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WIP: co-de bruijn #12

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rhi wants to merge 12 commits from 🥚🛁 into 🐉
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lib/Quox/NatExtra.idr
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@ -9,6 +9,11 @@ import Syntax.PreorderReasoning
%default total %default total
infixl 8 `shiftL`, `shiftR`
infixl 7 .&.
infixl 6 `xor`
infixl 5 .|.
public export public export
data LTE' : Nat -> Nat -> Type where data LTE' : Nat -> Nat -> Type where
@ -119,3 +124,86 @@ spread mask subj = go 1 (halfRec mask) subj 0 where
go bit (HalfRecOdd _ rec) subj res = case half subj of go bit (HalfRecOdd _ rec) subj res = case half subj of
HalfOdd subj => go (bit + bit) rec subj (res + bit) HalfOdd subj => go (bit + bit) rec subj (res + bit)
HalfEven subj => go (bit + bit) rec subj res HalfEven subj => go (bit + bit) rec subj res
public export
data BitwiseRec : Nat -> Nat -> Type where
BwDone : BitwiseRec 0 0
Bw00 : (m, n : Nat) -> Lazy (BitwiseRec m n) ->
BitwiseRec (m + m) (n + n)
Bw01 : (m, n : Nat) -> Lazy (BitwiseRec m n) ->
BitwiseRec (m + m) (S (n + n))
Bw10 : (m, n : Nat) -> Lazy (BitwiseRec m n) ->
BitwiseRec (S (m + m)) (n + n)
Bw11 : (m, n : Nat) -> Lazy (BitwiseRec m n) ->
BitwiseRec (S (m + m)) (S (n + n))
export
bitwiseRec : (m, n : Nat) -> BitwiseRec m n
bitwiseRec m n = go (halfRec m) (halfRec n) where
go : forall m, n. HalfRec m -> HalfRec n -> BitwiseRec m n
go HalfRecZ HalfRecZ = BwDone
go HalfRecZ (HalfRecEven n nr) = Bw00 0 n $ go HalfRecZ nr
go HalfRecZ (HalfRecOdd n nr) = Bw01 0 n $ go HalfRecZ nr
go (HalfRecEven m mr) HalfRecZ = Bw00 m 0 $ go mr HalfRecZ
go (HalfRecEven m mr) (HalfRecEven n nr) = Bw00 m n $ go mr nr
go (HalfRecEven m mr) (HalfRecOdd n nr) = Bw01 m n $ go mr nr
go (HalfRecOdd m mr) HalfRecZ = Bw10 m 0 $ go mr HalfRecZ
go (HalfRecOdd m mr) (HalfRecEven n nr) = Bw10 m n $ go mr nr
go (HalfRecOdd m mr) (HalfRecOdd n nr) = Bw11 m n $ go mr nr
export
bitwise : (Bool -> Bool -> Bool) -> Nat -> Nat -> Nat
bitwise f m n = go 1 (bitwiseRec m n) 0 where
one : Bool -> Bool -> Nat -> Nat -> Nat
one p q bit res = if f p q then bit + res else res
go : forall m, n. Nat -> BitwiseRec m n -> Nat -> Nat
go bit BwDone res = res
go bit (Bw00 m n rec) res = go (bit + bit) rec $ one False False bit res
go bit (Bw01 m n rec) res = go (bit + bit) rec $ one False True bit res
go bit (Bw10 m n rec) res = go (bit + bit) rec $ one True False bit res
go bit (Bw11 m n rec) res = go (bit + bit) rec $ one True True bit res
export
(.&.) : Nat -> Nat -> Nat
(.&.) = bitwise $ \p, q => p && q
private %foreign "scheme:blodwen-and"
primAnd : Nat -> Nat -> Nat
%transform "NatExtra.(.&.)" NatExtra.(.&.) m n = primAnd m n
export
(.|.) : Nat -> Nat -> Nat
(.|.) = bitwise $ \p, q => p || q
private %foreign "scheme:blodwen-or"
primOr : Nat -> Nat -> Nat
%transform "NatExtra.(.|.)" NatExtra.(.|.) m n = primOr m n
export
xor : Nat -> Nat -> Nat
xor = bitwise (/=)
private %foreign "scheme:blodwen-xor"
primXor : Nat -> Nat -> Nat
%transform "NatExtra.xor" NatExtra.xor m n = primXor m n
export
shiftL : Nat -> Nat -> Nat
shiftL n 0 = n
shiftL n (S i) = shiftL (n + n) i
private %foreign "scheme:blodwen-shl"
primShiftL : Nat -> Nat -> Nat
%transform "NatExtra.shiftL" NatExtra.shiftL n i = primShiftL n i
export
shiftR : Nat -> Nat -> Nat
shiftR n 0 = n
shiftR n (S i) = shiftL (floorHalf n) i
private %foreign "scheme:blodwen-shr"
primShiftR : Nat -> Nat -> Nat
%transform "NatExtra.shiftR" NatExtra.shiftR n i = primShiftR n i