Questions tagged [denotational-semantics]
34 questions
17
votes
2 answers
What questions can denotational semantics answer that operational semantics can't?
I am familiar with operational semantics (both small-step and big-step) for defining programming languages. I'm interested in learning denotational semantics as well, but I'm not sure if it will be worth the effort. Will I just be learning the same…
gardenhead
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12
votes
1 answer
Why are computable functions continuous?
I am working on writing an easy to read document about denotational semantics of the lambda calculus. For that I introduce CPOs, monotonicity and continuity.
A CPO is a set $M$ with a partial order $\leq$ and a bottom element $\bot$, requiring…
user3389669
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11
votes
4 answers
What does the leading turnstile operator mean?
I know that different authors use different notation to represent programming language semantics. As a matter of fact Guy Steele addresses this problem in an interesting video.
I'd like to know if anyone knows whether the leading turnstile operator…
Jim Newton
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11
votes
0 answers
Denotational semantics of object-oriented languages
I am interested in denotational semantics of object oriented languages. Namely, what are the common/typical denotations of objects used in the literature? Is this an interesting topic these days?
The most comprehensive article I've found dates back…
zpavlinovic
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11
votes
1 answer
What's the difference between: operational, denotational and axiomatic semantics?
Recap of the terms from the dictionary:
semantics: the study of meaning in a language (words, phrases, etc) and of language constructs in programming languages (basically any syntactically valid part of a program that generates an instruction or a…
George
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8
votes
1 answer
What was the major breakthrough between Hoare-Floyd logic and Scott–Strachey semantics?
I'm reading through a commentary on Milner's "The use of machines to assist in rigorous proof" by Mike Gordon. In this paper, he explains how LCF was born from the ideas of denotational semantics by Dana Scott and Strachey.
It seems to me that…
user1868607
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6
votes
0 answers
Is there relation between K-Framework and structural operational semantics?
K-framework strives to give one (instead of two - operational and denotational) semantics for industrial programming languages. The same unification is done by structural operational semantic as well. Are those two frameworks related somehow? Such…
TomR
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5
votes
1 answer
Domain theory: Definition of isomorphisms
Consider the following definitions of CPOs, monotonicity and continuity:
The pair $(M, \leq)$ is called CPO (complete partial order), if
$M$ is a set,
$\leq$ is a partial order on $M$,
there exists a least element according to $\leq$ in $M$ (called…
user3389669
- 337
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5
votes
1 answer
What is a predicate transformer?
I'm reading Programming - The derivation of algorithms, and I want to understand the purpose of a predicate transformer. This is the excerpt (p. 14-15):
A more precise way in which constructs may be introduced is as follows. For each construct $S$…
InfZero
- 183
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5
votes
1 answer
Defining a "repeat until"-construct in Denotational semantics
My Problem is: to define a "repeat until"-construct in terms of Denotational semantics. I made an attempt and now i need to know if i made it right.
The Conditions are: i used the language "While" as specified in "Semantics with Applications" by…
Toralf Westström
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4
votes
0 answers
How to decide between operational, denotational, and axiomatic semantics?
Context
I'm designing a language which implements lambda calculus and (first-order) predicate calculus, where lambdas behave as the abstraction encapsulating logic, compositionally forming a computational model for higher-order logic.
Question
How…
Phizo
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4
votes
1 answer
Denotational semantics of expressions with side effects
I'm doing revision for a module on programming language semantics and
I'm having trouble understanding the introduction of side-effects in
expressions.
We assume a standard syntax for arithmetic expression, with the four
usual operations, plus the…
user2320239
- 235
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- 2
4
votes
0 answers
Can `D = (D→ D)_⊥` be solved in the domain of DCPOs with monotonic functions?
A denotational semantic for the lambda calculus can be given by solving the domain equation
$$
D \simeq [D →_c D]_\bot
$$
in the category of $\omega$-complete CPOs, where $→_c$ denotes the space of $\omega$-continuous functions. The existence of an…
Joachim Breitner
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3
votes
2 answers
Why does the denotational semantics for a while loop have a existence quantifier?
I was going through these notes and they have the following operator on partial functions:
$$
\mathcal F^{k}(\bot)(\sigma) =
\left\{
\begin{array}{ll}
\alpha( [\![s]\!]\sigma ) & [\![b]\!]\sigma=true \\
\sigma & [\![b]\!]\sigma=false \\
…
Charlie Parker
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3
votes
0 answers
What Happened to "Top" in Denotational Semantics?
Has "top" ($\top$) been removed from or relegated to a much more minor role in denotational semantics? If so, when and why?
I see older papers and books talking about both "top" and "bottom" ("bot", $\bot$), but it seems like newer work only refers…
joeA
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