LAWS.causal: law of bendtorch@1.3.0.0
Import: import bendtorch@1.3.0.0/LAWS.bend as LAWS
Lines 102-119 of bendtorch@1.3.0.0/LAWS.bend: https://jend.leeeet.dev/read.txt?path=bendtorch@1.3.0.0/LAWS.bend&start_line=102&end_line=119

import Base
import bendtorch@1.3.0.0/main.bend as T

# LAW (causal): in T.Attention, row i of a head's probabilities is a softmax over exactly i + 1 positions. T.prow
# writes the query's scores from the start of its row and runs the softmax over as many positions as it wrote; the count
# is the one the softmax's own division loop reports (T.psmc), and this law says it is i + 1, the keys 0..i of
# causal_keys. P starts as zeros and nothing else writes the row, so its other t - (i + 1) positions stay 0: no
# probability lands on a later position.
law causal:
  for +i: Nat
  for +t: Nat
  for +hd: Nat
  for +sc: F32
  for +qs: U32
  for +qc: U32
  for +ks: U32
  for +kc: U32
  for q: Array<F32>
  for k: Array<F32>
  for p: Array<F32>
  {T.pr_n(T.prow(i, t, hd, sc, qs, qc, ks, kc, q, k, p)) == 1n+i : Nat}

Uses (15):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.mul
  https://jend.leeeet.dev/definition.txt?path=bend-ml-nat-lemmas@0.1.2.0/main.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/PROOF.bend&name=cnt_drow
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=dot0
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=pr_n
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=prow