This is way better
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The definition of `Atom` is as given in the Preserves text syntax.
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```text
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Document := Expr* sp
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Expr := sp (Atom | Compound | Punct | Embedded | Annotated)
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Compound := Sequence | Record | Block | Group | Set
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Punct := `,` | `;` | `:`+
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sp := (space | tab | cr | lf)*
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Sequence := `[` Expr* Trailer sp `]`
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Record := `<` Expr* Trailer sp `>`
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Block := `{` Expr* Trailer sp `}`
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Group := `(` Expr* Trailer sp `)`
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Set := `#{` Expr* Trailer sp `}`
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Trailer := Annotation*
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Embedded := `#!` Expr
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Annotated := Annotation Expr
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Annotation := `@` Expr | `#` ((space | tab) linecomment) (cr | lf)
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```
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@ -3,128 +3,105 @@ title: "P-expressions"
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---
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Tony Garnock-Jones <tonyg@leastfixedpoint.com>
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October 2023. Version 0.2.0.
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October 2023. Version 0.3.0.
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[text syntax]: preserves-text.html
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This document defines a grammar called *Preserves Expressions*
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(*P-expressions*, *pexprs*) that includes [ordinary Preserves text
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syntax](preserves-text.html) but offers extensions sufficient to support
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a Lisp- or Haskell-like programming notation.
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syntax][text syntax] but offers extensions sufficient to support a Lisp-
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or Haskell-like programming notation.
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**Motivation.** The [text syntax](preserves-text.html) for Preserves
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works well for writing `Value`s, i.e. data. However, in some contexts,
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Preserves applications need a broader grammar that allows interleaving
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of *expressions* with data. Two examples are the [Preserves Schema
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**Motivation.** The [text syntax][] for Preserves works well for writing
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`Value`s, i.e. data. However, in some contexts, Preserves applications
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need a broader grammar that allows interleaving of *expressions* with
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data. Two examples are the [Preserves Schema
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language](preserves-schema.html) and the [Synit configuration scripting
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language](https://synit.org/book/operation/scripting.html), both of
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which (ab)use Preserves text syntax as a kind of programming notation.
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## Preliminaries
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The P-expression grammar takes the text syntax grammar as its base and
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modifies it.
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The P-expression grammar includes by reference the definition of `Atom` from the
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[text syntax][], as well as the definitions that `Atom` depends on.
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P-expressions take their own approach to inter-token whitespace,
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however.
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<a id="whitespace">
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**Whitespace.** Whitespace is redefined as any number of spaces, tabs,
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carriage returns, or line feeds. Commas are *not* considered whitespace
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in P-expressions.
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**Whitespace.** Whitespace `sp` is defined as any number of spaces,
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tabs, carriage returns, or line feeds. Commas are *not* considered
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whitespace in P-expressions, and so class `sp` is different to class
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`ws` from the text syntax.
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ws = *(%x20 / %x09 / CR / LF)
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sp = *(%x20 / %x09 / CR / LF)
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<a id="delimiters"></a>
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**Delimiters.** Because commas are no longer included in class `ws`,
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class `delimiter` is widened to include them explicitly.
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delimiter = ws / ","
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/ "<" / ">" / "[" / "]" / "{" / "}"
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/ "#" / ":" / DQUOTE / "|" / "@" / ";"
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No changes to [the Preserves semantic model](preserves.html) are made.
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Every Preserves text-syntax term can be parsed as a valid P-expression,
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but in general P-expressions must be rewritten or otherwise interpreted
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before a meaningful Preserves value can be arrived at ([see
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below](#reading-preserves)).
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## Grammar
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P-expressions add comma, semicolon, and sequences of one or more colons
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to the syntax class `Value`.
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Standalone documents containing P-expressions are sequences of
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individual `Expr`s, followed by trailing whitespace.
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Value =/ Comma / Semicolon / Colons
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Comma = ","
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Semicolon = ";"
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Colons = 1*":"
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Document = *Expr sp
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Now that colon is in `Value`, the syntax for `Dictionary` is replaced
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with `Block` everywhere it is mentioned.
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A single P-expression `Expr` can be an `Atom` from the [text syntax][],
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a compound expression, special punctuation, an `Embedded` expression, or
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an `Annotated` expression.
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Block = "{" *Value ws "}"
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Expr = sp (Atom | Compound | Punct | Embedded | Annotated)
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Syntax for `Record` is loosened to allow empty angle brackets.
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Embedded and annotated values are as in the text syntax, differing only
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in that uses of `Value` are replaced with `Expr`.
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Record = "<" *Value ws ">"
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Embedded = "#!" Expr
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Annotated = Annotation Expr
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Annotation = "@" Expr / "#" [(%x20 / %x09) linecomment] (CR / LF)
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New syntax for explicit uninterpreted grouping of sequences of values is
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introduced, and added to class `Value`.
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P-expression special punctuation marks are comma, semicolon, and sequences of one or more colons.
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Value =/ ws Group
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Group = "(" *Value ws ")"
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Punct = "," / ";" / 1*":"
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Finally, class `Document` is replaced in order to allow standalone
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documents to directly comprise a sequence of multiple values.
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Compound expressions are sequences of `Expr`s with optional trailing
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`Annotation`s, surrounded by various kinds of parentheses.
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Document = *Value ws
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Compound = Sequence / Record / Block / Group / Set
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Sequence = "[" *Expr Trailer sp "]"
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Record = "<" *Expr Trailer sp ">"
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Block = "{" *Expr Trailer sp "}"
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Group = "(" *Expr Trailer sp ")"
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Set = "#{" *Expr Trailer sp "}"
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No changes to [the Preserves semantic model](preserves.html) are made.
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Every Preserves text-syntax term is a valid P-expression, but in general
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P-expressions must be rewritten or otherwise interpreted before a
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meaningful Preserves value can be arrived at ([see
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below](#reading-preserves)).
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In an `Annotated` P-expression, annotations and comments attach to the
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term following them, just as in the ordinary text syntax. However, it is
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common in programming notations to allow comments at the end of a file
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or other sequential construct. The ordinary text syntax forbids comments
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in these positions, but P-expressions allow them.
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## <a id="annotations"></a>Annotations and Comments
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Annotations and comments attach to the term following them, just as in
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the ordinary text syntax. However, it is common in programming notations
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to allow comments at the end of a file or other sequential construct:
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{
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key: value
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# example of a comment at the end of a dictionary
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}
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# example of a comment at the end of the input file
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While the ordinary text syntax forbids comments in these positions,
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P-expressions allow them:
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Document =/ *Value Trailer ws
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Record =/ "<" *Value Trailer ws ">"
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Sequence =/ "[" *Value Trailer ws "]"
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Set =/ "#{" *Value Trailer ws "}"
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Block =/ "{" *Value Trailer ws "}"
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Group =/ "(" *Value Trailer ws ")"
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Trailer = 1*Annotation
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Trailer = *Annotation
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## <a id="encoding-pexprs"></a>Encoding P-expressions as Preserves
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We write ⌜*p*⌝ for the encoding into Preserves of P-expression *p*.
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{:.pseudocode.equations}
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| ⌜·⌝ : **P-expression** | ⟶ | **Preserves** |
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Aside from `Group`, `Block`, `Comma`, `Semicolon`, `Colons`, `Trailer`,
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and `Record`, P-expressions are encoded directly as Preserves data.
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{:.pseudocode.equations}
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| ⌜`[`*p* ...`]`⌝ | = | `[`⌜*p*⌝ ...`]` |
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| ⌜`#{`*p* ...`}`⌝ | = | `#{`⌜*p*⌝ ...`}` |
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| ⌜`#!`*p*⌝ | = | `#!`⌜*p*⌝ |
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| ⌜`@`*p* *q*⌝ | = | `@`⌜*p*⌝ ⌜*q*⌝ |
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| ⌜*p*⌝ | = | *p* when *p* ∈ **Atom** |
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Everything else is encoded as Preserves records.
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{:.pseudocode.equations}
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| ⌜`<`*p* ...`>`⌝ | = | `<r` ⌜*p*⌝ ...`>` |
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| ⌜`(`*p* ...`)`⌝ | = | `<g` ⌜*p*⌝ ...`>` |
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| ⌜`{`*p* ...`}`⌝ | = | `<b` ⌜*p*⌝ ...`>` |
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| ⌜`,`⌝ | = | `<s |,|>` |
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| ⌜`;`⌝ | = | `<s |;|>` |
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| ⌜`:` ...⌝ | = | `<s |:` ...`|>` |
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| ⌜*t*⌝ | = | ⌜*a*⌝ ... `<a>`, where *a* ... are the annotations in *t* and *t* ∈ **Trailer** |
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| ⌜·⌝ : **Expr** | ⟶ | **Value** |
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| ⌜`[`*p* ...`]`⌝ | = | `[`⌜*p*⌝ ...`]` |
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| ⌜`<`*p* ...`>`⌝ | = | `<r` ⌜*p*⌝ ...`>` |
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| ⌜`{`*p* ...`}`⌝ | = | `<b` ⌜*p*⌝ ...`>` |
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| ⌜`(`*p* ...`)`⌝ | = | `<g` ⌜*p*⌝ ...`>` |
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| ⌜`#{`*p* ...`}`⌝ | = | `<s `⌜*p*⌝ ...`>` |
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| ⌜`#!`*p*⌝ | = | `#!`⌜*p*⌝ |
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| ⌜`@`*p* *q*⌝ | = | `@`⌜*p*⌝ ⌜*q*⌝ |
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| ⌜*p*⌝ | = | *p* | when *p* ∈ **Atom** |
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| ⌜`,`⌝ | = | `<p |,|>` |
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| ⌜`;`⌝ | = | `<p |;|>` |
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| ⌜`:` ...⌝ | = | `<p |:` ...`|>` |
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| ⌜*t*⌝ | = | ⌜*a*⌝ ... `<a>` | where *a* ... are the annotations in *t* and *t* ∈ **Trailer** |
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The record `<a>` acts as an anchor for the annotations in a `Trailer`.
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@ -145,18 +122,19 @@ using Preserves text syntax and then (3) read as a P-expression can be
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A reader for P-expressions can be adapted to yield a reader for
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Preserves terms by processing (subterms of) each P-expression that the
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reader produces. The only subterms that need processing are the special
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classes mentioned above.
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reader produces.
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1. Every `Group` or `Semicolon` that appears is an error.
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2. Every `Colons` with two or more colons in it is an error.
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3. Every `Comma` that appears is discarded.
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1. Every `(`..`)` or `;` that appears is an error.
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2. Every `:`, `::`, `:::`, ... is an error, except in context of `Block`s as described below.
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3. Every `,` that appears is discarded.
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4. Every `Trailer` that appears is an error.[^discard-trailers-instead-of-error]
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5. Every `Record` with no values in it is an error.
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6. Every `Block` must contain triplets of `Value`, `Colons` (with a
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single colon), `Value`. Any `Block` not following this pattern is an
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6. Every `Block` must contain zero or more repeating triplets of
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`Expr`, `:`, `Expr`. Any `Block` not following this pattern is an
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error. Each `Block` following the pattern is translated to a
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`Dictionary` containing a key/value pair for each triplet.
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`Dictionary` containing a key/value pair for each triplet. Any
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`Block` with duplicate keys (under interpretation) is an error.
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7. Every `Set` containing any duplicate expressions (under interpretation) is an error.
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[^discard-trailers-instead-of-error]: **Implementation note.** When
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implementing parsing of P-expressions into Preserves, consider
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@ -168,7 +146,7 @@ classes mentioned above.
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Examples are given as pairs of P-expressions and their Preserves
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text-syntax encodings.
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### Individual P-expression `Value`s
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### Individual P-expression `Expr`s
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```preserves
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⌜<date 1821 (lookup-month "February") 3>⌝
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@ -203,19 +181,27 @@ text-syntax encodings.
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tearDown();
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}⌝
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= <b
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setUp <g> <s |;|>
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setUp <g> <p |;|>
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# Now enter the loop
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loop <s |:|> <b
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greet <g "World"> <s |;|>
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loop <p |:|> <b
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greet <g "World"> <p |;|>
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>
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tearDown <g> <s |;|>
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tearDown <g> <p |;|>
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>
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```
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```preserves
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⌜[1 + 2.0, print "Hello", predicate: #t, foo, #!remote, bar]⌝
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= [1 + 2.0 <s |,|> print "Hello" <s |,|> predicate <s |:|> #t <s |,|>
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foo <s |,|> #!remote <s |,|> bar]
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= [1 + 2.0 <p |,|> print "Hello" <p |,|> predicate <p |:|> #t <p |,|>
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foo <p |,|> #!remote <p |,|> bar]
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```
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```preserves
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⌜#{1 2 3}⌝
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= <s 1 2 3>
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⌜#{(read) (read) (read)}⌝
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= <s <g read> <g read> <g read>>
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```
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```preserves
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@ -224,8 +210,8 @@ text-syntax encodings.
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address: Address,
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}⌝
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= <b
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optional name <s |:|> string <s |,|>
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address <s |:|> Address <s |,|>
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optional name <p |:|> string <p |,|>
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address <p |:|> Address <p |,|>
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>
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```
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@ -238,7 +224,7 @@ text-syntax encodings.
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}
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# example of a comment at the end of the input file⌝
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= [ <b
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key <s |:|> value
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key <p |:|> value
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@"example of a comment at the end of a dictionary" <a>
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>
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@"example of a comment at the end of the input file"
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@ -273,7 +259,7 @@ generic P-expression reader can then feed into special-purpose
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program, and the parser refines this.
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Often, a parser will wish to extract structure from sequences of
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P-expression `Value`s.
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P-expression `Expr`s.
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- A simple technique is repeated splitting of sequences; first by
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`Semicolon`, then by `Comma`, then by increasingly high binding-power
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@ -286,10 +272,39 @@ P-expression `Value`s.
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to build a parse tree using an extensible specification of the pre-,
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in-, and postfix operators involved.
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- Finally, if you treat sequences of `Value`s as pre-lexed token
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- Finally, if you treat sequences of `Expr`s as pre-lexed token
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streams, almost any parsing formalism (such as [PEG
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parsing](https://en.wikipedia.org/wiki/Parsing_expression_grammar),
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[Ometa](https://en.wikipedia.org/wiki/OMeta), etc.) can be used to
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extract further syntactic structure.
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## Appendix: Equations for interpreting P-expressions as Preserves
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The partial function **uncomma**(*p*) removes all occurrences of `,`
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from a P-expression *p*.
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{:.pseudocode.equations}
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| **uncomma** : **Expr** | ⇀ | **Expr** | |
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| **uncomma**(`[`*p* ...`]`) | = | `[`**uncomma**(*p*) ...`]` | omitting any *p* = `,` |
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| **uncomma**(`<`*p* ...`>`) | = | `<`**uncomma**(*p*) ...`>` | omitting any *p* = `,` |
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| **uncomma**(`{`*p* ...`}`) | = | `{`**uncomma**(*p*) ...`}` | omitting any *p* = `,` |
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| **uncomma**(`(`*p* ...`)`) | = | `(`**uncomma**(*p*) ...`)` | omitting any *p* = `,` |
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| **uncomma**(`#{`*p* ...`}`) | = | `#{`**uncomma**(*p*) ...`}` | omitting any *p* = `,` |
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| **uncomma**(`#!`*p*) | = | `#!`**uncomma**(*p*) ...`}` | |
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| **uncomma**(`@`*p* *q*) | = | `@`**uncomma**(*p*) **uncomma**(*q*) | |
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| **uncomma**(*p*) | = | *p* | if *p* ∈ **Atom** ∪ **Punct** - {`,`} |
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We write ⌞**uncomma**(*p*)⌟ for the partial function mapping a
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P-expression *p* ∈ `Expr` to a corresponding Preserves `Value`.
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{:.pseudocode.equations}
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| ⌞·⌟ : **Expr** | ⇀ | **Value** | |
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| ⌞`[`*p* ...`]`⌟ | = | `[`⌞*p*⌟ ...`]` | |
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| ⌞`<`ℓ *p* ...`>`⌟ | = | `<`⌞ℓ⌟ ⌞*p*⌟ ...`>` | |
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| ⌞`{`*k*`:`*v* ...`}`⌟ | = | `{`⌞*k*⌟`:`⌞*v*⌟ ...`}` | if all ⌞*k*⌟ ... are distinct |
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| ⌞`#{`*p* ...`}`⌟ | = | `#{`⌞*p*⌟ ...`}` | if all ⌞*p*⌟ ... are distinct |
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| ⌞`#!`*p*⌟ | = | `#!`⌞*p*⌟ | |
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| ⌞`@`*p* *q*⌟ | = | `@`⌞*p*⌟ ⌞*q*⌟ | |
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| ⌞*p*⌟ | = | *p* | when *p* ∈ **Atom** |
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## Notes
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