# Questions tagged [denotational-semantics]

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### Results in denotational semantics from model theory?

Denotational semantics interpret the theories of various lambda calculi in various (set-theoretic, domain-theoretic, category-theoretic, game...) models. Let $T$ be the theory of one such lambda ...
306 views

### Typed Lambda Calculus models and denotations

I'm trying to draw a general mental picture about the models and the denotational semantics of the typed lambda calculus, in its different variants. I'm particularly interested in how the semantics ...
229 views

### Denotational semantics of System $F_\omega$ with recursive types and general recursion

Is there a denotational semantics for System $F_\omega$ in literature that supports both recursive types and general recursion? I'm looking for a model of Ralf Hinze's variant of System $F_\omega$ ...
108 views

### Observational Equivalence of open terms in PCF

The notion of observational equivalence is rather intuitive, but formally I'm having some doubts in the particular case of open terms. Lets consider the simple case where the terms ...
312 views

### Precise definition of syntatic categories / syntatic domains in abstract syntax

I have read the introductory parts of a couple of books on programming language semantics (Gordon, Winskel, Nielson & Nielson, Allison, Stump, Schmidt), and while I do understand what they mean by ...
82 views

### Categorical way of factoring out points

Major rewrite justifiably asked for: I'm currently trying to get a categorical way of doing something called the Gelfond-Lifschitz reduct on a set of single-headed Horn clauses. The semantics is the ...
131 views

### What is contextual equivalence ignoring non-termination called?

Contextual equivalence ($M_1 \cong_{ctx} M_2$) is often defined as: $C[M_1] \Downarrow V \iff C[M_2] \Downarrow V$ Which is to say for any context $C$, $C[M_1]$ terminates with value $V$ iff $C[M_2]$...
1k views

### What is the relation/difference between axiomatic and denotational semantics one one side, and the data flow analysis(DFA) on the other sied?

I am supposed to write a small paper about DFA in OOP for a CS class in theory. But I am required to connect that (DFA) to axiomatic and denotational semantics! I read few resources about axiomatic/...
113 views

### In which posets is the set of compact elements downwards closed?

In a poset $(D, \sqsubseteq)$, a compact element is an element $d \in D$ such that for every directed set $A$ which happens to have a supremum $\bigsqcup A \in D$ with $d \sqsubseteq \bigsqcup A$, it ...
172 views

### What are Zhang's molecules?

I'm currently looking into the representation theory of Scott domains. In his paper "dI-Domains as prime information systems" (1992), Guo-Qiang Zhang uses prime information systems to represent dI-...
510 views

### Is there any known CCC closed under a probabilistic powerdomain operation?

Equivalently, is there a known denotational semantics for probabilistic higher-order functional programming languages? Specifically, is there a domain model of pure untyped $\lambda$-calculus extended ...
365 views

### Flat vs non-flat domains

My understanding is that, more often than not, when people use domain theory for higher-type computability or the denotational semantics of functional programming languages, they tend to prefer flat ...
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### Reference for the undefinability of modulus of continuity functional in PCF?

Can someone point me to the reference for the non-definability of the modulus of continuity functional in PCF? $\newcommand{\N}{\mathbb{N}}$ $\newcommand{\bool}{\mathsf{bool}}$ Andrej Bauer has ...
367 views

### Reasoning about non-deterministically terminating loops

Here's a "track B" question if there ever was one. Summary: the first thing I think of when I try to give a semantics to non-deterministic programs results in a semantics where I can't prove things ...
825 views

### What is the origin of logical relations?

I actually have two questions: Who first used logical relations to relate semantics? I traced them back to Reynold's "On the Relation Between Direct and Continuation Semantics", but I can't claim to ...
203 views

### Has anyone studied “polynomially compact” metric spaces?

A subspace $S$ of a metric space $A$ is compact if it is complete and totally bounded. Here, complete means that every Cauchy sequence in $S$ has a limit also in $S$. For $S$ to be totally bounded, ...
572 views

### Fixed point theorems for constructive metric spaces?

Banach's fixed point theorem says that if we have a nonempty complete metric space $A$, then any uniformly contractive function $f : A \to A$ it has a unique fixed point $\mu(f)$. However, the proof ...
299 views

### Is Escardó's metric semantic for PCF+timeouts fully abstract ?

In his 1999 workshop paper "A Metric Model of PCF", Martín Escardó showed that it is possible to give a simple interpretation of PCF in the category of complete ultrametric spaces and ...
6k views

### What constitutes denotational semantics?

On a different thread, Andrej Bauer defined denotational semantics as: the meaning of a program is a function of the meanings of its parts. What bothers me about this definition is that it doesn't ...
7k views

### Books on programming language semantics

I've been reading Nielson & Nielson's "Semantics with Applications", and I really like the subject. I'd like to have one more book on programming language semantics -- but I really can get only ...
375 views

### In domain theory, what can the extra structure present in metric spaces be used for?

Smyth's chapter in the handbook of logic in computer science and other references describe how metric spaces can be used as domains. I do understand that complete metric spaces give unique fixed ...
942 views

### What is a good Category Theory-Domain Theory dictionary?

When dealing with the domain theoretic categories (say CPO and $\omega$CPO), I frequently wish for a dictionary for the language of category theory in domain theory. That is, given a concept, say ...