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Page 5288 of Mathematical Reviews Vol. , Issue 2000h
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2000
Mathematical Reviews
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“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
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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
2009
Electronical Notes in Theoretical Computer Science
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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
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2000
Mathematical Reviews
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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?
1982
Information and Control
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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
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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]
2012
Lecture Notes in Computer Science
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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
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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
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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]
2009
arXiv
pre-print
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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
2005
Mathematical Structures in Computer Science
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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
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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
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1996
Mathematical Reviews
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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
1998
Journal of functional programming
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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
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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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