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Logical relations for monadic types

JEAN GOUBAULT-LARRECQ, SŁAWOMIR LASOTA, DAVID NOWAK
2008 Mathematical Structures in Computer Science  
We propose a natural notion of logical relations able to deal with the monadic types of Moggi's computational lambda-calculus.  ...  Logical relations and their generalizations are a fundamental tool in proving properties of lambda-calculi, e.g., yielding sound principles for observational equivalence.  ...  Logical relations for monadic types are given by [2] : c 1 R Tτ c 2 ⇐⇒ (∀k 1 , k 2 .  ... 
doi:10.1017/s0960129508007172 fatcat:kdwv2ozha5hvnfbxer7uckbu34

Logical Relations for Monadic Types [chapter]

Jean Goubault-Larrecq, Slawomir Lasota, David Nowak
2002 Lecture Notes in Computer Science  
Whereas pre-logical relations are complete at all types, logical relations are only complete up to firstorder types.  ...  We propose a notion of contextual equivalence for Moggi's computational lambda calculus, and define pre-logical and logical relations for this calculus.  ...  Logical relations for monadic types are given by [2] : c 1 R Tτ c 2 ⇐⇒ (∀k 1 , k 2 .  ... 
doi:10.1007/3-540-45793-3_37 fatcat:n643ql2kdjbnxpqdcqpn3b43g4

On Completeness of Logical Relations for Monadic Types [chapter]

Sławomir Lasota, David Nowak, Yu Zhang
2007 Lecture Notes in Computer Science  
We have already defined logical relations for the computational lambda-calculus in previous work.  ...  Contextual equivalence is difficult to prove directly, but we can often use logical relations as a tool to establish it in lambda-calculi.  ...  Logical relations for monadic types are given by [2] : c 1 R Tτ c 2 ⇐⇒ (∀k 1 , k 2 .  ... 
doi:10.1007/978-3-540-77505-8_17 fatcat:v2vdxu6nofh5dlg3qtuef4w72y

Factorisation systems for logical relations and monadic lifting in type-and-effect system semantics [article]

Ohad Kammar, Dylan McDermott
2018 arXiv   pre-print
We relate the derived semantics to the original semantics using fibrations for logical relations. Our proof uses a folklore technique for lifting monads with operations.  ...  A semantics for type-and-effect systems involves a parameterised family of monads whose size is exponential in the number of effects.  ...  Well-powered factorisation systems for logical relations induce categories of partial maps via Fiore's axiomatic domain theory [6] .  ... 
arXiv:1804.03460v1 fatcat:epdkdup5lzfy5fjdpgecjwnszu

Factorisation Systems for Logical Relations and Monadic Lifting in Type-and-effect System Semantics

Ohad Kammar, Dylan McDermott
2018 Electronical Notes in Theoretical Computer Science  
We relate the derived semantics to the original semantics using fibrations for logical relations. Our proof uses a folklore technique for lifting monads with operations.  ...  A semantics for type-and-effect systems involves a parameterised family of monads whose size is exponential in the number of effects.  ...  The codomain functor cod : M → C is a fibration for logical relations iff (E, M) is a factorisation system for logical relations.  ... 
doi:10.1016/j.entcs.2018.11.012 fatcat:xube7wtyf5eubb3g5ltbr7gj7a

The Next 700 Relational Program Logics [article]

Kenji Maillard, Catalin Hritcu, Exequiel Rivas, Antoine Van Muylder
2019 arXiv   pre-print
We propose the first framework for defining relational program logics for arbitrary monadic effects. The framework is embedded within a relational dependent type theory and is highly expressive.  ...  For an arbitrary relational effect observation, we generically define the core of a sound relational program logic, and explain how to complete it to a full-fledged logic for the monadic effect at hand  ...  ACKNOWLEDGMENTS We thank Alejandro Aguirre, Danel Ahman, Robert Atkey, Gilles Barthe, Shin-ya Katsumata, Satoshi Kura, Guido Martínez, Ramkumar Ramachandra, Nikhil Swamy, Éric Tanter, and the anonymous reviewers for  ... 
arXiv:1907.05244v3 fatcat:72sokhhbwndifi6r53ooeabkdi

Completeness of Global Evaluation Logic [chapter]

Sergey Goncharov, Lutz Schröder, Till Mossakowski
2006 Lecture Notes in Computer Science  
logics such as monad-based Hoare logic or dynamic logic.  ...  We prove completeness of global evaluation logic for models in cartesian categories with a distinguished Heyting algebra object.  ...  ] , a monad-based Hoare logic [13] , and a monad-based dynamic logic related to evaluation logic [14] .  ... 
doi:10.1007/11821069_39 fatcat:x34mtae7jnfkjo43ql4jfswuk4

A functional-logic library for wired

Matthew Naylor, Emil Axelsson, Colin Runciman
2007 Proceedings of the ACM SIGPLAN workshop on Haskell workshop - Haskell '07  
Compared to a previous library for logic programming by Claessen and Ljunglöf, we support residuation, easier creation of logical data types, and pattern matching.  ...  We develop a Haskell library for functional-logic programming, motivated by the implementation of Wired, a relational embedded domain-specific language for describing and analysing digital circuits at  ...  We would like to thank Mary Sheeran and the anonymous referees for substantial constructive suggestions and comments.  ... 
doi:10.1145/1291201.1291207 dblp:conf/haskell/NaylorAR07 fatcat:4eoc6otg2fhsljcnbj2qnxqpsy

Proof-Producing Synthesis of CakeML with I/O and Local State from Monadic HOL Functions [chapter]

Son Ho, Oskar Abrahamsson, Ramana Kumar, Magnus O. Myreen, Yong Kiam Tan, Michael Norrish
2018 Lecture Notes in Computer Science  
We introduce an automatic method for producing stateful ML programs together with proofs of correctness from monadic functions in HOL.  ...  We apply this approach to several non-trivial examples, including the type inferencer and register allocator of the otherwise pure CakeML compiler, which now benefits from better runtime performance.  ...  The second and fourth authors were partly supported by the Swedish Foundation for Strategic Research. The fifth author was supported by an A*STAR National Science Scholarship (PhD), Singapore.  ... 
doi:10.1007/978-3-319-94205-6_42 fatcat:45lqenczprgkdlnuftku6uh76y

Building verification condition generators by compositional extensions

I.S.W.B. Prasetya, A.A. Fakultas, T.E.J. Vos, A. van Leeuwen
2005 Third IEEE International Conference on Software Engineering and Formal Methods (SEFM'05)  
This paper describes a technique that combines algebraic datatypes and monads to build derivative verification condition generators (VCGs) by extending a base VCG.  ...  To deal with exceptions, not only the logic of L 0 has to be extended with new rules, its structure also needs to be changed.  ...  Related Work One way monads can be useful for program verification is to use them in the semantics of the target language.  ... 
doi:10.1109/sefm.2005.11 dblp:conf/sefm/PrasetyaAVL05 fatcat:bvxo23rfnzbmbnuejqd7pfhy4q

Higher-Order Syntax and Saturation Algorithms for Hybrid Logic

Moritz Hardt, Gert Smolka
2007 Electronical Notes in Theoretical Computer Science  
We present modal logic on the basis of the simply typed lambda calculus with a system of equational deduction.  ...  Once HL(@) is characterized as the monadic fragment of MFI, we develop a tableau calculus and a tableau-based decision procedure for this logic. The first such algorithm is due to Tzakova [15].  ...  Acknowledgments We thank an anonymous referee for pointing out a flaw in a previous version of the paper. We appreciate the time the editors gave us for reorganizing the results.  ... 
doi:10.1016/j.entcs.2006.11.023 fatcat:l3er2uovyjgzxiv6bha6qahxa4

Proof-Producing Synthesis of CakeML from Monadic HOL Functions

Oskar Abrahamsson, Son Ho, Hrutvik Kanabar, Ramana Kumar, Magnus O. Myreen, Michael Norrish, Yong Kiam Tan
2020 Journal of automated reasoning  
We introduce an automatic method for producing stateful ML programs together with proofs of correctness from monadic functions in HOL.  ...  The following is a recursion equation for a function, fib, in higher-order logic (HOL) that does the job: fib n def = if n < 2 then n else fib (n − 1) + fib (n − 2) A hand-written implementation (shown  ...  The first and fifth authors were partly supported by the Swedish Foundation for Strategic Research. The seventh author was supported by an A*STAR National Science Scholarship (Ph.D.), Singapore.  ... 
doi:10.1007/s10817-020-09559-8 fatcat:p7djm6ixgjcfpmaceb7gkrdnji

Computational Semantics for Monadic Quantifiers

Marcin Mostowski
1998 Journal of Applied Non-Classical Logics  
The paper gives a survey of known results related to computational devices (finite and push-down automata) recognizing monadic generalized quantifiers in finite models.  ...  Additionally a new result characterizing monadic quantifiers recognized by push down automata is proven. * The research reported here has been supported by the research grant of Polish National Commitee  ...  More precisely for each n-ary monadic quantifier Q we define the logic L(Q) as an extension of elementary (first order) logic.  ... 
doi:10.1080/11663081.1998.10510934 fatcat:4lcydm6gfnhw5n3kcndb2go2he

Monadic Second-Order Logic for Graphs: Algorithmic and Language Theoretical Applications [chapter]

Bruno Courcelle
2009 Lecture Notes in Computer Science  
This tutorial will present an overview of the use of Monadic Second-Order Logic to describe sets of finite graphs and graph transformations, in relation with the notions of tree-width and clique-width.  ...  A graph, either finite or infinite, can be considered as a logical structure whose domain (the ground set of the logical structure) consists of the set of vertices ; a binary relation on this set represents  ...  They can also replace finite automata for defining graph transformations, that we call transductions, as in Language Theory. However, monadic second-order logic alone yields no interesting results.  ... 
doi:10.1007/978-3-642-00982-2_2 fatcat:ryjvoaa7dnefrcruygfnpqso2i

Composition Theorems for Generalized Sum and Recursively Defined Types

Alexander Rabinovich
2005 Electronical Notes in Theoretical Computer Science  
In [6] several composition theorems for monadic-second order logic over trees were given. Two important applications of the compositional methods to algebra and logics are related to  ...  In [24] the composition theorem for linear orders was one of the main tools for obtaining remarkable decidability results for the monadic theory of linear orders.  ...  In [6] several composition theorems for monadic-second order logic over trees were given. Two important applications of the compositional methods to algebra and logics are related to Decidability.  ... 
doi:10.1016/j.entcs.2004.04.049 fatcat:awwxobdvubhrxmgi6rpsjhkxga
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