# SPEAR: Shared Pidgin for Expressive Abstraction and Requirements

SPEAR is a task-specification protocol for reducing residual intent ambiguity without forcing the human to describe the entire world.

## Core schema

```text
TASK
  Verb + target transformation or decision.

OBJECTS & TYPES
  Name important objects and state their types, units, domains, and interfaces.

ABSTRACTION
  PRESERVE: invariants and distinctions the answer must retain.
  IGNORE: degrees of freedom that may be discarded.
  ASSUME: idealizations, priors, operating regime, and “spherical cow” model.

OBJECTIVE
  Quantity or ordering to optimize; include trade-off weights when known.

CONSTRAINTS
  HARD: must never be violated.
  SOFT: preferences with penalties or priority order.

UNCERTAINTY
  What is unknown, estimated, disputed, or allowed to vary.

OUTPUT
  Required artifact, structure, audience, length, notation, and precision.

EVALUATION
  Acceptance tests, metrics, counterexamples, tolerances, and failure conditions.

INTERACTION
  Clarification policy: ask only when expected reduction in task loss exceeds query cost.

EXAMPLES
  Positive examples, negative examples, and boundary cases.
```

## Compact mathematical objective

Let \(\Theta\) be latent intent, \(M\) the specification, \(C_H(M)\) its human production cost, and \(d(\Theta,\hat\Theta)\) task distortion. A task-optimal pidgin seeks a language and encoder minimizing

\[
\mathbb E[d(\Theta,\hat\Theta)]
+\lambda\,\mathbb E[C_H(M)]
+\gamma\,\mathbb E[C_{\mathrm{interaction}}],
\]

or, under a human cost budget \(B\), maximizing task-relevant mutual information

\[
\sup_{\mathbb E[C_H(M)]\le B} I(Z_T;M\mid C),
\]

where \(Z_T\) is the coarsest abstraction sufficient for the task.

## Example: systems optimization

```text
TASK
  Reduce anomaly-detector serving latency.

OBJECTS & TYPES
  Input: event stream, 1–5 million events/s.
  Output: anomaly score in [0,1] and optional alert flag.

ABSTRACTION
  PRESERVE: recall on labeled critical incidents; event order within each source.
  IGNORE: exact score calibration when alert ordering is unchanged.
  ASSUME: current traffic mix and CPU-only deployment.

OBJECTIVE
  Minimize p99 end-to-end latency.

CONSTRAINTS
  HARD: recall >= 0.98; no event loss; memory <= 64 GB.
  SOFT: minimize cloud cost after latency target is met.

OUTPUT
  Ranked intervention plan plus estimated latency/cost effects.

EVALUATION
  Replay benchmark on the supplied trace; report p50, p95, p99, recall, and cost.

INTERACTION
  Ask before changing the anomaly definition or dropping fields.
```

## Example: mathematical abstraction

```text
TASK
  Estimate convective cooling time.

ABSTRACTION
  ASSUME: body is a sphere of radius R with uniform temperature T(t).
  PRESERVE: total heat capacity, exposed area, ambient temperature, convection coefficient.
  IGNORE: limbs, internal temperature gradients, radiation, and airflow anisotropy.

MODEL
  m c_p dT/dt = -h (4 pi R^2) (T - T_inf).

OUTPUT
  Closed-form T(t), characteristic time constant, and validity limits.
```

The abstraction is good only if it preserves the variables sufficient for the requested decision. Correct mathematics on the wrong quotient produces false precision.