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Equal values and distinct positions

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# Equal values and distinct positions

## Intention

I want to keep equal amounts of different charges when summing.

Equal values of different entities collapse in a Set; the scenes repeat the case on two charges of 500 KZT.

## Incorrect form and why it stays silent

```text title="Incorrect form"
sum(collect x: Money, c: Charge where amount(c, x))
```

Set collapses equal amount values even when the charges are different. List keeps every substitution; the number of charges is counted over the entities themselves.

## Correct form

```law
language "law.core" version "0.2";
package recipes.l.r11 version "0.1.0";
namespace "urn:recipe:l-calc:11";

entity Charge;
relation amount(c: Charge, x: Money) { key(c); }
relation total(x: Money);
rule Total strict { when true; then total(sum(collect all x: Money, c: Charge where amount(c, x))); }
```

## Frozen execution scene

| Facts and choice | Question | Answer |
|---|---|---|
| 1. two equal positions, List | `truth(total(1000 KZT))` | `TRUE_ONLY` / `COMPUTED` |
| 2. counterfactual: duplicate preservation removed | `truth(total(500 KZT))` | `TRUE_ONLY` / `COMPUTED` |
| 3. number of amount values | `count(collect x: Money, c: Charge where amount(c, x))` | `1` / `COMPUTED` |
| 4. number of charges | `count(collect c: Charge, x: Money where amount(c, x))` | `2` / `COMPUTED` |

```law
test "two equal positions as list" {
    given {
        context {
            legal_time @2026-09-13;
            decision_time @2026-09-13T09:00:00+05:00;
            knowledge_time @2026-09-13T09:00:00+05:00;
            timezone "Asia/Almaty";
        }
        assert amount(entity_ref("urn:recipe:l-calc:11:a"), 500 KZT); assert amount(entity_ref("urn:recipe:l-calc:11:b"), 500 KZT);
    }
    evaluate truth(total(1000 KZT));
    expect truth_status == TRUE_ONLY;
    expect evaluation_status == COMPUTED;
    
}
```

```law
test "duplicate preservation removed" {
    given {
        context {
            legal_time @2026-09-13;
            decision_time @2026-09-13T09:00:00+05:00;
            knowledge_time @2026-09-13T09:00:00+05:00;
            timezone "Asia/Almaty";
        }
        assert amount(entity_ref("urn:recipe:l-calc:11:a"), 500 KZT); assert amount(entity_ref("urn:recipe:l-calc:11:b"), 500 KZT);
    }
    evaluate truth(total(500 KZT));
    expect truth_status == TRUE_ONLY;
    expect evaluation_status == COMPUTED;
    
}
```

```law
test "count of sum values" {
    given {
        context {
            legal_time @2026-09-13;
            decision_time @2026-09-13T09:00:00+05:00;
            knowledge_time @2026-09-13T09:00:00+05:00;
            timezone "Asia/Almaty";
        }
        assert amount(entity_ref("urn:recipe:l-calc:11:a"), 500 KZT); assert amount(entity_ref("urn:recipe:l-calc:11:b"), 500 KZT);
    }
    evaluate count(collect x: Money, c: Charge where amount(c, x));
    expect value == 1;
    expect evaluation_status == COMPUTED;
    
}
```

```law
test "count of charges" {
    given {
        context {
            legal_time @2026-09-13;
            decision_time @2026-09-13T09:00:00+05:00;
            knowledge_time @2026-09-13T09:00:00+05:00;
            timezone "Asia/Almaty";
        }
        assert amount(entity_ref("urn:recipe:l-calc:11:a"), 500 KZT); assert amount(entity_ref("urn:recipe:l-calc:11:b"), 500 KZT);
    }
    evaluate count(collect c: Charge, x: Money where amount(c, x));
    expect value == 2;
    expect evaluation_status == COMPUTED;
    
}
```



## Counterfactual

Mutation: `x: Money, c: Charge where amount(c, x)` → `x: Money where amount(c, x)`; expected `LDC-E1317`. Additional counterfactuals are shown as separate table rows.

## Boundary

collect all does not remove extra substitutions over grounds — that is [Sum over items, not over grounds](/recipes/l-calc/count-items/). Choosing List for the sum and Set for entities does not replace a completeness check of input facts.

## Pitfall

Two equal charges are one value but two positions: count them over the entities, not the amounts.