Type theory

Subject reduction

In type theory, a type system has the property of subject reduction (also subject evaluation, type preservation or simply preservation) if evaluation of expressions does not cause their type to change. Formally, if Γ ⊢ e1 : τ and e1 → e2 then Γ ⊢ e2 : τ. Intuitively, this means one would not like to write a expression, in say Haskell, of type Int, and have it evaluate to a value v, only to find out that v is a string. Together with , it is an important meta-theoretical property for establishing type soundness of a type system. The opposite property, if Γ ⊢ e2 : τ and e1 → e2 then Γ ⊢ e1 : τ, is called subject expansion. It often does not hold as evaluation can erase ill-typed sub-terms of an expression, resulting in a well-typed one. (Wikipedia).

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From playlist Data-Driven Control with Machine Learning

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This is part of an online course on covariance-based dimension-reduction and source-separation methods for multivariate data. The course is appropriate as an intermediate applied linear algebra course, or as a practical tutorial on multivariate neuroscience data analysis. More info here:

From playlist Dimension reduction and source separation

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From playlist Linear Algebra

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From playlist Transformations

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Reductions in JuliaDB

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From playlist Julia on Coursera

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From playlist Limits

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From playlist A Level Physics Revision

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https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. In this video

From playlist Advanced Circuit Design

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From playlist ELECTRICAL ENGINEERING 12 AC POWER

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From playlist AP® Statistics Exam: Free Response Questions

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From playlist Research Spotlights

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From playlist Research Spotlights

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From playlist Smooth And Homogeneous Dynamics

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From playlist Free Will, Determinism, & Action

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From playlist Research Spotlights

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From playlist Group Algebras, Representations And Computation

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Representations of finite groups of Lie type (Lecture 1) by Dipendra Prasad

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From playlist Group Algebras, Representations And Computation

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From playlist Calculus for Machine Learning

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From playlist Total Synthesis

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From playlist Philosophy of Science

Related pages

Type theory