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Results tagged with programming-languages
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user 12623
Questions related to design, implementation, and analysis of programming languages. NOT for questions about how to program, which are off-topic on this site.
1
vote
2
answers
305
views
How is it that programs can be identified with partial functions for programming language se...
I was reading about denotational semantics
Broadly speaking, denotational semantics is concerned with finding mathematical objects called domains that represent what programs do. For example, pro …
- 3,090
0
votes
How is it that programs can be identified with partial functions for programming language se...
The point is to express what a piece "means"/semantics. To define what it means we map syntax **at a given state ** (that takes in a state $\sigma$) to a mathematical object. This mathematical object …
- 3,090
0
votes
How does one formally show that two lambda functions are $\alpha$ equivalent?
My confusion was that the definition is not that there exists a variable name such that the two functions are equal (which I believe is a better definition, probably equivalent to the one provided). I …
- 3,090
2
votes
1
answer
144
views
How do we show $\lambda x . x (\lambda y .y) \equiv_{\alpha} \lambda y.y (\lambda x . x)$ in...
How do we show $$\lambda x . x (\lambda y .y) \equiv_{\alpha} \lambda y.y (\lambda x . x)$$?
I was going through the slides here and it asked to do the above but by page 16 of the slides we have not …
- 3,090
1
vote
1
answer
58
views
What are $(S,\Sigma)$-CCCs?
I was reading this and I was trying to understand the definition of $(S,\Sigma)$-CCC. The first requirement says:
a mapping [[_]] : S → |C|, associating some object [[s]] ∈ |C| to
any s ∈ S;
w …
- 3,090
2
votes
1
answer
72
views
What is the denotation for identifiers?
I am trying to understand what is the domain for denotational semantics.
Right now the way I understand denotational semantics is that given some syntax of a program that maps to some mathematical ob …
- 3,090
2
votes
4
answers
695
views
How does one formally show that two lambda functions are $\alpha$ equivalent?
I was going through the following slides and I wanted to show the following:
$$ \lambda x. x \equiv_{\alpha} \lambda y . y$$
formally. They define a an $\alpha$-conversion on page 15 as follows:
$$ …
- 3,090
2
votes
2
answers
110
views
How does one show $(\lambda x . (\lambda y.x))yx \equiv_{\beta} y$ in lambda calculus?
I wanted to show:
$$ (\lambda x . (\lambda y.x))yx \equiv_{\beta} y $$
the definition of beta equivalence is on page 17 of these notes.
I did a few attempts but got different things like $x$. I thi …
- 3,090
3
votes
2
answers
318
views
Why does the denotational semantics for a while loop have a existence quantifier?
I was going through these notes and they have the following operator on partial functions:
$$
\mathcal F^{k}(\bot)(\sigma) =
\left\{
\begin{array}{ll}
\alpha( [\![s]\!]\sigma ) & [\![b]\!]\sigm …
- 3,090
0
votes
0
answers
125
views
Why is Combinatorial Sketching for Finite programs possible?
I was reading Combinatorial Sketching for Finite Programs and wanted to understand why synthesis of the sketching language was possible/feasible.
As far as I understand a partial program is transfor …
- 3,090
2
votes
1
answer
810
views
What is the definition of a redex and what are they for in programming languages literature?
I saw the word "redex" in the context of proramming language theory/semantics in 2018 and now when I was reading a neurosymbolic research paper (machine learning with neural nets + symbolic algorithms …
- 3,090
3
votes
1
answer
338
views
Proper algorithm for resolving ambiguity in grammars via enforcing associativity and precede...
I was told there is a algorithm that always resolves ambiguity for grammars that have issues with precedence and associativity. I know ambiguity in general is undecidable, so I only want to resolve th …
- 3,090
5
votes
1
answer
134
views
What does $ \forall \alpha_1, \dots , \alpha_n . \tau $ mean formally as a type?
I was learning about polymorphic types but I couldn't understand the notation, can someone explain it means (context cs421 UIUC):
$$ \forall \alpha_1, \dots , \alpha_n . \tau $$
its supposed to be a …
- 3,090
2
votes
2
answers
89
views
Are type variables really only used in mathematical conversation about types?
Are type variables really only used in mathematical conversation about types? i.e. are type variables (meta-variables that only contain the type classification label) only exist in proofs for types bu …
- 3,090
3
votes
Accepted
Why is the assignment rule the way it is in Hoare Logic?
So after reading and thinking about it more this is my explanation (thanks software foundations):
The key confusion for me seems to be the meaning of $P[e/x]$ (replaces every free instance of x with …
- 3,090