I have an assignment that I have to do for school which involves using foldleft to find the length of a list. My question lies in the implementation of foldleft. We were given some example code that uses foldleft to multiply every item in a list by x.
implement
list0_mult(xs) =
list0_foldleft<int><int>(xs, 1, lam(res, x) => res*x)
In the third line, what does mean? We have to get the length function to work with any datatype, and I'm assuming to do that I may need to change one or both of those.
I think I've figured out the answer to my own question:
The first refers to the datatype that the foldleft is going to return, and the second refers to the datatype that is in the list that the foldleft is dealing with. For foldright, the first and second 's swap locations.
Your TA here.
list0_foldleft has the following definition. (You can find this in your assignment.)
extern fun {res:t#ype}{a:t#ype} list0_foldleft
(xs: list0 a, ini: res, fopr: (res, a) -<cloref1> res): res
Here, {res:t#ype} is the first template argument representing the type of return value, and {a:t#ype} is the second template argument representing the type of the element of the list. For fopr, its type is (res, a) -<cloref1> res, which is a closure (function + environment) taking two arguments of type res and a, and return a value of type res.
In the call site,
list0_foldleft<int><int>(xs, 1, lam(res, x) => res*x)
the first <int> is indicating that return type res is int, and the second <int> is indicating that the type of list element is int (which is probably not what you want).
I believe you can figure out what goes wrong from here.
Related
If I define a new struct as
mutable struct myStruct
data::AbstractMatrix
labels::Vector{String}
end
and I want to throw an error if the length of labels is not equal to the number of columns of data, I know that I can write a constructor that enforces this condition like
myStruct(data, labels) = length(labels) != size(data)[2] ? error("Labels incorrect length") : new(data,labels)
However, once the struct is initialized, the labels field can be set to the incorrect length:
m = myStruct(randn(2,2), ["a", "b"])
m.labels = ["a"]
Is there a way to throw an error if the labels field is ever set to length not equal to the number of columns in data?
You could use StaticArrays.jl to fix the matrix and vector's sizes to begin with:
using StaticArrays
mutable struct MatVec{R, C, RC, VT, MT}
data::MMatrix{R, C, MT, RC} # RC should be R*C
labels::MVector{C, VT}
end
but there's the downside of having to compile for every concrete type with a unique permutation of type parameters R,C,MT,VT. StaticArrays also does not scale as well as normal Arrays.
If you don't restrict dimensions in the type parameters (with all those downsides) and want to throw an error at runtime, you got good and bad news.
The good news is you can control whatever mutation happens to your type. m.labels = v would call the method setproperty!(object::myStruct, name::Symbol, v), which you can define with all the safeguards you like.
The bad news is that you can't control mutation to the fields' types. push!(m.labels, 1) mutates in the push!(a::Vector{T}, item) method. The myStruct instance itself doesn't actually change; it still points to the same Vector. If you can't guarantee that you won't do something like x = m.labels; push!(x, "whoops") , then you really do need runtime checks, like iscorrect(m::myStruct) = length(m.labels) == size(m.data)[2]
A good option is to not access the fields of your struct directly. Instead, do it using a function. Eg:
mutable struct MyStruct
data::AbstractMatrix
labels::Vector{String}
end
function modify_labels(s::MyStruct, new_labels::Vector{String})
# do all checks and modifications
end
You should check chapter 8 from "Hands-On Design Patterns and Best Practices with Julia: Proven solutions to common problems in software design for Julia 1.x"
I'm struggling to understand parametric type creation in julia. I know that I can create a type with the following:
type EconData
values
dates::Array{Date}
colnames::Array{ASCIIString}
function EconData(values, dates, colnames)
if size(values, 1) != size(dates, 1)
error("Date/data dimension mismatch.")
end
if size(values, 2) != size(colnames, 2)
error("Name/data dimension mismatch.")
end
new(values, dates, colnames)
end
end
ed1 = EconData([1;2;3], [Date(2014,1), Date(2014,2), Date(2014,3)], ["series"])
However, I can't figure out how to specify how values will be typed. It seems reasonable to me to do something like
type EconData{T}
values::Array{T}
...
function EconData(values::Array{T}, dates, colnames)
...
However, this (and similar attempts) simply produce and error:
ERROR: `EconData{T}` has no method matching EconData{T}(::Array{Int64,1}, ::Array{Date,1}, ::Array{ASCIIString,2})
How can I specify the type of values?
The answer is that things get funky with parametric types and inner constructors - in fact, I think its probably the most confusing thing in Julia. The immediate solution is to provide a suitable outer constructor:
using Dates
type EconData{T}
values::Vector{T}
dates::Array{Date}
colnames::Array{ASCIIString}
function EconData(values, dates, colnames)
if size(values, 1) != size(dates, 1)
error("Date/data dimension mismatch.")
end
if size(values, 2) != size(colnames, 2)
error("Name/data dimension mismatch.")
end
new(values, dates, colnames)
end
end
EconData{T}(v::Vector{T},d,n) = EconData{T}(v,d,n)
ed1 = EconData([1,2,3], [Date(2014,1), Date(2014,2), Date(2014,3)], ["series"])
What also would have worked is to have done
ed1 = EconData{Int}([1,2,3], [Date(2014,1), Date(2014,2), Date(2014,3)], ["series"])
My explanation might be wrong, but I think the probably is that there is no parametric type constructor method made by default, so you have to call the constructor for a specific instantiation of the type (my second version) or add the outer constructor yourself (first version).
Some other comments: you should be explicit about dimensions. i.e. if all your fields are vectors (1D), use Vector{T} or Array{T,1}, and if their are matrices (2D) use Matrix{T} or Array{T,2}. Make it parametric on the dimension if you need to. If you don't, slow code could be generated because functions using this type aren't really sure about the actual data structure until runtime, so will have lots of checks.
If I want to change a value on a list, I will return a new list with the new value instead of changing the value on the old list.
Now I have four types. I need to update the value location in varEnd, instead of changing the value, I need to return a new type with the update value
type varEnd = {
v: ctype;
k: varkind;
l: location;
}
;;
type varStart = {
ct: ctype;
sy: sTable;
n: int;
stm: stmt list;
e: expr
}
and sEntry = Var of varEnd | Fun of varStart
and sTable = (string * sEntry) list
type environment = sTable list;;
(a function where environment is the only parameter i can use)
let allocateMem (env:environment) : environment =
I tried to use List.iter, but it changes the value directly, which type is also not mutable. I think List.fold will be a better option.
The biggest issue i have is there are four different types.
I think you're saying that you know how to change an element of a list by constructing a new list.
Now you want to do this to an environment, and an environment is a list of quite complicated things. But this doesn't make any difference, the way to change the list is the same. The only difference is that the replacement value will be a complicated thing.
I don't know what you mean when you say you have four types. I see a lot more than four types listed here. But on the other hand, an environment seems to contain things of basically two different types.
Maybe (but possibly not) you're saying you don't know a good way to change just one of the four fields of a record while leaving the others the same. This is something for which there's a good answer. Assume that x is something of type varEnd. Then you can say:
{ x with l = loc }
If, in fact, you don't know how to modify an element of a list by creating a new list, then that's the thing to figure out first. You can do it with a fold, but in fact you can also do it with List.map, which is a little simpler. You can't do it with List.iter.
Update
Assume we have a record type like this:
type r = { a: int; b: float; }
Here's a function that takes r list list and adds 1.0 to the b fields of those records whose a fields are 0.
let incr_ll rll =
let f r = if r.a = 0 then { r with b = r.b +. 1.0 } else r in
List.map (List.map f) rll
The type of this function is r list list -> r list list.
For a list, you can do pattern matching and iterate until the nth element, but for a tuple, how would you grab the nth element?
TL;DR; Stop trying to access directly the n-th element of a t-uple and use a record or an array as they allow random access.
You can grab the n-th element by unpacking the t-uple with value deconstruction, either by a let construct, a match construct or a function definition:
let ivuple = (5, 2, 1, 1)
let squared_sum_let =
let (a,b,c,d) = ivuple in
a*a + b*b + c*c + d*d
let squared_sum_match =
match ivuple with (a,b,c,d) -> a*a + b*b + c*c + d*d
let squared_sum_fun (a,b,c,d) =
a*a + b*b + c*c + d*d
The match-construct has here no virtue over the let-construct, it is just included for the sake of completeness.
Do not use t-uples, Don¹
There are only a few cases where using t-uples to represent a type is the right thing to do. Most of the times, we pick a t-uple because we are too lazy to define a type and we should interpret the problem of accessing the n-th field of a t-uple or iterating over the fields of a t-uple as a serious signal that it is time to switch to a proper type.
There are two natural replacements to t-uples: records and arrays.
When to use records
We can see a record as a t-uple whose entries are labelled; as such, they are definitely the most natural replacement to t-uples if we want to access them directly.
type ivuple = {
a: int;
b: int;
c: int;
d: int;
}
We then access directly the field a of a value x of type ivuple by writing x.a. Note that records are easily copied with modifications, as in let y = { x with d = 0 }. There is no natural way to iterate over the fields of a record, mostly because a record do not need to be homogeneous.
When to use arrays
A large² homogeneous collection of values is adequately represented by an array, which allows direct access, iterating and folding. A possible inconvenience is that the size of an array is not part of its type, but for arrays of fixed size, this is easily circumvented by introducing a private type — or even an abstract type. I described an example of this technique in my answer to the question “OCaml compiler check for vector lengths”.
Note on float boxing
When using floats in t-uples, in records containing only floats and in arrays, these are unboxed. We should therefore not notice any performance modification when changing from one type to the other in our numeric computations.
¹ See the TeXbook.
² Large starts near 4.
Since the length of OCaml tuples is part of the type and hence known (and fixed) at compile time, you get the n-th item by straightforward pattern matching on the tuple. For the same reason, the problem of extracting the n-th element of an "arbitrary-length tuple" cannot occur in practice - such a "tuple" cannot be expressed in OCaml's type system.
You might still not want to write out a pattern every time you need to project a tuple, and nothing prevents you from generating the functions get_1_1...get_i_j... that extract the i-th element from a j-tuple for any possible combination of i and j occuring in your code, e.g.
let get_1_1 (a) = a
let get_1_2 (a,_) = a
let get_2_2 (_,a) = a
let get_1_3 (a,_,_) = a
let get_2_3 (_,a,_) = a
...
Not necessarily pretty, but possible.
Note: Previously I had claimed that OCaml tuples can have at most length 255 and you can simply generate all possible tuple projections once and for all. As #Virgile pointed out in the comments, this is incorrect - tuples can be huge. This means that it is impractical to generate all possible tuple projection functions upfront, hence the restriction "occurring in your code" above.
It's not possible to write such a function in full generality in OCaml. One way to see this is to think about what type the function would have. There are two problems. First, each size of tuple is a different type. So you can't write a function that accesses elements of tuples of different sizes. The second problem is that different elements of a tuple can have different types. Lists don't have either of these problems, which is why you can have List.nth.
If you're willing to work with a fixed size tuple whose elements are all the same type, you can write a function as shown by #user2361830.
Update
If you really have collections of values of the same type that you want to access by index, you should probably be using an array.
here is a function wich return you the string of the ocaml function you need to do that ;) very helpful I use it frequently.
let tup len n =
if n>=0 && n<len then
let rec rep str nn = match nn<1 with
|true ->""
|_->str ^ (rep str (nn-1))in
let txt1 ="let t"^(string_of_int len)^"_"^(string_of_int n)^" tup = match tup with |" ^ (rep "_," n) ^ "a" and
txt2 =","^(rep "_," (len-n-2)) and
txt3 ="->a" in
if n = len-1 then
print_string (txt1^txt3)
else
print_string (txt1^txt2^"_"^txt3)
else raise (Failure "Error") ;;
For example:
tup 8 6;;
return:
let t8_6 tup = match tup with |_,_,_,_,_,_,a,_->a
and of course:
val t8_6 : 'a * 'b * 'c * 'd * 'e * 'f * 'g * 'h -> 'g = <fun>
I have an Ocaml function that is giving me errors.
What I am trying to do:
Recursively create a List of random numbers (0-2) of size "limit".
Here's what I have:
let rec carDoorNumbers = fun limit ->
match limit with
| [1] -> Random.int 3
| [] -> Random.int 3 :: carDoorNumbers (limit-1);;
I am getting this error:
Error: This expression has type 'a list
but an expression was expected of type int
Think about what your function has to do: given a limit, you have to create a list of numbers. So your type is something like carDoorNumbers : int -> int list.
Looking at that, it seems you have two errors. First, you're matching limit (which should be an int) against a list pattern. [1] -> ... matches a list containing only the element 1 and [] matches the empty list; you really want to match against the number 1 and any other number n.
The second error is that you return two different types in your match statement. Remember that you are supposed to be returning a list. In the first case, you are returning Random.int 3, which is an int rather than an int list. What you really want to return here is something like [Random.int 3].
The error you got is a little confusing. Since the first thing you returned was an int, it expects your second thing to also be an int. However, your second case was actually correct: you do return an int list! However, the compiler does not know what you meant, so its error is backwards; rather than changing the int list to an int, you need to change the int to an int list.
Your match expression treats limit like a list. Both [1] and [] are lists. That's what the compiler is telling you. But it seems limit should be an integer.
To match an integer, just use an integer constant. No square brackets.
(As a side comment, you might want to be sure the function works well when you pass it 0.)