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## Filters

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The Girard Translation extended with recursion
[chapter]

1995
*
Lecture Notes in Computer Science
*

*The*embedding of proofs of IL into proofs of ILL given by

*the*

*Girard*

*Translation*is

*extended*

*with*

*the*rules for

*recursion*, such that an embedding of terms of

*the*λ rec -calculus into terms of

*the*linear ... This paper

*extends*Curry-Howard interpretations of Intuitionistic Logic (IL) and Intuitionistic Linear Logic (ILL)

*with*rules for

*recursion*. ...

*The*

*Girard*

*Translation*

*Extended*

*with*

*Recursion*

*The*

*Girard*

*Translation*still works if we

*extend*it

*with*

*the*rules for

*recursion*given in Appendix B and Appendix D. ...

##
###
The Girard Translation Extended with Recursion

1995
*
BRICS Report Series
*

*The*embedding of proofs of IL into proofs of ILL given by

*the*

*Girard*

*Translation*is

*extended*

*with*

*the*rules for

*recursion*, such that an embedding of terms of

*the*rec-calculus into terms of

*the*linear rec-calculus ... <p>This paper

*extends*Curry-Howard interpretations of Intuitionistic Logic (IL) and Intuitionistic Linear Logic (ILL)

*with*rules for

*recursion*. ...

*The*

*Girard*

*Translation*

*Extended*

*with*

*Recursion*

*The*

*Girard*

*Translation*still works if we

*extend*it

*with*

*the*rules for

*recursion*given in Appendix B and Appendix D. ...

##
###
Page 1568 of Mathematical Reviews Vol. , Issue 2003C
[page]

2003
*
Mathematical Reviews
*

of

*the*A-terms typable*with*IT.” ...*The*assignment of types to A-terms*extends*naturally*the*basic type assignment system. ...##
###
Page 6651 of Mathematical Reviews Vol. , Issue 90K
[page]

1990
*
Mathematical Reviews
*

We also

*extend*part of Gi- rard’s results by investigating*the*consequence relations associated*with*linear logic and by proving corresponding strong complete- ness theorems. ...*Girard*in order to provide a logical basis for*the*study of parallelism. It is described and investigated in a paper by*Girard*[same journal 50 (1987), no. 1; MR 89m:03057]. ...##
###
The Limits of Computation

2021
*
Axiomathes
*

It is argued that

doi:10.1007/s10516-021-09561-8
fatcat:w6nlldlpxvblpjgxp37u6jejke
*the*power of algorithms is at least as strong as functions that can be proved to be totally computable in type-theoretic*translations*of subsystems of second-order Zermelo Fraenkel set ... Moreover, it is claimed that typed systems of*the*lambda calculus give rise naturally to a functional interpretation of rich systems of types and to a hierarchy of ordinal*recursive*functionals of arbitrary ... 6.7. d*Girard*proved that System F has*the*same provably total*recursive*functions as full second-order Peano arithmetic, see*Girard*(1989) . ...##
###
Page 2745 of Mathematical Reviews Vol. , Issue 98E
[page]

1998
*
Mathematical Reviews
*

*Girard*

*translation*

*extended*

*with*

*recursion*. ...

*The*embedding of proofs in intuitionistic logic into proofs in intuitionistic linear logic given by

*the*

*Girard*

*translation*is ex- tended by rules for

*recursion*such that an embedding of terms of

*the*A£ ...

##
###
Page 5937 of Mathematical Reviews Vol. , Issue 90J
[page]

1990
*
Mathematical Reviews
*

Summary (

*translated*from*the*Russian): “We give an algorithm that is regularizing*with*respect to a functional for solving crite- rial problems of least squares of*the*form ||w(x) —£z;9i(x)||? ... Second a spatial cubic Bézier curve*with*no repetitive apex is regular and has no double point and no stationary point. Ming Gen Cui (Harbin) Numerical approximation 90j:65031 65D10 65D07*Girard*, D. ...##
###
Call-by-name, call-by-value, call-by-need and the linear lambda calculus

1999
*
Theoretical Computer Science
*

Our results

doi:10.1016/s0304-3975(98)00358-2
fatcat:wpm6kbycovabhlkibythzok3mu
*extend*neatly to*translations*of extensions for*recursion*in*the*call-by-name and call-by-value calculi, and in general to extensions for products and for*the*corresponding untyped systems. ...*Girard*devotes several pages to*the*ÿrst*translation*and less than a paragraph to*the*second, stating that "its interest is limited". ...*Extending**the**translations*for Name rec and Val rec is straightforward. Both*extended**translations*are sound and complete for*the*respective calculi*with**recursion*. ...##
###
Page 8396 of Mathematical Reviews Vol. , Issue 2000m
[page]

2000
*
Mathematical Reviews
*

Let T be any re. arithmetic theory

*extending*primitive*recursive*arithmetic. ... It was*translated*from Russian by*the*author. ...##
###
Inheritance as implicit coercion

1991
*
Information and Computation
*

Many of

doi:10.1016/0890-5401(91)90055-7
fatcat:qlzvfdnfpfhgxggyfkdbpxorta
*the*results of this paper were obtained during Coquand's visit to*the*University of Pennsylvania, partially sponsored by Scedrov's funds from*the*Natural Sciences Association. ... Scedrov's research was partially supported by NSF Grant CCR-87-05596, by ONR Grant N00014-88-K-0635, and by*the*1987 Young Faculty Award from*the*Natural Sciences Association of*the*University of Pennsylvania ...*The*method we propose proceeds first*with*a*translation*of Fun into an*extended*polymorphic lambda calculus*with**recursive*types. ...##
###
A Simple Semantics for Polymorphic Recursion
[chapter]

2005
*
Lecture Notes in Computer Science
*

Polymorphic

doi:10.1007/11575467_4
fatcat:px3c3sa7v5axfpahgrjgcqe6wi
*recursion*is a useful extension of Hindley-Milner typing and has been incorporated in*the*functional programming language Haskell. ...*The*semantics reported here also contributes an essential building block to any semantics of Haskell: a model for first-order polymorphic*recursion*. ... Acknowledgements*The*author wishes to thank Dick Kieburtz, Brian Dunphy, and Mark Jones for their encouragement and for numerous discussions on aspects of polymorphic*recursion*, its relationship to*the*...##
###
Page 4022 of Mathematical Reviews Vol. , Issue 87h
[page]

1987
*
Mathematical Reviews
*

*The*same sets of ordinals are, for example, represented by

*recursive*, primitive

*recursive*, and elementary

*recursive*well-orderings of

*the*natural numbers. ...

*The*author proves, for example, that

*the*sup of

*the*ordinals constructed by primitive

*recursive*functors is

*the*least primitive

*recursively*closed ordinal, and

*the*sup of those obtained by ¢o-

*recursive*...

##
###
Page 4264 of Mathematical Reviews Vol. , Issue 85j
[page]

1985
*
Mathematical Reviews
*

*Girard*, for PI

*with*

*the*Bachmann/Howard ordinal replacing

*the*smaller ¢9.

*The*tools used are

*the*fast-growing and slow-growing hierarchies, {F,,} and {G.}. ... Mints (Tallinn) 85j:03101 Visser, Albert (NL-UTRE) 85j:03102

*The*provability logics of

*recursively*enumerable theories

*extending*Peano arithmetic at arbitrary theories

*extending*Peano arithmetic. J. ...

##
###
Page 1937 of Mathematical Reviews Vol. , Issue 95d
[page]

1995
*
Mathematical Reviews
*

*The*notion of ptyx was introduced by J.-Y.

*Girard*and J.-P. Ressayre [in

*Recursion*theory (Ithaca, N.Y., 1982), 389-445, Proc. Sympos. Pure Math., 42, Amer. Math. ... They then go on to show that

*the*interpretation of a A-term in ¥ is equal to

*the*interpretation of its pure proof net

*translation*. ...

##
###
Page 2229 of Mathematical Reviews Vol. , Issue 91D
[page]

1991
*
Mathematical Reviews
*

Summary: “It is shown that a class of standard schemes

*with*one counter and a finite number of finite-turn stacks can be*translated*in*the*class of standard schemes. ...*The*problem of freedom is proved to be unsolvable for metalinear*recursive*schemes*with*an individual constant.” ...
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