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-rw-r--r--subprojects/docs/src/learn/language/logic/AssertionsError.svg20
-rw-r--r--subprojects/docs/src/learn/language/logic/AssertionsExample.svg99
-rw-r--r--subprojects/docs/src/learn/language/logic/DefaultAssertions.svg129
-rw-r--r--subprojects/docs/src/learn/language/logic/MultiObjects.svg81
-rw-r--r--subprojects/docs/src/learn/language/logic/ObjectScopes.svg58
-rw-r--r--subprojects/docs/src/learn/language/logic/StrongerObjectScopes.svg58
-rw-r--r--subprojects/docs/src/learn/language/logic/index.md256
7 files changed, 701 insertions, 0 deletions
diff --git a/subprojects/docs/src/learn/language/logic/AssertionsError.svg b/subprojects/docs/src/learn/language/logic/AssertionsError.svg
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diff --git a/subprojects/docs/src/learn/language/logic/MultiObjects.svg b/subprojects/docs/src/learn/language/logic/MultiObjects.svg
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index 00000000..a5232575
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1---
2SPDX-FileCopyrightText: 2024 The Refinery Authors
3SPDX-License-Identifier: EPL-2.0
4description: Four-valued logic abstraction
5sidebar_position: 1
6---
7
8# Partial modeling
9
10Refinery allow precisely expressing _unknown,_ _uncertain_ or even _contradictory_ information using [four-valued logic](https://en.wikipedia.org/wiki/Four-valued_logic#Belnap).
11During model generation, unknown aspects of the partial model get _refined_ into concrete (true or false) facts until the generated model is completed, or a contradiction is reached.
12
13The _Belnap--Dunn four-valued logic_ supports the following truth values:
14
15* `true` values correspond to facts known about the model, e.g., that a node is the instance of a given class or there is a reference between two nodes.
16* `false` values correspond to facts that are known not to hold, e.g., that a node is _not_ an instance of a given class or there is _no_ reference between two nodes.
17* `unknown` values express uncertain properties and design decisions yet to be made. During model refinement, `unknown` values are gradually replaced with `true` and `false` values until a consistent and concrete model is derived.
18* `error` values represent contradictions and validation failures in the model. One a model contains an error value, it can't be refined into a consistent model anymore.
19
20## Assertions
21
22_Assertions_ express facts about a partial model. An assertion is formed by a _symbol_ and an _argument list_ of _nodes_ in parentheses.
23Possible symbols include [classes](../classes/#classes), [references](../classes/#references), and [predicates](../predicates).
24Nodes appearing in the argument list are automatically added to the model.
25
26A _negative_ assertion with a `false` truth value is indicated by prefixing it with `!`.
27
28---
29
30Consider the following metamodel:
31
32```refinery
33class Region {
34 contains Vertex[] vertices
35}
36class Vertex.
37class State extends Vertex.
38```
39
40Along with the following set of assertions:
41
42```refinery
43Region(r1).
44Vertex(v1).
45Vertex(v2).
46!State(v2).
47vertices(r1, v1).
48vertices(r1, v2).
49!vertices(Region::new, v1).
50!vertices(Region::new, v2).
51```
52
53import AssertionsExample from './AssertionsExample.svg';
54
55<AssertionsExample />
56
57It is `true` that `r1` is an instance of the class `Region`, while `v1` and `v2` are instances of the class `Vertex`.
58We also assert that `v2` is _not_ an instance of the class `State`, but it is unknown whether `v1` is an instance of the class `State`.
59Types that are `unknown` are shown in a lighter color and with an outlined icon.
60
61It is `true` that there is a `vertices` reference between `r1` and `v1`, as well as `r1` and `v2`, but there is no such reference from `Region::new` to the same vertices.
62As no information is provided, it is `unknown` whether `State::new` is a vertex of any `Region` instance.
63References that are `unknown` are shown in a lighter color and with a dashed line.
64
65### Propagation
66
67Refinery can automatically infer some facts about the partial model based on the provided assertions by information _propagation._
68The set of assertions in the [example above](#assertions) is equivalent to the following:
69
70```refinery
71vertices(r1, v1).
72vertices(r1, v2).
73!State(v2).
74```
75
76By the type constraints of the `vertices` reference, Refinery can infer that `r1` is a `Region` instance and `v1` and `v2` are `Vertex` instances.
77Since `State` is a subclass of `Vertex`, it is still unknown whether `v1` is a `State` instance,
78but `v2` is explicitly forbidden from being such by the negative assertion `!State(v2)`.
79We may omit `!vertices(Region::new, v1)` and `!vertices(Region::new, v2)`, since `v1` and `v2` may be a target of only one [containment](../classes/#containment-hierarchy) reference.
80
81Contradictory assertions lead to `error` values in the partial model:
82
83```refinery
84State(v1).
85!Vertex(v1).
86```
87
88import AssertionsError from './AssertionsError.svg';
89
90<AssertionsError />
91
92### Default assertions
93
94Assertions marked with the `default` keyword have _lower priority_ that other assertions.
95They may contain wildcard arguments `*` to specify information about _all_ nodes in the graph.
96However, they can be overridden by more specific assertions that are not marked with the `default` keyword.
97
98---
99
100To make sure that the reference `vertices` is `false` everywhere except where explicitly asserted, we may add a `default` assertion:
101
102```refinery
103default !vertices(*, *).
104vertices(r1, v1).
105vertices(r2, v2).
106vertices(r3, v3).
107?vertices(r1, State::new).
108```
109
110import DefaultAssertions from './DefaultAssertions.svg';
111
112<DefaultAssertions />
113
114We can prefix an assertion with `?` to explicitly assert that some fact about the partial model is `unknown`.
115This is useful for overriding negative `default` assertions.
116
117## Multi-objects
118
119The special symbols `exists` and `equals` control the _number of graph nodes_ represented by an object in a partial model.
120
121By default, `exists` is `true` for all objects.
122An object `o` with `?exists(o)` (i.e., `exists(o)` explicitly set to `unknown`) may be _removed_ from the partial model.
123Therefore, it represents _at least 0_ graph nodes.
124
125By default, `equals` is `true` for its _diagonal_, i.e., we have `equals(o, o)` for all object `o`.
126For off-diagonal pairs, i.e., `(p, q)` with `p` not equal to `q`, we always have `!equals(p, q)`: distinct objects can never be _merged._
127If we set a _diagonal_ entry to `unknown` by writing `?equals(o, o)`, the object `o` becomes a **multi-object:** it can be freely _split_ into multiple graph nodes.
128Therefore, multi-objects represent _possibly more than 1_ graph nodes.
129
130| `exists(o)` | `equals(o, o)` | Number of nodes | Description |
131|:-:|:-:|-:|:-|
132| `true` | `true` | `1` | graph node |
133| `unknown` | `true` | `0..1` | removable graph node |
134| `true` | `unknown` | `1..*` | multi-object |
135| `unknown` | `unknown` | `0..*` | removable multi-object |
136
137In the Refinery web UI, `?exists(o)` is represented with a _dashed_ border, while `?equals(o, o)`
138
139```refinery
140node(node).
141
142node(removable).
143?exists(removable).
144
145node(multi).
146?equals(multi, multi).
147
148node(removableMulti).
149?exists(removableMulti).
150?equals(removableMulti, removableMulti).
151```
152
153import MultiObjects from './MultiObjects.svg';
154
155<MultiObjects />
156
157import TuneIcon from '@material-icons/svg/svg/tune/baseline.svg';
158import LabelIcon from '@material-icons/svg/svg/label/baseline.svg';
159import LabelOutlineIcon from '@material-icons/svg/svg/label/outline.svg';
160
161:::info
162
163You may use the <TuneIcon style={{ fill: 'currentColor', verticalAlign: 'text-top' }} title="Filter panel icon" />&nbsp;_filter panel_ icon in Refinery to toggle the visibility of special symbols like `exists` and `equals`.
164You may either show <LabelOutlineIcon style={{ fill: 'currentColor', verticalAlign: 'text-top' }} title="Unknown value icon" />&nbsp;_both true and unknown_ values or <LabelIcon style={{ fill: 'currentColor', verticalAlign: 'text-top' }} title="True value icon" />&nbsp;_just true_ values.
165The _object scopes_ toggle will also show the number of graph nodes represented by an object in square brackets after its name, like in the figure above.
166:::
167
168By default, a **new object** `C::new` is added for each non-`abstract` [class](../classes#classes) `C` with `?exists(C::new)` and `?equals(C::new, C::new)`.
169This multi-object represents all potential instances of the class.
170To assert that no new instances of `C` should be added to the generated model, you may write `!exists(C::new)`.
171
172You may use the `multi` keyword to quickly defined a (removable) multi-object:
173
174```refinery
175multi removableMulti.
176% This is equivalent to:
177% ?exists(removableMulti).
178% ?equals(removableMulti, removableMulti).
179```
180
181## Type scopes
182
183_Type scopes_ offer finer-grained control over the number of graph nodes in the generated model (as represented by the multi-objects) that `exists` or `equals` assertions.
184
185A _type scope constraint_ is formed by a unary symbol (a [class](../classes/#classes) or a [predicate](../predicates) with a single parameter) and _scope range._
186Ranges have a form similar to [multiplicity constraints](../classes#multiplicity): a range `n..m` indicates a lower bound of `n` and an upper bound of `m`.
187While an upper bound of `*` indicates a possibly unbounded number of objects, generated models will always be finite.
188Like for multiplicity constraints, the case `n..n` can be abbreviated as `n`.
189
190The number of nodes in the generated model can be controlled using the `node` special symbol.
191For example, we may write the following to generate a model with at least 100 at and most 120 nodes:
192
193```refinery
194scope node = 100..200.
195```
196
197A `scope` declaration may prescribe type scope constraint for any number of symbols, separated by `,`.
198Multiple `scope` declarations are also permitted.
199Multiple ranges provided for the same symbol will be intersected, i.e., they influence the generated model simultaneously.
200
201In other words,
202```
203scope Region = 10, State = 80..120.
204scope State = 100..150.
205% Equivalent to:
206scope Region = 10, State = 100..120.
207```
208
209The _object scopes_ option in the <TuneIcon style={{ fill: 'currentColor', verticalAlign: 'text-top' }} title="Filter panel icon" />&nbsp;_filter panel_ may help in exploring the effects of object scopes.
210
211---
212
213Consider the example
214
215```refinery
216class Region {
217 contains Vertex[] vertices
218}
219class Vertex.
220class State extends Vertex.
221scope node = 100..120, Vertex = 50..*.
222```
223
224import ObjectScopes from './ObjectScopes.svg';
225
226<ObjectScopes />
227
228Notice that Refinery could determine that there can be no more than 70 `Region` instances in the generated model, since at least 50 of the `100..120` nodes in the model must be `Vertex` instances.
229However, since `State` is a subclass of `Vertex` (i.e., `State::new` is also an instance of `Vertex`), the range `50..*` is shared between both `Vertex::new` and `State::new`, resulting in both representing `0..120` nodes.
230Nevertheless, every generated model will obey the scope constraint exactly, i.e., will have between 100 and 120 node, at least 50 of which are `Vertex` instances.
231
232By providing more information, Refinery can determine more precise ranges for multi-objects.
233For example, we may strengthen the scope constraints as follows:
234
235```refinery
236scope node = 100..120, Vertex = 50..*, State = 20.
237```
238
239import StrongerObjectScopes from './StrongerObjectScopes.svg';
240
241<StrongerObjectScopes />
242
243### Incremental scopes
244
245We may specify an _incremental_ object scope with the `+=` operator to determine the number of new instances to be added to the model.
246This is only allowed for symbol that are classes with no subclasses, as it directly influences the number of nodes represented by the corresponding `::new` object.
247
248For example, to ensure that between 5 and 7 `State` instances are added to the model, we may write:
249
250```refinery
251State(s1).
252State(s2).
253scope State += 5..7.
254```
255
256Since `s1` and `s2` are also instances of the `State` class, the generated concrete model will have between 7 and 9 `State` instances altogether.
generated by cgit v1.2.3-54-g00ecf (git 2.45.2) at 2024-06-25 18:53:35 +0000