namespace Homework$3$

open System.Reflection.Metadata

open System.Runtime.Intrinsics.Arm

module HW$3=$

type SET $=$

$|$ I of int list $//$ I $[1$;$2$;$3]$

$|$ S of string list $//$ S $["$a$"$;$"$b$"$;$"$c$"]$

$|$ IS of $($int $*$ string$)$ list $//$ IS $[(1,"$a$")$;$(2,"$b$")]$

$|$ II of $($int $*$ int$)$ list $//$ II $[(1,2)$; $(3,4)$; $(5,6)]$

$|$ SS of $($string $*$ string$)$ list $//$ SS $[("$a$","$b$")$; $("$c$","$d$")]$

$|$ SI of $($string $*$ int$)$ list $//$ SI $[("$a$",1)$; $("$b$",2)$; $("$c$",3)]$

$|$ SISI of $(($string $*$ int$)*($string $*$ int$))$ list $//$ SISI $[(("$a$",1),("$b$",2))$; $(("$c$",3),"$d$",4))]$

$|$ SIIS of $(($string $*$ int$)*($int $*$ string$))$ list $//$ SIIS $[(("$a$",1),(2,"$b$"))$; $(("$c$",3),(4,"$d$"))]$

$//$ complete this function

let pairs L$1$ L$2=$

$[]$

$//$ complete this function

let dist a L $=[]$

$//$ cartesian product

let product s$1$ s$2=$

match $($s$1,$ s$2)$ with

$|($I s$1,$ I s$2)->$ II $($pairs s$1$ s$2)//$ you need to write pairs

$|($S s$1,$ S s$2)->$ SS $($pairs s$1$ s$2)$

$|($I s$1,$ S s$2)->$ IS $($pairs s$1$ s$2)$

$//$ you need to complete these cases

$//$ The following four methods are incorrect and must be replaced!

let gtSx x y $=$ true

$//$ to do

let eqxIxx x y $=$ true

$//$ ot do

let selectSI x y $=$ I $[]$

$//$ to do

let selectSIIS x y $=$ I $[]$

$//$ to do

let rec isMember a L $=$

match L with

$|[]->$ false

$|$ h::t when a$=$h $->$ true

$|$ h::t $->$ isMember a t

let rec unionList l$1$ l$2=$

match l$1$ with

$|[]->$ l$2$

$|$ h::t when not $($isMember h l$2)->$ h::unionList t l$2$

$|$ h::t $->$ unionList t l$2$

let union s$1$ s$2=$

match $($s$1,$ s$2)$ with

$|($I l$1,$ I l$2)->$ I $($unionList l$1$ l$2)$

$|($IS l$1,$ IS l$2)->$ IS $($unionList l$1$ l$2)$

$|($SISI l$1,$ SISI l$2)->$ SISI $($unionList l$1$ l$2)$

$//$ you need to complete these cases

$//$ to do

let gtIx x $($a$,\_)=$ a $>$ x

let gtxxxI x $((\_,\_),(\_,$ a$))=$ a $>$ x

$//$ let gtSx $???=???$

$//$ to do

$//$ let eqIxx $???=???$

$//$ to do

let rec filter f L $=$

match L with

$|[]->[]$

$|$ h::t when f h $->$ h::filter f t

$|$ h::t $->$ filter f t

let selectIS s f $=$

match s with

$|$ IS i $->$ IS $($filter f i$)$

let selectSISI s f $=$

match s with

$|$ SISI i $->$ SISI $($filter f i$)$

let minus L$1$ L$2=[]$

$//$ to do

let difference s$1$ s$2=$

match $($s$1,$s$2)$ with

$|($I s$1,$ I s$2)->$ I $($minus s$1$ s$2)//$ write the minus function

$|($SI s$1,$ SI s$2)->$ SI $($minus s$1$ s$2)$

$|($SISI s$1,$ SISI s$2)->$ SISI $($minus s$1$ s$2)$

$//$ complete these cases