---
title: Example of composing two multi-relations
...

A span from Bundle to Item and from Bundle to Category. 

```clafer
abstract Bundle
    contains ->> Item +
    uniqueCategory -> Category 2..* = contains . category
    allCategory ->> Category 4..* 
```

We would like to write the following but it's not supported in Clafer currently (as of 0.4.3). 
We'll do that in an Alloy escape later.

```
  allCategory = this <: contains >< category
```

One bundle.

```clafer
B1 : Bundle
    [ contains = Bread, Muffin, Milk, Butter ] 
```

Every item belongs to a product category.

```clafer
abstract Item
    category ->> Category
```

Categories.

```clafer
enum Category = Bakery | Dairy
```

And four items:

```clafer
Bread : Item
    [ category = Bakery ]
Muffin : Item
    [ category = Bakery ]
Butter : Item 
    [ category = Dairy ]
Milk : Item
    [ category = Dairy ]

[alloy|
fact {
     compose
     [ c0_contains,    ~r_c0_contains,    c0_contains_ref
     , c0_category,    ~r_c0_category,    c0_category_ref
     , c0_allCategory, ~r_c0_allCategory, c0_allCategory_ref
     ]
}
pred compose[
  hd1: univ, sleg1: hd1->univ, tleg1: hd1->univ,
  hd2: univ, sleg2: hd2->univ, tleg2: hd2->univ,
  res: univ, slegr: res->univ, tlegr: res->univ ]
{
  some r1: res->hd1 | some r2: res->hd2 |
   all a: hd1, b: hd2 |
    a.tleg1 = b.sleg2 implies { one r: res | r.r1 = a && r.r2 = b } &&
    #res = #(hd1<:tleg1).~(hd2<:sleg2) &&
    res<:slegr = r1.(hd1<:sleg1) && res<:tlegr = r2.(hd2<:tleg2)
}
|]

```
Escape to Alloy to compose `all b : Bundle | b.allCategory = b <: contains >< category`:

```
[alloy|
fact {
     compose
     [ c0_contains,    ~r_c0_contains,    c0_contains_ref
     , c0_category,    ~r_c0_category,    c0_category_ref
     , c0_allCategory, ~r_c0_allCategory, c0_allCategory_ref
     ]
}
pred compose[
  hd1: univ, sleg1: hd1->univ, tleg1: hd1->univ,  // span
  hd2: univ, sleg2: hd2->univ, tleg2: hd2->univ,  // span
  res: univ, slegr: res->univ, tlegr: res->univ ] // span
{
  some r1: res->hd1 | some r2: res->hd2 |
   all a: hd1, b: hd2 |
    a.tleg1 = b.sleg2 implies { one r: res | r.r1 = a && r.r2 = b } &&
    #res = #(hd1<:tleg1).~(hd2<:sleg2) &&
    res<:slegr = r1.(hd1<:sleg1) && res<:tlegr = r2.(hd2<:tleg2)
}
|]
```

```{.clafer .ide}
```

Go back to [composing a multi-set with a multi-relation](multi-relation-composition).