wk5: Higher order functions, Modelling (pt.2)

2024-03-22 22:24:09 +01:00
parent 8eb9c65aa6
commit 303d110b90
4 changed files with 296 additions and 0 deletions
--- a/wk5/src/Modelling2.elm
+++ b/wk5/src/Modelling2.elm
@@ -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