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# Shared affine storage operations. Shape descriptors do not own another buffer.import Baseimport ./traversal_array.bend as Traversalimport ./proofs/storage_certificate.bend as Certificatetype Buffer<-Element: Data> is Type:  Buffer{storage: Array<Element>,length: Nat,certificate: Certificate.Certificate<Element,storage>}# Construction records evidence once, without visiting the owner or carrying# certificates through the elementwise loop.def allocate(~Element: Data,+depth: Nat,+value: Element,length: Nat) -> Buffer<Element>:  Buffer{Array.new(Element,depth,value),length,Certificate.allocated(Element,depth,value)}def from_list(~Element: Data,+values: List<&2,Element>,+depth: Nat,+fallback: Element,length: Nat) -> Buffer<Element>:  Buffer{Traversal.write_list(~Element,values,0,Array.new(Element,depth,fallback)),length,    Certificate.write_list(~Element,values,0,Array.new(Element,depth,fallback),Certificate.allocated(Element,depth,fallback))}# The values written from the offset on; the certificate follows the storage.def write_at(~Element: Data,+values: List<&2,Element>,+offset: U32,buffer: Buffer<Element>) -> Buffer<Element>:  Buffer{storage,length,certificate} = buffer  Buffer{Traversal.write_list(~Element,values,offset,storage),length,Certificate.write_list(~Element,values,offset,storage,certificate)}def capacity(~Element: Data,-storage: Array<Element>,certificate: Certificate.Certificate<Element,storage>) -> U32:  Certificate.Certificate{depth,equation} = certificate  U32.shln(1,depth)def bind_pair(~First: Type,~Second: Type,~Result: Type,pair: First & Second,body: First -> Second -> Result) -> Result:  (first,second) = pair  body(first,second)# At most 32 word steps, independent of the allocation length.def bit_length(remaining_bits: Nat,+value: U32) -> Nat:  match remaining_bits:    case 0n: 0n    case 1n+rest:      Bool.pick(Nat,U32.is_zero(value),0n,1n+bit_length(rest,U32.shr(value)))# Positive requested lengths round to the next power-of-two capacity.# The caller establishes the machine allocation limit before calling Array.new.def allocation_depth(length: U32) -> Nat:  bit_length(32n,(length - 1 : U32))# Shared runtime depth calculation. The tail call stops at the significant# word bits; allocation_depth remains the arithmetic model used by proofs.def significant_bits(remaining: Nat,+value: U32,+bits: Nat,zero: Bool) -> Nat:  match remaining zero:    case 0n zero: bits    case 1n+rest True{}: bits    case 1n+rest False{}:      +next = U32.shr(value)      significant_bits(rest,next,1n+bits,U32.is_zero(next))def depth_for(+count: U32) -> Nat:  +value = (U32.max(count,1) - 1 : U32)  significant_bits(32n,value,0n,U32.is_zero(value))def write_list(~Element: Data,values: List<&2,Element>,+offset: U32,storage: Array<Element>) -> Array<Element>:  Traversal.write_list(~Element,values,offset,storage)def read_list(~Element: Data,count: Nat,+offset: U32,storage: Array<Element>) -> List<&2,Element>:  match count:    case 0n: []    case 1n+rest:      bind_pair(Array<Element>,Element,List<&2,Element>,Array.get(Element,storage,offset),storage => value =>        value <> read_list(Element,rest,(offset + 1 : U32),storage))def read_when(~Element: Data,fallback: Element,valid: Bool,storage: Array<Element>,index: U32) -> Array<Element> & Element:  match valid:    case False{}: (storage,fallback)    case True{}: Array.get(Element,storage,index)def read_sized(~Element: Data,fallback: Element,+index: U32,+logical_length: U32,sized: Array<Element> & U32) -> Array<Element> & Element:  (storage,capacity) = sized  read_when(Element,fallback,U32.is_lt(index,logical_length) && U32.is_le(logical_length,capacity),storage,index)def read_or(~Element: Data,fallback: Element,storage: Array<Element>,index: U32,logical_length: U32) -> Array<Element> & Element:  read_sized(Element,fallback,index,logical_length,Array.size(Element,storage))