HigherOrderCO/Kind
1
1
Fork 0
mirror of https://github.com/HigherOrderCO/Kind.git synced 2024-07-14 22:30:30 +03:00
Code Issues Packages Projects Releases Wiki Activity

BBT updates

Browse Source
This commit is contained in:
Derenash 2024-02-20 17:08:37 -03:00
parent c6be73b582
commit 95e65c55a6
7 changed files with 93 additions and 20 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

10
book/BBT.balance.kind2
View File

@ -51,12 +51,12 @@ BBT.balance.lft_heavier
let P = λx ∀(new_size: #U60) ∀(key: K) ∀(val: V) ∀(lft.key: K) ∀(lft.val: V) ∀(lft.lft: (BBT K V)) ∀(lft.rgt: (BBT K V)) ∀(rgt: (BBT K V)) (BBT K V)
// key > lft.key
let true = λnew_size λkey λval λlft.key λlft.val λlft.lft λlft.rgt λrgt // Parent Lambdas
let true = λnew_size λkey λval λlft.key λlft.val λlft.lft λlft.rgt λrgt
let lft = (BBT.lft_rotate K V lft.size lft.key lft.val lft.lft lft.rgt)
(BBT.rgt_rotate K V new_size key val lft rgt)
// key < lft.key
let false = λnew_size λkey λval λlft.key λlft.val λlft.lft λlft.rgt λrgt // Parent Lambdas
let false = λnew_size λkey λval λlft.key λlft.val λlft.lft λlft.rgt λrgt
let lft = (BBT.bin K V lft.size lft.key lft.val lft.lft lft.rgt)
(BBT.rgt_rotate K V new_size key val lft rgt)
@ -78,21 +78,21 @@ BBT.balance_rgt_heavier
∀(lft: (BBT K V))
∀(rgt: (BBT K V))
(BBT K V)
= λK λV λcmp λnew_size λnode_key λset_key λval λlft λrgt // Parent Lambdas
= λK λV λcmp λnew_size λnode_key λset_key λval λlft λrgt
let P = λx(BBT K V)
let bin = λrgt.size λrgt.key λrgt.val λrgt.lft λrgt.rgt
let P = λx ∀(new_size: #U60) ∀(key: K) ∀(val: V) ∀(lft: (BBT K V)) ∀(rgt.key: K) ∀(rgt.val: V) ∀(rgt.lft: (BBT K V)) ∀(rgt.rgt: (BBT K V)) (BBT K V)
// key > rgt.key
// rotating parent once to the left
let true = λnew_size λkey λval λlft λrgt.key λrgt.val λrgt.lft λrgt.rgt // Parent Lambdas
let true = λnew_size λkey λval λlft λrgt.key λrgt.val λrgt.lft λrgt.rgt
let rgt = (BBT.bin K V rgt.size rgt.key rgt.val rgt.lft rgt.rgt)
(BBT.lft_rotate K V new_size key val lft rgt)
// key < rgt.key
// rotating parent once to the left
// rotating right child once to the right
let false = λnew_size λkey λval λlft λrgt.key λrgt.val λrgt.lft λrgt.rgt // Parent Lambdas
let false = λnew_size λkey λval λlft λrgt.key λrgt.val λrgt.lft λrgt.rgt
let rgt = (BBT.rgt_rotate K V rgt.size rgt.key rgt.val rgt.lft rgt.rgt)
(BBT.lft_rotate K V new_size key val lft rgt)
((~(Cmp.is_gtn (cmp set_key rgt.key)) P true false) new_size node_key val lft rgt.key rgt.val rgt.lft rgt.rgt)

10
book/BBT.get.kind2
View File

@ -8,10 +8,10 @@ BBT.get
= λK λV λcmp λkey λmap
let P = λx(Maybe V)
let bin = λ_size λnext.key λnext.val λnext.lft λnext.rgt
let P = λx(Maybe V)
let ltn = (BBT.get K V cmp key next.lft)
let eql = (Maybe.some V next.val)
let gtn = (BBT.get K V cmp key next.rgt)
(~(cmp key next.key) P ltn eql gtn)
let P = λx ∀(cmp: ∀(a: K) ∀(b: K) Cmp) ∀(key: K) (Maybe V)
let ltn = λcmp λkey (BBT.get K V cmp key next.lft)
let eql = λcmp λkey (Maybe.some V next.val)
let gtn = λcmp λkey (BBT.get K V cmp key next.rgt)
((~(cmp key next.key) P ltn eql gtn) cmp key)
let tip = (Maybe.none V)
(~map P bin tip)

31
book/BBT.got.kind2 Normal file
View File

@ -0,0 +1,31 @@
BBT.got
: ∀(K: *)
∀(V: *)
∀(cmp: ∀(a: K) ∀(b: K) Cmp)
∀(key: K)
∀(map: (BBT K V))
(Pair (Maybe V) (BBT K V))
= λK λV λcmp λkey λmap
let P = λx(Pair (Maybe V) (BBT K V))
let bin = λsize λnext.key λnext.val λnext.lft λnext.rgt
let P = λx ∀(cmp: ∀(a: K) ∀(b: K) Cmp) ∀(key: K) (Pair (Maybe V) (BBT K V))
let ltn = λcmp λkey
let new_pair = (BBT.got K V cmp key next.lft)
let P = λx(Pair (Maybe V) (BBT K V))
let new = λval λlft
let map = (BBT.bin K V size next.key next.val lft next.rgt)
(Pair.new (Maybe V) (BBT K V) val map)
(~new_pair P new)
let eql = λcmp λkey
let map = (BBT.bin K V size next.key next.val next.lft next.rgt)
(Pair.new (Maybe V) (BBT K V) (Maybe.some V next.val) map)
let gtn = λcmp λkey
let new_pair = (BBT.got K V cmp key next.rgt)
let P = λx(Pair (Maybe V) (BBT K V))
let new = λval λrgt
let map = (BBT.bin K V size next.key next.val next.lft rgt)
(Pair.new (Maybe V) (BBT K V) val map)
(~new_pair P new)
((~(cmp key next.key) P ltn eql gtn) cmp key)
let tip = (Pair.new (Maybe V) (BBT K V) (Maybe.none V) (BBT.tip K V))
(~map P bin tip)

4
book/BBT.lft_rotate.kind2
View File

@ -13,11 +13,11 @@ BBT.lft_rotate
= λK λV λsize λkey λval λlft λrgt
let P = λx ∀(key: K) ∀(val: V) ∀(lft: (BBT K V)) (BBT K V)
let bin = λ_size λrgt.key λrgt.val λrgt.lft λrgt.rgt
λkey λval λlft // Parent lambdas
λkey λval λlft
let b = (BBT.new_node K V key val lft rgt.lft)
let a = (BBT.new_node K V rgt.key rgt.val b rgt.rgt)
a
let tip =
λkey λval λlft // Parent lambdas
λkey λval λlft
(BBT.bin K V size key val lft (BBT.tip K V))
((~rgt P bin tip) key val lft)

4
book/BBT.rgt_rotate.kind2
View File

@ -13,11 +13,11 @@ BBT.rgt_rotate
= λK λV λsize λkey λval λlft λrgt
let P = λx ∀(key: K) ∀(val: V) ∀(rgt: (BBT K V)) (BBT K V)
let bin = λ_size λlft.key λlft.val λlft.lft λlft.rgt
λkey λval λrgt // Parent lambdas
λkey λval λrgt
let b = (BBT.new_node K V key val lft.rgt rgt)
let a = (BBT.new_node K V lft.key lft.val lft.lft b )
a
let tip =
λkey λval λrgt // Parent lambdas
λkey λval λrgt
(BBT.bin K V size key val (BBT.tip K V) rgt)
((~lft P bin tip) key val rgt)

11
book/BBT.set.kind2
View File

@ -8,21 +8,26 @@ BBT.set
(BBT K V)
= λK λV λcmp λkey λval λmap
let P = λx ∀(key: K) ∀(val: V) (BBT K V)
let bin = λsize λnext.key λnext.val λnext.lft λnext.rgt
λkey λval // Parent Lambdas
let bin = λsize λnext.key λnext.val λnext.lft λnext.rgt λkey λval
let P = λx ∀(key: K) ∀(next.key: K) ∀(next.val: V) ∀(next.lft: (BBT K V)) ∀(next.rgt: (BBT K V)) (BBT K V)
// Go left
let ltn = λkey λnext.key λnext.val λnext.lft λnext.rgt
let new_lft = (BBT.set K V cmp key val next.lft)
(BBT.balance K V cmp key next.key next.val new_lft next.rgt)
// Same key, update value
let eql = λkey λnext.key λnext.val λnext.lft λnext.rgt
(BBT.bin K V size next.key val next.lft next.rgt)
// Go right
let gtn = λkey λnext.key λnext.val λnext.lft λnext.rgt
let new_rgt = (BBT.set K V cmp key val next.rgt)
(BBT.balance K V cmp key next.key next.val next.lft new_rgt)
((~(cmp key next.key) P ltn eql gtn) key next.key next.val next.lft next.rgt)
let tip = λkey λval // Parent Lambdas
// Empty tree, create new node
let tip = λkey λval
(BBT.singleton K V key val)
((~map P bin tip) key val)

43
book/testbbt.kind2
View File

@ -50,6 +50,14 @@ U60.get
= λV λkey λmap
(BBT.get #U60 V U60.cmp key map)
U60.got
: ∀(V: *)
∀(key: #U60)
∀(map: (BBT #U60 V))
(Pair (Maybe V) (BBT #U60 V))
= λV λkey λmap
(BBT.got #U60 V U60.cmp key map)
U60.set
: ∀(V: *)
∀(key: #U60)
@ -219,6 +227,7 @@ testbbt
// : (List.Map #U60 String)
// : (BBT #U60 String)
: (#U60)
// : (Maybe #U60)
=
// let map = (BBT.tip #U60 String)
// let map = ~λP λbin λtip (tip)
@ -237,7 +246,6 @@ testbbt
// val
// map
// let map = (U60.map_gen #1024)
// let ext = λx (~x λx(#U60) λsome(#2) #0)
// let val1 = (U60.get String #5 map)
// let val2 = (U60.get String #10 map)
// #(+ val1 val2)
@ -273,8 +281,37 @@ testbbt
let map = (U60.set #U60 #8 #8 map) // 23469 +4320 5set 4bal 1rot_lft
let map = (U60.set #U60 #9 #9 map) // 27789 +4484 5set 4bal 1rot_lft
let map = (U60.set #U60 #10 #10 map) // 32281 +4492 5set 4bal 1rot_lft
let sum = (U60.add_all map)
sum
let P = λx(#U60)
let new = λval1 λmap
let val1 =
let P = λx(#U60)
let some = λval (val)
let none = #0
(~val1 P some none)
let P = λx(#U60)
let new = λval2 λmap
let val2 =
let P = λx(#U60)
let some = λval (val)
let none = #0
(~val2 P some none)
#(+ val1 val2)
(~(U60.got #U60 #3 map) P new)
(~(U60.got #U60 #3 map) P new)
// #(+ val1 val2)
// #3
// #(+ (ext val1) (ext val1))
// let mymap = λ_ λx0 λ_ (x0 #4 #3 #3 λ_ λx1 λ_ (x1 #2 #1 #1 λ_ λx2 λ_ (x2 #1 #0 #0 λ_ λ_ λx3 x3 λ_ λ_ λx4 x4) λ_ λx5 λ_ (x5 #1 #2 #2 λ_ λ_ λx6 x6 λ_ λ_ λx7 x7)) λ_ λx8 λ_ (x8 #3 #7 #7 λ_ λx9 λ_ (x9 #2 #5 #5 λ_ λx10 λ_ (x10 #1 #4 #4 λ_ λ_ λx11 x11 λ_ λ_ λx12 x12) λ_ λx13 λ_ (x13 #1 #6 #6 λ_ λ_ λx14 x14 λ_ λ_ λx15 x15)) λ_ λx16 λ_ (x16 #2 #9 #9 λ_ λx17 λ_ (x17 #1 #8 #8 λ_ λ_ λx18 x18 λ_ λ_ λx19 x19) λ_ λx20 λ_ (x20 #1 #10 #10 λ_ λ_ λx21 (x21 λ_ λ_ λx22 x22)))))
// mymap
// let sum = (U60.add_all map)
// sum
// let map = (U60.map_gen_u60 #1023)
// let map = (U60.set #U60 #3 #3 map)
// let sum = (U60.add_all map)