catlog/stdlib/
models.rs

1//! Standard library of models of double theories.
2
3use std::sync::Arc;
4use ustr::{Ustr, ustr};
5
6use crate::dbl::{model::*, theory::*};
7use crate::one::fin_category::FinMor;
8
9/** The positive self-loop.
10
11A signed graph or free [signed category](super::theories::th_signed_category),
12possibly with delays or indeterminates.
13 */
14pub fn positive_loop(th: Arc<UstrDiscreteDblTheory>) -> UstrDiscreteDblModel {
15    loop_of_type(th, ustr("Object"), FinMor::Id(ustr("Object")))
16}
17
18/** The negative self-loop.
19
20A signed graph or free [signed category](super::theories::th_signed_category),
21possibly with delays or indeterminates.
22 */
23pub fn negative_loop(th: Arc<UstrDiscreteDblTheory>) -> UstrDiscreteDblModel {
24    loop_of_type(th, ustr("Object"), FinMor::Generator(ustr("Negative")))
25}
26
27/** The delayed positive self-loop.
28
29A free [delayable signed category](super::theories::th_delayable_signed_category).
30 */
31pub fn delayed_positive_loop(th: Arc<UstrDiscreteDblTheory>) -> UstrDiscreteDblModel {
32    loop_of_type(th, ustr("Object"), FinMor::Generator(ustr("PositiveSlow")))
33}
34
35/** The delayed negative self-loop.
36
37A free [delayable signed category](super::theories::th_delayable_signed_category).
38 */
39pub fn delayed_negative_loop(th: Arc<UstrDiscreteDblTheory>) -> UstrDiscreteDblModel {
40    loop_of_type(th, ustr("Object"), FinMor::Generator(ustr("NegativeSlow")))
41}
42
43/// Creates a self-loop with given object and morphism types.
44fn loop_of_type(
45    th: Arc<UstrDiscreteDblTheory>,
46    ob_type: Ustr,
47    mor_type: FinMor<Ustr, Ustr>,
48) -> UstrDiscreteDblModel {
49    let mut model = UstrDiscreteDblModel::new(th);
50    let x = ustr("x");
51    model.add_ob(x, ob_type);
52    model.add_mor(ustr("loop"), x, x, mor_type);
53    model
54}
55
56/** The positive feedback loop between two objects.
57
58A signed graph or free [signed category](super::theories::th_signed_category).
59 */
60pub fn positive_feedback(th: Arc<UstrDiscreteDblTheory>) -> UstrDiscreteDblModel {
61    let mut model = UstrDiscreteDblModel::new(th);
62    let (x, y) = (ustr("x"), ustr("y"));
63    model.add_ob(x, ustr("Object"));
64    model.add_ob(y, ustr("Object"));
65    model.add_mor(ustr("positive1"), x, y, FinMor::Id(ustr("Object")));
66    model.add_mor(ustr("positive2"), y, x, FinMor::Id(ustr("Object")));
67    model
68}
69
70/** The negative feedback loop between two objects.
71
72A signed graph or free [signed category](super::theories::th_signed_category).
73 */
74pub fn negative_feedback(th: Arc<UstrDiscreteDblTheory>) -> UstrDiscreteDblModel {
75    let mut model = UstrDiscreteDblModel::new(th);
76    let (x, y) = (ustr("x"), ustr("y"));
77    model.add_ob(x, ustr("Object"));
78    model.add_ob(y, ustr("Object"));
79    model.add_mor(ustr("positive"), x, y, FinMor::Id(ustr("Object")));
80    model.add_mor(ustr("negative"), y, x, FinMor::Generator(ustr("Negative")));
81    model
82}
83
84/** The "walking attribute" schema.
85
86A schema with one entity type, one attribute type, and one attribute.
87 */
88pub fn walking_attr(th: Arc<UstrDiscreteDblTheory>) -> UstrDiscreteDblModel {
89    let mut model = UstrDiscreteDblModel::new(th);
90    let (entity, attr_type) = (ustr("entity"), ustr("type"));
91    model.add_ob(entity, ustr("Entity"));
92    model.add_ob(attr_type, ustr("AttrType"));
93    model.add_mor(ustr("attr"), entity, attr_type, FinMor::Generator(ustr("Attr")));
94    model
95}
96
97/** The "walking" backward link.
98
99The free category with links having a link from the codomain of a morphism back
100to the morphism itself.
101
102In the system dynamics jargon, a backward link defines a "reinforcing loop,"
103assuming the link has a positive effect on the flow. An example is an infection
104flow in a model of an infectious disease, where increasing the number of
105infectives increases the rate of infection of the remaining susceptibles (other
106things equal).
107 */
108pub fn backward_link(th: Arc<UstrDiscreteTabTheory>) -> UstrDiscreteTabModel {
109    let mut model = UstrDiscreteTabModel::new(th.clone());
110    let (x, y, f) = (ustr("x"), ustr("y"), ustr("f"));
111    let ob_type = TabObType::Basic(ustr("Object"));
112    model.add_ob(x, ob_type.clone());
113    model.add_ob(y, ob_type.clone());
114    model.add_mor(f, TabOb::Basic(x), TabOb::Basic(y), th.hom_type(ob_type));
115    model.add_mor(
116        ustr("link"),
117        TabOb::Basic(y),
118        model.tabulated_gen(f),
119        TabMorType::Basic(ustr("Link")),
120    );
121    model
122}
123
124#[cfg(test)]
125mod tests {
126    use super::super::theories::*;
127    use super::*;
128    use crate::validate::Validate;
129
130    #[test]
131    fn signed_categories() {
132        let th = Arc::new(th_signed_category());
133        assert!(positive_loop(th.clone()).validate().is_ok());
134        assert!(negative_loop(th.clone()).validate().is_ok());
135        assert!(positive_feedback(th.clone()).validate().is_ok());
136        assert!(negative_feedback(th.clone()).validate().is_ok());
137    }
138
139    #[test]
140    fn delayable_signed_categories() {
141        let th = Arc::new(th_delayable_signed_category());
142        assert!(positive_loop(th.clone()).validate().is_ok());
143        assert!(negative_loop(th.clone()).validate().is_ok());
144        assert!(delayed_positive_loop(th.clone()).validate().is_ok());
145        assert!(delayed_negative_loop(th.clone()).validate().is_ok());
146    }
147
148    #[test]
149    fn schemas() {
150        let th = Arc::new(th_schema());
151        assert!(walking_attr(th).validate().is_ok());
152    }
153
154    #[test]
155    fn categories_with_links() {
156        let th = Arc::new(th_category_links());
157        assert!(backward_link(th).validate().is_ok());
158    }
159}
catlog/stdlib/models.rs

catlog/stdlib/
models.rs
