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Which simple types have a unique inhabitant?

Gabriel Scherer, Didier Rémy
2015 SIGPLAN notices  
We study the question of whether a given type has a unique inhabitant modulo program equivalence.  ...  Backward search in this logic gives an effective algorithm that returns either zero, one or two distinct inhabitants for any given type.  ...  Introduction In this article, we answer an instance of the following question: "Which types have a unique inhabitant"? In other words, for which type is there exactly one program of this type?  ... 
doi:10.1145/2858949.2784757 fatcat:g5ik2xr4dbfz5k5d2ewc6fdu44

Which simple types have a unique inhabitant?

Gabriel Scherer, Didier Rémy
2015 Proceedings of the 20th ACM SIGPLAN International Conference on Functional Programming - ICFP 2015  
We study the question of whether a given type has a unique inhabitant modulo program equivalence.  ...  Backward search in this logic gives an effective algorithm that returns either zero, one or two distinct inhabitants for any given type.  ...  Introduction In this article, we answer an instance of the following question: "Which types have a unique inhabitant"? In other words, for which type is there exactly one program of this type?  ... 
doi:10.1145/2784731.2784757 dblp:conf/icfp/SchererR15 fatcat:adazx34yafdctcjyrgftd5cekm

Solvability = Typability + Inhabitation [article]

Antonio Bucciarelli, Delia Kesner, Simona Ronchi Della Rocca
2021 arXiv   pre-print
We show first that the system P characterizes the set of terms having canonical form, i.e. that a term is typable if and only if it reduces to a canonical form.  ...  We then prove that typability, together with inhabitation, provides a full characterization of solvability, in the sense that a term is solvable if and only if it is typable and the types of all its arguments  ...  As a matter of fact the unique type A such that Γ p : A could have been denoted by Γ(p), as we do for variables.  ... 
arXiv:1812.06009v4 fatcat:vwqd6yqtx5fyzollm5vtqr64ha

Inhabited Intelligent Environments

V Callaghan, G Clarke, M Colley, H Hagras, J S Y Chin, F Doctor
2004 BT technology journal  
We also introduce a more human-directed approach to programming in pervasive environments which we refer to as task-oriented programming (TOP). † All authors are from the University of Essex Inhabited  ...  In this paper we discuss a solution based on embeddedagents which enables emergent intelligent behaviour by predominantly implicit processes.  ...  To explore this aspect of our inhabited intelligent environment work we have recently opened up a complementary strand of research which we refer to as task-oriented programming.  ... 
doi:10.1023/b:bttj.0000047137.42670.4d fatcat:sionrqsjufabdeh55r45e4mdfq

Solvability = Typability + Inhabitation

Antonio Bucciarelli, Delia Kesner, Simona Ronchi Della Rocca
2018 Logical Methods in Computer Science  
We show first that the system P characterizes the set of terms having canonical form, i.e. that a term is typable if and only if it reduces to a canonical form.  ...  We then prove that typability, together with inhabitation, provides a full characterization of solvability, in the sense that a term is solvable if and only if it is typable and the types of all its arguments  ...  As a matter of fact the unique type A such that Γ p : A could have been denoted by Γ(p), as we do for variables.  ... 
doi:10.23638/lmcs-17(1:7)2021 fatcat:enx3kw5a6zacfkr5j45yfipeae

Inhabitation for Non-idempotent Intersection Types [article]

Antonio Bucciarelli and Delia Kesner and Simona Ronchi Della Rocca
2018 arXiv   pre-print
The inhabitation problem for intersection types in the lambda-calculus is known to be undecidable.  ...  We study the problem in the case of non-idempotent intersection, considering several type assignment systems, which characterize the solvable or the strongly normalizing lambda-terms.  ...  Considering the λ-calculus as a general paradigm for functional programming languages, a virtuous example is the simple type assignment system, for which both problems are decidable, and which is the basis  ... 
arXiv:1712.03829v4 fatcat:bki7a4ktorgjpjzg4ytubzct3i

Inhabiting the solar system

Brent Sherwood
2011 Open Engineering  
Foreseeable options for 21st century developments in human space flight provide a framework to tease out potential space architecture opportunities for the next century.  ...  Defined as the "theory and practice of designing and building inhabited environments in outer space," the field synthesizes human space flight systems engineering subjects with the long tradition of making  ...  Almost all asteroids have ultra-low gravity, so asteroidal architecture would be a hybrid of orbital and planet-surface types and is thus not treated here.  ... 
doi:10.2478/s13531-011-0004-y fatcat:ekkj7bf2mnglhmqhar6x63gqdy

A Unifying Framework for Type Inhabitation

Sandra Alves, Sabine Broda, Michael Wagner
2018 International Conference on Rewriting Techniques and Applications  
In this paper we define a framework to address different kinds of problems related to type inhabitation, such as type checking, the emptiness problem, generation of inhabitants and counting, in a uniform  ...  Our framework uses an alternative representation for types, called the pre-grammar of the type, on which different methods for these problems are based.  ...  For instance, an inhabited type may have only a finite number of normal inhabitants, but has always an infinite number of (not necessarily normal) inhabitants.  ... 
doi:10.4230/lipics.fscd.2018.5 dblp:conf/rta/AlvesB18 fatcat:a5f5vez3inbgjo5qnsi6iad7da

Inhabitation of Low-Rank Intersection Types [chapter]

Paweł Urzyczyn
2009 Lecture Notes in Computer Science  
We prove that the inhabitation problem ("Does there exist a closed term of a given type?")  ...  (Roughly speaking, an intersection of simple types is of rank 1, and a rank n + 1 type has arguments of rank n.) In [20] it is shown that the inhabitation problem is undecidable for types of rank 4.  ...  The natural partial algorithm to find inhabitants of a given intersection type [3, 10, 20] is similar to the Wajsberg/Ben-Yelles algorithm for simple types [18] .  ... 
doi:10.1007/978-3-642-02273-9_26 fatcat:brffyidd3fccjkc67egifbb3tm

The Habitable Zone of Inhabited Planets [article]

Jorge I. Zuluaga, Juan F. Salazar (GIGA/Escuela Ambiental/UdeA), Pablo Cuartas-Restrepo, German Poveda
2014 arXiv   pre-print
We do not provide here definitive limits to the InHZ but we show through simple numerical models (as a parable of an inhabited planet) how the limits of the AHZ could be modified by including plausible  ...  Although previous authors have explored the effects of life on habitability there is a gap in research developing the reasons why life should be systematically included at determining the HZ limits.  ...  We want to especially thank to our colleagues Victor Gorshkov, Anastassia Makarieva, Rene Heller, Dave Waltham and Peter Bunyard for a preliminary revision of the manuscript.  ... 
arXiv:1405.4576v1 fatcat:ys6mvtuzxvhmrhhz2j4lwzosm4

The Habitable Zone of Inhabited Planets

J. I. Zuluaga, J. F. Salazar, P. Cuartas-Restrepo, G. Poveda
2014 Biogeosciences Discussions  
We do not provide here definitive limits to the InHZ but we show through simple numerical models (as a parable of an inhabited planet) how the limits of the AHZ could be modified by including plausible  ...  Although previous authors have explored the effects of life on habitability there is a gap in research developing the reasons why life should be systematically included at determining the HZ limits.  ...  Although including life in all its complexity in a realistic model of the environment of any inhabited planet is challenging, we have 20 shown trhough simple albeit illustrative conceptual and numerical  ... 
doi:10.5194/bgd-11-8443-2014 fatcat:eou37zds4zc6xcipwz3od3soi4

The Complexity of Inhabitation with Explicit Intersection [chapter]

Jakob Rehof, Paweł Urzyczyn
2012 Lecture Notes in Computer Science  
It is shown that the inhabitation problem for intersection types without the intersection introduction rule is Expspace-complete and that the further restriction without subtyping is Pspace-complete.  ...  Conclusion We have considered the question of complexity of inhabitation for a natural fragment of the intersection typed λ-calculus, in which intersections are explicit, in the sense of "Church-style"  ...  It therefore follows from Lemma 6 that an inhabited type must have a normal inhabitant. Lemma 7. If Γ M : σ then there is a normal form M with Γ M : σ.  ... 
doi:10.1007/978-3-642-29485-3_16 fatcat:ybxwumbofjhknkoe6yc7zwazxa

Gluing resource proof-structures: inhabitation and inverting the Taylor expansion [article]

Giulio Guerrieri, Luc Pellissier, Lorenzo Tortora de Falco
2022 arXiv   pre-print
We also prove semi-decidability of the type inhabitation problem for cut-free MELL proof-structures.  ...  A Multiplicative-Exponential Linear Logic (MELL) proof-structure can be expanded into a set of resource proof-structures: its Taylor expansion.  ...  Inhabitation. We can characterize type inhabitation in MELL proof-structures.  ... 
arXiv:2008.03103v8 fatcat:ucxwnjhvwrculh26psbr3o5ksy

Tutorial on Inhabited Virtual Heritage [article]

Nadia Magnenat-Thalmann, Alan Chalmers, Pascal Fua, Daniel Thalmann
2002 Eurographics State of the Art Reports  
Finally we show applications of our system in a virtual reality training and a virtual heritage reconstruction.  ...  We define a modular behavioral architecture of a multi-agent system allowing autonomous and scripted behavior of agents supporting variety.  ...  different forms or types").  ... 
doi:10.2312/egt.20021059 fatcat:je5fnfvlmbcopgn2day32x5djm

Fungi Inhabiting the Wheat Endosphere

Błaszczyk Lidia, Salamon Sylwia, Mikołajczak Katarzyna
2021 Pathogens  
This paper reviews the literature in the context of the general characteristics of endophytic fungi inhabiting the internal tissues of wheat.  ...  Wheat production is influenced by changing environmental conditions, including climatic conditions, which results in the changing composition of microorganisms interacting with this cereal.  ...  Identification is simple when the nucleotide sequence is constant within each species and unique to one species [61] .  ... 
doi:10.3390/pathogens10101288 pmid:34684238 fatcat:2mfw2mob65at5ou6zs2725kp6m
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