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Page 3871 of Mathematical Reviews Vol. , Issue 81J [page]

1981 Mathematical Reviews  
(pp. 503-510); Richard Statman, On the existence of closed terms in the typed A-calculus, I (pp. 511-534); M.  ...  Scott, Relating theories of the A-calculus (pp. 403-450). Typed terms: R. O. Gandy, An early proof of normalization by A. M. Turing (pp. 453-455); R. O.  ... 

The semantics of second-order lambda calculus

Kim B. Bruce, Albert R. Meyer, John C. Mitchell
1990 Information and Computation  
In the second-order (polymorphic) typed lambda calculus, lambda abstraction over type variables leads to terms denoting polymorphic functions.  ...  We verify that some specific interpretations of the calculus proposed in the literature indeed yield models in our sense.  ...  We will now concentrate on Girard's model HEO,, which is a particular model of second-order lambda calculus based on partial equivalence relations.  ... 
doi:10.1016/0890-5401(90)90044-i fatcat:c3bzzkjwvbcblhprguedtljc6a

Page 1307 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
Summary: “Extensions of the simply typed lambda calculus have been used as a metalanguage to represent ‘higher order term algebras’, such as, for instance, formulas of the predicate calculus.  ...  We illustrate the system by considering typed programs to reduce to normal form terms of the untyped lambda calculus, encoded as elements of a second order term algebra.  ... 

Easiness in graph models

C. Berline, A. Salibra
2006 Theoretical Computer Science  
In this paper we concentrate on the semantics G of lambda calculus given in terms of graph models, graph semantics for short.  ...  This semantical result extends to other classes of models and to some other terms which share with enough of its good will (cf. [14] for a survey of such results).  ...  For example, the open problem of the order-incompleteness of lambda calculus [49, 47] asks for the existence of a lambda theory not arising as the equational theory of a nontrivially partially ordered  ... 
doi:10.1016/j.tcs.2005.11.005 fatcat:367kbdjdh5cerfzoybtblycmvi

Scott Is Always Simple [chapter]

Antonino Salibra
2012 Lecture Notes in Computer Science  
In this paper we give an outline of recent algebraic results concerning theories and models of the untyped lambda calculus.  ...  partially ordered model of lambda calculus.  ...  It is sufficient to find out two closed λ-terms, whose denotations in the model M are related by the partial ordering.  ... 
doi:10.1007/978-3-642-32589-2_3 fatcat:jqadnhzb5jcudfucqdvxbirasa

TILC: The Interactive Lambda-Calculus Tracer

David Ruiz, Mateu Villaret
2009 Electronical Notes in Theoretical Computer Science  
This is achieved by allowing users to graphically interact with a sort of parse-tree of the lambda-terms and automatically reproducing these interactions in the lambda-term.  ...  This graphical interaction encourages students to practice with lambda-terms easing the learning of the syntax and of the operational semantics of lambda-calculus.  ...  We would also like to acknowledge the suggestions for improving the tool that we have received from people using it in their lectures like Salvador Lucas from Universitat Politècnica de València, Temur  ... 
doi:10.1016/j.entcs.2009.07.067 fatcat:uinkyjhjt5e7biyos42hxecvtm

Page 17 of Mathematical Reviews Vol. , Issue 93i [page]

1993 Mathematical Reviews  
lambda calculus, internal partial 17 NONASSOCIATIVE RINGS AND ALGEBRAS 4790 equivalence relation (per) models, etc.  ...  Chapters 11 and 12 are a very formal treatment of categorical models of Girard’s second-order lambda calculus, and a detailed comparison of external Seely models (using indexed categories) versus the somewhat  ... 

Some aspects of categories in computer science [chapter]

P.J. Scott
2000 Handbook of Algebra  
We now introduce Girard's second order lambda calculus. We use the notation FV (t) and BV (t) for the set of free and bound variables of term t, respectively.  ...  (ii) It is a fundamental property that lambda calculus is a higher-order functional language: terms of type B A can use an arbitrary term of type A as an argument, and A and B themselves may be very complex  ...  (iii) Although Manes and Arbib use the Limit Axiom to prove existence of Elgot-style iteration (see below), Kuro s did not have it. And for many aspects of the theory below, it is not needed.  ... 
doi:10.1016/s1570-7954(00)80027-3 fatcat:oeaqbcqgzjhuzl2ddangzergr4

Models and theories of lambda calculus [article]

Giulio Manzonetto
2009 arXiv   pre-print
In this paper we briefly summarize the contents of Manzonetto's PhD thesis which concerns denotational semantics and equational/order theories of the pure untyped lambda-calculus.  ...  algebras; (iii) a proof that no effective lambda-model can have lambda-beta or lambda-beta-eta as its equational theory (this can be seen as a partial answer to an open problem introduced by Honsell-Ronchi  ...  In each of these semantics all the models come equipped with a partial order, and some of them, called webbed models, are built from lower level structures called "webs".  ... 
arXiv:0904.4756v1 fatcat:7j47i72zebaoxkltk6fqul5bsi

Anagopos: A Reduction Graph Visualizer for Term Rewriting and Lambda Calculus

Niels Bjørn Bugge Grathwohl, Jeroen Ketema, Jens Duelund Pallesen, Jakob Grue Simonsen, Marc Herbstritt
2011 International Conference on Rewriting Techniques and Applications  
We present Anagopos, an open source tool for visualizing reduction graphs of terms in lambda calculus and term rewriting.  ...  Anagopos allows step-by-step generation of reduction graphs under six different graph drawing algorithms. We provide ample examples of graphs drawn with the tool.  ...  Acknowledgments The authors thank Jan Willem Klop, Peter Sestoft, and the anonymous referees for useful feedback.  ... 
doi:10.4230/lipics.rta.2011.61 dblp:conf/rta/GrathwohlKPS11 fatcat:wjr3phbg6ne4zavrklslj37f4a

Page 4079 of Mathematical Reviews Vol. , Issue 98G [page]

1998 Mathematical Reviews  
S. van Benthem Jutting, The language theory of A., a typed A-calculus where terms are types (655-683); N. G. de Bruijn, Example of a text written in Automath (687 700); L.  ...  G. de Bruijn, Generalizing Automath by means of a lambda-typed lambda calculus [MR 89b:03026] (313-337); H.  ... 

Applying Universal Algebra to Lambda Calculus

G. Manzonetto, A. Salibra
2008 Journal of Logic and Computation  
From one side we survey the knowledge we have acquired these last ten years about the lattice of all λ-theories (= equational extensions of untyped λ-calculus) and the models of lambda calculus via universal  ...  Central elements are also used to provide applications of the representation theorem to lambda calculus.  ...  partially ordered model of lambda calculus.  ... 
doi:10.1093/logcom/exn085 fatcat:muo26iplxbe2diepxtlnnutdxi

Aspects of categorical recursion theory [article]

Pieter Hofstra, Philip Scott
2020 arXiv   pre-print
We present a survey of some developments in the general area of category-theoretic approaches to the theory of computation, with a focus on topics and ideas particularly close to the interests of Jim Lambek  ...  We also hope to have conveyed to the reader that there are still many interesting unanswered questions and relatively unexplored facets of categorical recursion theory that deserve further investigation  ...  Conclusion We hope that we have shown in this -admittedly biased-overview of categorical recursion theory how various of Lambek's seminal ideas have initiated and inspired numerous strands of research  ... 
arXiv:2001.05778v1 fatcat:orhmpipltngtdcnkuq2y7rvqaa

Open problems in rewriting [chapter]

Nachum Dershowitz, Jean-Pierre Jouannaud, Jan Willem Klop
1991 Lecture Notes in Computer Science  
Acknowledgements We thank all the individuals mentioned above who contributed questions, F.-J. de Vries for helping prepare this list, and Ron Book, for going out of his way t o m a k e it possible.  ...  One of the outstanding open problems in typed lambda calculi is the following: Given a term in ordinary untyped lambda calculus, is it decidable whether it can be typed in the second-order 2 calculus  ...  in a set of lecture notes on Term Rewriting Systems" by one of us Klop for a seminar on reduction machines Ustica, 1985, another list by one of us Jouannaud in the Bulletin of the European Association  ... 
doi:10.1007/3-540-53904-2_120 fatcat:bsnbx2vghrc2tmv6xcywwijbjq

Graph easy sets of mute lambda terms

A. Bucciarelli, A. Carraro, G. Favro, A. Salibra
2016 Theoretical Computer Science  
Alongside, we provide a brief survey of the notion of undefinedness in the lambda calculus.  ...  Among the unsolvable terms of the lambda calculus, the mute ones are those having the highest degree of undefinedness.  ...  Introduction Undefinedness in the lambda calculus is an important issue, tackled since the inception of recursion theory: in order to show that the lambda calculus is Turing-complete, a sensible notion  ... 
doi:10.1016/j.tcs.2015.12.024 fatcat:4ronvkej6vfw7lpptda55gql4q
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