def continued

stelliferous@0.0.2.0 · proofs/traversal_batch_refinement.bend:74

import Base
import stelliferous@0.0.2.0/proofs/traversal_map_readback.bend as MapReadback
import stelliferous@0.0.2.0/proofs/storage_tree_model.bend as Tree
import stelliferous@0.0.2.0/proofs/storage_shape.bend as Shape
import stelliferous@0.0.2.0/proofs/nat_to_u32_bounds.bend as Bounds
import stelliferous@0.0.2.0/proofs/nat_order.bend as Order
import stelliferous@0.0.2.0/proofs/natural_addition.bend as Addition
import stelliferous@0.0.2.0/proofs/nat_interval.bend as Interval

74# A batch that continues done steps of the map completes the map.
75def continued(~Element: Data,~Context: Data,~map: Context -> U32 -> Element -> Element,+remaining: Nat,+done: Nat,+start: Nat,+context: Context,+input: Tree.Tree<Element>,
76  +depth: Nat,+capacity: U32,+capacity_equal: {Tree.capacity(Element,input) == capacity : U32},+balanced: Shape.Balanced(Element,depth,input),
77  +limit: {Nat.is_le(depth,31n) == True{} : Bool},+capacity_ok: {U32.is_le(capacity,2147483648) == True{} : Bool},
78  +room: {Nat.is_le(Nat.add(Nat.add(start,done),remaining),U32.to_nat(capacity)) == True{} : Bool}) ->
79  {batch(~Element,~Context,~map,remaining,U32.from_nat(Nat.add(start,done)),context,input,MapReadback.run_indexed(~Element,~Context,~map,done,U32.from_nat(start),context,input)) ==
80    MapReadback.run_indexed(~Element,~Context,~map,Nat.add(done,remaining),U32.from_nat(start),context,input) : Tree.Tree<Element>}:
81  match remaining:
82    case 0n:
83      %Equal.sym(Nat,Nat.add(done,0n),done,Addition.zero_right(done)) :
84        {MapReadback.run_indexed(~Element,~Context,~map,done,U32.from_nat(start),context,input) == MapReadback.run_indexed(~Element,~Context,~map,_,U32.from_nat(start),context,input) : Tree.Tree<Element>}
85      {==}
86    case 1n+ +rest:
87      +reached = Nat.add(start,done)
88      +query = U32.from_nat(reached)
89      +mapped = MapReadback.run_indexed(~Element,~Context,~map,done,U32.from_nat(start),context,input)
90      +inside = Order.room_index(reached,rest,U32.to_nat(capacity),room)
91      +within = Bounds.strict_le(reached,U32.to_nat(capacity),inside)
92      +unread = MapReadback.outside_indexed(~Element,~Context,~map,done,start,query,context,input,depth,capacity,capacity_equal,balanced,limit,capacity_ok,within,
93        MapReadback.address_inside(reached,capacity,capacity_ok,inside),
94        Interval.After{
95          %Equal.sym(Nat,U32.to_nat(query),reached,Bounds.roundtrip(reached,capacity,capacity_ok,within)) : {Nat.is_le(reached,_) == True{} : Bool}
96          Order.reflexive(reached)})
97      %Equal.sym(Nat,Nat.add(done,1n+rest),1n+Nat.add(done,rest),Addition.successor_right(done,rest)) :
98        {batch(~Element,~Context,~map,rest,(query + 1 : U32),context,input,Tree.write(Element,mapped,query,map(context,query,Tree.read(Element,input,query)))) ==
99          MapReadback.run_indexed(~Element,~Context,~map,_,U32.from_nat(start),context,input) : Tree.Tree<Element>}
100      %unread :
101        {batch(~Element,~Context,~map,rest,(query + 1 : U32),context,input,Tree.write(Element,mapped,query,map(context,query,_))) ==
102          MapReadback.run_indexed(~Element,~Context,~map,1n+Nat.add(done,rest),U32.from_nat(start),context,input) : Tree.Tree<Element>}
103      %extended(~Element,~Context,~map,done,start,context,input) :
104        {batch(~Element,~Context,~map,rest,(query + 1 : U32),context,input,_) ==
105          MapReadback.run_indexed(~Element,~Context,~map,1n+Nat.add(done,rest),U32.from_nat(start),context,input) : Tree.Tree<Element>}
106      %Equal.sym(U32,(query + 1 : U32),U32.from_nat(1n+reached),Bounds.add_one(query)) :
107        {batch(~Element,~Context,~map,rest,_,context,input,MapReadback.run_indexed(~Element,~Context,~map,1n+done,U32.from_nat(start),context,input)) ==
108          MapReadback.run_indexed(~Element,~Context,~map,1n+Nat.add(done,rest),U32.from_nat(start),context,input) : Tree.Tree<Element>}
109      %Addition.successor_right(start,done) :
110        {batch(~Element,~Context,~map,rest,U32.from_nat(_),context,input,MapReadback.run_indexed(~Element,~Context,~map,1n+done,U32.from_nat(start),context,input)) ==
111          MapReadback.run_indexed(~Element,~Context,~map,1n+Nat.add(done,rest),U32.from_nat(start),context,input) : Tree.Tree<Element>}
112      continued(~Element,~Context,~map,rest,1n+done,start,context,input,depth,capacity,capacity_equal,balanced,limit,capacity_ok,
113        %Equal.sym(Nat,Nat.add(start,1n+done),1n+reached,Addition.successor_right(start,done)) : {Nat.is_le(Nat.add(_,rest),U32.to_nat(capacity)) == True{} : Bool}
114        Order.advance_room(reached,rest,U32.to_nat(capacity),room))