Matches in SemOpenAlex for { <https://semopenalex.org/work/W2155132509> ?p ?o ?g. }
Showing items 1 to 87 of
87
with 100 items per page.
- W2155132509 endingPage "107" @default.
- W2155132509 startingPage "65" @default.
- W2155132509 abstract "Functions play a central role in type theory, logic and computation. We describe how the notions of functionalisation (the way in which functions can be constructed) and instantiation (the process of applying a function to an argument) have been developed in the last century. We explain how both processes were implemented in Frege’s Begriffschrift , Russell’s Ramified Type Theory , and the λ -calculus (originally introduced by Church) showing that the λ -calculus misses a crucial aspect of functionalisation. We then pay attention to some special forms of function abstraction that do not exist in the λ -calculus and we show that various logical constructs (e.g., let expressions and definitions and the use of parameters in mathematics), can be seen as forms of the missing part of functionalisation. Our study of the function concept leads to: (a) an extension of the Barendregt cube [4] with all of definitions, Π -reduction and explicit substitutions giving all their advantages in one system; and (b) a natural refinement of the cube with parameters. We show that in the refined Barendregt cube, systems like A utomath , LF, and ML, can be described more naturally and accurately than in the original cube." @default.
- W2155132509 created "2016-06-24" @default.
- W2155132509 creator A5003863800 @default.
- W2155132509 creator A5031944209 @default.
- W2155132509 creator A5036895724 @default.
- W2155132509 date "2003-01-01" @default.
- W2155132509 modified "2023-09-26" @default.
- W2155132509 title "Revisiting the notion of function" @default.
- W2155132509 cites W145869046 @default.
- W2155132509 cites W1483170865 @default.
- W2155132509 cites W1543641760 @default.
- W2155132509 cites W1589690886 @default.
- W2155132509 cites W159082583 @default.
- W2155132509 cites W1595372275 @default.
- W2155132509 cites W1603543937 @default.
- W2155132509 cites W1607953571 @default.
- W2155132509 cites W187110443 @default.
- W2155132509 cites W1986402635 @default.
- W2155132509 cites W1996404651 @default.
- W2155132509 cites W2044758536 @default.
- W2155132509 cites W2062081760 @default.
- W2155132509 cites W2067024462 @default.
- W2155132509 cites W2087917645 @default.
- W2155132509 cites W2104816023 @default.
- W2155132509 cites W2110373727 @default.
- W2155132509 cites W2118420900 @default.
- W2155132509 cites W2134669912 @default.
- W2155132509 cites W2136446682 @default.
- W2155132509 cites W2147896991 @default.
- W2155132509 cites W2151872924 @default.
- W2155132509 cites W2153926566 @default.
- W2155132509 cites W2154273644 @default.
- W2155132509 cites W2155411851 @default.
- W2155132509 cites W2275166338 @default.
- W2155132509 cites W2323803659 @default.
- W2155132509 cites W2522041776 @default.
- W2155132509 cites W4861723 @default.
- W2155132509 cites W62953528 @default.
- W2155132509 cites W65564231 @default.
- W2155132509 cites W78235646 @default.
- W2155132509 doi "https://doi.org/10.1016/s1567-8326(02)00016-4" @default.
- W2155132509 hasPublicationYear "2003" @default.
- W2155132509 type Work @default.
- W2155132509 sameAs 2155132509 @default.
- W2155132509 citedByCount "2" @default.
- W2155132509 crossrefType "journal-article" @default.
- W2155132509 hasAuthorship W2155132509A5003863800 @default.
- W2155132509 hasAuthorship W2155132509A5031944209 @default.
- W2155132509 hasAuthorship W2155132509A5036895724 @default.
- W2155132509 hasBestOaLocation W21551325091 @default.
- W2155132509 hasConcept C111472728 @default.
- W2155132509 hasConcept C138885662 @default.
- W2155132509 hasConcept C14036430 @default.
- W2155132509 hasConcept C199360897 @default.
- W2155132509 hasConcept C33923547 @default.
- W2155132509 hasConcept C41008148 @default.
- W2155132509 hasConcept C78458016 @default.
- W2155132509 hasConcept C86803240 @default.
- W2155132509 hasConceptScore W2155132509C111472728 @default.
- W2155132509 hasConceptScore W2155132509C138885662 @default.
- W2155132509 hasConceptScore W2155132509C14036430 @default.
- W2155132509 hasConceptScore W2155132509C199360897 @default.
- W2155132509 hasConceptScore W2155132509C33923547 @default.
- W2155132509 hasConceptScore W2155132509C41008148 @default.
- W2155132509 hasConceptScore W2155132509C78458016 @default.
- W2155132509 hasConceptScore W2155132509C86803240 @default.
- W2155132509 hasIssue "1-2" @default.
- W2155132509 hasLocation W21551325091 @default.
- W2155132509 hasOpenAccess W2155132509 @default.
- W2155132509 hasPrimaryLocation W21551325091 @default.
- W2155132509 hasRelatedWork W1527862632 @default.
- W2155132509 hasRelatedWork W2109507516 @default.
- W2155132509 hasRelatedWork W2112962394 @default.
- W2155132509 hasRelatedWork W2118300983 @default.
- W2155132509 hasRelatedWork W2135396778 @default.
- W2155132509 hasRelatedWork W2382501300 @default.
- W2155132509 hasRelatedWork W2740990710 @default.
- W2155132509 hasRelatedWork W3137189469 @default.
- W2155132509 hasRelatedWork W4235530921 @default.
- W2155132509 hasRelatedWork W4243252198 @default.
- W2155132509 hasVolume "54" @default.
- W2155132509 isParatext "false" @default.
- W2155132509 isRetracted "false" @default.
- W2155132509 magId "2155132509" @default.
- W2155132509 workType "article" @default.