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A Curry-Howard foundation for functional computation with control

1997
*
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '97
*

*Computationally*they give succinct expression to

*a*kind of generic (forward) \jump" operator, which may be regarded as

*a*unifying

*control*construct

*for*

*functional*

*computation*. ... We study the behavioural properties of pcf v and show that, though simple, it is

*a*very general language

*for*

*functional*

*computation*

*with*

*control*: it can express all the main

*control*constructs such as ... Acknowledgements We are grateful to Tony Hoare

*for*detailed comments on an earlier draft of the paper. ...

##
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Page 5757 of Mathematical Reviews Vol. , Issue 95j
[page]

1995
*
Mathematical Reviews
*

Intuitively,

*a*verifier of*a*formula*for**a*model-theoretic structure is*a*program or*computable**function*which provides constructive evidence*for*the truth of the formula in the structure. ... The fact that*Curry*-*Howard*terms are verifiers, combined*with*the Church-Rosser property and strong normalization, means that proofs in natural deduction systems can always be reduced to*Curry*-*Howard*terms ...##
###
The rôle of linear logic in coalgebraical approach of computing

2011
*
Journal of Information and Organizational Sciences
*

*Curry*-

*Howard*correspondence is

*a*correspondence between logic and

*computing*in informatics. ... In this contribution we present two ways of

*computations*which correctness we prove by

*Curry*-

*Howard*correspondence. ... Acknowledgments This work has been supported by VEGA Grant No.1/0015/10: Principles and methods of semantic enrichment and adaptation of knowledge-based languages

*for*automatic software development. ...

##
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Page 3611 of Mathematical Reviews Vol. , Issue 95f
[page]

1995
*
Mathematical Reviews
*

*For*Church and

*Curry*,

*a*fundamental question was whether

*functions*should be defined as sets or sets defined as

*functions*. ... And as the fore- word reveals, the book can also be enjoyed by the nonspecialist mathematician

*with*

*a*fascination

*for*logic and

*computer*science. ...

##
###
Types for TiPES - Applying Type Theory to Climate Impact Research

2020
*
Zenodo
*

Presentation given at the RD4 seminar of the Potsdam Institute

doi:10.5281/zenodo.4554684
fatcat:fnxttpwd6jcylivqspul7upu5m
*for*Climate Impact Research (PIK) about dependent type theory and its application to climate impact research. ... of M Val (e.g.*computes*the expected value*for*M = SimpleProb) Question: Does this*function**compute*the same value as*a**function*val which measures the sum of the rewards along the possible trajectories ... transition*function*next which calculates the next state(s) depending on time, Val of Values*A**function*reward which determines the value of*a*transition depending on the current state, the*control*and ...##
###
Linearity, Control Effects, and Behavioral Types
[chapter]

2017
*
Lecture Notes in Computer Science
*

example of

doi:10.1007/978-3-662-54434-1_9
fatcat:hk5yagycr5f55f2gigbs5hwl7a
*a**Curry*-*Howard*interpretation of*a*realistic programming language*with*built-in internal non-determinism. ... Remarkably, our type system builds on*a**Curry*-*Howard*correspondence*with*(classical) linear logic conservatively extended*with*two dual modalities capturing an additive (co)monad, and provides*a*first ... Introduction In this paper, we study*a*principled, typeful*foundation*to represent*a*relevant class of*control*effects within*a*behavioral type system*for*stateful concurrent programs. ...##
###
Proofs-as-Programs in Computable Analysis

2009
*
Electronic Communications of the EASST
*

In

doi:10.14279/tuj.eceasst.23.332
dblp:journals/eceasst/Berger09
fatcat:nihg2u2vobbmhgxto2k7vzq7wy
*Computer*Science this idea is known as the "proofs-as-programs paradigm" or "*Curry*-*Howard*correspondence". ... Since the work of Brouwer, Kolmogorov, Goedel, Kleene and many others we know that constructive proofs have*computational*meaning. ... "*Curry*-*Howard*correspondence" which is the observation that -under certain conditions-formal proofs can be viewed and executed as programs. ...##
###
On Correspondence between Selective CPS Transformation and Selective Double Negation Translation

2021
*
Mathematics
*

*A*selective CPS transformation uses

*a*type and effect system to selectively translate only nontrivial expressions possibly

*with*

*computational*effects into CPS

*functions*. ... We believe that our work can serve as

*a*reference point

*for*further study on the

*Curry*-

*Howard*isomorphism between CPS transformations and DNTs. ... The main contributions of our paper are summarized as follows: • We review the

*Curry*-

*Howard*isomorphism between the standard call-by-value (CBV) CPS transformation

*with*

*control*operators and the corresponding ...

##
###
When Logic Meets Engineering: Introduction to Logical Issues in the History and Philosophy of Computer Science

2015
*
History and Philosophy of Logic
*

1 See Tedre 2015

doi:10.1080/01445340.2015.1084183
fatcat:5uu53ql7szf6jo5p4vj5i7kqga
*for**a*recent in-depth study of the past and ongoing debates on what*computer*science is. ... to the implicational fragment of Intuitionistic Logic (and hence the typed λ-calculus), as suggested by*Curry*; this equivalence was later rediscovered by*Howard**for*natural deduction,*a*correspondence ...*With*the need*for*logical*control*over dynamically performed*computations*came also the need to develop communication means, feasible*for*both machine and human user. ...##
###
CONSTRUCTIVE CLASSICAL LOGIC AS CPS-CALCULUS

2000
*
International Journal of Foundations of Computer Science
*

We establish the

doi:10.1142/s0129054100000065
fatcat:qt4xrvsvsrc5xf62vheeqvavkq
*Curry*-*Howard*isomorphism between constructive classical logic and CPS-calculus. CPS-calculus exactly means the target language of Continuation Passing Style(CPS) transforms. ... Continuation Passing Style (CPS) transforms are widely used in the semantics of*functional*programming languages*with**control*operators. ... The Importance of the Isomorphism Second-Order system and its*computational*strength: The*Curry*-*Howard*isomorphism can be extended to the second-order. ...##
###
PhD Abstracts

2017
*
Journal of functional programming
*

As

doi:10.1017/s0956796817000181
fatcat:xbdgckkjpnaathslfgakegj3ka
*a*service to the community, the Journal of*Functional*Programming publishes the abstracts from PhD dissertations completed during the previous year. ... Many students complete PhDs in*functional*programming each year. ... Our approach is based on the*Curry*-*Howard*isomorphism which says that programs following*a*specification are the same as proofs*for*mathematical theorems. ...##
###
Page 1424 of Mathematical Reviews Vol. , Issue 2000b
[page]

2000
*
Mathematical Reviews
*

The target is

*a*simple*functional*language extended*with*basic primitives*for*actor*computation*. ... The Ay-calculus is an extension of the typed*A*-calculus which corresponds via the*Curry*-*Howard*correspondence to classical logic. ...##
###
Natural Deduction for Intuitionistic Non-commutative Linear Logic
[chapter]

1999
*
Lecture Notes in Computer Science
*

We present

doi:10.1007/3-540-48959-2_21
fatcat:trfe35vz2nfg7dxu4zgxtwgtpm
*a*system of natural deduction and associated term calculus*for*intuitionistic non-commutative linear logic (INCLL) as*a*conservative extension of intuitionistic linear logic. ... This establishes the connection to*functional**computation*by an extension of the*Curry*-*Howard*isomorphism. ... Introduction Intuitionistic logic captures pure*functional**computation*in*a*logical way, as can be seen from the*Curry*-*Howard*isomorphism between constructive proofs and*functional*programs. ...##
###
The Logical Abstract Machine: A Curry-Howard Isomorphism for Machine Code
[chapter]

1999
*
Lecture Notes in Computer Science
*

We then establish

doi:10.1007/10705424_20
fatcat:vtbv4axyb5b35fdljip4gexziu
*a**Curry*-*Howard*isomorphism between this proof system and machine code based on the following observation. ... An ordinary machine instruction corresponds to*a*polymorphic proof transformer that extends*a*given proof*with*one inference step. ... Acknowledgments The author would like to thank Shin'ya Katsumata*for*stimulating discussion on logic and*computer*hardware, and*for*comments on*a*draft of this paper. ...##
###
Page 2808 of Mathematical Reviews Vol. , Issue 82g
[page]

1982
*
Mathematical Reviews
*

Miinster, Miinster, 1978] to other

*functional*interpretations. {*For*the entire collection see MR 81j:03005.} H. Schwichtenberg (Munich) 82g:03094 82g:03093*Howard*, W.*A*. ... Theorem 3.7: If F: L* > L” is*a*concave fuzz*function*, then*for*any convex fuzzy set*A*in X, its image F(*A*) is*a*convex fuzzy set in Y. ...
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