def h.wf_put

bend-kit-collections@0.1.4.1 · PROOF.bend:3784

import Base
import bend-mathlib@0.7.4.0/bool.bend as MBool
import bend-kit-collections@0.1.4.1/LAWS.bend as Laws
import bend-kit-collections@0.1.4.1/hmap.bend as M

3784def h.wf_put(
3785  ~K: Data, ~V: Data, ~hash: K -> U32, ~eq: K -> K -> Bool, ~refl: @x: K -> {eq(x, x) == True{} : Bool},
3786  ~sound: @x: K -> @y: K -> {eq(x, y) == True{} : Bool} -> {x == y : K},
3787  n: Nat, +mask: U32, m: M.HMap<K, V>, +k: K, +v: V,
3788  +wf: {h.WF(~K, ~V, ~hash, ~eq, n, m) == True{} : Bool}
3789) -> {h.WF(~K, ~V, ~hash, ~eq, n, h.P(~K, ~V, ~eq, n, mask, m, hash(k), k, v)) == True{} : Bool}:
3790  match n:
3791    case 0n:
3792      match m:
3793        case M.HNil{}:
3794          {==}
3795        case M.HLeaf{o, es}:
3796          h.distinct_put(~K, ~V, ~eq, ~refl, ~sound, es, k, v, wf)
3797        case M.HBranch{lo, hi}:
3798          wf
3799    case 1n+(+p):
3800      match m:
3801        case M.HNil{}:
3802          h.wf_fresh(~K, ~V, ~hash, ~eq, 1n+p, k, v)
3803        case M.HLeaf{+o, +es}:
3804          h.wf_put.lf(~K, ~V, ~hash, ~eq, ~refl, ~sound, p, mask, o, es, k, v,
3805            MBool.eq_true_of_and_left(Laws.hmap_hashed(~K, ~V, ~hash, es, o), Laws.hmap_distinct(~K, ~V, ~eq, es), wf),
3806            MBool.eq_true_of_and_right(Laws.hmap_hashed(~K, ~V, ~hash, es, o), Laws.hmap_distinct(~K, ~V, ~eq, es), wf),
3807            U32.is_eq(o, hash(k)), {==},
3808            h.split_wf(~K, ~V, ~hash, ~eq, ~refl, ~sound, 1n+p, mask, o, es, k, v,
3809              MBool.eq_true_of_and_left(Laws.hmap_hashed(~K, ~V, ~hash, es, o), Laws.hmap_distinct(~K, ~V, ~eq, es), wf),
3810              MBool.eq_true_of_and_right(Laws.hmap_hashed(~K, ~V, ~hash, es, o), Laws.hmap_distinct(~K, ~V, ~eq, es), wf)))
3811        case M.HBranch{+lo, +hi}:
3812          h.wf_put.br(~K, ~V, ~hash, ~eq, p, mask, lo, hi, hash(k), k, v, U32.is_eq((hash(k) .&. mask : U32), 0),
3813            MBool.eq_true_of_and_left(h.WF(~K, ~V, ~hash, ~eq, p, lo), h.WF(~K, ~V, ~hash, ~eq, p, hi), wf),
3814            MBool.eq_true_of_and_right(h.WF(~K, ~V, ~hash, ~eq, p, lo), h.WF(~K, ~V, ~hash, ~eq, p, hi), wf),
3815            h.wf_put(~K, ~V, ~hash, ~eq, ~refl, ~sound, p, (mask << 1n : U32), lo, k, v,
3816              MBool.eq_true_of_and_left(h.WF(~K, ~V, ~hash, ~eq, p, lo), h.WF(~K, ~V, ~hash, ~eq, p, hi), wf)),
3817            h.wf_put(~K, ~V, ~hash, ~eq, ~refl, ~sound, p, (mask << 1n : U32), hi, k, v,
3818              MBool.eq_true_of_and_right(h.WF(~K, ~V, ~hash, ~eq, p, lo), h.WF(~K, ~V, ~hash, ~eq, p, hi), wf)))