!.
=>  %a50
~%  %a.50  ~  ~
|%
::  Types
::
+$  ship  @p
+$  life  @ud
+$  rift  @ud
+$  pass  @
+$  bloq  @
+$  step  _`@u`1
+$  bite  $@(bloq [=bloq =step])
+$  octs  [p=@ud q=@]
+$  mold  $~(* $-(* *))
++  unit  |$  [item]  $@(~ [~ u=item])
++  list  |$  [item]  $@(~ [i=item t=(list item)])
++  lest  |$  [item]  [i=item t=(list item)]
++  tree  |$  [node]  $@(~ [n=node l=(tree node) r=(tree node)])
++  pair  |$  [head tail]  [p=head q=tail]
++  map
  |$  [key value]
  $|  (tree (pair key value))
  |=(a=(tree (pair)) ?:(=(~ a) & ~(apt by a)))
::
++  set
  |$  [item]
  $|  (tree item)
  |=(a=(tree) ?:(=(~ a) & ~(apt in a)))
::
++  jug   |$  [key value]  (map key (set value))
::
::  Biblical
::
++  ruth  |=([a=* b=*] ?>(?=(@ b) b))
::
::  Bits
::
++  dec                                                 ::  decrement
  ~/  %dec
  |=  a=@
  ~_  leaf+"decrement-underflow"
  ?<  =(0 a)
  =+  b=0
  |-  ^-  @
  ?:  =(a +(b))  b
  $(b +(b))
::
++  add                                                 ::  plus
  ~/  %add
  |=  [a=@ b=@]
  ^-  @
  ?:  =(0 a)  b
  $(a (dec a), b +(b))
::
++  sub                                                 ::  subtract
  ~/  %sub
  |=  [a=@ b=@]
  ~_  leaf+"subtract-underflow"
  ::  difference
  ^-  @
  ?:  =(0 b)  a
  $(a (dec a), b (dec b))
::
++  mul                                                 ::  multiply
  ~/  %mul
  |:  [a=`@`1 b=`@`1]
  ^-  @
  =+  c=0
  |-
  ?:  =(0 a)  c
  $(a (dec a), c (add b c))
::
++  div                                                 ::  divide
  ~/  %div
  |:  [a=`@`1 b=`@`1]
  ^-  @
  ~_  leaf+"divide-by-zero"
  ?<  =(0 b)
  =+  c=0
  |-
  ?:  (lth a b)  c
  $(a (sub a b), c +(c))
::
++  mod                                                 ::  modulus
  ~/  %mod
  |:  [a=`@`1 b=`@`1]
  ^-  @
  ?<  =(0 b)
  (sub a (mul b (div a b)))
::
++  bex                                                 ::  binary exponent
  ~/  %bex
  |=  a=bloq
  ^-  @
  ?:  =(0 a)  1
  (mul 2 $(a (dec a)))
::
++  lsh                                                 ::  left-shift
  ~/  %lsh
  |=  [a=bite b=@]
  =/  [=bloq =step]  ?^(a a [a *step])
  (mul b (bex (mul (bex bloq) step)))
::
++  rsh                                                 ::  right-shift
  ~/  %rsh
  |=  [a=bite b=@]
  =/  [=bloq =step]  ?^(a a [a *step])
  (div b (bex (mul (bex bloq) step)))
::
++  con                                                 ::  binary or
  ~/  %con
  |=  [a=@ b=@]
  =+  [c=0 d=0]
  |-  ^-  @
  ?:  ?&(=(0 a) =(0 b))  d
  %=  $
    a   (rsh 0 a)
    b   (rsh 0 b)
    c   +(c)
    d   %+  add  d
          %+  lsh  [0 c]
          ?&  =(0 (end 0 a))
              =(0 (end 0 b))
          ==
  ==
::
++  dis                                                 ::  binary and
  ~/  %dis
  |=  [a=@ b=@]
  =|  [c=@ d=@]
  |-  ^-  @
  ?:  ?|(=(0 a) =(0 b))  d
  %=  $
    a   (rsh 0 a)
    b   (rsh 0 b)
    c   +(c)
    d   %+  add  d
          %+  lsh  [0 c]
          ?|  =(0 (end 0 a))
              =(0 (end 0 b))
          ==
  ==
::
++  mix                                                 ::  binary xor
  ~/  %mix
  |=  [a=@ b=@]
  ^-  @
  =+  [c=0 d=0]
  |-
  ?:  ?&(=(0 a) =(0 b))  d
  %=  $
    a   (rsh 0 a)
    b   (rsh 0 b)
    c   +(c)
    d   (add d (lsh [0 c] =((end 0 a) (end 0 b))))
  ==
::
++  lth                                                 ::  less
  ~/  %lth
  |=  [a=@ b=@]
  ^-  ?
  ?&  !=(a b)
      |-
      ?|  =(0 a)
          ?&  !=(0 b)
              $(a (dec a), b (dec b))
  ==  ==  ==
::
++  lte                                                 ::  less or equal
  ~/  %lte
  |=  [a=@ b=@]
  |(=(a b) (lth a b))
::
++  gte                                                 ::  greater or equal
  ~/  %gte
  |=  [a=@ b=@]
  ^-  ?
  !(lth a b)
::
++  gth                                                 ::  greater
  ~/  %gth
  |=  [a=@ b=@]
  ^-  ?
  !(lte a b)
::
++  swp                                                 ::  naive rev bloq order
  ~/  %swp
  |=  [a=bloq b=@]
  (rep a (flop (rip a b)))
::
++  met                                                 ::  measure
  ~/  %met
  |=  [a=bloq b=@]
  ^-  @
  =+  c=0
  |-
  ?:  =(0 b)  c
  $(b (rsh a b), c +(c))
::
++  end                                                 ::  tail
  ~/  %end
  |=  [a=bite b=@]
  =/  [=bloq =step]  ?^(a a [a *step])
  (mod b (bex (mul (bex bloq) step)))
::
++  cat                                                 ::  concatenate
  ~/  %cat
  |=  [a=bloq b=@ c=@]
  (add (lsh [a (met a b)] c) b)
::
++  cut                                                 ::  slice
  ~/  %cut  ::  TODO: jet
  |=  [a=bloq [b=step c=step] d=@]
  (end [a c] (rsh [a b] d))
::
++  dad                                                 ::  concatenate fixed
  ~/  %dad
  |=  [=bite a=@ b=@]
  (add a (lsh bite b))
::
++  can                                                 ::  assemble
  ~/  %can
  |=  [a=bloq b=(list [p=step q=@])]
  ^-  @
  ?~  b  0
  (add (end [a p.i.b] q.i.b) (lsh [a p.i.b] $(b t.b)))
::
++  cad                                                 ::  assemble specific
  ~/  %cad
  |=  [a=bloq b=(list [p=step q=@])]
  ^-  [=step @]
  :_  (can a b)
  |-
  ?~  b
    0
  (add p.i.b $(b t.b))
::
++  rep                                                 ::  assemble fixed
  ~/  %rep
  |=  [a=bite b=(list @)]
  =/  [=bloq =step]  ?^(a a [a *step])
  =|  i=@ud
  |-  ^-  @
  ?~  b   0
  %+  add  $(i +(i), b t.b)
  (lsh [bloq (mul step i)] (end [bloq step] i.b))
::
++  rip                                                 ::  disassemble
  ~/  %rip
  |=  [a=bite b=@]
  ^-  (list @)
  ?:  =(0 b)  ~
  [(end a b) $(b (rsh a b))]
::
::
::  Lists
::
++  lent                                                ::  length
  ~/  %lent
  |=  a=(list)
  ^-  @
  =+  b=0
  |-
  ?~  a  b
  $(a t.a, b +(b))
::
++  slag                                                ::  suffix
  ~/  %slag
  |*  [a=@ b=(list)]
  |-  ^+  b
  ?:  =(0 a)  b
  ?~  b  ~
  $(b t.b, a (dec a))
::
++  snag                                                ::  index
  ~/  %snag
  |*  [a=@ b=(list)]
  |-  ^+  ?>(?=(^ b) i.b)
  ?~  b
    ~_  leaf+"snag-fail"
    !!
  ?:  =(0 a)  i.b
  $(b t.b, a (dec a))
::
++  homo                                                ::  homogenize
  |*  a=(list)
  ^+  =<  $
    |@  ++  $  ?:(*? ~ [i=(snag 0 a) t=$])
    --
  a
::
++  flop                                                ::  reverse
  ~/  %flop
  |*  a=(list)
  =>  .(a (homo a))
  ^+  a
  =+  b=`_a`~
  |-
  ?~  a  b
  $(a t.a, b [i.a b])
::
++  welp                                                ::  concatenate
  ~/  %welp
  =|  [* *]
  |@
  ++  $
    ?~  +<-
      +<-(. +<+)
    +<-(+ $(+<- +<->))
  --
::
++  turn                                                ::  transform
  ~/  %turn
  |*  [a=(list) b=$-(* *)]
  =>  .(a (homo a))
  ^-  (list _?>(?=(^ a) (b i.a)))
  |-
  ?~  a  ~
  [i=(b i.a) t=$(a t.a)]
::
++  levy                                                ::  all of
  ~/  %levy
  |*  [a=(list) b=$-(* ?)]
  |-  ^-  ?
  ?~  a  &
  ?.  (b i.a)  |
  $(a t.a)
::
++  reap                                                ::  replicate
  ~/  %reap
  |*  [a=@ b=*]
  |-  ^-  (list _b)
  ?~  a  ~
  [b $(a (dec a))]
::
::  Modular arithmetic
::
++  fe                                                  ::  modulo bloq
  |_  a=bloq
  ++  rol  |=  [b=bloq c=@ d=@]  ^-  @                  ::  roll left
           =+  e=(sit d)
           =+  f=(bex (sub a b))
           =+  g=(mod c f)
           (sit (con (lsh [b g] e) (rsh [b (sub f g)] e)))
  ++  sum  |=([b=@ c=@] (sit (add b c)))                ::  wrapping add
  ++  sit  |=(b=@ (end a b))                            ::  enforce modulo
  --
::
::  Hashes
::
++  muk                                                 ::  standard murmur3
  ~%  %muk  ..muk  ~
  =+  ~(. fe 5)
  |=  [syd=@ len=@ key=@]
  =.  syd      (end 5 syd)
  =/  pad      (sub len (met 3 key))
  =/  data     (welp (rip 3 key) (reap pad 0))
  =/  nblocks  (div len 4)  ::  intentionally off-by-one
  =/  h1  syd
  =+  [c1=0xcc9e.2d51 c2=0x1b87.3593]
  =/  blocks  (rip 5 key)
  =/  i  nblocks
  =.  h1  =/  hi  h1  |-
    ?:  =(0 i)  hi
    =/  k1  (snag (sub nblocks i) blocks)  ::  negative array index
    =.  k1  (sit (mul k1 c1))
    =.  k1  (rol 0 15 k1)
    =.  k1  (sit (mul k1 c2))
    =.  hi  (mix hi k1)
    =.  hi  (rol 0 13 hi)
    =.  hi  (sum (sit (mul hi 5)) 0xe654.6b64)
    $(i (dec i))
  =/  tail  (slag (mul 4 nblocks) data)
  =/  k1    0
  =/  tlen  (dis len 3)
  =.  h1
    ?+  tlen  h1  ::  fallthrough switch
      %3  =.  k1  (mix k1 (lsh [0 16] (snag 2 tail)))
          =.  k1  (mix k1 (lsh [0 8] (snag 1 tail)))
          =.  k1  (mix k1 (snag 0 tail))
          =.  k1  (sit (mul k1 c1))
          =.  k1  (rol 0 15 k1)
          =.  k1  (sit (mul k1 c2))
          (mix h1 k1)
      %2  =.  k1  (mix k1 (lsh [0 8] (snag 1 tail)))
          =.  k1  (mix k1 (snag 0 tail))
          =.  k1  (sit (mul k1 c1))
          =.  k1  (rol 0 15 k1)
          =.  k1  (sit (mul k1 c2))
          (mix h1 k1)
      %1  =.  k1  (mix k1 (snag 0 tail))
          =.  k1  (sit (mul k1 c1))
          =.  k1  (rol 0 15 k1)
          =.  k1  (sit (mul k1 c2))
          (mix h1 k1)
    ==
  =.  h1  (mix h1 len)
  |^  (fmix32 h1)
  ++  fmix32
    |=  h=@
    =.  h  (mix h (rsh [0 16] h))
    =.  h  (sit (mul h 0x85eb.ca6b))
    =.  h  (mix h (rsh [0 13] h))
    =.  h  (sit (mul h 0xc2b2.ae35))
    =.  h  (mix h (rsh [0 16] h))
    h
  --
::
++  mug                                                 ::  mug with murmur3
  ~/  %mug
  |=  a=*
  |^  ?@  a  (mum 0xcafe.babe 0x7fff a)
      =/  b  (cat 5 $(a -.a) $(a +.a))
      (mum 0xdead.beef 0xfffe b)
  ::
  ++  mum
    |=  [syd=@uxF fal=@F key=@]
    =/  wyd  (met 3 key)
    =|  i=@ud
    |-  ^-  @F
    ?:  =(8 i)  fal
    =/  haz=@F  (muk syd wyd key)
    =/  ham=@F  (mix (rsh [0 31] haz) (end [0 31] haz))
    ?.(=(0 ham) ham $(i +(i), syd +(syd)))
  --
::
++  gor                                                 ::  mug order
  ~/  %gor
  |=  [a=* b=*]
  ^-  ?
  =+  [c=(mug a) d=(mug b)]
  ?:  =(c d)
    (dor a b)
  (lth c d)
::
++  mor                                                 ::  more mug order
  ~/  %mor
  |=  [a=* b=*]
  ^-  ?
  =+  [c=(mug (mug a)) d=(mug (mug b))]
  ?:  =(c d)
    (dor a b)
  (lth c d)
::
++  dor                                                 ::  tree order
  ~/  %dor
  |=  [a=* b=*]
  ^-  ?
  ?:  =(a b)  &
  ?.  ?=(@ a)
    ?:  ?=(@ b)  |
    ?:  =(-.a -.b)
      $(a +.a, b +.b)
    $(a -.a, b -.b)
  ?.  ?=(@ b)  &
  (lth a b)
::
++  por                                                 ::  parent order
  ~/  %por
  |=  [a=@p b=@p]
  ^-  ?
  ?:  =(a b)  &
  =|  i=@
  |-
  ?:  =(i 2)
    ::  second two bytes
    (lte a b)
  ::  first two bytes
  =+  [c=(end 3 a) d=(end 3 b)]
  ?:  =(c d)
    $(a (rsh 3 a), b (rsh 3 b), i +(i))
  (lth c d)
::
::  Maps
::
++  by
  ~/  %by
  =|  a=(tree (pair))  ::  (map)
  =*  node  ?>(?=(^ a) n.a)
  |@
  ++  get
    ~/  %get
    |*  b=*
    =>  .(b `_?>(?=(^ a) p.n.a)`b)
    |-  ^-  (unit _?>(?=(^ a) q.n.a))
    ?~  a
      ~
    ?:  =(b p.n.a)
      `q.n.a
    ?:  (gor b p.n.a)
      $(a l.a)
    $(a r.a)
  ::
  ++  has
    ~/  %has
    |*  b=*
    !=(~ (get b))
  ::
  ++  put
    ~/  %put
    |*  [b=* c=*]
    |-  ^+  a
    ?~  a
      [[b c] ~ ~]
    ?:  =(b p.n.a)
      ?:  =(c q.n.a)
        a
      a(n [b c])
    ?:  (gor b p.n.a)
      =+  d=$(a l.a)
      ?>  ?=(^ d)
      ?:  (mor p.n.a p.n.d)
        a(l d)
      d(r a(l r.d))
    =+  d=$(a r.a)
    ?>  ?=(^ d)
    ?:  (mor p.n.a p.n.d)
      a(r d)
    d(l a(r l.d))
  ::
  ++  del
    ~/  %del
    |*  b=*
    |-  ^+  a
    ?~  a
      ~
    ?.  =(b p.n.a)
      ?:  (gor b p.n.a)
        a(l $(a l.a))
      a(r $(a r.a))
    |-  ^-  [$?(~ _a)]
    ?~  l.a  r.a
    ?~  r.a  l.a
    ?:  (mor p.n.l.a p.n.r.a)
      l.a(r $(l.a r.l.a))
    r.a(l $(r.a l.r.a))
  ::
  ++  apt
    =<  $
    ~/  %apt
    =|  [l=(unit) r=(unit)]
    |.  ^-  ?
    ?~  a   &
    ?&  ?~(l & &((gor p.n.a u.l) !=(p.n.a u.l)))
        ?~(r & &((gor u.r p.n.a) !=(u.r p.n.a)))
        ?~  l.a   &
        &((mor p.n.a p.n.l.a) !=(p.n.a p.n.l.a) $(a l.a, l `p.n.a))
        ?~  r.a   &
        &((mor p.n.a p.n.r.a) !=(p.n.a p.n.r.a) $(a r.a, r `p.n.a))
    ==
  --
::
++  on                                                  ::  ordered map
  ~/  %on
  |*  [key=mold val=mold]
  =>  |%
      +$  item  [key=key val=val]
      --
  ::
  ~%  %comp  +>+  ~
  |=  compare=$-([key key] ?)
  ~%  %core    +  ~
  |%
  ::
  ++  apt
    ~/  %apt
    |=  a=(tree item)
    =|  [l=(unit key) r=(unit key)]
    |-  ^-  ?
    ?~  a  %.y
    ?&  ?~(l %.y (compare key.n.a u.l))
        ?~(r %.y (compare u.r key.n.a))
        ?~(l.a %.y &((mor key.n.a key.n.l.a) $(a l.a, l `key.n.a)))
        ?~(r.a %.y &((mor key.n.a key.n.r.a) $(a r.a, r `key.n.a)))
    ==
  ::
  ++  gas
    ~/  %gas
    |=  [a=(tree item) b=(list item)]
    ^-  (tree item)
    ?~  b  a
    $(b t.b, a (put a i.b))
  ::
  ++  get
    ~/  %get
    |=  [a=(tree item) b=key]
    ^-  (unit val)
    ?~  a  ~
    ?:  =(b key.n.a)
      `val.n.a
    ?:  (compare b key.n.a)
      $(a l.a)
    $(a r.a)
  ::
  ++  has
    ~/  %has
    |=  [a=(tree item) b=key]
    ^-  ?
    !=(~ (get a b))
  ::
  ++  lot
    ~/  %lot
    |=  $:  tre=(tree item)
            start=(unit key)
            end=(unit key)
        ==
    ^-  (tree item)
    |^
    ?:  ?&(?=(~ start) ?=(~ end))
      tre
    ?~  start
      (del-span tre %end end)
    ?~  end
      (del-span tre %start start)
    ?>  (compare u.start u.end)
    =.  tre  (del-span tre %start start)
    (del-span tre %end end)
    ::
    ++  del-span
      |=  [a=(tree item) b=?(%start %end) c=(unit key)]
      ^-  (tree item)
      ?~  a  a
      ?~  c  a
      ?-  b
          %start
        ?:  =(key.n.a u.c)
          (nip a(l ~))
        ?:  (compare key.n.a u.c)
          $(a (nip a(l ~)))
        a(l $(a l.a))
      ::
          %end
        ?:  =(u.c key.n.a)
          (nip a(r ~))
        ?:  (compare key.n.a u.c)
          a(r $(a r.a))
        $(a (nip a(r ~)))
      ==
    --
  ::
  ++  nip
    ~/  %nip
    |=  a=(tree item)
    ^-  (tree item)
    ?>  ?=(^ a)
    |-  ^-  (tree item)
    ?~  l.a  r.a
    ?~  r.a  l.a
    ?:  (mor key.n.l.a key.n.r.a)
      l.a(r $(l.a r.l.a))
    r.a(l $(r.a l.r.a))
  ::
  ++  put
    ~/  %put
    |=  [a=(tree item) =key =val]
    ^-  (tree item)
    ?~  a  [n=[key val] l=~ r=~]
    ?:  =(key.n.a key)  a(val.n val)
    ?:  (compare key key.n.a)
      =/  l  $(a l.a)
      ?>  ?=(^ l)
      ?:  (mor key.n.a key.n.l)
        a(l l)
      l(r a(l r.l))
    =/  r  $(a r.a)
    ?>  ?=(^ r)
    ?:  (mor key.n.a key.n.r)
      a(r r)
    r(l a(r l.r))
  ::
  ++  tap
    ~/  %tap
    |=  a=(tree item)
    ^-  (list item)
    =|  b=(list item)
    |-  ^+  b
    ?~  a  b
    $(a l.a, b [n.a $(a r.a)])
  --
::
::  Sets
::
++  in
  ~/  %in
  =|  a=(tree)  :: (set)
  |@
  ++  put
    ~/  %put
    |*  b=*
    |-  ^+  a
    ?~  a
      [b ~ ~]
    ?:  =(b n.a)
      a
    ?:  (gor b n.a)
      =+  c=$(a l.a)
      ?>  ?=(^ c)
      ?:  (mor n.a n.c)
        a(l c)
      c(r a(l r.c))
    =+  c=$(a r.a)
    ?>  ?=(^ c)
    ?:  (mor n.a n.c)
      a(r c)
    c(l a(r l.c))
  ::
  ++  del
    ~/  %del
    |*  b=*
    |-  ^+  a
    ?~  a
      ~
    ?.  =(b n.a)
      ?:  (gor b n.a)
        a(l $(a l.a))
      a(r $(a r.a))
    |-  ^-  [$?(~ _a)]
    ?~  l.a  r.a
    ?~  r.a  l.a
    ?:  (mor n.l.a n.r.a)
      l.a(r $(l.a r.l.a))
    r.a(l $(r.a l.r.a))
  ::
  ++  apt
    =<  $
    ~/  %apt
    =|  [l=(unit) r=(unit)]
    |.  ^-  ?
    ?~  a   &
    ?&  ?~(l & (gor n.a u.l))
        ?~(r & (gor u.r n.a))
        ?~(l.a & ?&((mor n.a n.l.a) $(a l.a, l `n.a)))
        ?~(r.a & ?&((mor n.a n.r.a) $(a r.a, r `n.a)))
    ==
  --
::
::  Jugs
::
++  ju
  =|  a=(tree (pair * (tree)))  ::  (jug)
  |@
  ++  get
    |*  b=*
    =+  c=(~(get by a) b)
    ?~(c ~ u.c)
  ::
  ++  del
    |*  [b=* c=*]
    ^+  a
    =+  d=(get b)
    =+  e=(~(del in d) c)
    ?~  e
      (~(del by a) b)
    (~(put by a) b e)
  ::
  ++  put
    |*  [b=* c=*]
    ^+  a
    =+  d=(get b)
    (~(put by a) b (~(put in d) c))
  --
--