def write_spec

bendtorch-core@0.1.0.0 · src/autograd/reduce_replayed_proof.bend:333

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/model.bend as Model
import bendtorch-core@0.1.0.0/src/storage/LAWS.bend as StorageLaws
import bendtorch-core@0.1.0.0/src/storage/array.bend as ArrayCore
import bendtorch-core@0.1.0.0/src/storage/api.bend as Api
import bendtorch-core@0.1.0.0/src/shape/index_proofs.bend as Index

333# Writing cell k at the path whose position is k turns the spec for k into
334# the spec for 1 + k.
335def write_spec(+plan: Shape.BroadcastPlan, +map: PlanMap(plan), +shape: Shape.Shape, +fill: F32, +ops: List<&2, StorageLaws.Op>, +k: Nat, +depth: Nat, +base: Nat, +path: Model.Path(depth),
336  +h: {Nat.add(Model.offset(depth, path), base) == k : Nat}) ->
337  {ArrayCore.write_path(F32, depth, out_spec(plan, map, shape, fill, ops, k, depth, base), path, cell_word(plan, map, shape, fill, ops, k)) == out_spec(plan, map, shape, fill, ops, 1n+k, depth, base) : Array<F32>}:
338  match depth:
339    case 0n:
340      %h : {ALeaf{cell_word(plan, map, shape, fill, ops, _)} == ALeaf{out_leaf(plan, map, shape, fill, ops, base, Nat.is_lt(base, 1n+_))} : Array<F32>}
341      %Equal.sym(Bool, Nat.is_lt(base, 1n+base), True{}, lt_self_succ(base)) :
342        {ALeaf{cell_word(plan, map, shape, fill, ops, base)} == ALeaf{out_leaf(plan, map, shape, fill, ops, base, _)} : Array<F32>}
343      {==}
344    case 1n+inner:
345      Model.Step{+bit, +rest} = path
346      match bit:
347        case False{}:
348          +c = Model.capacity(inner)
349          +high = Nat.add(c, base)
350          +inside = Equal.trans(Bool, Nat.is_lt(k, high), Nat.is_lt(Nat.add(Model.offset(inner, rest), base), high), True{},
351            Equal.cong(Nat, Bool, x => Nat.is_lt(x, high), k, Nat.add(Model.offset(inner, rest), base),
352              Equal.sym(Nat, Nat.add(Model.offset(inner, rest), base), k, h)),
353            lt_add_right(Model.offset(inner, rest), c, base, Api.offset_lt(inner, rest)))
354          %Equal.sym(Array<F32>, ArrayCore.write_path(F32, inner, out_spec(plan, map, shape, fill, ops, k, inner, base), rest, cell_word(plan, map, shape, fill, ops, k)),
355            out_spec(plan, map, shape, fill, ops, 1n+k, inner, base), write_spec(plan, map, shape, fill, ops, k, inner, base, rest, h)) :
356            {ANode{_, out_spec(plan, map, shape, fill, ops, k, inner, high)} == out_spec(plan, map, shape, fill, ops, 1n+k, 1n+inner, base) : Array<F32>}
357          %Equal.sym(Array<F32>, out_spec(plan, map, shape, fill, ops, k, inner, high), out_spec(plan, map, shape, fill, ops, 1n+k, inner, high), above(plan, map, shape, fill, ops, k, inner, high, inside)) :
358            {ANode{out_spec(plan, map, shape, fill, ops, 1n+k, inner, base), _} == out_spec(plan, map, shape, fill, ops, 1n+k, 1n+inner, base) : Array<F32>}
359          {==}
360        case True{}:
361          +c = Model.capacity(inner)
362          +high = Nat.add(c, base)
363          +off = Model.offset(inner, rest)
364          +lower = Equal.trans(Bool, Nat.is_le(high, k), Nat.is_le(high, Nat.add(c, Nat.add(off, base))), True{},
365            Equal.cong(Nat, Bool, x => Nat.is_le(high, x), k, Nat.add(c, Nat.add(off, base)),
366              Equal.trans(Nat, k, Nat.add(Nat.add(c, off), base), Nat.add(c, Nat.add(off, base)),
367                Equal.sym(Nat, Nat.add(Nat.add(c, off), base), k, h),
368                Equal.sym(Nat, Nat.add(c, Nat.add(off, base)), Nat.add(Nat.add(c, off), base), Index.add_assoc(c, off, base)))),
369            le_add_cong(c, base, Nat.add(off, base), Api.le_add_left(off, base)))
370          +shifted = Equal.trans(Nat, Nat.add(off, high), Nat.add(Nat.add(c, off), base), k, position_step(c, off, base), h)
371          %Equal.sym(Array<F32>, out_spec(plan, map, shape, fill, ops, k, inner, base), out_spec(plan, map, shape, fill, ops, 1n+k, inner, base), below(plan, map, shape, fill, ops, k, inner, base, lower)) :
372            {ANode{_, ArrayCore.write_path(F32, inner, out_spec(plan, map, shape, fill, ops, k, inner, high), rest, cell_word(plan, map, shape, fill, ops, k))} == out_spec(plan, map, shape, fill, ops, 1n+k, 1n+inner, base) : Array<F32>}
373          %Equal.sym(Array<F32>, ArrayCore.write_path(F32, inner, out_spec(plan, map, shape, fill, ops, k, inner, high), rest, cell_word(plan, map, shape, fill, ops, k)),
374            out_spec(plan, map, shape, fill, ops, 1n+k, inner, high), write_spec(plan, map, shape, fill, ops, k, inner, high, rest, shifted)) :
375            {ANode{out_spec(plan, map, shape, fill, ops, 1n+k, inner, base), _} == out_spec(plan, map, shape, fill, ops, 1n+k, 1n+inner, base) : Array<F32>}
376          {==}