proofs/containers/deque/state.bend source

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

import Baseimport ../../../spec/lib/common.bend as SCimport ../../../src/containers/deque.bend as DQ# The two-list deque DE{front, back, nf, nb} as a Data shadow: the two# lists, with the counts their lengths (so the count invariant holds by# construction).#   model(sh) = front ++ reverse(back)   the elements, front 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>) -> DQ.Deque<T>:  match sh:    case Sh{+f, +b}:      DQ.DE{f, b, 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, d: DQ.Deque<T>) -> Shadow<T>:  DQ.DE{f, b, nf, nb} = d  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 deque determines its shadowdef real_inj(-T: Data, +a: Shadow<T>, +b: Shadow<T>, +e: {real(T, a) == real(T, b) : DQ.Deque<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(DQ.Deque<T>, Shadow<T>, d => unreal(T, d), real(T, a), real(T, b), e), unreal_real(T, b)))