scholarly journals Explicit Substitutions for Contextual Type Theory

2010 ◽  
Vol 34 ◽  
pp. 5-20 ◽  
Author(s):  
Andreas Abel ◽  
Brigitte Pientka
Keyword(s):  
Type Theory ◽  
Explicit Substitutions

scholarly journals Contextual modal types for algebraic effects and handlers

2021 ◽  
Vol 5 (ICFP) ◽  
pp. 1-29
Author(s):  
Nikita Zyuzin ◽  
Aleksandar Nanevski
Keyword(s):  
Programming Languages ◽  
Type Theory ◽  
Operational Semantics ◽  
Algebraic Theory ◽  
Type System ◽  
Effect Theory ◽  
Explicit Substitutions ◽  
Type And Effect Systems ◽  
Modal Type ◽  
Modal Types

Programming languages with algebraic effects often track the computations’ effects using type-and-effect systems. In this paper, we propose to view an algebraic effect theory of a computation as a variable context; consequently, we propose to track algebraic effects of a computation with contextual modal types . We develop ECMTT, a novel calculus which tracks algebraic effects by a contextualized variant of the modal □ (necessity) operator, that it inherits from Contextual Modal Type Theory (CMTT). Whereas type-and-effect systems add effect annotations on top of a prior programming language, the effect annotations in ECMTT are inherent to the language, as they are managed by programming constructs corresponding to the logical introduction and elimination forms for the □ modality. Thus, the type-and-effect system of ECMTT is actually just a type system. Our design obtains the properties of local soundness and completeness, and determines the operational semantics solely by β-reduction, as customary in other logic-based calculi. In this view, effect handlers arise naturally as a witness that one context (i.e., algebraic theory) can be reached from another, generalizing explicit substitutions from CMTT. To the best of our knowledge, ECMTT is the first system to relate algebraic effects to modal types. We also see it as a step towards providing a correspondence in the style of Curry and Howard that may transfer a number of results from the fields of modal logic and modal type theory to that of algebraic effects.

Basic Simple Type Theory

1997 ◽  
Author(s):  
J. Roger Hindley
Keyword(s):  
Type Theory ◽  
Simple Type ◽  
Simple Type Theory

Type Theory and Formal Proof

2009 ◽  
Author(s):  
Rob Nederpelt ◽  
Herman Geuvers
Keyword(s):  
Type Theory ◽  
Formal Proof

Computational Models for Multilayered Composite Shells with Application to Tires

1996 ◽  
Vol 24 (1) ◽  
pp. 11-38 ◽  
Author(s):  
G. M. Kulikov
Keyword(s):  
Type Theory ◽  
Computational Models ◽  
Geometrical Nonlinearity ◽  
Higher Order ◽  
Stress Strain ◽  
Strain Fields ◽  
First Order ◽  
Timoshenko Type ◽  
Joint Influence ◽  
Discrete Layer

Abstract This paper focuses on four tire computational models based on two-dimensional shear deformation theories, namely, the first-order Timoshenko-type theory, the higher-order Timoshenko-type theory, the first-order discrete-layer theory, and the higher-order discrete-layer theory. The joint influence of anisotropy, geometrical nonlinearity, and laminated material response on the tire stress-strain fields is examined. The comparative analysis of stresses and strains of the cord-rubber tire on the basis of these four shell computational models is given. Results show that neglecting the effect of anisotropy leads to an incorrect description of the stress-strain fields even in bias-ply tires.

Campus Social Climate Correlates of Environmental Type Dimensions

NASPA Journal ◽  
2004 ◽  
Vol 41 (4) ◽  
Author(s):  
Daniel W. Salter ◽  
Reynol Junco ◽  
Summer D. Irvin
Keyword(s):  
Work Environment ◽  
Personal Growth ◽  
Type Theory ◽  
General Purpose ◽  
Myers Briggs Type Indicator ◽  
Environment Scale ◽  
Type Indicator ◽  
Group Environment ◽  
System Maintenance ◽  
Environment Type

To address the ability of the Salter Environment Type Assessment (SETA) to measure different kinds of campus environments, data from three studies of the SETA with the Work Environment Scale, Group Environment Scale, and University Residence Environment Scale were reexamined (n = 534). Relationship dimension scales were very consistent with extraversion and feeling from environmental type theory. System maintenance and systems change scales were associated with judging and perception on the SETA, respectively. Results from the SETA and personal growth dimension scales were mixed. Based on this analysis, the SETA may serve as a general purpose environmental assessment for use with the Myers-Briggs Type Indicator.

Coq plugin for the Reasonably Exceptional Type Theory

2019 ◽  
Author(s):  
Pierre-Marie P�drot ◽  
Nicolas Tabareau ◽  
Hans Jacob Fehrmann ◽  
�ric Tanter
Keyword(s):  
Type Theory

Propositions and specifications of programs in Martin-Löf's type theory

1984 ◽  
Vol 24 (3) ◽  
pp. 288-301 ◽  
Author(s):  
Bengt Nordström ◽  
Jan Smith
Keyword(s):  
Type Theory

scholarly journals $$ T\overline{T} $$-like flows in non-linear electrodynamic theories and S-duality

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
H. Babaei-Aghbolagh ◽  
Komeil Babaei Velni ◽  
Davood Mahdavian Yekta ◽  
H. Mohammadzadeh
Keyword(s):  
Type Theory ◽  
Free Action ◽  
Momentum Tensor ◽  
Flow Equation ◽  
Supersymmetric Model ◽  
Deformation Problem ◽  
Dimensional Spacetime ◽  
Non Linear ◽  
The Relationship ◽  
Simple Integration

Abstract We investigate the $$ T\overline{T} $$ T T ¯ -like flows for non-linear electrodynamic theories in D(=2n)-dimensional spacetime. Our analysis is restricted to the deformation problem of the classical free action by employing the proposed $$ T\overline{T} $$ T T ¯ operator from a simple integration technique. We show that this flow equation is compatible with $$ T\overline{T} $$ T T ¯ deformation of a scalar field theory in D = 2 and of a non-linear Born-Infeld type theory in D = 4 dimensions. However, our computation discloses that this kind of $$ T\overline{T} $$ T T ¯ flow in higher dimensions is essentially different from deformation that has been derived from the AdS/CFT interpretations. Indeed, the gravity that may be exist as a holographic dual theory of this kind of effective Born-Infeld action is not necessarily an AdS space. As an illustrative investigation in D = 4, we shall also show that our construction for the $$ T\overline{T} $$ T T ¯ operator preserves the original SL(2, ℝ) symmetry of a non-supersymmetric Born-Infeld theory, as well as $$ \mathcal{N} $$ N = 2 supersymmetric model. It is shown that the corresponding SL(2, ℝ) invariant action fixes the relationship between the $$ T\overline{T} $$ T T ¯ operator and quadratic form of the energy-momentum tensor in D = 4.

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