fv-vector-algebra-composition

IN premise — summaries/2026/08/24/todd-2023-function-vectors-s0-abstract-chunk-1.md

Created 2026-08-25T02:58:40+00:00

Function Vectors support partial vector algebra: Last-Capital* = Last-Copy + First-Capital − First-Copy, producing a vector that triggers the composed 'Last-Capital' task.

Summary

You can synthesize a "capitalize the last character" task simply by adding and subtracting existing primitive task vectors (like copy and capitalize-first), without defining it from scratch. This means the system's task space behaves at least partially like a vector space, so new capabilities can be discovered through basic arithmetic on known ones rather than requiring separate definitions for every possible task.