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Expanding on the naming conventions #793

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expanding naming conventions
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Expand Up @@ -190,19 190,19 @@ pointwise equal to `tr-Ω` as `compute-tr-Ω`.
To give a sense of the kind of general descriptors we use, we list some common
descriptors in the table below.

| Descriptor | Purpose |
| ---------------- | -------------------------------------------------------------------------------------------------------------- |
| `coh` | Used for proofs of coherence |
| `coherence` | Used to assert coherence |
| `compute` | Used for proofs of computation, which may be an identification or an element of any other identity system |
| `Eq` | Used for identity systems on types of a particular form |
| `eq` | Used as a descriptor for the identity type |
| `equiv` | Used for equivalences, and also for names of identity systems of universe-like types |
| `extensionality` | Used for computations of identity types |
| `htpy` | Used for constructions of homotopies, and also for names of identity systems of function-like types |
| `is-property` | Used when `is-prop` is unavailable |
| `map` | Used in two ways: as the functorial action of a type constructor, but also as the underlying map of a morphism |
| `type` | Used for the underlying type of an object |
| Descriptor | Purpose |
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Add statement

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I think it would be very good to have an example column for this table as well. That's what I did for the sHoTT project

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Another descriptor pair we use a lot is is/has :)

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Why do you think of them as descriptors? That seems grammatically very weird.

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They are modifiers signifying that the type is a property/structure, and then we omit them for the associated total types. It just seems consistent with the scheme.

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I'm willing to come up with our own naming convention, but I'm not willing to come up with a new theory that the verbs to be and to have are modifiers. That idea seems out of this world to me.

| ---------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| `coh` | Used for proofs of coherence |
| `coherence` | Used to assert coherence |
Comment on lines 195 to 196
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Seems like the need for coh is obsoleted by introducing statement.

| `compute` | Used for proofs of computation, which may be an identification or an element of any other identity system |
| `Eq` | Used for identity systems on types where `htpy` or `equiv` is not an appropriate descriptor of the identity system. `Eq` is commonly used as a descriptor for identity systems on number systems. |
| `eq` | Used as a descriptor for the identity type |
| `equiv` | Used for equivalences, and also for names of identity systems of universe-like types |
| `extensionality` | Used for computations of identity types |
| `htpy` | Used for constructions of homotopies, and also for names of identity systems of function-like types |
| `is-property` | Used when `is-prop` is unavailable |
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I don't remember if I already mentioned this, but did you know we actually define is-property in foundation-core.subtypes? Although IIRC it is not referred to anywhere.

| `map` | Used in two ways: as the functorial action of a type constructor, but also as the underlying map of a morphism |
| `type` | Used for the underlying type of an object |

## Overview of our naming conventions

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