# Abstract interpretation

In computer science, abstract interpretation is a theory of sound approximation of the semantics of computer programs, based on monotonic functions over ordered sets, especially lattices. It can be viewed as a partial execution of a computer program which gains information about its semantics (e.g., control-flow, data-flow) without performing all the calculations. Its main concrete application is formal static analysis, the automatic extraction of information about the possible executions of computer programs; such analyses have two main usages: * inside compilers, to analyse programs to decide whether certain optimizations or transformations are applicable; * for debugging or even the certification of programs against classes of bugs. Abstract interpretation was formalized by the French computer scientist working couple Patrick Cousot and Radhia Cousot in the late 1970s. (Wikipedia).

Group Definition (expanded) - Abstract Algebra

The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin

From playlist Abstract Algebra

Quotient group example

Now that we know what a quotient group is, let's take a look at an example to cement our understanding of the concepts involved.

From playlist Abstract algebra

What is Abstract Algebra? (Modern Algebra)

Abstract Algebra is very different than the algebra most people study in high school. This math subject focuses on abstract structures with names like groups, rings, fields and modules. These structures have applications in many areas of mathematics, and are being used more and more in t

From playlist Abstract Algebra

06 More about mappings

In this tutorial I show a few more notations and share a few more thoughts on mappings.

From playlist Abstract algebra

10 Relations (still with the not-so-exciting-stuff)

This video introduces relations between pairs of elements.

From playlist Abstract algebra

Equivalence Relations Definition and Examples

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Equivalence Relations Definition and Examples. This video starts by defining a relation, reflexive relation, symmetric relation, transitive relation, and then an equivalence relation. Several examples are given.

From playlist Abstract Algebra

Ruby Conf 2013 - Compilers For Free by Tom Stuart

Partial evaluation is a powerful tool for timeshifting some aspects of a program's execution from the future into the present. Among other things, it gives us an automatic way to turn a general, abstract program into a faster, more specialized one. This math-free talk uses Ruby to explain

From playlist RubyConf 2013

Marx’s Abstract Theory of Value and Money in Volume 1 of Capital

Fred Moseley is Professor Emeritus of Economics at Mount Holyoke College.  He has published extensively on Marxian theory and Marxian analysis of the US economy. His latest book is Money and Totality: A Macro-Monetary Interpretation of Marx’s Logic in “Capital” and the End of the Transform

From playlist Whitney Humanities Center

16 You have made it to the first exciting video Operations

To be honest, the topics have been very dry up to now. Here is the first bit of excitement. Operations. Understanding operations is a fundamental priority in abstract algebra.

From playlist Abstract algebra

Lie Groups and Lie Algebras: Lesson 8 - the Classical Groups part VI

Lie Groups and Lie Algebras: Lesson 8 - the Classical Groups part VI

From playlist Lie Groups and Lie Algebras

RubyConf 2016 - Lies by Ernie Miller

RubyConf 2016 - Lies by Ernie Miller All abstractions are lies, if they are abstractions at all, and as developers, we live our lives surrounded by them. What makes a some abstractions better than others? This will be an opinionated and empowering look at the value and nature of abstracti

From playlist RubyConf 2016

01 Introduction

Video series introducing abstract algebra. As promised, here's a link to one of my favorite channels: https://www.youtube.com/playlist?list=PLi01XoE8jYoi3SgnnGorR_XOW3IcK-TP6

From playlist Abstract algebra

ElixirConf 2016 - Abstractions: A Tale of Keys and Values by Ernie Miller

Due to technical difficulties the audio had to be taken from the camera. We apologize for the poor audio quality. Abstractions: A Tale of Keys and Values by Ernie Miller As programmers, we know that the right abstraction unlocks new ways of thinking about the problems we solve. But can t

From playlist ElixirConf 2016

Quantifying Interpretability of Models Trained on Coi… | Jorge Orbay | OpenAI Scholars Demo Day 2020

From playlist Events and Talks

22C3: PyPy - the new Python implementation on the block

Speakers: Armin Rigo, Carl Friedrich Bolz, Holger Krekel Language/VM R&D, whole program type inference, translation to low level backends, fun We present our first self-contained Python virtual machine that uses parts of itself to translate itself to low level languages ("the Muenchhause

From playlist 22C3: Private Investigations

Lecture 7B: Metacircular Evaluator, Part 2

MIT 6.001 Structure and Interpretation of Computer Programs, Spring 2005 Instructor: Harold Abelson, Gerald Jay Sussman, Julie Sussman View the complete course: https://ocw.mit.edu/6-001S05 YouTube Playlist: https://www.youtube.com/playlist?list=PLE18841CABEA24090 Metacircular Evaluator,

From playlist MIT 6.001 Structure and Interpretation, 1986

Perception, Abstraction & Idealism - General Philosophy (Peter Millican)

In this lecture on General Philosophy, Professor Peter Millican discusses the problem of perception, the distinction between primary and secondary qualities, resemblance, abstraction, and idealism. This comes from a 2010 series on General Philosophy. The slides have been added. This serie

From playlist Philosophy of Mind

Dynamic Inference with Neural Interpreters (w/ author interview)

#deeplearning #neuralinterpreter #ai This video includes an interview with the paper's authors! What if we treated deep networks like modular programs? Neural Interpreters divide computation into small modules and route data to them via a dynamic type inference system. The resulting model

From playlist Papers Explained

Homomorphisms in abstract algebra examples

Yesterday we took a look at the definition of a homomorphism. In today's lecture I want to show you a couple of example of homomorphisms. One example gives us a group, but I take the time to prove that it is a group just to remind ourselves of the properties of a group. In this video th

From playlist Abstract algebra