def fork_cells

bendtorch-core@0.1.0.0 · src/tensor/parallel_proofs.bend:188

import Base
import bendtorch-core@0.1.0.0/src/tensor/parallel.bend as Build

188def fork_cells(~Q: Data, ~P: Data, ~A: Type, ~B: Type, ~prepare: @+q: Q -> P, ~split: (A & B) -> (A & B) & (A & B),
189  ~cell: @+p: P -> @+position: Nat -> (A & B) -> Bool -> F32 & (A & B),
190  +q: Q, -start: (A & B), +inner: Nat, +count: Nat, +base: Nat, -state: (A & B), pair: (A & B) & (A & B),
191  -exact: {pair == split(state) : (A & B) & (A & B)},
192  -low: A -> B -> Array<F32>, -high: A -> B -> Array<F32>, -at: {state == start : (A & B)},
193  -first: {Pair.fst((A & B), (A & B), split(start)) == start : (A & B)}, -second: {Pair.snd((A & B), (A & B), split(start)) == start : (A & B)},
194  -low_cells: @l: A -> @r: B -> @-at: {(l, r) == start : (A & B)} -> Fact<Cells(~P, ~A, ~B, ~cell, prepare(q), start, inner, count, base, low(l, r))>,
195  -high_cells: @l: A -> @r: B -> @-at: {(l, r) == start : (A & B)} ->
196    Fact<Cells(~P, ~A, ~B, ~cell, prepare(q), start, inner, count, Build.upper(inner, base), high(l, r))>) ->
197  Fact<Cells(~P, ~A, ~B, ~cell, prepare(q), start, 1n+inner, count, base, Build.fork(~A, ~B, pair, low, high))>:
198  (one, two) = pair
199  (l1, r1) = one
200  (l2, r2) = two
201  node_cells(~P, ~A, ~B, ~cell, prepare(q), start, inner, count, base, low(l1, r1), high(l2, r2),
202    low_cells(l1)(r1)(half_equal((A & B), start, state, (l1, r1), split, h => Pair.fst((A & B), (A & B), h),
203      Equal.cong((A & B) & (A & B), (A & B), h => Pair.fst((A & B), (A & B), h), ((l1, r1), (l2, r2)), split(state), exact), at, first)),
204    high_cells(l2)(r2)(half_equal((A & B), start, state, (l2, r2), split, h => Pair.snd((A & B), (A & B), h),
205      Equal.cong((A & B) & (A & B), (A & B), h => Pair.snd((A & B), (A & B), h), ((l1, r1), (l2, r2)), split(state), exact), at, second)))