Isabelle: changing an element inside a list - isabelle

In VDM, we can do something like the following
someSequence(index) := someSequence(index) union {x}
where someSequence is a sequence of sets.
In Isabelle, how can I access an element inside a list and modify it like the above example? Is there a way to do this?
Thank you for your help!

You talk about a sequenced set, but you ask about a list. Here's the list function:
value "(list_update [1,2,3,4,5::nat] 2 0) = [1,2,0,4,5]"
There is main.pdf, which gives a quick overview of functions and syntax for common types. On page 9 is the overview of lists:
https://isabelle.in.tum.de/website-Isabelle2015/dist/Isabelle2015/doc/main.pdf#page=9
I looked at the function signatures until I saw something that looked like it took and returned the right kind of arguments.
Their is a PDF for the Isabelle/HOL logic. Chapter 66 is where they define lists for Isabelle2015. Page numbers and chapters can change for a new release.
On page 1033, there is a list of checks they do that serve as examples of some common list functions:
https://isabelle.in.tum.de/website-Isabelle2015/dist/library/HOL/HOL/document.pdf#page=1033
They don't try to make the list function library exhaustive. You can use what they've done, for examples of how to define your own.

Related

Is attributes() a function in R?

Help files call attributes() a function. Its syntax looks like a function call. Even class(attributes) calls it a function.
But I see I can assign something to attributes(myobject), which seems unusual. For example, I cannot assign anything to log(myobject).
So what is the proper name for "functions" like attributes()? Are there any other examples of it? How do you tell them apart from regular functions? (Other than trying supposedfunction(x)<-0, that is.)
Finally, I guess attributes() implementation overrides the assignment operator, in order to become a destination for assignments. Am I right? Is there any usable guide on how to do it?
Very good observation Indeed. It's an example of replacement function, if you see closely and type apropos('attributes') in your R console, It will return
"attributes"
"attributes<-"
along with other outputs.
So, basically the place where you are able to assign on the left sign of assignment operator, you are not calling attributes, you are actually calling attributes<- , There are many functions in R like that for example: names(), colnames(), length() etc. In your example log doesn't have any replacement counterpart hence it doesn't work the way you anticipated.
Definiton(from advanced R book link given below):
Replacement functions act like they modify their arguments in place,
and have the special name xxx<-. They typically have two arguments (x
and value), although they can have more, and they must return the
modified object
If you want to see the list of these functions you can do :
apropos('<-$') and you can check out similar functions, which has similar kind of properties.
You can read about it here and here
I am hopeful that this solves your problem.

What is the Julia's best approximation to R objects' attributes?

I store important metadata in R objects as attributes. I want to migrate my workflow to Julia and I am looking for a way to represent at least temporarily the attributes as something accessible by Julia. Then I can start thinking about extending the RData package to fill this data structure with actual objects' attributes.
I understand, that annotating with things like label or unit in DataFrame - I think the most important use for object' attributes - is probably going to be implemented in the DataFrames package some time (https://github.com/JuliaData/DataFrames.jl/issues/35). But I am asking about about more general solution, that doesn't depend on this specific use case.
For anyone interested, here is a related discussion in the RData package
In Julia it is ideomatic to define your own types - you'd simply make fields in the type to store the attributes. In R, the nice thing about storing things as attributes is that they don't affect how the type dispatches - e.g. adding metadata to a Vector doesn't make it stop behaving like a Vector. In julia, that approach is a little more complicated - you'd have to define the AbstractVector interface for your type https://docs.julialang.org/en/latest/manual/interfaces/#man-interface-array-1 to have it behave like a Vector.
In essence, this means that the workflow solutions are a little different - e.g. often the attribute metadata in R is used to associate metadata to an object when it's returned from a function. An easy way to do something similar in Julia is to have the function return a tuple and assign the result to a tuple:
function ex()
res = rand(5)
met = "uniformly distributed random numbers"
res, met
end
result, metadata = ex()
I don't think there are plans to implement attributes like in R.

R use list as function argument

I come from a C# background and try to migrate some of my time series library to R.
One of the benefits of OOP is that I can tuck away variables in a class and pass this as reference.
I read up on R environments, lists, ... and I'm still not sure about the right approach. If I would use a list then I would need to check the function argument:
exists()
(btw: Is there also a function to test for the elements in a list)
I could create a list, pass it as an argument and then write the result back in a list. But is this the right approach?
Any comments ...
exists is seldom used. If you need it, maybe you do something wrong.
missing is sometimes used.
Functions sometimes, but not very often, receive lists as parameters, and often return lists.
To test whether a list foo has an element bar, use is.null(foo$bar). This is FALSE if the list has the element, TRUE otherwise.

In R, looking for a more detailed str() showing full names or a tree

I want to change parts of a ggplot2 object made by a function and returned as a result, to remove the Y-axis label. No, the function does not allow that to be specified in the first place so I want to change it after the fact.
str(theObject) ## shows the nested structure with parts shortened to ".." and I want to be able to type something like:
theObject$A$B$C$myLabel <- ""
So how can I either make an str -like listing with full paths like that or perhaps draw a tree structure showing the inner working of the object?
Yes, I can figure things out using names(theObject) and finding which branch leads to what I am looking for, then switching to that branch and repeating but it looks like there could be a better automated way to find a leaf node such as:
leaf_str(obj=theObject, leaf="myLabel")
might return zero or more lines like:
theObject$A$B$C$myLabel
theObject$A$X$Y$Z$myLabel
Or, the entire structure could be put out as a series of such lines.
I have searched and found nothing quite like this. I can see lots of uses especially in teaching what an object is. Yes, S4 objects might also use # as well as $.
The
tree
function in the xfun package may be useful.
See here for more details
https://yihui.org/xfun/

Trying to understand R structure: what does a dot in function names signify?

I am trying to learn how to use R. I can use it to do basic things like reading in data and running a t-test. However, I am struggling to understand the way R is structured (I am have a very mediocre java background).
What I don't understand is the way the functions are classified.
For example in is.na(someVector), is is a class? Or for read.csv, is csv a method of the read class?
I need an easier way to learn the functions than simply memorizing them randomly. I like the idea of things belonging to other things. To me it seems like this gives a language a tree structure which makes learning more efficient.
Thank you
Sorry if this is an obvious question I am genuinely confused and have been reading/watching quite a few tutorials.
Your confusion is entirely understandable, since R mixes two conventions of using (1) . as a general-purpose word separator (as in is.na(), which.min(), update.formula(), data.frame() ...) and (2) . as an indicator of an S3 method, method.class (i.e. foo.bar() would be the "foo" method for objects with class attribute "bar"). This makes functions like summary.data.frame() (i.e., the summary method for objects with class data.frame) especially confusing.
As #thelatemail points out above, there are some other sets of functions that repeat the same prefix for a variety of different options (as in read.table(), read.delim(), read.fwf() ...), but these are entirely conventional, not specified anywhere in the formal language definition.
dotfuns <- apropos("[a-z]\\.[a-z]")
dotstart <- gsub("\\.[a-zA-Z]+","",dotfuns)
head(dotstart)
tt <- table(dotstart)
head(rev(sort(tt)),10)
## as is print Sys file summary dev format all sys
## 118 51 32 18 17 16 16 15 14 13
(Some of these are actually S3 generics, some are not. For example, Sys.*(), dev.*(), and file.*() are not.)
Historically _ was used as a shortcut for the assignment operator <- (before = was available as a synonym), so it wasn't available as a word separator. I don't know offhand why camelCase wasn't adopted instead.
Confusingly, methods("is") returns is.na() among many others, but it is effectively just searching for functions whose names start with "is."; it warns that "function 'is' appears not to be generic"
Rasmus Bååth's presentation on naming conventions is informative and entertaining (if a little bit depressing).
extra credit: are there any dot-separated S3 method names, i.e. cases where a function name of the form x.y.z represents the x.y method for objects with class attribute z ?
answer (from Hadley Wickham in comments): as.data.frame.data.frame() wins. as.data.frame is an S3 generic (unlike, say, as.numeric), and as.data.frame.data.frame is its method for data.frame objects. Its purpose (from ?as.data.frame):
If a data frame is supplied, all classes preceding ‘"data.frame"’
are stripped, and the row names are changed if that argument is
supplied.

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