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Journal articles on the topic 'Lambda-Pi calculus'

Author: Grafiati

Published: 25 May 2024

Last updated: 31 July 2025

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1

van Bakel, Steffen, and Maria Grazia Vigliotti. "A fully-abstract semantics of lambda-mu in the pi-calculus." Electronic Proceedings in Theoretical Computer Science 164 (September 9, 2014): 33–47. http://dx.doi.org/10.4204/eptcs.164.3.

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2

Fu, Weili, Fabian Krause, and Peter Thiemann. "Label dependent lambda calculus and gradual typing." Proceedings of the ACM on Programming Languages 5, OOPSLA (2021): 1–29. http://dx.doi.org/10.1145/3485485.

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Dependently-typed programming languages are gaining importance, because they can guarantee a wide range of properties at compile time. Their use in practice is often hampered because programmers have to provide very precise types. Gradual typing is a means to vary the level of typing precision between program fragments and to transition smoothly towards more precisely typed programs. The combination of gradual typing and dependent types seems promising to promote the widespread use of dependent types. We investigate a gradual version of a minimalist value-dependent lambda calculus. Compile-tim

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3

Laustsen, Niels Jakob, and Vladimir G. Troitsky. "Vector Lattices Admitting a Positively Homogeneous Continuous Function Calculus." Quarterly Journal of Mathematics 71, no. 1 (2020): 281–94. http://dx.doi.org/10.1093/qmathj/haz031.

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Abstract We characterize the Archimedean vector lattices that admit a positively homogeneous continuous function calculus by showing that the following two conditions are equivalent for each $n$-tuple $\boldsymbol{x} = (x_1,\ldots ,x_n)\in X^n$, where $X$ is an Archimedean vector lattice and $n\in{\mathbb{N}}$: • there is a vector lattice homomorphism $\Phi _{\boldsymbol{x}}\colon H_n\to X$ such that $$\begin{equation*}\Phi_{\boldsymbol{x}}(\pi_i^{(n)}) = x_i\qquad (i\in\{1,\ldots,n\}),\end{equation*}$$where $H_n$ denotes the vector lattice of positively homogeneous, continuous, real-valued fu

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4

Sangiorgi, Davide, and Xian Xu. "Trees from Functions as Processes." Logical Methods in Computer Science Volume 14, Issue 3 (August 27, 2018). https://doi.org/10.23638/lmcs-14(3:11)2018.

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Levy-Longo Trees and Bohm Trees are the best known tree structures on the {\lambda}-calculus. We give general conditions under which an encoding of the {\lambda}-calculus into the {\pi}-calculus is sound and complete with respect to such trees. We apply these conditions to various encodings of the call-by-name {\lambda}-calculus, showing how the two kinds of tree can be obtained by varying the behavioural equivalence adopted in the {\pi}-calculus and/or the encoding.

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5

Hirschowitz, André, Tom Hirschowitz, and Ambroise Lafont. "Modules over monads and operational semantics (expanded version)." Logical Methods in Computer Science Volume 18, Issue 3 (August 2, 2022). http://dx.doi.org/10.46298/lmcs-18(3:3)2022.

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This paper is a contribution to the search for efficient and high-level mathematical tools to specify and reason about (abstract) programming languages or calculi. Generalising the reduction monads of Ahrens et al., we introduce transition monads, thus covering new applications such as lambda-bar-mu-calculus, pi-calculus, Positive GSOS specifications, differential lambda-calculus, and the big-step, simply-typed, call-by-value lambda-calculus. Moreover, we design a suitable notion of signature for transition monads.

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6

Paulus, Joseph W. N., Daniele Nantes-Sobrinho, and Jorge A. Pérez. "Non-Deterministic Functions as Non-Deterministic Processes (Extended Version)." Logical Methods in Computer Science Volume 19, Issue 4 (October 10, 2023). http://dx.doi.org/10.46298/lmcs-19(4:1)2023.

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We study encodings of the lambda-calculus into the pi-calculus in the unexplored case of calculi with non-determinism and failures. On the sequential side, we consider lambdafail, a new non-deterministic calculus in which intersection types control resources (terms); on the concurrent side, we consider spi, a pi-calculus in which non-determinism and failure rest upon a Curry-Howard correspondence between linear logic and session types. We present a typed encoding of lambdafail into spi and establish its correctness. Our encoding precisely explains the interplay of non-deterministic and fail-pr

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7

Madiot, Jean-Marie, Damien Pous, and Davide Sangiorgi. "Modular coinduction up-to for higher-order languages via first-order transition systems." Logical Methods in Computer Science Volume 17, Issue 3 (September 17, 2021). http://dx.doi.org/10.46298/lmcs-17(3:25)2021.

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The bisimulation proof method can be enhanced by employing `bisimulations up-to' techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and bisimilarity, based on abstract fixed-point theory and compatible functions. We transport this theory onto languages whose bisimilarity and LTS go beyond those of first-order models. The approach consists in exhibiting fully abstract translations of the more sophisticated LTSs and bisimilarities onto the first-order ones. This allows us to reuse directly the large corpu

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8

Emmerson, Parker. "Cyclic Patterns of Pi : A Pattern We've All Been Searching." December 10, 2022. https://doi.org/10.5281/zenodo.7422783.

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To detect patterns in the transcendental number pi, we can use the following formula : r{Ξ, Π, Ρ, Σ}{Θ,Λ,Μ,Ν}∞, ∞ ⊃ -1+⍵kxb.b2{κ,Θ,Λ,Μ,Ν}∞ {ω,Ξ,Π,Ρ,Σ}∞ &&μ{g} ,f,g,h,i,j⃝⇈<Ω ⍺ a,b,c,d,e⃝⇈ σ[{υ, φ, χ, ψ}, {ω, Ξ, Π, Ρ, Σ}∞]∞ This formula uses the notion of subsets, the Greek letters Ξ, Π, Ρ, Σ and Θ, Λ, Μ, Ν to calculate the sum of the transcendental number pi over an

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9

Quaglia, Paola. "On the Finitary Characterization of pi-Congruences." BRICS Report Series 4, no. 52 (1997). http://dx.doi.org/10.7146/brics.v4i52.19273.

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Some alternative characterizations of late full congruences, either strong or weak, are presented. Those congruences are classically defined by requiring the corresponding ground bisimilarity under all name substitutions. <br />We first improve on those infinitary definitions by showing that congruences can be alternatively characterized in the pi-calculus by sticking to a finite<br />number of carefully identified substitutions, and hence, by resorting to only a finite number of ground bisimilarity checks.<br />Then we investigate the same issue in both the ground and the no

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10

Foster, Camaron. "V03 - Achefield Cosmology and Recursive Symbolic Intelligence." April 18, 2025. https://doi.org/10.5281/zenodo.15238490.

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<strong>Achefield Cosmology</strong> <em>Glyphogenetic Autopoiesis and the Birth of Zeta‑Recursive Symbolic Intelligence</em> <em>A Torsion-Based Model of Meaning Emergence in Recursive Symbolic Fields</em>  This work extends glyphic intelligence into a cosmological regime, formalizing <strong>zeta-recursive glyphogenesis</strong> as a unifying driver of symbolic, physical, and ethical dynamics. <strong>Core Construct</strong> Zeta-recursive duality couples a glyph’s <strong>achefield potential</strong> Γ(𝒜, m) with its <strong>tension gradient</strong> Ξ(𝒜, m) = ∂&Gam

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11

Heuvel, Bas van den, Daniele Nantes-Sobrinho, Joseph W. N. Paulus, and Jorge A. Pérez. "Typed Non-determinism in Concurrent Calculi: The Eager Way." Electronic Notes in Theoretical Informatics and Computer Science Volume 4 - Proceedings of... (December 11, 2024). https://doi.org/10.46298/entics.14735.

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We consider the problem of designing typed concurrent calculi with non-deterministic choice in which types leverage linearity for controlling resources, thereby ensuring strong correctness properties for processes. This problem is constrained by the delicate tension between non-determinism and linearity. Prior work developed a session-typed {\pi}-calculus with standard non-deterministic choice; well-typed processes enjoy type preservation and deadlock-freedom. Central to this typed calculus is a lazy semantics that gradually discards branches in choices. This lazy semantics, however, is comple

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12

Blanqui, Frédéric, Gilles Dowek, Emilie Grienenberger, Gabriel Hondet, and François Thiré. "A modular construction of type theories." Logical Methods in Computer Science Volume 19, Issue 1 (February 14, 2023). http://dx.doi.org/10.46298/lmcs-19(1:12)2023.

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The lambda-Pi-calculus modulo theory is a logical framework in which many type systems can be expressed as theories. We present such a theory, the theory U, where proofs of several logical systems can be expressed. Moreover, we identify a sub-theory of U corresponding to each of these systems, and prove that, when a proof in U uses only symbols of a sub-theory, then it is a proof in that sub-theory.

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13

Stark, Ian. "Names, Equations, Relations: Practical Ways to Reason about new." BRICS Report Series 4, no. 39 (1997). http://dx.doi.org/10.7146/brics.v4i39.18965.

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<p>The nu-calculus of Pitts and Stark is a typed lambda-calculus, extended with state<br />in the form of dynamically-generated names. These names can be created locally, passed around, and compared with one another. Through the interaction between<br />names and functions, the language can capture notions of scope, visibility and sharing. Originally motivated by the study of references in Standard ML, the nu-calculus<br />has connections to local declarations in general; to the mobile processes of the pi-calculus; and to security protocols in the spi-calculus. <br /

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14

Durier, Adrien, Daniel Hirschkoff, and Davide Sangiorgi. "Divergence and unique solution of equations." Logical Methods in Computer Science Volume 15, Issue 3 (August 7, 2019). https://doi.org/10.23638/lmcs-15(3:12)2019.

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We study proof techniques for bisimilarity based on unique solution of equations. We draw inspiration from a result by Roscoe in the denotational setting of CSP and for failure semantics, essentially stating that an equation (or a system of equations) whose infinite unfolding never produces a divergence has the unique-solution property. We transport this result onto the operational setting of CCS and for bisimilarity. We then exploit the operational approach to: refine the theorem, distinguishing between different forms of divergence; derive an abstract formulation of the theorems, on generic

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15

Stark, Ian. "Names, Equations, Relations: Practical Ways to Reason about 'new'." BRICS Report Series 3, no. 31 (1996). http://dx.doi.org/10.7146/brics.v3i31.21675.

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The nu-calculus of Pitts and Stark is a typed lambda-calculus, extended with state in the form of dynamically-generated names. These names can be created locally, passed around, and compared with one another. Through the interaction between names and functions, the language can capture notions of scope, visibility and sharing. Originally motivated by the study of references in Standard ML, the nu-calculus has connections to other kinds of local declaration, and to the mobile processes of the pi-calculus.<br /> <br />This paper introduces a logic of equations and relations which all

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16

Derakhshan, Farzaneh, and Frank Pfenning. "Circular Proofs as Session-Typed Processes: A Local Validity Condition." Logical Methods in Computer Science Volume 18, Issue 2 (May 10, 2022). http://dx.doi.org/10.46298/lmcs-18(2:8)2022.

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Proof theory provides a foundation for studying and reasoning about programming languages, most directly based on the well-known Curry-Howard isomorphism between intuitionistic logic and the typed lambda-calculus. More recently, a correspondence between intuitionistic linear logic and the session-typed pi-calculus has been discovered. In this paper, we establish an extension of the latter correspondence for a fragment of substructural logic with least and greatest fixed points. We describe the computational interpretation of the resulting infinitary proof system as session-typed processes, and

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17

Emmerson, Parker. "Programmatic Sketches for Spatio-Temporal Aspect Ratios." March 27, 2023. https://doi.org/10.5281/zenodo.7772803.

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Abstract : Infer the conclusion from these three statements in layman' s terms . The conclusion is that the value of a function, f\[Delta]a (x), which is dependent on a set of parameters (\[CapitalTheta]inf, \[CapitalOmega], \[CapitalLambda], \[Mu], \[Nu], \[Xi], \[Pi], \[Rho], \[Sigma], \[Upsilon], \[Phi], \[Chi], \[Psi]) and the derivatives of a function (\[CurlyPhi]) with respect to each of the parameters (a1, a2, ..., an) is equal to the sum of two terms . The first term is a product of the derivatives of the function (\[CurlyPhi]) with respect to each of the parameters (a1, a2, ..., a

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18

Mahillo, Alejandro, and Pedro J. Miana. "Catalan Generating Functions for Generators of Uni-parametric Families of Operators." Mediterranean Journal of Mathematics 19, no. 5 (2022). http://dx.doi.org/10.1007/s00009-022-02155-7.

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AbstractIn this paper we study solutions of the quadratic equation $$AY^2-Y+I=0$$ A Y 2 - Y + I = 0 where A is the generator of a one parameter family of operator ($$C_0$$ C 0 -semigroup or cosine functions) on a Banach space X with growth bound $$w_0 \le \frac{1}{4}$$ w 0 ≤ 1 4 . In the case of $$C_0$$ C 0 -semigroups, we show that a solution, which we call Catalan generating function of A, C(A), is given by the following Bochner integral, $$\begin{aligned} C(A)x := \int _{0}^\infty c(t) T(t)x \; \mathrm{d}t, \quad x\in X, \end{aligned}$$ C ( A ) x : = ∫ 0 ∞ c ( t ) T ( t ) x d t , x ∈ X , wh

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19

Santosh, Kr. Choudhary. "Fractional Order Feedback Control of a Ball and Beam System." July 3, 2014. https://doi.org/10.5281/zenodo.1094207.

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In this paper, fractional order feedback control of a ball beam model is investigated. The ball beam model is a particular example of the double Integrator system having strongly nonlinear characteristics and unstable dynamics which make the control of such system a challenging task. Most of the work in fractional order control systems are in theoretical nature and controller design and its implementation in practice is very small. In this work, a successful attempt has been made to design a fractional order PIλDμcontroller for a benchmark laboratory ball and beam model. Better perfo

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20

Yamada, Norihiro. "Game semantics of Martin-Löf type theory." Mathematical Structures in Computer Science, July 31, 2023, 1–42. http://dx.doi.org/10.1017/s0960129523000154.

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Abstract This work presents game semantics of Martin-Löf type theory (MLTT) equipped with the One, the Zero, the N, Pi, Sigma and Id types. Game semantics interprets a wide range of logic and computation, even the polymorphic $\lambda$ -calculus; however, it has remained a well-known challenge in the past 25 years to achieve game semantics of dependent type theories such as MLTT, and past attempts lack directness or generality. For instance, the approach taken by Abramsky et al. interprets Sigma types indirectly by formal lists, not by games, making an interpretation of universes hopeless, and

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