6 leaf nodes in Racket - racket

So I have the code below which perfectly implements(define myleaf (interior-node 'a (leaf-node 5) (leaf-node 6))). thats defined already
How can I implement a 6 leaf node for more data?
define-datatype bintree bintree?
(leaf-node
(datum number?)
)
(interior-node
(key symbol?)
(left bintree?)
(right bintree?)
)
)

I assume by "6-leaf node" that you mean a 6-ary tree, in which every non-leaf node has 6 children.
(define-datatype bintree bintree?
(leaf-node
(datum number?)
)
(interior-node
(key symbol?)
(first bintree?)
(second bintree?)
(third bintree?)
(fourth bintree?)
(fifth bintree?)
(sixth bintree?)
)
)
define-datatype basically works like this:
first argument: name of new datatype
second argument: the name of the function you will use to test if something is an instance of that type
next: all the different kinds of this datatype that can exist, their members their types
So in this case you would just add new members for each of the 6 children you want.

Related

How does an instance of "Arbitrary" looks for a tree?

In our CS-Lectures we currently learn about QuickCheck in Haskell. Now I got a task to use QuickCheck with the following tree-type:
data Tree = Leaf Int | Node Tree Tree
deriving (Eq, Show)
I have already written some necessery equations to check different properties of trees.
I know, that I need an instance of "Arbitrary" to run the whole thing.
So tried this:
instance Arbitrary Tree where
arbitrary = sized tree'
where tree' 0 = do a <- arbitrary
oneof [return (Leaf a)]
tree' n = do a <- arbitrary
oneof [return (Leaf a), return (Node (tree' (n-1)) (tree' (n-1)))]
But now I am getting some errors such as:
Couldn't match type `Gen Tree' with `Tree'
Expected type: a -> Tree
Actual type: a -> Gen Tree
* In an equation for `arbitrary':
arbitrary
= sized tree'
where
tree' 0
= do a <- arbitrary
....
tree' n
= do a <- arbitrary
....
In the instance declaration for `Arbitrary Tree'
|
61 | where tree' 0 = do a <- arbitrary
| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^...
or:
* Couldn't match type `Tree' with `Gen Tree'
Expected type: Int -> Gen Tree
Actual type: Int -> Tree
* In the first argument of `sized', namely tree'
In the expression: sized tree'
In an equation for `arbitrary':
arbitrary
= sized tree'
where
tree' 0
= do a <- arbitrary
....
tree' n
= do a <- arbitrary
....
|
60 | arbitrary = sized tree'
| ^^^^^
I think the problem is that I am doing some kind of recursion when choosing a Node. Because in that case the subtrees of that node are not trees but more like "return trees". Hopefully you know, what I mean.
Can somebody help me with this?
Thank you :)
The simplest way to implement this is with:
instance Arbitrary Tree where
arbitrary = frequency [
(3, Leaf <$> arbitrary)
, (1, Node <$> arbitrary <*> arbitrary)
]
Here the arbitrary functions in bold are the ones implement for the Tree instance. The arbitrary for Leaf is the arbitrary instance for an Int.
Here we thus specify that an arbitrary tree is a leaf with an arbitrary Int, or it is a Node with an arbitrary left and right sub-Tree.
or with sized :: (Int -> Gen a) -> Gen a:
instance Arbitrary Tree where
arbitrary = sized go
where go 0 = Leaf <$> arbitrary
go n = oneof [Leaf <$> arbitrary, Node <$> go' <*> go']
where go' = go (n-1)
here the size specifies the depth of the tree, not the number of elements.
This can be derived using the generic-random library
{-# Language DataKinds #-}
{-# Language DeriveGeneric #-}
{-# Language DerivingVia #-}
import GHC.Generics
import Generic.Random.DerivingVia
import Test.QuickCheck
-- ghci> :set -XTypeApplications
-- ghci> sample #Tree arbitrary
-- Node (Leaf 0) (Node (Leaf 0) (Node (Leaf 0) (Node (Node (Leaf 0) (Leaf 0)) (Leaf 0))))
-- Leaf 0
-- Leaf (-2)
-- Leaf 5
-- Leaf 0
-- Leaf 2
-- Leaf 1
-- Leaf 7
-- Node (Leaf (-7)) (Leaf (-2))
-- Node (Leaf 4) (Node (Leaf 0) (Leaf 3))
-- Node (Leaf 5) (Leaf (-2))
data Tree = Leaf Int | Node Tree Tree
deriving
stock (Eq, Show, Generic)
deriving Arbitrary
via GenericArbitraryRec '[2, 1] Tree
Let me know if there is something wrong with the distribution!

Bizarre Contract Violation in Judgment

I have a judgement with the following contract:
(define-judgment-form DynamicLam
#:mode (down I I O O)
#:contract (down Γ e Γ e)
[----------------"Lambda"
(down Γ_0 z_0 Γ_0 z_0)]
;; rest of the code ...
)
When I run this:
(define empty (term ()))
(redex-match? DynamicLam Γ empty)
(redex-match? DynamicLam e lam1^*)
(redex-match? DynamicLam z lam1^*)
(judgment-holds (down empty lam1^* empty lam1^*))
I get back:
#t
#t
#t
. . down: judgment input values do not match its contract;
(unknown output values indicated by _)
contract: (down Γ e Γ e)
values: (down empty lam1^* _ _)
But this does not make sense, because I clearly used redex-match? above to test:
That empty matches Γ
That lam1^* matches e
And furthermore that lam1^* matches z.
What am I missing? Is there more to the meaning of #:contract than just matching Γ e Γ e?
I solved the problem by changing the #:mode to (down I I I I) instead of (down I I O O), and changing
(judgment-holds (down empty lam1^* empty lam1^*))
to
(judgment-holds (down ,empty ,lam1^* ,empty ,lam1^*))
The , change makes a lot of sense to me but I still do not understand why the two outputs needed to be inputs, so if someone can either edit this answer to explain that, or provide a comment or another answer explaining that subtlety, that would be fantastic.

equivalent of assoc-in(clojure) in scala

I am trying to find an equivalent of assoc-in (clojure) in scala. I am trying to convert
(defn- organiseDataByTradeId [data]
(reduce #(let [a (assoc-in %1
[(%2 "internaltradeid") (read-string (%2 "paramseqnum")) "levelcols"]
(reduce (fn [m k](assoc m k (get %2 k)))
{}
(string/split xmlLevelAttributesStr #",")))
b (assoc-in a
[(%2 "internaltradeid") (read-string (%2 "paramseqnum")) "subLevelCols" (read-string (%2 "cashflowseqnum"))]
(reduce (fn [m k] (assoc m k (get %2 k)))
{}
(string/split xmlSubLevelAttributesStr #","))
)]
b)
{}
data))
to scala.
Have tried this :
def organiseDataByTradeId(data: List[Map[String, String]]) = {
data.map { entry => Map(entry("internaltradeid") -> Map(entry("paramseqnum").toInt -> Map("levelcols" -> (xmlLevelAttributesStr.split(",")).map{key=> (key,entry(key))}.toMap,
"subLevelCols" -> Map(entry("cashflowseqnum").asInstanceOf[String].toInt -> (xmlSubLevelAttributesStr.split(",")).map{key=> (key,entry(key))}.toMap)))) }
}
Not sure how to merge the list of maps I got without overwriting.
Here data List[Map[String,String]] is basically describing a table.Each entry is a row.Column names are keys of the maps and values are values.xmlLevelAttributeStr and xmlSubLevelAttributeStr are two Strings where column names are separated by comma.
I am fairly new to scala. I converted each row(Map[String,String]) to a scala Map and now not sure how to merge them so that previous data is not overwritten and behaves exactly as the clojure code.Also I am not allowed to use external libraries such as scalaz.
This Clojure code is not a good pattern to copy: it has a lot of duplication, and little explanation of what it is doing. I would write it more like this:
(defn- organiseDataByTradeId [data]
(let [level-reader (fn [attr-list]
(let [levels (string/split attr-list #",")]
(fn [item]
(into {} (for [level levels]
[level (get item level)])))))
attr-levels (level-reader xmlLevelAttributesStr)
sub-levels (level-reader xmlSubLevelAttributesStr)]
(reduce (fn [acc item]
(update-in acc [(item "internaltradeid"),
(read-string (item "paramseqnum"))]
(fn [trade]
(-> trade
(assoc "levelcols" (attr-levels item))
(assoc-in ["subLevelCols", (read-string (item "cashflowseqnum"))]
(sub-levels item))))))
{}, data)))
It's more lines of code than your original, but I've taken the opportunity to name a number of useful concepts and extract the repetition into a local function so that it's more self-explanatory.
It's even easier if you know there will be no duplication of internaltradeid: you can simply generate a number of independent maps and merge them together:
(defn- organiseDataByTradeId [data]
(let [level-reader (fn [attr-list]
(let [levels (string/split attr-list #",")]
(fn [item]
(into {} (for [level levels]
[level (get item level)])))))
attr-levels (level-reader xmlLevelAttributesStr)
sub-levels (level-reader xmlSubLevelAttributesStr)]
(apply merge (for [item data]
{(item "internaltradeid")
{(read-string (item "paramseqnum"))
{"levelcols" (attr-levels item),
"subLevelCols" {(read-string (item "cashflowseqnum")) (sub-levels item)}}}}))))
But really, neither of these approaches will work well in Scala, because Scala has a different data modeling philosophy than Clojure does. Clojure encourages loosely-defined heterogeneous maps like this, where Scala would prefer that your maps be homogeneous. When you will have data mixing multiple types, Scala suggests you define a class (or perhaps a case class - I'm no Scala expert) and then create instances of that class.
So here you'd want a Map[String, Map[Int, TradeInfo]], where TradeInfo is a class with two fields, levelcols : List[Attribute], and subLevelCols as some sort of pair (or perhaps a single-element map) containing a cashflowseqnum and another List[Attribute].
Once you've modeled your data in the Scala way, you'll be quite far away from using anything that looks like assoc-in because your data won't be a single giant map, so the question won't arise.

Pass a data structure in to a macro for filling in

I'm trying to solve a problem: I need to create a map from passed-in values, but while the symbol names for the values are consistent, the keys they map to are not. For instance: I might be passed a value that is a user ID. In the code, I can always use the symbol user-id -- but depending on other factors, I might need to make a map {"userId" user-id} or {"user_id" user-id} or {:user-id user-id} or -- well, you get the picture.
I can write a macro that gets me part-way there:
(defmacro user1 [user-id] `{"userId" ~user-id}
(defmacro user2 [user-id] `{"user_id" ~user-id}
But what I'd much rather do is define a set of maps, then combine them with a given set of symbols:
(def user-id-map-1 `{"userId" `user-id}
(defn combiner [m user-id] m) ;; <-- Around here, a miracle occurs.
I can't figure out how to get this evaluation to occur. It seems like I should be able to make a map containing un-evaluated symbols, then look up those symbols in the lexical scope of a function or macro that binds those symbols as locals -- but how?
Instead of standardizing your symbolic names, use maps with standard keyword keys. You don't need to go near macros, and you can turn your maps into records if need be without much trouble.
What you know as
(def user1 {:id 3124, :surname "Adabolo", :forenames ["Julia" "Frances"]})
... can be transformed by mapping the keys with whatever function you choose:
(defn map-keys [keymap m]
(zipmap (map keymap (keys m)) (vals m)))
For example,
(map-keys name user1)
;{"id" 3124, "surname" "Adabolo", "forenames" ["Julia" "Frances"]}
or
(map-keys {:id :user-id, :surname :family-name} user1)
;{:user-id 3124, :family-name "Adabolo", nil ["Julia" "Frances"]}
If you want rid of the nil entry, wrap the expression in (dissoc ... nil):
(defn map-keys [keymap m]
(dissoc
(zipmap (map keymap (keys m)) (vals m))
nil))
Then
(map-keys {:id :user-id, :surname :family-name} user1)
;{:user-id 3124, :family-name "Adabolo"}
I see from Michał Marczyk's answer, which has priority, that the above essentially rewrites clojure.set/rename-keys, which, however ...
leaves missing keys untouched:
For example,
(clojure.set/rename-keys user1 {:id :user-id, :surname :family-name})
;{:user-id 3124, :forenames ["Julia" "Frances"], :family-name "Adabolo"}
doesn't work with normal functions:
For example,
(clojure.set/rename-keys user1 name)
;IllegalArgumentException Don't know how to create ISeq from: clojure.core$name ...
If you forego the use of false and nil as keys, you can leave missing keys untouched and still use normal functions:
(defn map-keys [keymap m]
(zipmap (map #(or (keymap %) %) (keys m)) (vals m)))
Then
(map-keys {:id :user-id, :surname :family-name} user1)
;{:user-id 3124, :family-name "Adabolo", :forenames ["Julia" "Frances"]}
How about putting your passed-in values in a map keyed by keywords forged from the formal parameter names:
(defmacro zipfn [map-name arglist & body]
`(fn ~arglist
(let [~map-name (zipmap ~(mapv keyword arglist) ~arglist)]
~#body)))
Example of use:
((zipfn argmap [x y z]
argmap)
1 2 3)
;= {:z 3, :y 2, :x 1}
Better yet, don't use macros:
;; could take varargs for ks (though it would then need another name)
(defn curried-zipmap [ks]
#(zipmap ks %))
((curried-zipmap [:x :y :z]) [1 2 3])
;= {:z 3, :y 2, :x 1}
Then you could rekey this map using clojure.set/rename-keys:
(clojure.set/rename-keys {:z 3, :y 2, :x 1} {:z "z" :y "y" :x "x"})
;= {"x" 1, "z" 3, "y" 2}
The second map here is the "translation map" for the keys; you can construct in by merging maps like {:x "x"} describing how the individual keys ought to be renamed.
For the problem you described I can't find a reason to use macros.
I'd recommend something like
(defn assoc-user-id
[m user-id other-factors]
(assoc m (key-for other-factors) user-id))
Where you implement key-for so that it selects the key based on other-factors.

let vs def in clojure

I want to make a local instance of a Java Scanner class in a clojure program. Why does this not work:
; gives me: count not supported on this type: Symbol
(let s (new Scanner "a b c"))
but it will let me create a global instance like this:
(def s (new Scanner "a b c"))
I was under the impression that the only difference was scope, but apparently not. What is the difference between let and def?
The problem is that your use of let is wrong.
let works like this:
(let [identifier (expr)])
So your example should be something like this:
(let [s (Scanner. "a b c")]
(exprs))
You can only use the lexical bindings made with let within the scope of let (the opening and closing parens). Let just creates a set of lexical bindings. I use def for making a global binding and lets for binding something I want only in the scope of the let as it keeps things clean. They both have their uses.
NOTE: (Class.) is the same as (new Class), it's just syntactic sugar.
LET is not "make a lexical binding in the current scope", but "make a new lexical scope with the following bindings".
(let [s (foo whatever)]
;; s is bound here
)
;; but not here
(def s (foo whatever))
;; s is bound here
Simplified: def is for global constants, let is for local variables.
Correct syntax:
(let [s (Scanner. "a b c")] ...)
The syntax for them is different, even if the meanings are related.
let takes a list of bindings (name value pairs) followed by expressions to evaluate in the context of those binding.
def just takes one binding, not a list, and adds it to the global context.
You could think of let as syntactic sugar for creating a new lexical scope with fn then applying it immediately:
(let [a 3 b 7] (* a b)) ; 21
; vs.
((fn [a b] (* a b)) 3 7) ; 21
So you could implement let with a simple macro and fn:
(defmacro fnlet [bindings & body]
((fn [pairs]
`((fn [~#(map first pairs)] ~#body) ~#(map last pairs)))
(partition 2 bindings)))
(fnlet [a 3 b 7] (* a b)) ; 21