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A Curry-Howard foundation for functional computation with control

C.-H. L. Ong, C. A. Stewart
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.  ... 
doi:10.1145/263699.263722 dblp:conf/popl/OngS97 fatcat:k4e4l3thefhhdf2kgvpmsbex7y

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

Viliam Slodičák, Pavol Macko
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.  ... 
doaj:75bab1b9dc2b46558af226dcb0ae2cd8 fatcat:3ftl4xi2evgwxfizt45gjduxyq

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

Nuria Brede
2020 Zenodo  
Presentation given at the RD4 seminar of the Potsdam Institute 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  ... 
doi:10.5281/zenodo.4554684 fatcat:fnxttpwd6jcylivqspul7upu5m

Linearity, Control Effects, and Behavioral Types [chapter]

Luís Caires, Jorge A. Pérez
2017 Lecture Notes in Computer Science  
example of 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.  ... 
doi:10.1007/978-3-662-54434-1_9 fatcat:hk5yagycr5f55f2gigbs5hwl7a

Proofs-as-Programs in Computable Analysis

Ulrich Berger
2009 Electronic Communications of the EASST  
In 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.  ... 
doi:10.14279/tuj.eceasst.23.332 dblp:journals/eceasst/Berger09 fatcat:nihg2u2vobbmhgxto2k7vzq7wy

On Correspondence between Selective CPS Transformation and Selective Double Negation Translation

Hyeonseung Im
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  ... 
doi:10.3390/math9040385 fatcat:bxoyxm5ezjasfpzoyu2kqmxgsm

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

Liesbeth De Mol, Giuseppe Primiero
2015 History and Philosophy of Logic  
1 See Tedre 2015 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.  ... 
doi:10.1080/01445340.2015.1084183 fatcat:5uu53ql7szf6jo5p4vj5i7kqga

CONSTRUCTIVE CLASSICAL LOGIC AS CPS-CALCULUS

ICHIRO OGATA
2000 International Journal of Foundations of Computer Science  
We establish the 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.  ... 
doi:10.1142/s0129054100000065 fatcat:qt4xrvsvsrc5xf62vheeqvavkq

PhD Abstracts

GRAHAM HUTTON
2017 Journal of functional programming  
As 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.  ... 
doi:10.1017/s0956796817000181 fatcat:xbdgckkjpnaathslfgakegj3ka

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]

Jeff Polakow, Frank Pfenning
1999 Lecture Notes in Computer Science  
We present 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.  ... 
doi:10.1007/3-540-48959-2_21 fatcat:trfe35vz2nfg7dxu4zgxtwgtpm

The Logical Abstract Machine: A Curry-Howard Isomorphism for Machine Code [chapter]

Atsushi Ohori
1999 Lecture Notes in Computer Science  
We then establish 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.  ... 
doi:10.1007/10705424_20 fatcat:vtbv4axyb5b35fdljip4gexziu

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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