PROOFS AND TYPES JEAN-YVES GIRARD Translated and with appendices by PAUL TAYLOR

Source URL: www.cs.man.ac.uk

• Logic
• Mathematical logic
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• Proof theory
• Logic in computer science
• Models of computation
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• Metalogic
• Denotational semantics
• Linear logic
• Natural deduction
• Cut-elimination theorem

B Web appendix Proofs for Stress and Coping - An Economic Approach Klaus Wälde49 September 22, 2015

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• Dynamic programming
• Bellman equation
• Control theory
• Equations
• Mathematical optimization

Effective bounds from ineffective proofs in analysis: an application of functional interpretation and majorization∗ Ulrich Kohlenbach Fachbereich Mathematik, J.W.Goethe–Universitt Robert–Mayer–Str. 6–10, 6000 F

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• Computability theory
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• Logic
• Primitive recursive functional
• Proof theory
• Symbol
• Mathematics
• Table of stars with Bayer designations

Analyzing proofs in analysis∗ Ulrich Kohlenbach Fachbereich Mathematik, J.W.Goethe–Universit¨at Robert–Mayer–Str. 6–10, D–60054 Frankfurt am Main, Germany 1

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• Logic
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• Automated theorem proving
• Logic programming
• Logical truth
• Propositional calculus
• Substitution
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• operator
• Spectral theory of ordinary differential equations

On the computational content of convergence proofs via Banach limits U. Kohlenbach1∗, L. Leu¸stean2 1 Department of Mathematics, Technische Universit¨

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• Mathematics
• Mathematical analysis
• Topology
• Banach spaces
• Convex analysis
• Calculus
• Modulus and characteristic of convexity
• Continuous function
• Banach fixed-point theorem
• Uniformly smooth space
• Metric space
• Open set

A Hundred Impossibility Proofs for Distributed Computing Nancy A. Lynch * Lab for Computer Science MIT, Cambridge, MAlynchQtds.Ics.mit.edu

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• Fault-tolerant computer systems
• Mathematical logic
• Distributed computing
• Consensus
• Failure
• Theory of computation
• Proof of impossibility
• Algorithm
• Byzantine fault tolerance
• Parallel computing
• Shared register

Probabilistic Algorithms and Ramsey-Type Principles in Reverse Mathematics Laurent Bienvenu Ludovic Patey

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• Mathematics
• Logic
• Proof theory
• Mathematical proofs
• Lemma
• Theorem
• Abstraction
• Reverse mathematics
• BPP

Telling cause from effect in deterministic linear dynamical systems Supplementary Material We have prepared an appendix to address the proofs for Proposition 3, Theorems 1 and 2 which we provide in the following sections

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• Mathematical analysis
• Mathematics
• Analysis
• Operator theory
• Algebra of random variables
• Covariance
• Covariance and correlation
• Variance
• Monotone convergence theorem
• Pi
• Harmonic analysis
• Proof that is irrational

First proofs: Elementary set theory7 6 As mathematicians and students of mathematics, it is our job to separate those mathematical assertions that are true from those that are false. The method that mathematicians use t

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Programs and Proofs Mechanizing Mathematics with Dependent Types Lecture Notes Ilya Sergey Draft of August 19, 2015

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• Mathematical logic
• Theoretical computer science
• Mathematics
• Type theory
• Logic in computer science
• Automated theorem proving
• Formal methods
• Coq
• Automated reasoning
• Proof assistant
• Separation logic
• Functional programming