def right_pair

bendtorch-core@0.1.0.0 · src/tensor/matmul_PROOF.bend:149

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/matmul.bend as Matrix
import bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend as Laws

149def right_pair(+fuel: Nat, +left: Shape.Shape, +right: Shape.Shape, -a: Core.Tensor<left>, -b: Core.Tensor<right>,
150  -ra: Core.Tensor<left>, rb: Core.Tensor<right>, result: Result<&2, &2, Core.Error, F32>,
151  +row: U32, +column: U32, +cursor: Nat, +accumulator: F32, +lv: F32,
152  -rec: @a: Core.Tensor<left> -> @b: Core.Tensor<right> -> @+value: F32 ->
153    Laws.SourceDot<fuel, left, right, a, b, row, column, 1n+cursor, value, Matrix.natural_dot(fuel, left, right, a, b, row, column, 1n+cursor, value)>,
154  -exact: {U32.to_nat(U32.from_nat(cursor)) == cursor : Nat},
155  -lo: {Laws.coordinate_observe(left, a, [row, U32.from_nat(cursor)]) == Some{lv} : Maybe<&2, F32>},
156  -meaning: @unit: Unit -> {Core.result_value(result) == Laws.coordinate_observe(right, b, [U32.from_nat(cursor), column]) : Maybe<&2, F32>},
157  -left_kept: @+other: U32 -> {Core.checked_observe(left, ra, other) == Core.checked_observe(left, a, other) : Maybe<&2, F32>},
158  -right_kept: @+other: U32 -> {Core.checked_observe(right, rb, other) == Core.checked_observe(right, b, other) : Maybe<&2, F32>}) ->
159  Laws.SourceDot<1n+fuel, left, right, a, b, row, column, cursor, accumulator, Matrix.right_read(left, right,
160    a => b => value => Matrix.natural_dot(fuel, left, right, a, b, row, column, 1n+cursor, value), ra, lv, accumulator, (rb, result))>:
161  match result:
162    case Fail{error}:
163      Laws.SourceDot{unit => Unit{}}
164    case Done{+rv}:
165      Laws.SourceDot{unit =>
166        claim : @certificate: Laws.SourceDot<fuel, left, right, ra, rb, row, column, 1n+cursor, F32.add(accumulator, F32.mul(lv, rv)),
167          Matrix.natural_dot(fuel, left, right, ra, rb, row, column, 1n+cursor, F32.add(accumulator, F32.mul(lv, rv)))> ->
168          Laws.DotResultMeaning(fuel, left, right, ra, rb, row, column, 1n+cursor, F32.add(accumulator, F32.mul(lv, rv)),
169            Matrix.natural_dot(fuel, left, right, ra, rb, row, column, 1n+cursor, F32.add(accumulator, F32.mul(lv, rv)))) =
170          \{Laws.SourceDot: proof => proof(Unit{})}
171        dot_extend(fuel, left, right, a, b, ra, rb, row, column, cursor, accumulator, lv, rv,
172          Matrix.natural_dot(fuel, left, right, ra, rb, row, column, 1n+cursor, F32.add(accumulator, F32.mul(lv, rv))),
173          claim(rec(ra, rb, F32.add(accumulator, F32.mul(lv, rv)))), exact, lo,
174          Equal.sym(Maybe<&2, F32>, Some{rv}, Laws.coordinate_observe(right, b, [U32.from_nat(cursor), column]), meaning(Unit{})), left_kept, right_kept)}