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brendanzab committed Aug 25, 2022
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4 changes: 2 additions & 2 deletions experiments/idris/src/Fathom/Closed/InductiveRecursive.idr
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||| the descriptions and their in-memory representation. This closely matches
||| the current implementation of format descriptions in Fathom.
|||
||| [Induction recusion](https://en.wikipedia.org/wiki/Induction-recursion) is
||| [Induction recursion](https://en.wikipedia.org/wiki/Induction-recursion) is
||| where an inductive datatype is defined simultaneously with a function that
||| operates on that type (see the @Format and @Rep definitions below).
|||
||| The universe is ‘closed’ in the sense tha new format descriptions cannot be
||| added to the type theory, although they can be composed out of other formats)
|||
||| This is similar to the approach used when defining type theories with
||| Tarski-style universes. In-fact inductive-recusrive datatypes as a language
||| Tarski-style universes. In-fact inductive-recursive datatypes as a language
||| feature were apparently originally motivated by this use case (see: [“A
||| General Formulation of Simultaneous Inductive-Recursive Definitions in Type
||| Theory”](https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.4575) by
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||| Experimenting with an approach to extending inductive-recusive format
||| Experimenting with an approach to extending inductive-recursive format
||| descriptions with custom formats.

module Fathom.Closed.InductiveRecursiveCustom
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||| A custom format description.
|||
||| We’d prefer to just import `Fathom.Open.Record`, but Idris’ imports are a
||| bit tempramental and result in ambiguities when importing modules that
||| bit temperamental and result in ambiguities when importing modules that
||| contain types of the same name as those defined in the current module.
public export
record CustomFormat where
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6 changes: 3 additions & 3 deletions experiments/idris/src/Fathom/Open/Record.idr
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||| Open format universe
|||
||| This module defines an open universe of binary format descriptions using
||| records to define an inderface. By defining formats in this way, the
||| records to define an interface. By defining formats in this way, the
||| universe of formats is open to extension.
|||
||| I’m not sure, but this reminds me a little of the ‘coinductive universes’
||| that [some type theorists were proposing for HoTT](https://www.cmu.edu/dietrich/philosophy/hott/slides/shulman-2022-05-12.pdf#page=79),
||| I’m not sure, but this reminds me a little of the ‘coinductively defined
||| universes’ that [some type theorists were proposing](https://www.cmu.edu/dietrich/philosophy/hott/slides/shulman-2022-05-12.pdf#page=79),
||| but I may be mistaken.

module Fathom.Open.Record
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4 changes: 2 additions & 2 deletions experiments/idris/src/Playground.idr
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Expand Up @@ -13,7 +13,7 @@ import Fathom.Open.Record as Record
-- Experiment with converting between the different styles of format universes


||| Convert an inductive-recusive format universe into a record format
||| Convert an inductive-recursive format universe into a record format
public export
format : IndRec.Format -> Record.Format
format f = Record.MkFormat
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}


||| Conver an indexed-inductive format universe into a record format
||| Convert an indexed-inductive format universe into a record format
public export
formatOf : {Rep : Type} -> Indexed.FormatOf Rep -> Record.Format
formatOf f = Record.MkFormat
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