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Graded Hoare Logic and its Categorical Semantics [article]

Marco Gaboardi, Shin-ya Katsumata, Dominic Orchard, Tetsuya Sato
2021 arXiv   pre-print
We develop a semantic framework for modelling GHL such that grading, logical assertions (pre- and post-conditions) and the underlying effectful semantics of an imperative language can be integrated together  ...  We propose Graded Hoare Logic (GHL), a parameterisable framework for augmenting program logics with a preordered monoidal analysis.  ...  Conclusion We have presented a Graded Hoare Logic as a parameterisable framework for reasoning about programs and their side effects, and studied its categorical semantics.  ... 
arXiv:2007.11235v2 fatcat:c3blnxcfu5hfzae2z6e6v26gjm

Teaching Experience: Logic and Formal Methods with Coq [chapter]

Martin Henz, Aquinas Hobor
2011 Lecture Notes in Computer Science  
We also document some of the teaching materials we have developed for the course to date, and what our experiences have been like.  ...  We explain our goals for adding mechanized provers to the course, and illustrate how we have integrated the provers into our syllabus to meet those goals.  ...  in teaching logic to computer science students.  ... 
doi:10.1007/978-3-642-25379-9_16 fatcat:ci5jngydf5an7eyleobywj2kta

Higher-order probabilistic adversarial computations: Categorical semantics and program logics [article]

Alejandro Aguirre, Gilles Barthe, Marco Gaboardi, Deepak Garg, Shin-ya Katsumata, Tetsuya Sato
2021 arXiv   pre-print
We prove the soundness of the logics in the category of quasi-Borel spaces, using a general notion of graded predicate liftings, and we use logical relations over graded predicate liftings to establish  ...  Our logics are built on top of a simply typed λ-calculus extended with a graded monad for probabilities and state.  ...  We also introduce a novel concept of stateful lifting, which combines graded monad liftings with the state monad. This gives a categorical semantics of our new Hoare-triple type (c.f.  ... 
arXiv:2107.01155v1 fatcat:pvfuaokk3rcrtlkd63hdtkzn7i

Generalising KAT to verify weighted computations [article]

Leandro Gomes, Alexandre Madeira, Luís Soares Barbosa
2019 arXiv   pre-print
On this context, and in analogy to Kozen's encoding of Propositional Hoare Logic (PHL) in KAT [22], we discuss the encoding of a graded PHL in I-GKAT and of its while-free fragment in GKAT.  ...  Moreover, to establish semantics for these structures four new algebras are defined: FSET(T), FREL(K,T) and FLANG(K,T) over complete residuated lattices K and T, and M(n,A) over a GKAT or I-GKAT A.  ...  This reinterpretation leads to a generalised version we shall refer to as graded propositional Hoare logic (GPHL).  ... 
arXiv:1911.01146v1 fatcat:45sut6pllbfjpjca3t7nrrb4u4

Page 205 of Behavior Research Methods Vol. 40, Issue 1 [page]

2008 Behavior Research Methods  
Washington, DC: American Psycho¬ logical Association. Steyvers, M., & ItNENBAUM, J. (2005). The large-scale structure of se¬ mantic networks: Statistical analyses and a model of semantic growth.  ...  Word as¬ sociation spaces for predicting semantic similarity effects in episodic memory. In A. F. Healy (Ed.), Experimental cognitive psychology and its applications (pp. 237-249).  ... 

Unifying graded and parameterised monads [article]

Dominic Orchard, Philip Wadler, Harley Eades III
2020 arXiv   pre-print
Most notably, graded monads, indexed by a monoid, model effect systems and parameterised monads, indexed by pairs of pre- and post-conditions, model program logics.  ...  Using this as a basis, we show how graded and parameterised monads can be unified, studying their similarities and differences along the way.  ...  Section 7 shows that the apex of 2-category-graded monads plus generalised units capture analyses and semantics that have both graded and parameterised monad components, using an example of a Hoare logic  ... 
arXiv:2001.10274v1 fatcat:3ts6khvqgbgvvbkc6rkydt6oce

iiOSProTrain: An Interactive Intelligent Online System for Programming Training

Tho Thanh Quan, Phung H Nguyen, Thang H Bui, Thuan Dinh Le, An Nhu Nguyen, Duc L.N. Hoang, Vu Huu Nguyen, Binh Thien Nguyen
2012 Journal of Advances in Information Technology  
More importantly, iiOSProTrain adopts the concept of structured error-flow to give students traceable feedbacks on their mistakes, thus allowing them to track and correct the logic errors in a flexible  ...  and convenient manner.  ...  Axiomatic Problem Description Axiomatic semantic is closely based on Hoare logic [34] , which gives axioms and inference rules for imperative programming languages.  ... 
doi:10.4304/jait.3.1.10-20 fatcat:7jhl3mctvbdufh22mukhpfijxi

A method of programming

Ali Mili
1989 Science of Computer Programming  
Glaser, Hankin and Till.  ...  reviews 165 On numerous occasions Diller relies on references to provide supplementary information, particularly to the "classic" texts on functional programming such as those by Henderson, Peyton Jones, and  ...  and the SECD machine is referred to merely as an influence behind Curien's categorical abstract machine.  ... 
doi:10.1016/0167-6423(89)90043-9 fatcat:aq3vvg2odbhxjhwbokxap37iuq

Approximate Relational Hoare Logic for Continuous Random Samplings

Tetsuya Sato
2016 Electronical Notes in Theoretical Computer Science  
Approximate relational Hoare logic (apRHL) is a logic for formal verification of the differential privacy of databases written in the programming language pWHILE.  ...  We extend the logic apRHL with this graded lifting to deal with continuous random samplings. We give a generic method to give proof rules of apRHL for continuous random samplings.  ...  Acknowledgement The author thanks Shin-ya Katsumata for many valuable comments and stimulating discussions, Marco Gaboardi for helpful suggestions and the introduction of his preprint of [1] in arXiv  ... 
doi:10.1016/j.entcs.2016.09.043 fatcat:c3c7r2aq6vhcnk2q7lvmzkgmd4

Coupling proofs are probabilistic product programs

Gilles Barthe, Benjamin Grégoire, Justin Hsu, Pierre-Yves Strub
2017 SIGPLAN notices  
Our proof rule can capture examples of shift couplings, and the logic is relatively complete for deterministic programs. We show soundness of ×pRHL and use it to analyze two classes of examples.  ...  Recent developments in formal verification identify a close connection between couplings and pRHL, a relational program logic motivated by applications to provable security, enabling formal construction  ...  More recently, Sousa and Dillig [52] propose Cartesian Hoare Logic, an extension of relational Hoare logic to an arbitrary finite number of executions.  ... 
doi:10.1145/3093333.3009896 fatcat:udnq6ofcu5dhhj564oncrfel6u

Coupling proofs are probabilistic product programs [article]

Gilles Barthe, Benjamin Grégoire, Justin Hsu, Pierre-Yves Strub
2016 arXiv   pre-print
Our proof rule can capture examples of shift couplings, and the logic is relatively complete for deterministic programs. We show soundness of xpRHL and use it to analyze two classes of examples.  ...  Recent developments in formal verification identify a close connection between couplings and pRHL, a relational program logic motivated by applications to provable security, enabling formal construction  ...  More recently, Sousa and Dillig [52] propose Cartesian Hoare Logic, an extension of relational Hoare logic to an arbitrary finite number of executions.  ... 
arXiv:1607.03455v4 fatcat:pcessntahnbvxgbxhk5flchfte

Weighted programming : a programming paradigm for specifying mathematical models

Kevin Batz, Adrian Gallus, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Tobias Winkler
2022 ACM SIGPLAN International Conference on Object-Oriented Programming Systems  
More specifically, the weighted programs we investigate are like usual imperative programs with two additional features: (1) nondeterministic branching and (2) weighting execution traces.  ...  We develop weakest-precondition-and weakest-liberal-precondition-style calculi à la Dijkstra for reasoning about mathematical models specified by weighted programs. We present several case studies.  ...  We thank Lena Verscht and Linpeng Zhang for the fruitful discussions at Schloss Dagstuhl.  ... 
doi:10.18154/rwth-2022-04445 fatcat:axpfhudn35azvemwdq53y37hsm

Weighted programming: a programming paradigm for specifying mathematical models

Kevin Batz, Adrian Gallus, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Tobias Winkler
2022 Proceedings of the ACM on Programming Languages (PACMPL)  
More specifically, the weighted programs we investigate are like usual imperative programs with two additional features: (1) nondeterministic branching and (2) weighting execution traces.  ...  We develop weakest-precondition- and weakest-liberal-precondition-style calculi à la Dijkstra for reasoning about mathematical models specified by weighted programs. We present several case studies.  ...  We thank Lena Verscht and Linpeng Zhang for the fruitful discussions at Schloss Dagstuhl.  ... 
doi:10.1145/3527310 fatcat:43vxsumlmjgyhctekgjqrj6q4a

A decade of TAPSOFT [chapter]

Hartmut Ehrig, Bernd Mahr
1995 Lecture Notes in Computer Science  
and attempts to adapt to practical needs was dominant after 1985.  ...  The relationship between theory and practice of software development on the background of the driving forces in the 70'ies and 80'ies was the main topic of the ftrst TAPSOFT conference in 1985.  ...  In [MM 82/84] it was shown that the logic of universal Horn formulas was the most general one within first order logic to admit initial semantics.  ... 
doi:10.1007/3-540-59293-8_184 fatcat:vydozuun3fajhpxgakow7btv64

Design, Analysis and Reasoning about Tools: Abstracts from the Third Workshop

Flemming Nielson
1993 DAIMI Report Series  
CLICS Winskel's Esprit BRA "Categorical Logic in Computer Science" funds the category theorist and proof theorist Sergei Soloviev (on leave from the University of St.  ...  Common properties, which seem to have called for a full Hoare logic beyond the reach of type checking and decidability, can now be expressed in a uniform descriptive language integrating types and program  ... 
doi:10.7146/dpb.v22i457.6930 fatcat:qqr3ybpuqrc3fmwjlsamx3kuwu
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