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An Elementary Fragment of Second-Order Lambda Calculus
[article]

2004
*
arXiv
*
pre-print

A

arXiv:cs/0210022v3
fatcat:7zywa2andzc3boacifjgb2dy6i
*fragment**of**second*-*order**lambda**calculus*(System F) is defined that characterizes the*elementary*recursive functions. ... ., the types are assigned levels, and a quantified variable can only be instantiated by a type*of*smaller level, with a slightly liberalized treatment*of*the level zero. ... Á Γ ⊢ r : τ Ò r r ′¸Ø Ò Γ ⊢ r ′ : τº Statement*of*the main result. ÓÖ Ú ÖÝ ØÝÔ τ¸Û ¬Ò Ø ØÝÔ τ * := (τ → τ) → (τ → τ) . ...##
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Page 4129 of Mathematical Reviews Vol. , Issue 92h
[page]

1992
*
Mathematical Reviews
*

Girard proved both these results for his system F (the

*second*-*order*polymorphic*lambda*-*calculus*). ... The author puts forward a formal system which arises as*an*exten- sion*of*the*second*-*order**lambda**calculus*(e.g., Girard’s F system), obtained by adding two type constructors uw and v. ...##
###
Page 4689 of Mathematical Reviews Vol. , Issue 93i
[page]

1993
*
Mathematical Reviews
*

*lambda*-

*calculus*whose types are formulas

*of*

*second*-

*order*predicate

*calculus*is introduced. ... This paper is primarily a survey

*of*the use

*of*category-theoretic techniques in the modelling

*of*the

*second*-

*order*

*lambda*

*calculus*and some

*of*its closer relatives (such as Girard’s F,,). ...

##
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Lambda terms for natural deduction, sequent calculus and cut elimination

2000
*
Journal of functional programming
*

Moreover, the

doi:10.1017/s0956796899003524
fatcat:aj53epzfdjephcolxilmi2mmye
*second*type assignment system has a 'cut-free'*fragment*()..L cf ) . This*fragment*generates exactly the typeable*lambda*terms in normal form. ... The cut elimination theorem becomes a simple consequence*of*the fact that typed*lambda*terms posses a normal form. Acknowledgment. ... Moreover, as the cut-free deduct ion is*of*the same*order**of*complexity as the corresponding normal*lambda*term, the size*of*the cut-free version*of*a derivation is non*elementary*in the size*of*the original ...##
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Page 2287 of Mathematical Reviews Vol. , Issue 86f
[page]

1986
*
Mathematical Reviews
*

Séedrov, Andrej (1-PA) 86f:03022 On some nonclassical extensions

*of**second*-*order*intuitionistic propositional*calculus*. Ann. Pure Appl. Logic 27 (1984), no. 2, 155-164. ... t1,t2) then for all se R,, t,(r,s) = te(r,s); with respect to the*second*, it is shown that there is a recursive function B: L x L — N such that for arbitrary t,,t2 € L and*an*arbitrary set*of*true identities ...##
###
Page 4126 of Mathematical Reviews Vol. , Issue 93h
[page]

1993
*
Mathematical Reviews
*

Tauts (Tallinn)
93h:03014 03B40 06A23 Honsell, Furio (I-UDIN); Ronchi Della Rocca, Simona (I-TRIN-IF)

*An*approximation theorem for topological*lambda*models and the topological incompleteness*of**lambda*... (The*second*-*order*properties defining K have in some sense then been reduced to first-*order*properties.) ...##
###
Page 8 of Mathematical Reviews Vol. , Issue 92c
[page]

1992
*
Mathematical Reviews
*

The author concentrates on two important examples, the

*second*-*order**lambda**calculus**of*Girard and Reynolds, and the Coquand- Huet*calculus**of*constructions. ... There are detailed proofs*of*the Church-Rosser property and strong normalisation for the*second*-*order**lambda**calculus*, and*an*extensive discussion*of*models for both calculi. ...##
###
Böhm Trees, Krivine's Machine and the Taylor Expansion of Lambda-Terms
[chapter]

2006
*
Lecture Notes in Computer Science
*

This information is expressed as a term

doi:10.1007/11780342_20
fatcat:wdygzoafijfbheelv7l6rdefvy
*of*a resource*lambda*-*calculus*introduced by the authors in a recent article; this*calculus*can be seen as a*fragment**of*the differential*lambda*-*calculus*. ... We use this machine to show that Taylor expansion*of**lambda*-terms (*an*operation mapping*lambda*-terms to generally infinite linear combinations*of*resource*lambda*-terms) commutes with Böhm tree computation ... B k is*an**elementary*Böhm tree. ...##
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Page 1109 of Mathematical Reviews Vol. , Issue 96b
[page]

1996
*
Mathematical Reviews
*

The most natural LAAs are obtained by coordinatizing environ- ment models

*of*the*lambda**calculus*. ... Summary: “*Lambda*abstraction algebras (LAAs) are designed to algebraize the untyped*lambda**calculus*in the same way cylindric and polyadic algebras algebraize the first-*order*predicate logic. ...##
###
Page 17 of Mathematical Reviews Vol. , Issue 94a
[page]

1994
*
Mathematical Reviews
*

(PL-WASW-I; Warsaw) Type reconstruction in finite rank

*fragments**of*the*second*-*order*A-*calculus*. Selections from the 1990 IEEE Symposium on Logic in Computer Science. ... Visser, 1980) or a term*of**order*0 (Statman, 1987). It is proved that any nontrivial set*of*closed*lambda*terms which is co-r.e. and closed under =, can be used to represent ‘undefined’. ...##
###
Natural Language Semantics and Computability

2019
*
Journal of Logic, Language and Information
*

We also discuss the algorithmic complexity

doi:10.1007/s10849-019-09290-7
fatcat:xnkyltzmrngbdkuo73m5dcptqi
*of*this process. ... This paper is a reflexion on the computability*of*natural language semantics. ... We believe that natural language semantics uses a restricted*fragment**of*the*lambda**calculus*, soft*lambda**calculus*. ...##
###
Natural Language Semantics and Computability
[article]

2016
*
arXiv
*
pre-print

We also discuss the algorithmic complexity

arXiv:1605.04122v1
fatcat:6ir6tt2i2zh3jl2kbxtng3pjmi
*of*this process. ... This paper is a reflexion on the computability*of*natural language semantics. ... We believe that natural language semantics uses a restricted*fragment**of*the*lambda**calculus*, soft*lambda**calculus*. ...##
###
Page 1277 of Mathematical Reviews Vol. , Issue 95c
[page]

1995
*
Mathematical Reviews
*

The author gives a proof

*of*strong normalization for the closed terms*of*Girard’s system F*of**second*-*order*polymorphic*lambda**calculus*, using a modification*of*W. W. ... Assuming the existence*of**an**elementary*embedding j: VV — M with critical point x and V,.4.,; C M, where w < a < @, they use*an*idea*of*S. Shelah [in Surveys in set theory, 116-134, Cambridge Univ. ...##
###
A Finiteness Structure on Resource Terms

2010
*
2010 25th Annual IEEE Symposium on Logic in Computer Science
*

Such coherence properties are lost when one considers non-deterministic or algebraic extensions

doi:10.1109/lics.2010.38
dblp:conf/lics/Ehrhard10
fatcat:6lluz63tafaxderygh5etxb5zi
*of*the*lambda*-*calculus*(the algebraic*lambda*-*calculus*is*an*extension*of*the*lambda*-*calculus*where terms ... Roughly speaking, the ordinary*lambda*-*calculus*correspond to the*fragment**of*LL which contains the multiplicative, structural and promotion rules. ... This superposition*of**elementary*normal forms is controlled by the finiteness structures, but this is possible only in a typed setting (here,*second**order*types). ...##
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Page 627 of Mathematical Reviews Vol. , Issue 91B
[page]

1991
*
Mathematical Reviews
*

Zakharyashchev (Moscow)
91b:03029 03B40 03G30 68Q55
Jacobs, Bart (NL-NIJM-C)
On the semantics

*of**second**order**lambda**calculus*: from Bruce-Meyer-Mitchell models to hyperdoctrine models and vice-versa. ... In the paper under review, by changing the conditions defining PL-categories the author constructs (categorical) 42-models and gives*an*interpretation with valuation functions*of**second*-*order*A-*calculus*...
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