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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

2009
*
Electronical Notes in Theoretical Computer Science
*

This is achieved by allowing users to graphically interact with

doi:10.1016/j.entcs.2009.07.067
fatcat:uinkyjhjt5e7biyos42hxecvtm
*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 ...##
###
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?

1982
*
Information and Control
*

These definitions

doi:10.1016/s0019-9958(82)80087-9
fatcat:ws7l2zql4bg63jvyxe5w5zhx5y
*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*. ...##
###
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]

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. ...

##
###
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]

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] ). ...

##
###
A short survey of isomorphisms of types

2005
*
Mathematical Structures in Computer Science
*

Conclusions We have shown

doi:10.1017/s0960129505004871
fatcat:ifyjdheemragti56gremvwilxa
*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 ...##
###
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

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. ...

##
###
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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