wk5: Higher order functions, Modelling (pt.2)
This commit is contained in:
Dimitar Byalkov
24
wk5/elm.json
Normal file
24
wk5/elm.json
Normal file
@@ -0,0 +1,24 @@
|
||||
{
|
||||
"type": "application",
|
||||
"source-directories": [
|
||||
"src"
|
||||
],
|
||||
"elm-version": "0.19.1",
|
||||
"dependencies": {
|
||||
"direct": {
|
||||
"elm/browser": "1.0.2",
|
||||
"elm/core": "1.0.5",
|
||||
"elm/html": "1.0.0"
|
||||
},
|
||||
"indirect": {
|
||||
"elm/json": "1.1.3",
|
||||
"elm/time": "1.0.0",
|
||||
"elm/url": "1.0.0",
|
||||
"elm/virtual-dom": "1.0.3"
|
||||
}
|
||||
},
|
||||
"test-dependencies": {
|
||||
"direct": {},
|
||||
"indirect": {}
|
||||
}
|
||||
}
|
||||
65
wk5/src/HighOrder.elm
Normal file
65
wk5/src/HighOrder.elm
Normal file
@@ -0,0 +1,65 @@
|
||||
module HighOrder exposing (..)
|
||||
|
||||
{-
|
||||
Higher order functions
|
||||
Dimitar Byalkov and Kaloyan Stoykov
|
||||
-}
|
||||
|
||||
repeatUntil: (a -> Bool) -> (a -> a) -> a -> a
|
||||
repeatUntil p f init =
|
||||
let
|
||||
fResult = f init
|
||||
in
|
||||
if not(p fResult) then
|
||||
repeatUntil p f fResult
|
||||
else
|
||||
fResult
|
||||
|
||||
double: Int -> Int
|
||||
double a =
|
||||
a * 2
|
||||
|
||||
above100: Int -> Bool
|
||||
above100 x =
|
||||
x > 100
|
||||
|
||||
aboveN: Int -> (Int -> Bool)
|
||||
aboveN n =
|
||||
((<=) n)
|
||||
|
||||
log: Int -> Int -> Int
|
||||
log base result =
|
||||
if result == base then
|
||||
1
|
||||
else
|
||||
log base ((repeatUntil (aboveN result) (\x -> base * x) base)
|
||||
// base) + 1
|
||||
|
||||
myCollatz: List Int -> List Int
|
||||
myCollatz values =
|
||||
case values of
|
||||
[] ->
|
||||
[]
|
||||
x :: _ ->
|
||||
if modBy 2 x == 0 then
|
||||
x // 2 :: values
|
||||
else
|
||||
(3 * x + 1) :: values
|
||||
|
||||
myPredicate: List Int -> Bool
|
||||
myPredicate vals =
|
||||
case vals of
|
||||
[] ->
|
||||
False
|
||||
x :: _ ->
|
||||
x == 1
|
||||
|
||||
-- Tests
|
||||
|
||||
testCollatzEven: Bool
|
||||
testCollatzEven = repeatUntil myPredicate myCollatz [24] ==
|
||||
[1,2,4,8,16,5,10,3,6,12,24]
|
||||
|
||||
testCollatzOdd: Bool
|
||||
testCollatzOdd = repeatUntil myPredicate myCollatz [19] ==
|
||||
[1,2,4,8,16,5,10,20,40,13,26,52,17,34,11,22,44,88,29,58,19]
|
||||
114
wk5/src/Modelling1.elm
Normal file
114
wk5/src/Modelling1.elm
Normal file
@@ -0,0 +1,114 @@
|
||||
module Modelling1 exposing (..)
|
||||
|
||||
{-
|
||||
Modelling Math Functions (part 1)
|
||||
Dimitar Byalkov and Kaloyan Stoykov
|
||||
-}
|
||||
|
||||
type Function
|
||||
= Poly Function Int
|
||||
| Mult Function Function
|
||||
| Div Function Function
|
||||
| Plus Function Function
|
||||
| Minus Function Function
|
||||
| Const Int
|
||||
| X
|
||||
|
||||
print: Function -> String
|
||||
print f =
|
||||
case f of
|
||||
X ->
|
||||
"x"
|
||||
Const val ->
|
||||
String.fromInt val
|
||||
Poly func val ->
|
||||
"(" ++ print func ++ " ^ " ++ String.fromInt val ++ ")"
|
||||
Mult func1 func2 ->
|
||||
"(" ++ print func1 ++ " * " ++ print func2 ++ ")"
|
||||
Div func1 func2 ->
|
||||
"(" ++ print func1 ++ " / " ++ print func2 ++ ")"
|
||||
Plus func1 func2 ->
|
||||
"(" ++ print func1 ++ " + " ++ print func2 ++ ")"
|
||||
Minus func1 func2 ->
|
||||
"(" ++ print func1 ++ " - " ++ print func2 ++ ")"
|
||||
|
||||
eval: Float -> Function -> Float
|
||||
eval num f =
|
||||
case f of
|
||||
X ->
|
||||
num
|
||||
Const val ->
|
||||
toFloat val
|
||||
Poly func val ->
|
||||
eval num func ^ (toFloat val)
|
||||
Mult func1 func2 ->
|
||||
eval num func1 * eval num func2
|
||||
Div func1 func2 ->
|
||||
eval num func1 / eval num func2
|
||||
Plus func1 func2 ->
|
||||
eval num func1 + eval num func2
|
||||
Minus func1 func2 ->
|
||||
eval num func1 - eval num func2
|
||||
|
||||
-- Graph line drawing function
|
||||
graphLine: Function -> Int -> Int -> Int -> String
|
||||
graphLine func x ymin ymax =
|
||||
let
|
||||
-- value of f(x)
|
||||
funcValue = round (eval (toFloat x) func)
|
||||
-- number of points on the line
|
||||
ySpan = abs ymin + abs ymax
|
||||
in
|
||||
-- Check if the value of f(x) is in the specified range
|
||||
if (funcValue > ymin) && (funcValue < ymax) then
|
||||
stringFill (funcValue - ymin) "*" ++ stringFill (ySpan - (funcValue - ymin)) "-"
|
||||
else if (funcValue > ymin) then
|
||||
stringFill ySpan "*"
|
||||
else
|
||||
stringFill ySpan "-"
|
||||
|
||||
-- Recursive function to create a string of specified characters with a given length
|
||||
stringFill: Int -> String -> String
|
||||
stringFill n sym =
|
||||
if (n <= 0) then
|
||||
""
|
||||
else
|
||||
sym ++ stringFill (n - 1) sym
|
||||
|
||||
-- xmin < xmax; ymin < ymax
|
||||
graph: Function -> Int -> Int -> Int -> Int -> String
|
||||
graph func xmin xmax ymin ymax =
|
||||
-- Check if range is not possible
|
||||
if xmin > xmax || ymin > ymax then
|
||||
"Error: Range is negative"
|
||||
else if xmin == xmax then
|
||||
graphLine func xmin ymin ymax
|
||||
else
|
||||
graphLine func xmin ymin ymax ++ "\n" ++ graph func (xmin + 1) xmax ymin ymax
|
||||
|
||||
testPrint: Bool
|
||||
testPrint = print (Plus (Mult (Plus (Const 3) X) (Minus X (Poly X 5))) (Const 2)) == "(((3 + x) * (x - (x ^ 5))) + 2)"
|
||||
|
||||
testEval: Bool
|
||||
testEval = eval 2 (Plus (Mult (Plus (Const 3) X) (Minus X (Poly X 5))) (Const 2)) == -148
|
||||
|
||||
testGraph1: Bool
|
||||
testGraph1 = graph (Plus (Minus (Poly (Minus (Div X (Const 5)) (Const 1)) 4) (Poly (Plus (Div X (Const -2)) (Const 2)) 2)) (Const 6)) -10 20 -10 10 ==
|
||||
"********************\n********************\n********************\n*******************-\n**************------\n************--------\n**********----------\n**********----------\n***********---------\n************--------\n*************-------\n**************------\n***************-----\n****************----\n****************----\n****************----\n***************-----\n**************------\n************--------\n**********----------\n********------------\n******--------------\n****----------------\n**------------------\n*-------------------\n**------------------\n***-----------------\n*******-------------\n*************-------\n********************\n********************"
|
||||
|
||||
-- for reference 3x2-graph.png
|
||||
testGraph2: Bool
|
||||
testGraph2 = graph (Mult (Const 3) (Poly X 2)) -5 5 -1 10 == "***********\n***********\n***********\n***********\n****-------\n*----------\n****-------\n***********\n***********\n***********\n***********"
|
||||
|
||||
testEmptyParams: Bool
|
||||
testEmptyParams = graph (Mult (Const 3) (Poly X 2)) 0 0 0 0 == ""
|
||||
|
||||
testSingleLine: Bool
|
||||
testSingleLine = graph (Mult (Const 3) (Poly X 2)) 1 1 -1 10 == "****-------"
|
||||
|
||||
|
||||
testInvalidArgs: Bool
|
||||
testInvalidArgs = graph X 2 1 2 1 == "Error: Range is negative"
|
||||
|
||||
testAllGraphs : List Bool
|
||||
testAllGraphs = [testGraph1, testGraph2, testEmptyParams, testSingleLine, testInvalidArgs]
|
||||
93
wk5/src/Modelling2.elm
Normal file
93
wk5/src/Modelling2.elm
Normal file
@@ -0,0 +1,93 @@
|
||||
module Modelling2 exposing (..)
|
||||
import Modelling1 exposing (..)
|
||||
import HighOrder exposing (..)
|
||||
|
||||
{-
|
||||
Modelling Math Functions (part 2)
|
||||
Dimitar Byalkov and Kaloyan Stoykov
|
||||
-}
|
||||
|
||||
f: Function
|
||||
f = Plus (Mult (Plus (Const 3) X) (Minus X (Poly X 5))) (Const 2)
|
||||
|
||||
derivative: Function -> Function
|
||||
derivative func =
|
||||
case func of
|
||||
-- constant
|
||||
Const _ ->
|
||||
Const 0
|
||||
-- X
|
||||
X ->
|
||||
Const 1
|
||||
-- sum
|
||||
Plus left right ->
|
||||
Plus (derivative left) (derivative right)
|
||||
-- difference
|
||||
Minus left right ->
|
||||
Minus (derivative left) (derivative right)
|
||||
-- product
|
||||
Mult left right ->
|
||||
Plus (Mult (derivative left) right) (Mult left (derivative right))
|
||||
-- quotient
|
||||
Div left right ->
|
||||
Div (Minus (Mult (derivative left) right) (Mult left (derivative right)))
|
||||
(Poly right 2)
|
||||
-- power
|
||||
Poly X right ->
|
||||
Mult (Const right) (Poly X (right - 1))
|
||||
Poly left right ->
|
||||
Poly (derivative left) right
|
||||
|
||||
simplify: Function -> Function
|
||||
simplify func =
|
||||
-- tries to simplify until no further simplification is possible
|
||||
repeatUntil (\x -> x == simplifyHelp x) simplifyHelp func
|
||||
|
||||
simplifyHelp: Function -> Function
|
||||
simplifyHelp func =
|
||||
case func of
|
||||
-- arithmetics
|
||||
Mult (Const left) (Const right) ->
|
||||
Const (left * right)
|
||||
Div (Const left) (Const right) ->
|
||||
Const (left // right)
|
||||
Plus (Const left) (Const right) ->
|
||||
Const (left + right)
|
||||
Minus (Const left) (Const right) ->
|
||||
Const (left - right)
|
||||
-- nested addition and subtraction
|
||||
Poly left 1 ->
|
||||
left
|
||||
Poly _ 0 ->
|
||||
(Const 1)
|
||||
Poly (Const left) right ->
|
||||
Const (left ^ right)
|
||||
Poly left right ->
|
||||
Poly left right
|
||||
Mult (Const 1) right ->
|
||||
right
|
||||
Mult left (Const 1) ->
|
||||
left
|
||||
Mult _ (Const 0) ->
|
||||
(Const 0)
|
||||
Div (Const 0) _ ->
|
||||
(Const 0)
|
||||
Div left (Const 1) ->
|
||||
left
|
||||
Plus left (Const 0) ->
|
||||
left
|
||||
Plus (Const 0) right ->
|
||||
right
|
||||
Minus left (Const 0) ->
|
||||
left
|
||||
-- recursive simplification
|
||||
Mult left right ->
|
||||
Mult (simplify left) (simplify right)
|
||||
Div left right ->
|
||||
Div (simplify left) (simplify right)
|
||||
Plus left right ->
|
||||
Plus (simplify left) (simplify right)
|
||||
Minus left right ->
|
||||
Minus (simplify left) (simplify right)
|
||||
_ ->
|
||||
func
|
||||
Reference in New Issue
Block a user