-rule-v-conversion-logic-partial-functions" target="_blank" >http://www.klemens.sav.sk/fiusav/organon/?q=en/valid-rule-v-conversion-logic-partial-functions</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
A valid rule of beta-conversion for the logic of partial functions
Original language description
The goal of this paper is to examine the conditions of validity for the rule of β-conversion in TIL, which is a hyperintensional, typed lambda-calculus of partial functions. The rule of β-reduction is a fundamental computational rule of the lambda-calculi and functional programming languages. However, it is a well-known fact that the specification of this rule is ambiguous. There are two procedurally non-equivalent ways of executing the rule, namely β-conversion ‘by name’ and β-conversion ‘by value’. In the lambda-calculi conversion by name is usually applied, though it is known that such a conversion is not unconditionally valid when partial functions are involved. If a procedure that is typed to produce an argument value is improper by failing to produce one, conversion by name cannot be validly applied. On the other hand, conversion by value is valid even in the case of improperness. Moreover, we show that in a typed lambda-calculus the specification of lambda-closure is also not unambiguous. There is an interpretation of this specification under which beta-reduction by name is not valid even when the argument procedure does not fail to produce a value. As a result, we present a universally valid rule of beta-reduction by value.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA15-13277S" target="_blank" >GA15-13277S: Hyperintensional logic for natural language analysis</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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