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# MIT License, Copyright (c) 2022 Marvin Borner
# Lists in Church/Boehm-Berarducci encoding using pairs
:import std/Combinator .
:import std/Pair P
:import std/Logic .
:import std/Number .
# empty list element
empty false
# returns whether a list is empty
empty? [0 [[[false]]] true]
<>?( empty?
:test (<>?empty) (true)
:test (<>?(cons (+2) empty)) (false)
# prepends an element to a list
cons P.pair
(:) cons
:test ((+1) : ((+2) : empty)) (P.pair (+1) (P.pair (+2) empty))
:test ('a' : ('b' : ('c' : empty))) ("abc")
# returns the head of a list or empty
head P.fst
^( head
:test (^((+1) : ((+2) : empty))) ((+1))
# returns the tail of a list or empty
tail P.snd
~( tail
:test (~((+1) : ((+2) : empty))) ((+2) : empty)
# returns the length of a list in balanced ternary
length Z [[[case-some]]] case-empty
case-some <>?0 case-end case-inc
case-inc 2 ++1 ~0
case-end 1
case-empty (+0)
#( length
:test (#((+1) : ((+2) : empty))) ((+2))
:test (#empty) ((+0))
# returns the element at index in list
index Z [[[case-some]]]
case-some <>?0 case-end case-index
case-index =?1 ^0 (2 --1 ~0)
case-end empty
(!!) C index
:test (((+1) : ((+2) : ((+3) : empty))) !! (+0)) ((+1))
:test (((+1) : ((+2) : ((+3) : empty))) !! (+2)) ((+3))
:test (((+1) : ((+2) : ((+3) : empty))) !! (-1)) (empty)
:test (((+1) : ((+2) : ((+3) : empty))) !! (+3)) (empty)
# reverses a list
reverse Z [[[case-some]]] case-empty
case-some <>?0 case-end case-rev
case-rev 2 (^0 : 1) ~0
case-end 1
case-empty empty
<~>( reverse
:test (<~>((+1) : ((+2) : ((+3) : empty)))) ((+3) : ((+2) : ((+1) : empty)))
# creates list out of n terms
# TODO: fix for balanced ternary
list [0 [[[2 (0 : 1)]]] reverse empty]
# appends two lists
append Z [[[case-some]]]
case-some <>?1 case-end case-merge
case-merge ^1 : (2 ~1 0)
case-end 0
(++) append
:test (((+1) : ((+2) : ((+3) : empty))) ++ ((+4) : empty)) ((+1) : ((+2) : ((+3) : ((+4) : empty))))
# appends an element to a list
snoc [[1 ++ (0 : empty)]]
(;) snoc
:test (empty ; (+1)) ((+1) : empty)
:test (((+1) : empty) ; (+2)) ((+1) : ((+2) : empty))
# maps each element to a function
map Z [[[case-some]]]
case-some <>?0 case-end case-map
case-map (1 ^0) : (2 1 ~0)
case-end empty
(<$>) map
:test (inc <$> ((+1) : ((+2) : ((+3) : empty)))) ((+2) : ((+3) : ((+4) : empty)))
# applies a left fold on a list
foldl Z [[[[case-some]]]]
case-some <>?0 case-end case-fold
case-fold 3 2 (2 1 ^0) ~0
case-end 1
:test ((foldl add (+0) ((+1) : ((+2) : ((+3) : empty)))) =? (+6)) (true)
:test ((foldl sub (+6) ((+1) : ((+2) : ((+3) : empty)))) =? (+0)) (true)
# applies a right fold on a list
foldr [[[Z [[case-some]] case-empty]]]
case-some <>?0 case-end case-fold
case-fold 4 ^0 (1 ~0)
case-end 3
case-empty 0
:test ((foldr add (+0) ((+1) : ((+2) : ((+3) : empty)))) =? (+6)) (true)
:test ((foldr sub (+2) ((+1) : ((+2) : ((+3) : empty)))) =? (+0)) (true)
# filters a list based on a predicate
filter Z [[[case-some]]]
case-some <>?0 case-end case-filter
case-filter 1 ^0 (cons ^0) I (2 1 ~0)
case-end empty
(<#>) C filter
:test (((+1) : ((+0) : ((+3) : empty))) <#> zero?) ((+0) : empty)
# returns the last element of a list
last Z [[case-some]]
case-some <>?0 case-end case-last
case-last <>?(~0) ^0 (1 ~0)
case-end empty
_( last
:test (last ((+1) : ((+2) : ((+3) : empty)))) ((+3))
# returns everything but the last element of a list
init Z [[case-some]]
case-some <>?0 case-end case-init
case-init <>?(~0) empty (^0 : (1 ~0))
case-end empty
:test (init ((+1) : ((+2) : ((+3) : empty)))) ((+1) : ((+2) : empty))
# zips two lists discarding excess elements
zip Z [[[case-some]]]
case-some <>?1 case-end case-zip
case-zip <>?0 empty ((^1 : ^0) : (2 ~1 ~0))
case-end empty
:test (zip ((+1) : ((+2) : empty)) ((+2) : ((+1) : empty))) (((+1) : (+2)) : (((+2) : (+1)) : empty))
# applies pairs of the zipped list as arguments to a function
zip-with Z [[[[case-some]]]]
case-some <>?1 case-end case-zip
case-zip <>?0 empty ((2 ^1 ^0) : (3 2 ~1 ~0))
case-end empty
:test (zip-with add ((+1) : ((+2) : empty)) ((+2) : ((+1) : empty))) ((+3) : ((+3) : empty))
# returns first n elements of a list
take Z [[[case-some]]]
case-some <>?0 case-end case-take
case-take =?1 empty (^0 : (2 --1 ~0))
case-end empty
:test (take (+2) ((+1) : ((+2) : ((+3) : empty)))) ((+1) : ((+2) : empty))
# takes elements while a predicate is satisfied
take-while Z [[[case-some]]]
case-some <>?0 case-end case-take
case-take 1 ^0 (^0 : (2 1 ~0)) empty
case-end empty
:test (take-while zero? ((+0) : ((+0) : ((+1) : empty)))) ((+0) : ((+0) : empty))
# removes first n elements of a list
drop Z [[[case-some]]]
case-some <>?0 case-end case-drop
case-drop =?1 0 (2 --1 ~0)
case-end empty
:test (drop (+2) ((+1) : ((+2) : ((+3) : empty)))) ((+3) : empty)
# removes elements while a predicate is satisfied
drop-while Z [[[case-some]]]
case-some <>?0 case-end case-drop
case-drop 1 ^0 (2 1 ~0) 0
case-end empty
:test (drop-while zero? ((+0) : ((+0) : ((+1) : empty)))) ((+1) : empty)
# removes duplicates from list based on eq predicate (keeps only first occurrence)
nub Z [[[case-some]]]
case-some <>?0 case-end case-nub
case-nub ^0 : (2 1 (~0 <#> [!(2 0 ^1)]))
case-end empty
:test (nub eq? ((+1) : ((+2) : ((+3) : empty)))) (((+1) : ((+2) : ((+3) : empty))))
:test (nub eq? ((+1) : ((+2) : ((+1) : empty)))) (((+1) : ((+2) : empty)))
# returns a list with n-times a element
repeat Z [[[case-some]]]
case-some =?1 case-end case-repeat
case-repeat 0 : (2 --1 0)
case-end empty
:test (repeat (+5) (+4)) (((+4) : ((+4) : ((+4) : ((+4) : ((+4) : empty))))))
:test (repeat (+1) (+4)) (((+4) : empty))
:test (repeat (+0) (+4)) (empty)
# returns a list with infinite-times previous (or start) value applied to a function
iterate Z [[[case-some]]]
case-some case-iterate
case-iterate 0 : (2 1 (1 0))
:test (take (+5) (iterate inc (+0))) (((+0) : ((+1) : ((+2) : ((+3) : ((+4) : empty))))))
:test (take (+2) (iterate dec (+5))) (((+5) : ((+4) : empty)))
:test (take (+5) (iterate I (+4))) (repeat (+5) (+4))
:test (take (+0) (iterate inc (+0))) (empty)
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