Block-scaled representation capability #
Block-scaled codes store one scale shared by several significands. This proof-only capability relates that concrete decomposition to a system's finite block denotation while leaving the index, scale, stored significand, lane value, and scaling operation fully generic.
def
FloatLib.Numerics.BlockScaled
(system : NumericalSystem)
(Index : Type u)
(Scale : Type v)
(Stored : Type w)
(Lane : Type x)
(laneAt : system.Scalar → Index → Lane)
(scaleOf : system.Code → Scale)
(storedAt : system.Code → Index → Stored)
(applyScale : Scale → Stored → Lane)
:
A numerical system's finite denotation is lane-wise reconstruction from one shared scale.
All executable projections are explicit parameters. The proposition certifies them but does not force numerical kernels to access a typeclass dictionary in their inner loops.