Decorated proofs for computational effects: States

Dumas, J.; Duval, Dominique; Fousse, Laurent; Reynaud, Jean-Claude

doi:10.4204/eptcs.93.3

Cited by 8 publications

(27 citation statements)

References 12 publications

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“…• The distinction between the language for exceptions and its associated private core language (Definitions 3.1 and 3.2) allows to split the proofs in two successive parts; in addition, the private part can be directly dualized from the proofs on global states (relying on [3] and [4]).…”

Section: Discussionmentioning

confidence: 99%

“…• A proof assistant can be used for checking the decorated proofs on exceptions. Indeed the decorated proof system for states, as described in [4] has been implemented in Coq [2] and dualized for exceptions (see http://coqeffects.forge.imag.fr).…”

Section: Discussionmentioning

confidence: 99%

“…Lawvere theories were proposed for dealing with the operations and equations related to computational effects [15,12]. Another related approach, based on the fact that the state is observed, relies on the classification of expressions provided by the coKleisli category of comonad of states X × St and its associated Kleisli-on-coKleisli category [4].…”

Section: Introductionmentioning

confidence: 99%

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Certified proofs in programs involving exceptions

Dumas,

Duval,

Ekici

et al. 2013

Preprint

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Exception handling is provided by most modern programming languages. It allows to deal with anomalous or exceptional events which require special processing. In computer algebra, exception handling is an efficient way to implement the dynamic evaluation paradigm: for instance, in linear algebra, dynamic evaluation can be used for applying programs which have been written for matrices with coefficients in a field to matrices with coefficients in a ring. Thus, a proof system for computer algebra should include a treatement of exceptions, which must rely on a careful description of a semantics of exceptions. The categorical notion of monad can be used for formalizing the raising of exceptions: this has been proposed by Moggi and implemented in Haskell. In this paper, we provide a proof system for exceptions which involves both raising and handling, by extending Moggi's approach. Moreover, the core part of this proof system is dual to a proof system for side effects in imperative languages, which relies on the categorical notion of comonad. Both proof systems are implemented in the Coq proof assistant.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Certified proofs in programs involving exceptions

Dumas,

Duval,

Ekici

et al. 2013

Preprint

Self Cite

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show abstract

“…This can be generalized to an arbitrary number of locations. The logic L st and the theory T st have to be generalized as in [5], then Proposition A.2 has to be adapted using the basic properties of lookup and update, as stated in [17]; these properties can be deduced from the decorated theory for states, as proved in [9]. The rest of the proof generalizes accordingly, as in [16].…”

Section: Proofmentioning

confidence: 99%

Relative Hilbert-Post Completeness for Exceptions

Dumas

Duval

Ekici

et al. 2016

Mathematical Aspects of Computer and Information Sciences

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A theory is complete if it does not contain a contradiction, while all of its proper extensions do. In this paper, first we introduce a relative notion of syntactic completeness; then we prove that adding exceptions to a programming language can be done in such a way that the completeness of the language is not made worse. These proofs are formalized in a logical system which is close to the usual syntax for exceptions, and they have been checked with the proof assistant Coq.

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“…For instance, a pure term f (0) : X → Y in the logic which models the global state effect (decorated logic for the state [6]) is interpreted as a map f : X → Y in the base category C . An accessor term f (1) : X → Y as an arrow f : X → Y in C D which implicitly corresponds to a map f : X × S → Y in the base category C .…”

mentioning

confidence: 99%

Mac Lane’s Comparison Theorem for the Kleisli Construction Formalized in Coq

Ekici

Kaliszyk

2020

Math.Comput.Sci.

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co)Monads are used to encapsulate impure operations of a computation. A (co)monad is determined by an adjunction and further determines a specific type of adjunction called the (co)Kleisli adjunction. Mac Lane introduced the comparison theorem which allows comparing these adjunctions bridged by a (co)monad through a unique comparison functor. In this paper we specify the foundations of category theory in Coq and show that the chosen representations are useful by certifying Mac Lane's comparison theorem and its basic consequences. We also show that the foundations we use are equivalent to the foundations by Timany. The formalization makes use of Coq classes to implement categorical objects and the axiom uniqueness of identity proofs to close the gap between the contextual equality of objects in a categorical setting and the judgmental Leibniz equality of Coq. The theorem is used by Duval and Jacobs in their categorical settings to interpret the state effect in impure programming languages.

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Decorated proofs for computational effects: States

Abstract: The syntax of an imperative language does not mention explicitly the state, while its denotational semantics has to mention it. In this paper we show that the equational proofs about an imperative language may hide the state, in the same way as the syntax does

Cited by 8 publications

References 12 publications

Certified proofs in programs involving exceptions

Certified proofs in programs involving exceptions

Relative Hilbert-Post Completeness for Exceptions

Mac Lane’s Comparison Theorem for the Kleisli Construction Formalized in Coq

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