32 research outputs found
Probing wave function collapse models with a classically driven mechanical oscillator
We show that the interaction of a pulsed laser light with a mechanical
oscillator through the radiation pressure results in an opto-mechanical
entangled state in which the photon number is correlated with the oscillator
position. Interestingly, the mechanical oscillator can be delocalized over a
large range of positions when driven by an intense laser light. This provides a
simple yet sensitive method to probe hypothetic post-quantum theories including
an explicit wave function collapse model, like the Diosi and Penrose model. We
propose an entanglement witness to reveal the quantum nature of this
opto-mechanical state as well as an optical technique to record the decoherence
of the mechanical oscillator. We also report on a detailed feasibility study
giving the experimental challenges that need to be overcome to confirm or rule
out predictions from explicit wave function collapse models.Comment: 11 pages, 2 figures. Corrections, and added appendi
Modules over Monads and Operational Semantics
This paper is a contribution to the search for efficient and high-level mathematical tools to specify and reason about (abstract) programming languages or calculi. Generalising the reduction monads of Ahrens et al., we introduce transition monads, thus covering new applications such as ???-calculus, ?-calculus, Positive GSOS specifications, differential ?-calculus, and the big-step, simply-typed, call-by-value ?-calculus. Finally, we design a suitable notion of signature for transition monads
High-level signatures and initial semantics
We present a device for specifying and reasoning about syntax for datatypes,
programming languages, and logic calculi. More precisely, we study a notion of
signature for specifying syntactic constructions.
In the spirit of Initial Semantics, we define the syntax generated by a
signature to be the initial object---if it exists---in a suitable category of
models. In our framework, the existence of an associated syntax to a signature
is not automatically guaranteed. We identify, via the notion of presentation of
a signature, a large class of signatures that do generate a syntax.
Our (presentable) signatures subsume classical algebraic signatures (i.e.,
signatures for languages with variable binding, such as the pure lambda
calculus) and extend them to include several other significant examples of
syntactic constructions.
One key feature of our notions of signature, syntax, and presentation is that
they are highly compositional, in the sense that complex examples can be
obtained by assembling simpler ones. Moreover, through the Initial Semantics
approach, our framework provides, beyond the desired algebra of terms, a
well-behaved substitution and the induction and recursion principles associated
to the syntax.
This paper builds upon ideas from a previous attempt by Hirschowitz-Maggesi,
which, in turn, was directly inspired by some earlier work of
Ghani-Uustalu-Hamana and Matthes-Uustalu.
The main results presented in the paper are computer-checked within the
UniMath system.Comment: v2: extended version of the article as published in CSL 2018
(http://dx.doi.org/10.4230/LIPIcs.CSL.2018.4); list of changes given in
Section 1.5 of the paper; v3: small corrections throughout the paper, no
major change
For Finitary Induction-Induction, Induction is Enough
Inductive-inductive types (IITs) are a generalisation of inductive types in type theory. They allow the mutual definition of types with multiple sorts where later sorts can be indexed by previous ones. An example is the Chapman-style syntax of type theory with conversion relations for each sort where e.g. the sort of types is indexed by contexts. In this paper we show that if a model of extensional type theory (ETT) supports indexed W-types, then it supports finitely branching IITs. We use a small internal type theory called the theory of signatures to specify IITs. We show that if a model of ETT supports the syntax for the theory of signatures, then it supports all IITs. We construct this syntax from indexed W-types using preterms and typing relations and prove its initiality following Streicher. The construction of the syntax and its initiality proof were formalised in Agda
Modules over monads and operational semantics
This paper is a contribution to the search for efficient and high-level
mathematical tools to specify and reason about (abstract) programming languages
or calculi. Generalising the reduction monads of Ahrens et al., we introduce
transition monads, thus covering new applications such as
lambda-bar-mu-calculus, pi-calculus, Positive GSOS specifications, differential
lambda-calculus, and the big-step, simply-typed, call-by-value lambda-calculus.
Moreover, we design a suitable notion of signature for transition monads
High-level signatures and initial semantics
We present a device for specifying and reasoning about syntax for datatypes, programming languages, and logic calculi. More precisely, we consider a general notion of "signature" for specifying syntactic constructions. Our signatures subsume classical algebraic signatures (i.e., signatures for languages with variable binding, such as the pure lambda calculus) and extend to much more general examples.
In the spirit of Initial Semantics, we define the "syntax generated by a signature" to be the initial object - if it exists - in a suitable category of models. Our notions of signature and syntax are suited for compositionality and provide, beyond the desired algebra of terms, a well-behaved substitution and the associated inductive/recursive principles.
Our signatures are "general" in the sense that the existence of an associated syntax is not automatically guaranteed. In this work, we identify a large and simple class of signatures which do generate a syntax.
This paper builds upon ideas from a previous attempt by Hirschowitz-Maggesi, which, in turn, was directly inspired by some earlier work of Ghani-Uustalu-Hamana and Matthes-Uustalu.
The main results presented in the paper are computer-checked within the UniMath system
A categorical framework for congruence of applicative bisimilarity in higher-order languages
Applicative bisimilarity is a coinductive characterisation of observational
equivalence in call-by-name lambda-calculus, introduced by Abramsky (1990).
Howe (1996) gave a direct proof that it is a congruence, and generalised the
result to all languages complying with a suitable format. We propose a
categorical framework for specifying operational semantics, in which we prove
that (an abstract analogue of) applicative bisimilarity is automatically a
congruence. Example instances include standard applicative bisimilarity in
call-by-name, call-by-value, and call-by-name non-deterministic
-calculus, and more generally all languages complying with a variant
of Howe's format
Reduction Monads and Their Signatures
International audienc