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Page 5288 of Mathematical Reviews Vol. , Issue 2000h [page]

2000 Mathematical Reviews  
The proofs associated with these applications are based on an interpretation of the lambda calculus in a category-theoretic model in which all functions are polynomial time computable by construction.  ...  Summary: “We introduce a notion of Grothendieck logical relation and use it to characterise the definability of morphisms in stable bi- Cartesian closed categories by terms of the simply-typed lambda calculus  ... 

Page 4129 of Mathematical Reviews Vol. , Issue 92h [page]

1992 Mathematical Reviews  
Girard’s proof of CR for system F is syntactical and extends the Tait and Martin-Lof proof for the untyped lambda calculus.  ...  The assumption that a type is a type (the Type:Type assumption) is a very common one in the typed lambda-calculus. However, the problem arises of finding models for such a calculus.  ... 

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.  ...  TILC aims to be a friendly user graphical application that helps teaching/studying the main basic concepts of pure untyped 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 3847 of Mathematical Reviews Vol. , Issue 2000f [page]

2000 Mathematical Reviews  
This paper provides a syntactic proof of the conservativity of the higher-order polymorphically typed lambda calculus 2,, (Girard’s Fw) over the polymorphically typed lambda calculus 42 (Girard’s F), in  ...  Summary: “We survey a substantial body of knowledge about lambda calculus and pure type systems, formally developed in a constructive type theory using the LEGO proof system.  ... 

What is a model of the lambda calculus?

Albert R. Meyer
1982 Information and Control  
These definitions of model are consistent with, and yield a completeness theorem for, the standard axioms for lambda convertibility. A simple construction of models for lambda calculus is reviewed.  ...  An elementary, purely algebraic definition of model for the untyped lambda calculus is given. This definition is shown to be equivalent to the natural semantic definition based on environments.  ...  In the final section we cite some additional results connecting the model theory and proof theory of lambda calculus.  ... 
doi:10.1016/s0019-9958(82)80087-9 fatcat:ws7l2zql4bg63jvyxe5w5zhx5y

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

2003 Mathematical Reviews  
Finally, we consider interpretations of our typed systems in the pure lambda calculus and a new Gédelization of the pure lambda calculus.”  ...  The examples also show that a version of the intersection type disciplines can be helpful in some cases to prove the existence of a canonical form.  ... 

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.  ...  The proofs of the above results are syntactical and very difficult.  ...  The connection between the syntax and the semantics of lambda calculus is established by the completeness theorem of lambda calculus: every λ-theory is the equational theory of some λ-model.  ... 
doi:10.1007/978-3-642-32589-2_3 fatcat:jqadnhzb5jcudfucqdvxbirasa

Page 3523 of Mathematical Reviews Vol. , Issue 93g [page]

1993 Mathematical Reviews  
Intrigila [“Some results on numerical systems in A-calculus”, Notre Dame J.  ...  e2 such that o(e;) and o(e2) are equivalent under the conversion rules of the typed lambda-calculus.  ... 

Page 2361 of Mathematical Reviews Vol. , Issue 81F [page]

1981 Mathematical Reviews  
Berry, Gérard; Lévy, Jean-Jacques A survey of some syntactic results in the \-calculus. Mathematical foundations of computer science, 1979 (Proc.  ...  Therefore, one can say that the A- calculus framework is a generalisation of recursive program schemes to any functional order. “Here we look at syntactic results.  ... 

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.  ...  The main research achievements include: (i) a general construction of lambda-models from reflexive objects in (possibly non-well-pointed) categories; (ii) a Stone-style representation theorem for combinatory  ...  This problem is still open, but generated a wealth of interesting research and results (surveyed in [7] and [8] ).  ... 
arXiv:0904.4756v1 fatcat:7j47i72zebaoxkltk6fqul5bsi

A short survey of isomorphisms of types

ROBERTO DI COSMO
2005 Mathematical Structures in Computer Science  
Conclusions We have shown in this short survey that the study of isomorphisms of types is a very lively research subject, that has attracted the interest of researchers coming from very diverse fields,  ...  from logic to lambda calculus, to algorithmics and programming.  ...  While this work was done in the framework of the untyped lambda calculus, it turned out that this family of invertible terms can be typed in the simple typed lambda calculus, and this allowed Bruce and  ... 
doi:10.1017/s0960129505004871 fatcat:ifyjdheemragti56gremvwilxa

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

1993 Mathematical Reviews  
In the former case a large number of interesting results are obtained on conditions necessary for a mapping to be an automorphism, on relations between pairs of automorphisms, and on automorphisms in special  ...  The sections on internal and indexed categories are quite syntactical and may not please some categorists.  ... 

Page 4540 of Mathematical Reviews Vol. , Issue 96h [page]

1996 Mathematical Reviews  
From the text: “In this survey article we state some open problems and give appropriate background in the set-theoretic aspect of Boolean algebras.  ...  In particular, he discusses how the equations of his multilinear lambda calculus relate to logical rules as well as how to solve the decision problems above.  ... 

The call-by-need lambda calculus

JOHN MARAIST, MARTIN ODERSKY, PHILIP WADLER
1998 Journal of functional programming  
The call-byneed lambda calculus is confluent, has a notion of standard reduction, and entails the same observational equivalence relation as the call-by-name calculus.  ...  We present a calculus that captures the operational semantics of call-by-need.  ...  Turner and a number of anonymous referees for valuable comments and discussions.  ... 
doi:10.1017/s0956796898003037 fatcat:hzfbo4ki6bb4pjfuhxppuvqqw4

Page 4744 of Mathematical Reviews Vol. , Issue 85k [page]

1985 Mathematical Reviews  
Each term of the untyped lambda calculus can be assigned a set of types in such a way that the assignment of types to terms is complete, with respect to a natural semantics [see H.  ...  The other main result is a syntactic characterisation of the preorder defined on terms by the inclusion relation of the filter \- model.  ... 
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