preserves/preserves-schema.md

no_site_title	title
true	Preserves Schema

Tony Garnock-Jones tonyg@leastfixedpoint.com
May 2021. Version 0.1.0.

This document proposes a Schema language for the Preserves data model.

Introduction

A Preserves schema connects Preserves Values to host-language data structures. Each definition within a schema can be processed by a compiler to produce

• a host-language type definition;

• a partial parsing function from Values to instances of the produced type; and

• a total serialization function from instances of the type to Values.

Every parsed Value retains enough information to always be able to be serialized again, and every instance of a host-language data structure contains, by construction, enough information to be successfully serialized.

Example. Sending the schema

version 1 .
Date = <date @year int @month int @day int>.
Person = <person @name string @birthday Date>.

to the TypeScript schema compiler produces types,

type Date = {"year": number, "month": number, "day": number};
type Person = {"name": string, "birthday": Date};

constructors,

function Date({year, month, day}: {year: number, month: number, day: number}): Date;
function Person({name, birthday}: {name: string, birthday: Date}): Person;

partial parsing functions which throw on parse failure,

function asDate(v: _val): Date;
function asPerson(v: _val): Person;

total parsing functions which yield undefined on parse failure,

function toDate(v: _val): undefined | Date;
function toPerson(v: _val): undefined | Person;

and total serialization functions,

function fromDate(_v: Date): _val;
function fromPerson(_v: Person): _val;

Concepts

Bundle. A collection of schemas, each named by a module path.

Definition. A named pattern within a schema. When compiled, a definition will usually produce a type (plus associated constructors and predicates), a parser function, and a serializer function.

Metaschema. The Preserves metaschema is a schema describing the abstract syntax of all schema instances (including itself).

Module path. A sequence of symbols, denoting a leaf in a tree with symbol-labelled edges.

Pattern. A pattern describes a collection of Values as well as providing names for the portions of matching Values that should be captured in a host-language data type.

Schema abstract syntax tree (AST). Schema-manipulating tools will usually work with schema AST; that is, with Values conforming to the metaschema or instances of the corresponding host-language datastructures.

Schema domain-specific language (DSL). While human beings can work directly with Preserves documents matching the metaschema, the schema DSL provides an easier-to-read and -write language for working with schemas that can be translated into instances

Schema. A collection of definitions, plus an optional schema-wide reference to a schema describing embedded values.

Concrete (DSL) Syntax

In this section, we use an ABNF-like notation to define a textual syntax that is easy for people to read and write. Most of the examples in this document are written using this syntax. In the following section, we will define the abstract syntax that this surface syntax translates into.

Schema files and bundles.

Each schema should be placed in a single file. Schema files usually end with extension .prs, and consist of a sequence of Preserves Values¹ separated into clauses by the Preserves Symbol ".".

A bundle of schema files is a directory tree containing .prs files.

Clauses.

Clause            = (Version / EmbeddedTypeName / Definition) "."

Version           = "version" "1"
EmbeddedTypeName  = "embeddedType" ("#f" / Ref)
Definition        = symbol "=" (OrPattern / AndPattern / Pattern)

Version specification. Mandatory. Names the version of the schema language used in the file. This version of the specification is referred to in schema files as version 1.

Embedded type name. Optional. If given as #f (the default), it declares that values parsed by the schema do not contain embedded Values of any particular type. If given as a Ref, a reference to a definition in this or a neighbouring schema, it declares that embedded Values must themselves conform to the named definition.

Definition. Each definition clause implicitly connects a pattern with a type name and a set of associated functions.

Union definitions.

OrPattern = AltPattern "/" AltPattern *("/" AltPattern)

The right-hand-side of a definition may supply two or more alternatives. When parsing, the alternatives are tried in order; the result of the first successful alternative is the result of the entire parse.

The type corresponding to an OrPattern is a union type, a variant type, or an algebraic sum type, depending on the host language.

Each alternative with an OrPattern must have a definition-unique name. The name can either be given explicitly as @name (see discussion of NamedPattern below) or inferred. It can only be inferred from the label of a record pattern, from the name of a reference to another definition, or from the text of a "sufficiently stringlike" literal pattern - one that matches a string, symbol, number or boolean:

AltPattern = "@" symbol SimplePattern
           / "<" symbol *(NamedPattern) ">"
           / Ref
           / LiteralPattern  -- with a side condition

Intersection definitions.

AndPattern = NamedPattern "&" NamedPattern *("&" NamedPattern)

The right-hand-side of a definition may supply two or more patterns, the intersection of whose denotations is the denotation of the overall definition. When parsing, every pattern is tried; if all succeed, the resulting information is combined into a single record type.

When serializing, the terms resulting from serializing at each pattern are merged together.

Experimental.

Intersections are an experimental feature. They can be used to express optional dictionary entries:

MyDict = {a: int, b: string} & @c MaybeC .
MaybeC = @present {c: symbol} / @absent {} .

It is not yet clear whether they pull their weight. In particular, the semantics of serializing a value defined by intersection are not completely clear.

Patterns.

Pattern = SimplePattern / CompoundPattern

Patterns come in two kinds:

• the parsers for simple patterns yield a single host-language value such as a string, number, or pointer.

• the parsers for compound patterns yield zero or more fields which combine into an overall record type associated with a definition.

Simple patterns

SimplePattern = AnyPattern
              / AtomKindPattern
              / EmbeddedPattern
              / LiteralPattern
              / SequenceOfPattern
              / SetOfPattern
              / DictOfPattern
              / Ref

The any pattern matches any input Value:

AnyPattern = "any"

Specifying the name of a kind of Atom matches that kind of atom:

AtomKindPattern = "bool" / "float" / "double" / "int" / "string" / "bytes" / "symbol"

Specifying embedded matches an Embedded value, following the schema-wide embeddedType, if any:

EmbeddedPattern = "embedded"

A literal pattern may be expressed in any of three ways: non-symbol atoms stand for themselves directly; symbols, prefixed with an equal sign, are matched literally; and any Value at all may be quoted by placing it in a <<lit> ... > record:

LiteralPattern = "="symbol / "<<lit>" value ">" / non-symbol-atom

Brackets containing an item pattern and a literal ellipsis match a sequence of items, each matching the nested item pattern. Sets and uniform dictionaries are similar.

SequenceOfPattern = "[" SimplePattern "..." "]"
SetOfPattern = "#{" SimplePattern "}"
DictOfPattern = "{" SimplePattern ":" SimplePattern "...:..." "}"

Finally, a reference to some other definition, in this schema or a neighbouring schema within this bundle, is made by mentioning the possibly-qualified name of the definition as a bare symbol:

Ref = symbol

Periods "." in such symbols are special:

• Name refers to the definition named Name in the current schema.
• Mod.Submod.Name refers to definition Name in Mod.Submod, some other schema in the bundle.

Compound patterns

CompoundPattern = RecordPattern
                / TuplePattern
                / VariableTuplePattern
                / DictionaryPattern

A record pattern matches an input record. It may be specified as a record with a literal in the label position, or as a quoted <<rec> ... > record:

RecordPattern = "<" value *(NamedPattern) ">"
              / "<<rec>" NamedPattern *(NamedPattern) ">"

A tuple pattern matches a fixed-length sequence with specific patterns in each position. A variable tuple pattern is the same, but with an additional pattern for matching additional elements following the fixed-position patterns.

TuplePattern = "[" *(NamedPattern) "]"
VariableTuplePattern = "[" 1*(NamedPattern) NamedSimplePattern "..." "]"

A dictionary pattern matches specific literal keys in an input dictionary. If no explicit name is given for a particular NamedSimplePattern, but the key for the pattern is a symbol, then that symbol is used as the name for that dictionary entry.

DictionaryPattern = "{" *(value ":" NamedSimplePattern) "}"

Bindings: NamedPattern and NamedSimplePattern

Compound patterns specifications contain NamedPatterns or NamedSimplePatterns rather than ordinary Patterns:

NamedPattern       = "@" symbol SimplePattern / Pattern
NamedSimplePattern = "@" symbol SimplePattern / SimplePattern

Use of an @name prefix generally results in creation of a field with the given name in the overall record type for a definition. The type of value contained in the field will correspond to the Pattern or SimplePattern given.

Appendix: Metaschema

The metaschema defines the structure of the abstract syntax (AST) of schemas, using the concrete DSL syntax described above.

The text below is taken from schema/schema.prs in the source code repository.

A Bundle collects a number of Schemas, each named by a ModulePath:²

Bundle = <bundle @modules Modules>.
Modules = { ModulePath: Schema ...:... }.
ModulePath = [symbol ...].

Schema = <schema {
  version: Version
  embeddedType: EmbeddedTypeName
  definitions: Definitions
}>.

A Version names the version of the schema language in use. At present, it must be 1.

; version 1 .
Version = 1 .

An EmbeddedTypeName specifies the type of embedded values within values parsed by a given schema:

EmbeddedTypeName = Ref / #f.
Ref = <ref @module ModulePath @name symbol>.

The Definitions are a named collection of definitions within a schema. Note the special mention of pattern0 and pattern1: these ensure that each or or and record has at least two members.

Definitions = { symbol: Definition ...:... }.

Definition =
  ; Pattern / Pattern / ...
  / <or [@pattern0 NamedAlternative
         @pattern1 NamedAlternative
         @patternN NamedAlternative ...]>

  ; Pattern & Pattern & ...
  / <and [@pattern0 NamedPattern
          @pattern1 NamedPattern
          @patternN NamedPattern ...]>

  ; Pattern
  / Pattern
.

NamedAlternative = [@variantLabel string @pattern Pattern].

Each Pattern is either a simple or compound pattern:

Pattern = SimplePattern / CompoundPattern .

Simple patterns are as described above:

SimplePattern =
  ; any
  / =any

  ; special builtins: bool, float, double, int, string, bytes, symbol
  / <atom @atomKind AtomKind>

  ; matches an embedded value in the input: embedded
  / <embedded>

  ; =symbol, <<lit> any>, or plain non-symbol atom
  / <lit @value any>

  ; [p ...] ----> <seqof <ref p>>; see also tuple* below.
  / <seqof @pattern SimplePattern>

  ; #{p} ----> <setof <ref p>>
  / <setof @pattern SimplePattern>

  ; {k: v, ...:...} ----> <dictof <ref k> <ref v>>
  / <dictof @key SimplePattern @value SimplePattern>

  ; symbol, symbol.symbol, symbol.symbol.symbol, ...
  / Ref
.

AtomKind = =Boolean
         / =Float
         / =Double
         / =SignedInteger
         / =String
         / =ByteString
         / =Symbol .

Compound patterns involve optionally-named subpatterns:

CompoundPattern =
  ; <label a b c> ----> <rec <lit label> <tuple [<ref a> <ref b> <ref c>]>>
  ; except for record labels
  ; <<rec> x y> ---> <rec <ref x> <ref y>>
  / <rec @label NamedPattern @fields NamedPattern>

  ; [a b c] ----> <tuple [<ref a> <ref b> <ref c>]>
  / <tuple @patterns [NamedPattern ...]>

  ; [a b c ...] ----> <tuple* [<ref a> <ref b>] <seqof <ref c>>>
  / <tuple* @fixed [NamedPattern ...] @variable NamedSimplePattern>

  ; {a: b, c: d} ----> <dict {a: <ref b>, c: <ref d>}>
  / <dict @entries DictionaryEntries>
.

DictionaryEntries = { any: NamedSimplePattern ...:... }.

Explicitly-named subpatterns are always SimplePatterns; but, depending context, if a name is omitted, the pattern may be a Pattern or may be restricted to SimplePattern as well:

NamedSimplePattern = @named NamedSimplePattern_ / @anonymous SimplePattern .
NamedPattern = @named NamedSimplePattern_ / @anonymous Pattern .
NamedSimplePattern_ = <named @name symbol @pattern SimplePattern>.

Appendix: Metaschema instance

The following is a (lightly-reformatted) Preserves document which is the output of DSL-to-AST compilation of the DSL source text of the metaschema.

<schema {
  version: 1,
  embeddedType: #f,
  definitions: {

    Pattern: <or [
      ["SimplePattern", <ref [] SimplePattern>],
      ["CompoundPattern", <ref [] CompoundPattern>]
    ]>,

    CompoundPattern: <or [
      ["rec", <rec <lit rec> <tuple [
          <named label <ref [] NamedPattern>>,
          <named fields <ref [] NamedPattern>>
        ]>>],
      ["tuple", <rec <lit tuple> <tuple [<named patterns <seqof <ref [] NamedPattern>>>]>>],
      ["tuple*", <rec <lit tuple*> <tuple [
          <named fixed <seqof <ref [] NamedPattern>>>,
          <named variable <ref [] NamedSimplePattern>>
        ]>>],
      ["dict", <rec <lit dict> <tuple [<named entries <ref [] DictionaryEntries>>]>>]
    ]>,

    Modules: <dictof <ref [] ModulePath> <ref [] Schema>>,

    Ref: <rec <lit ref> <tuple [
      <named module <ref [] ModulePath>>,
      <named name <atom Symbol>>
    ]>>,

    Bundle: <rec <lit bundle> <tuple [<named modules <ref [] Modules>>]>>,

    NamedSimplePattern_: <rec <lit named> <tuple [
      <named name <atom Symbol>>,
      <named pattern <ref [] SimplePattern>>
    ]>>,

    Definition: <or [
      ["or", <rec <lit or> <tuple [<tuple* [
          <named pattern0 <ref [] NamedAlternative>>,
          <named pattern1 <ref [] NamedAlternative>>
        ] <named patternN <seqof <ref [] NamedAlternative>>>>]>>],
      ["and", <rec <lit and> <tuple [<tuple* [
          <named pattern0 <ref [] NamedPattern>>,
          <named pattern1 <ref [] NamedPattern>>
        ] <named patternN <seqof <ref [] NamedPattern>>>>]>>],
      ["Pattern", <ref [] Pattern>]
    ]>,

    NamedSimplePattern: <or [
      ["named", <ref [] NamedSimplePattern_>],
      ["anonymous", <ref [] SimplePattern>]
    ]>,

    EmbeddedTypeName: <or [
      ["Ref", <ref [] Ref>],
      ["false", <lit #f>]
    ]>,

    ModulePath: <seqof <atom Symbol>>,

    AtomKind: <or [
      ["Boolean", <lit Boolean>],
      ["Float", <lit Float>],
      ["Double", <lit Double>],
      ["SignedInteger", <lit SignedInteger>],
      ["String", <lit String>],
      ["ByteString", <lit ByteString>],
      ["Symbol", <lit Symbol>]
    ]>,

    DictionaryEntries: <dictof any <ref [] NamedSimplePattern>>,

    Version: <lit 1>,

    NamedPattern: <or [
      ["named", <ref [] NamedSimplePattern_>],
      ["anonymous", <ref [] Pattern>]
    ]>,

    SimplePattern: <or [
      ["any", <lit any>],
      ["atom", <rec <lit atom> <tuple [<named atomKind <ref [] AtomKind>>]>>],
      ["embedded", <rec <lit embedded> <tuple []>>],
      ["lit", <rec <lit lit> <tuple [<named value any>]>>],
      ["seqof", <rec <lit seqof> <tuple [<named pattern <ref [] SimplePattern>>]>>],
      ["setof", <rec <lit setof> <tuple [<named pattern <ref [] SimplePattern>>]>>],
      ["dictof", <rec <lit dictof> <tuple [
          <named key <ref [] SimplePattern>>,
          <named value <ref [] SimplePattern>>
        ]>>],
      ["Ref", <ref [] Ref>]
    ]>,

    NamedAlternative: <tuple [
      <named variantLabel <atom String>>,
      <named pattern <ref [] Pattern>>
    ]>,

    Definitions: <dictof <atom Symbol> <ref [] Definition>>,

    Schema: <rec <lit schema> <tuple [<dict {
      version: <named version <ref [] Version>>,
      embeddedType: <named embeddedType <ref [] EmbeddedTypeName>>,
      definitions: <named definitions <ref [] Definitions>>
    }>]>>
  }
}>

Appendix: Example generated types

The following are the (abridged) TypeScript and Racket generated type definitions for the metaschema.

TypeScript.

import * as _ from "@preserves/core";

// ...
export type _embedded = any;
export type _val = _.Value<_embedded>;
// ...

export type Bundle = {"modules": Modules};

export type Modules = _.KeyedDictionary<ModulePath, Schema, _embedded>;

export type Schema = {
    "version": Version,
    "embeddedType": EmbeddedTypeName,
    "definitions": Definitions
};

export type Version = null;

export type EmbeddedTypeName = ({"_variant": "Ref", "value": Ref} | {"_variant": "false"});

export type Definitions = _.KeyedDictionary<symbol, Definition, _embedded>;

export type Definition = (
    {
        "_variant": "or",
        "pattern0": NamedAlternative,
        "pattern1": NamedAlternative,
        "patternN": Array<NamedAlternative>
    } |
    {
        "_variant": "and",
        "pattern0": NamedPattern,
        "pattern1": NamedPattern,
        "patternN": Array<NamedPattern>
    } |
    {"_variant": "Pattern", "value": Pattern}
);

export type Pattern = (
    {"_variant": "SimplePattern", "value": SimplePattern} |
    {"_variant": "CompoundPattern", "value": CompoundPattern}
);

export type SimplePattern = (
    {"_variant": "any"} |
    {"_variant": "atom", "atomKind": AtomKind} |
    {"_variant": "embedded"} |
    {"_variant": "lit", "value": _val} |
    {"_variant": "seqof", "pattern": SimplePattern} |
    {"_variant": "setof", "pattern": SimplePattern} |
    {"_variant": "dictof", "key": SimplePattern, "value": SimplePattern} |
    {"_variant": "Ref", "value": Ref}
);

export type CompoundPattern = (
    {"_variant": "rec", "label": NamedPattern, "fields": NamedPattern} |
    {"_variant": "tuple", "patterns": Array<NamedPattern>} |
    {
        "_variant": "tuple*",
        "fixed": Array<NamedPattern>,
        "variable": NamedSimplePattern
    } |
    {"_variant": "dict", "entries": DictionaryEntries}
);

export type DictionaryEntries = _.KeyedDictionary<_val, NamedSimplePattern, _embedded>;

export type AtomKind = (
    {"_variant": "Boolean"} |
    {"_variant": "Float"} |
    {"_variant": "Double"} |
    {"_variant": "SignedInteger"} |
    {"_variant": "String"} |
    {"_variant": "ByteString"} |
    {"_variant": "Symbol"}
);

export type NamedAlternative = {"variantLabel": string, "pattern": Pattern};

export type NamedSimplePattern = (
    {"_variant": "named", "value": NamedSimplePattern_} |
    {"_variant": "anonymous", "value": SimplePattern}
);

export type NamedPattern = (
    {"_variant": "named", "value": NamedSimplePattern_} |
    {"_variant": "anonymous", "value": Pattern}
);

export type NamedSimplePattern_ = {"name": symbol, "pattern": SimplePattern};

export type Ref = {"module": ModulePath, "name": symbol};

export type ModulePath = Array<symbol>;

Racket.

(struct AtomKind-Symbol () #:prefab)
(struct AtomKind-ByteString () #:prefab)
(struct AtomKind-String () #:prefab)
(struct AtomKind-SignedInteger () #:prefab)
(struct AtomKind-Double () #:prefab)
(struct AtomKind-Float () #:prefab)
(struct AtomKind-Boolean () #:prefab)

(struct Bundle (modules) #:prefab)

(struct CompoundPattern-dict (entries) #:prefab)
(struct CompoundPattern-tuple* (fixed variable) #:prefab)
(struct CompoundPattern-tuple (patterns) #:prefab)
(struct CompoundPattern-rec (label fields) #:prefab)

(struct Definition-Pattern (value) #:prefab)
(struct Definition-and (pattern0 pattern1 patternN) #:prefab)
(struct Definition-or (pattern0 pattern1 patternN) #:prefab)

(struct EmbeddedTypeName-false () #:prefab)
(struct EmbeddedTypeName-Ref (value) #:prefab)

(struct NamedAlternative (variantLabel pattern) #:prefab)

(struct NamedPattern-anonymous (value) #:prefab)
(struct NamedPattern-named (value) #:prefab)

(struct NamedSimplePattern-anonymous (value) #:prefab)
(struct NamedSimplePattern-named (value) #:prefab)

(struct NamedSimplePattern_ (name pattern) #:prefab)

(struct Pattern-CompoundPattern (value) #:prefab)
(struct Pattern-SimplePattern (value) #:prefab)

(struct Ref (module name) #:prefab)

(struct Schema (definitions embeddedType version) #:prefab)

(struct SimplePattern-Ref (value) #:prefab)
(struct SimplePattern-dictof (key value) #:prefab)
(struct SimplePattern-setof (pattern) #:prefab)
(struct SimplePattern-seqof (pattern) #:prefab)
(struct SimplePattern-lit (value) #:prefab)
(struct SimplePattern-embedded () #:prefab)
(struct SimplePattern-atom (atomKind) #:prefab)
(struct SimplePattern-any () #:prefab)

Appendix: Future work

• There are side conditions on AST instances. It would be nice to eventually be able to express these within the metaschema.

• It'd be interesting to, Ometa-like, be able to specify the DSL-to-AST translation process as a schema. One challenge in doing so is the way schemas are required to be reversible at present.

Notes

---

1. That is, schema files use Preserves as a kind of S-expression! ↩︎

2. The semantics of module path references remain to be specified! ↩︎