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### Compiling Hilbert's epsilon operator

Rustan Leino
unpublished
Hilbert's epsilon operator is a binder that picks an arbitrary element froma nonempty set.  ...  More specifically, the paper presents the design choicesmade around supporting this operator in the verification-aware language Dafny.  ...  In this sense, it isn't really Hilbert's ε operator, because Hilbert's ε operator is axiomatized to be deterministic. We'll look at that next.  ...

### Using PVS to prove a Z refinement: A case study [chapter]

David W. J. Stringer-Calvert, Susan Stepney, Ian Wand
1997 Lecture Notes in Computer Science
a small, but non trivial compiler by hand in the Z specication language.  ...  This is especially true of compilers, which are a weak link between the source code produced and the ob ject code which is executed.  ...  The second option can be achieved by the use of Hilbert's epsilon operator [13] , which, given a predicate, returns a value which satises that predicate (if possible) and if it is not satisable returns  ...

### The Mechanical Verification of a DPLL-Based Satisfiability Solver

Natarajan Shankar, Marc Vaucher
2011 Electronical Notes in Theoretical Computer Science
It uses Hilbert's epsilon, axiomatized in the PVS prelude library so that for any predicate p over a nonempty type T, if there is any a such that p(a) holds, then p(epsilon(p)) holds The main DPLL search  ...  Examples of these include the McCarthy-Painter proof of correctness of a compiler for arithmetic expressions, the correctness of a satisfiability solver for conditional expressions, and the Turingcompleteness  ...

### Subtypes for specifications: predicate subtyping in PVS

J. Rushby, S. Owre, N. Shankar
1998 IEEE Transactions on Software Engineering
The first, epsilon, is simply Hilbert's ε operator. Given a set p over a nonempty type T, epsilon(p) is some member of p, if any such exist, otherwise it is just some value of type T.  ...  The full definition is actually choose(p): (p) = epsilon(p); this additionally specifies that choose(p) returns the same value as epsilon(p), which is useful in specifications that use both epsilon and  ...

### Verifying hybrid systems modeled as timed automata: A case study [chapter]

Myla Archer, Constance Heitmeyer
1997 Lecture Notes in Computer Science
Our ultimate solution, which t o o k a d v antage of this fact, uses PVS's implementation epsilon" of Hilbert's choice operator in expressing the transition relation as a function.  ...  Instead, we aim to compile a list of facts that can eventually be used automatically in an improved real-arithmetic" PVS strategy.  ...

### Verifying the Correctness and Amortized Complexity of a Union-Find Implementation in Separation Logic with Time Credits

Arthur Charguéraud, François Pottier
2017 Journal of automated reasoning
We define p(x) using Hilbert's ε operator: Definition p F x := epsilon (fun y ⇒ F x y).  ...  Hilbert's ε operator applies to a predicate P of type A → Prop, where A is an inhabited type.  ...

### A synthetic axiomatization of Map Theory

Chantal Berline, Klaus Grue
2016 Theoretical Computer Science
Map Theory axiomatizes lambda calculus plus Hilbert's epsilon operator.  ...  All theorems of ZFC set theory including the axiom of foundation are provable in Map Theory, and if one omits Hilbert's epsilon operator from Map Theory then one is left with a computer programming language  ...  Syntactically, Map Theory comprises a computer programming language plus Hilbert's epsilon operator.  ...

### A Most Interesting, but Revoked Draft for Hilbert and Bernays' "Grundlagen der Mathematik" that never found its way into any publication, and 2 CV of Gisbert Hasenjaeger [article]

Claus-Peter Wirth
2021 arXiv   pre-print
A simplified and improved free-variable framework for Hilbert's epsilon as an operator of indefinite committed choice. IFCoLog J. of Logics and Their Applications, 4:435-526. Received Oct. 23, 2015.  ...  Hilbert's program.  ...

### Abstracts

1974 Historia Mathematica
KEMENY, John G 1973 Mathematical models and the computer Pi Mu Epsilon Journal 5, 373-386 COMPUTERS. CURRENT HISTORY. MATHEMATICAL MODELS. PREDICTIONS.  ...  MITCHAM, Carl & MACKEY, Robert, Compilers 1973 Bibliography of the Philosophy of Technology Chicago (Univ of Chicago Press) 205 p BIBLIOGRAPHIES. TECHNOLOGY. PHILOSOPHY OF TECHNOLOGY.  ...

### Formalization and Execution of Linear Algebra: From Theorems to Algorithms [chapter]

Jesús Aransay, Jose Divasón
2014 Lecture Notes in Computer Science
(traversing its indexing type), algorithms traversing the universe of the rows or columns indexing types, and also operations that involve logical operators (∀, ∃) or the Hilbert's operator, such as every  ...  A priori, nite (enumerable) types have nice computational features, since mathematical and logical operations (traversing, epsilon operator, universal or existential quantiers) over them can be executed  ...

### Passages of Proof [article]

Cristian S. Calude, Elena Calude, Solomon Marcus
2004 arXiv   pre-print
However, from a practical point of view, the chance of a computer error that appears consistently in exactly the same way on all runs of our programs on all the compilers under all the operating systems  ...  In particular, we have not proved the correctness of the compiler we compiled our programs on, nor have we proved the infallibility of the hardware we ran our programs on.  ...

### A Proposal for a Formal OCL Semantics in Isabelle/HOL [chapter]

Achim D. Brucker, Burkhart Wolff
2002 Lecture Notes in Computer Science
specification into HOL-OCL 2 leads to the following specification triangle spec of the operation triangle(): For the actual test-case generation, we define triangle, which selects via Hilbert's epsilon  ...  The task of implementing a compiler that converts representations of UML-diagrams (for example, formats produced by ArgoUML) is desirable but not in the focus of this research.  ...

### ABSTRACTS

Glen Van Brummelen
2002 Historia Mathematica
Galois Theory in the Work of Serret [in Spanish], Epsilon 16 (3) (2000), 377-408.  ...  The texts are: 46 problems compiled by Francisco di Cortisi (1420); 35 problems compiled by Altovino da Firenzo (1446-1447); and an anonymous collection of 63 problems written circa 1420.  ...

### Formal Verification of an Executable LTL Model Checker with Partial Order Reduction [chapter]

Julian Brunner, Peter Lammich
2016 Lecture Notes in Computer Science
Performing a step like this in a formal proof requires precise reasoning and in our case the use of Hilbert's epsilon operator.  ...  Among other steps, this includes compilation of the model to a more efficient representation.  ...

### Verified Bytecode Subroutines [chapter]

Gerwin Klein, Martin Wildmoser
2003 Lecture Notes in Computer Science
Since succs returns lists and not sets, we use Hilbert's epsilon operator SOME to pick any list that converts to this set.  ...  List operations may be unfamiliar: the "cons" operator is the infix #, concatenation the infix @; head and tail are hd and tl.  ...
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