def extended

stelliferous@0.0.2.0 · proofs/traversal_batch_refinement.bend:54

import Base
import stelliferous@0.0.2.0/traversal_array.bend as Traversal
import stelliferous@0.0.2.0/traversal_loop.bend as Loop
import stelliferous@0.0.2.0/proofs/traversal_array_refinement.bend as ArrayLaws
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

54# One more step of the model map writes the position after the ones it mapped.
55def extended(~Element: Data,~Context: Data,~map: Context -> U32 -> Element -> Element,+done: Nat,+start: Nat,+context: Context,+input: Tree.Tree<Element>) ->
56  {MapReadback.run_indexed(~Element,~Context,~map,1n+done,U32.from_nat(start),context,input) ==
57    Tree.write(Element,MapReadback.run_indexed(~Element,~Context,~map,done,U32.from_nat(start),context,input),U32.from_nat(Nat.add(start,done)),
58      map(context,U32.from_nat(Nat.add(start,done)),Tree.read(Element,MapReadback.run_indexed(~Element,~Context,~map,done,U32.from_nat(start),context,input),U32.from_nat(Nat.add(start,done))))) : Tree.Tree<Element>}:
59  +initial = {Traversal.State{Unit{},input,U32.from_nat(start),context} : ModelState(~Element,~Context)}
60  %Equal.sym(ModelState(~Element,~Context),Loop.run(~ModelState(~Element,~Context),~ArrayLaws.model_map_step(~Element,~Context,~map),1n+done,initial),
61    ArrayLaws.model_map_step(~Element,~Context,~map,Loop.run(~ModelState(~Element,~Context),~ArrayLaws.model_map_step(~Element,~Context,~map),done,initial)),
62    last_step(~ModelState(~Element,~Context),~ArrayLaws.model_map_step(~Element,~Context,~map),done,initial)) :
63    {MapReadback.output(~Element,~Context,_) ==
64      Tree.write(Element,MapReadback.run_indexed(~Element,~Context,~map,done,U32.from_nat(start),context,input),U32.from_nat(Nat.add(start,done)),
65        map(context,U32.from_nat(Nat.add(start,done)),Tree.read(Element,MapReadback.run_indexed(~Element,~Context,~map,done,U32.from_nat(start),context,input),U32.from_nat(Nat.add(start,done))))) : Tree.Tree<Element>}
66  %Equal.sym(ModelState(~Element,~Context),Loop.run(~ModelState(~Element,~Context),~ArrayLaws.model_map_step(~Element,~Context,~map),done,initial),
67    Traversal.State{Unit{},MapReadback.run_indexed(~Element,~Context,~map,done,U32.from_nat(start),context,input),U32.from_nat(Nat.add(start,done)),context},
68    state_after(~Element,~Context,~map,done,start,context,input)) :
69    {MapReadback.output(~Element,~Context,ArrayLaws.model_map_step(~Element,~Context,~map,_)) ==
70      Tree.write(Element,MapReadback.run_indexed(~Element,~Context,~map,done,U32.from_nat(start),context,input),U32.from_nat(Nat.add(start,done)),
71        map(context,U32.from_nat(Nat.add(start,done)),Tree.read(Element,MapReadback.run_indexed(~Element,~Context,~map,done,U32.from_nat(start),context,input),U32.from_nat(Nat.add(start,done))))) : Tree.Tree<Element>}
72  {==}