proofs/containers/queue/state.bend source

proofs/containers/queue/state.bend on the hub · documented module

import Baseimport ../../../spec/lib/common.bend as SCimport ../../../src/containers/queue.bend as Q# The two-list queue QU{front, back, count} as a Data shadow: the two lists,# with the count their total length.#   model(sh) = front ++ reverse(back)   the elements, oldest firsttype Shadow<-T: Data> is Data:  Sh{front: List<&2, T>, back: List<&2, T>}def initial(-T: Data) -> Shadow<T>:  Sh{Nil{}, Nil{}}def real(-T: Data, sh: Shadow<T>) -> Q.Queue<T>:  match sh:    case Sh{+f, +b}:      Q.QU{f, b, Nat.add(SC.length(T, f), SC.length(T, b))}def model(-T: Data, sh: Shadow<T>) -> List<&2, T>:  match sh:    case Sh{f, b}:      SC.append(T, f, SC.reverse(T, b))def unreal(-T: Data, q: Q.Queue<T>) -> Shadow<T>:  Q.QU{f, b, n} = q  Sh{f, b}def unreal_real(-T: Data, +sh: Shadow<T>) -> {unreal(T, real(T, sh)) == sh : Shadow<T>}:  match sh:    case Sh{f, b}:      {==}# a queue determines its shadowdef real_inj(-T: Data, +a: Shadow<T>, +b: Shadow<T>, +e: {real(T, a) == real(T, b) : Q.Queue<T>}) -> {a == b : Shadow<T>}:  Equal.trans(Shadow<T>, a, unreal(T, real(T, a)), b, Equal.sym(Shadow<T>, unreal(T, real(T, a)), a, unreal_real(T, a)),    Equal.trans(Shadow<T>, unreal(T, real(T, a)), unreal(T, real(T, b)), b, Equal.cong(Q.Queue<T>, Shadow<T>, d => unreal(T, d), real(T, a), real(T, b), e), unreal_real(T, b)))