Logical relations for monadic types

Goubault-Larrecq, Jean; Lasota, Sławomir; Nowak, David

doi:10.1017/s0960129508007172

Cited by 47 publications

(56 citation statements)

References 39 publications

(53 reference statements)

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“…The work presented in this paper is a natural continuation of the authors' previous work [2,3]. In [2], we extend [9] and derive logical relations for monadic types which are sound in the sense that the Basic Lemma still holds.…”

Section: Resultsmentioning

confidence: 80%

“…A uniform framework for defining logical relations relies on the categorical notion of subscones [9], and a natural extension of logical relations able to deal with monadic types was introduced in [2]. The construction consists in lifting the CCC structure and the strong monad from the categorical model to the subscone.…”

Section: Logical Relations For λ Compmentioning

confidence: 99%

“…A list of instantiations of the above definition in concrete monads is also given in [2]. Figure 2 cites the relations for those monads defined in Figure 1.…”

Section: Logical Relations For λ Compmentioning

confidence: 99%

“…We were expecting to find a general proof following the general construction defined in [2]. However, this turns out extremely difficult although it might not be impossible with certain restrictions, on types for example.…”

Section: Toward a Proof On Completeness Of Logical Relations For λ Compmentioning

confidence: 99%

See 3 more Smart Citations

On Completeness of Logical Relations for Monadic Types

Lasota¹,

Nowak²

2007

Advances in Computer Science - ASIAN 2006. Secure Software and Related Issues

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Abstract. Software security can be ensured by specifying and verifying security properties of software using formal methods with strong theoretical bases. In particular, programs can be modeled in the framework of lambda-calculi, and interesting properties can be expressed formally by contextual equivalence (a.k.a. observational equivalence). Furthermore, imperative features, which exist in most real-life software, can be nicely expressed in the so-called computational lambdacalculus. Contextual equivalence is difficult to prove directly, but we can often use logical relations as a tool to establish it in lambda-calculi. We have already defined logical relations for the computational lambda-calculus in previous work. We devote this paper to the study of their completeness w.r.t. contextual equivalence in the computational lambda-calculus.

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Section: Resultsmentioning

confidence: 80%

Section: Logical Relations For λ Compmentioning

confidence: 99%

“…A list of instantiations of the above definition in concrete monads is also given in [2]. Figure 2 cites the relations for those monads defined in Figure 1.…”

Section: Logical Relations For λ Compmentioning

confidence: 99%

Section: Toward a Proof On Completeness Of Logical Relations For λ Compmentioning

confidence: 99%

See 2 more Smart Citations

On Completeness of Logical Relations for Monadic Types

Lasota¹,

Nowak²

2007

Advances in Computer Science - ASIAN 2006. Secure Software and Related Issues

Self Cite

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show abstract

“…It would be desirable, in particular with regard to a formalisation in a proof assistant, to lift the proof to the same abstract monadic level at which the functions P, eval and apply are defined. A framework for carrying this out might be provided by suitable versions of Moggi's Computational λ-Calculus, Pitts' Evaluation Logic [Pit91] and special logical relations for monads [GLN02].…”

Section: Main Theoremmentioning

confidence: 99%

A Provably Correct Translation of the λ-Calculus into a Mathematical Model of C++

2007

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We introduce a translation of the simply typed λ-calculus into C++, and give a mathematical proof of the correctness of this translation. For this purpose we develop a suitable fragment of C++ together with a denotational semantics. We introduce a formal translation of the λ-calculus into this fragment, and show that this translation is correct with respect to the denotational semantics. We show as well a completeness result, namely that by translating λ-terms we obtain essentially all C++ terms in this fragment. We introduce a mathematical model for the evaluation of programs of this fragment, and show that the evaluation computes the correct result with respect to this semantics.

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Effectful Normal Form Bisimulation

Lago

Gavazzo

2019

Programming Languages and Systems

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Normal form bisimulation, also known as open bisimulation, is a coinductive technique for higher-order program equivalence in which programs are compared by looking at their essentially infinitary tree-like normal forms, i.e. at their Böhm or Lévy-Longo trees. The technique has been shown to be useful not only when proving metatheorems about λ-calculi and their semantics, but also when looking at concrete examples of terms. In this paper, we show that there is a way to generalise normal form bisimulation to calculi with algebraic effects,à la Plotkin and Power. We show that some mild conditions on monads and relators, which have already been shown to guarantee effectful applicative bisimilarity to be a congruence relation, are enough to prove that the obtained notion of bisimilarity, which we call effectful normal form bisimilarity, is a congruence relation, and thus sound for contextual equivalence. Additionally, contrary to applicative bisimilarity, normal form bisimilarity allows for enhancements of the bisimulation proof method, hence proving a powerful reasoning principle for effectful programming languages.

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Logical relations for monadic types

Cited by 47 publications

References 39 publications

On Completeness of Logical Relations for Monadic Types

On Completeness of Logical Relations for Monadic Types

A Provably Correct Translation of the λ-Calculus into a Mathematical Model of C++

Effectful Normal Form Bisimulation

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