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WillowScript (.ws) is a proposed, not-yet-implemented language. Examples and library integrations here are illustrative design exercises, not verified runnable programs.

WillowScript Professional · Compare safe and unsafe transformed domains

Module project — Estimator specification

Account for domain restrictions: alternative solution challenge.

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PART I

Warm-up

Reconnect with a useful idea before starting account for domain restrictions. In one or two sentences, describe the input, output or host boundary from the previous exercise that this lesson builds on. If you are arriving directly, skim the worked example first; there is no locked prerequisite.

A rough note is enough. You can revise it after the example.

PART II

Instruction & guided example

Compare safe and unsafe transformed domains

Formula (x*x-1)/(x-1) simplifies to x+1 only for x≠1.

At x=2 both expressions give 3. At x=1 the original is undefined while the simplified expression gives 2. The transformed formula is equivalent only on the original domain. A UI allowing the newly defined point would change the feature contract.

Write the intermediate states explicitly before proposing a code change. The example below remains an illustrative source anchor; this new case changes the inputs or the host requirement. WillowScript and these library services are proposed and unimplemented here. Treat new policies as supplied exercise contracts, and keep hand predictions distinct from native execution evidence.

Worked reasoning and supplied artifact

// PAPER FIXTURE — Compare safe and unsafe transformed domains
// Manual worked artifact; comments below are not executable source.
// INPUT / CONTRACT: Formula (x*x-1)/(x-1) simplifies to x+1 only for x≠1.
// DERIVATION / EXPECTED ARTIFACT: At x=2 both expressions give 3. At x=1 the original is undefined while
// the simplified expression gives 2. The transformed formula is equivalent only on the original domain. A
// UI allowing the newly defined point would change the feature contract.

Illustrative example from the proposed WillowScript design. The language and WUIX/WMATH/WDB/WAUDIO/WTMP services are not implemented in the supplied source. This site has no interpreter, VM or native host and does not execute or certify the snippet.

Walk through the example, one line at a time
  1. // PAPER FIXTURE — Compare safe and unsafe transformed domains

    This comment explains intent for a reader. It is not an operation and should not be counted as an executed result.

  2. // Manual worked artifact; comments below are not executable source.

    This comment explains intent for a reader. It is not an operation and should not be counted as an executed result.

  3. // INPUT / CONTRACT: Formula (x*x-1)/(x-1) simplifies to x+1 only for x≠1.

    This comment explains intent for a reader. It is not an operation and should not be counted as an executed result.

  4. // DERIVATION / EXPECTED ARTIFACT: At x=2 both expressions give 3. At x=1 the original is undefined while

    This comment explains intent for a reader. It is not an operation and should not be counted as an executed result.

  5. // the simplified expression gives 2. The transformed formula is equivalent only on the original domain. A

    This comment explains intent for a reader. It is not an operation and should not be counted as an executed result.

  6. // UI allowing the newly defined point would change the feature contract.

    This comment explains intent for a reader. It is not an operation and should not be counted as an executed result.

Try the guided change

Reconstruct the supplied worked case first: list its inputs, intermediate decisions and final artifact. Compare each row with the explanation and identify exactly where the rejected alternative fails. Then use the changed inputs in Part IV for independent work.

  • Write the supplied inputs and initial state before following the example.
  • Reconstruct each intermediate calculation or host decision, then compare with the worked artifact.
  • Explain why the contrasting alternative fails before attempting the changed inputs in Part IV.

PART III

Take a breather

Step back after the guided example. Look away from the screen, stretch, or reread your prediction. This is an optional learning pause, not a timer or an assessment gate.

When you return, try to name the lesson’s key idea without copying its wording. If that feels difficult, return to Part II and trace one line rather than restarting the entire lesson.

Your drafts remain here. Continue whenever you are ready.

PART IV

Independent practice

Project context: Estimator specification. Build a small, understandable change around account for domain restrictions.

Produce a paired truth table at x=0,1,2 and state an equivalence claim with its domain qualifier.

What to produce

Produce a paired truth table at x=0,1,2 and state an equivalence claim with its domain qualifier.

  • State the intended behavior in a sentence before editing.
  • Use only source-backed syntax and the host services whose contract you have been given.
  • Record a normal case and a boundary or unavailable-resource case.
  • Label hand predictions separately from anything actually measured in a supplied toolchain.

Syntax colors are a reading aid, not a compiler. The line you are editing stays uncolored until you move to a different line; capitalization is never changed. Drafts stay on this browser and code is not executed.

Need a hint?

At x=2 both expressions give 3. At x=1 the original is undefined while the simplified expression gives 2. The transformed formula is equivalent only on the original domain. A UI allowing the newly defined point would change the feature contract.

The tempting answer “x=2” does not satisfy this case. At x=2 both expressions give 3. At x=1 the original is undefined while the simplified expression gives 2. The transformed formula is equivalent only on the original domain. A UI allowing the newly defined point would change the feature contract.

Original learning-path task and reference

Integrate every section in this module into Estimator specification. Submit .ws source, a list of approved host APIs, eight acceptance cases, and a short explanation. Demonstrate Evaluate a bound expression; Separate symbolic and numerical work; Recognize the slv equation-solving form; Account for domain restrictions.

import math;
domain Calculation {
    fnc sample() -> void {
        vary x: i32 = 2;
        vary value = [[ (x * 5) + 20 ]];
    }
}

Where the original task needs a host API that is not supplied here, write the contract and predictions. Do not invent a runtime result.

PART V

Self-check

Use this check to notice what to revisit. It does not award a private course grade, block another page or claim to verify compiled code. Every answer has a learning explanation.

Where must the equivalence exclude an input?

You may keep exploring even if you are unsure. Use the hint, compare the trace, and revise your explanation.

PART VI

Recap & small task

Bring the idea back to the mod feature you are building. A useful recap connects the mechanism to a decision you can make in your own code.

  • Compare safe and unsafe transformed domains
  • Formula (x*x-1)/(x-1) simplifies to x+1 only for x≠1.
  • Separate source-backed behavior, host requirements and untested predictions.

One small recap task

Change one input in this case and state which intermediate state or calculation must be recomputed. Explain why “x=2” is not justified.

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