GraphCoQL A mechanized formalization of GraphQL in Coq Toms Daz - - PowerPoint PPT Presentation

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GraphCoQL A mechanized formalization of GraphQL in Coq Toms Daz - - PowerPoint PPT Presentation

Jan 15, 2023 105 likes •641 views

GraphCoQL A mechanized formalization of GraphQL in Coq Toms Daz Federico Olmedo ric Tanter Millennium Institute Foundational Research on Data Certified Programs and Proofs New Orleans, USA January 2020 GraphQL Clases de ctedra

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GraphCoQL

Certified Programs and Proofs New Orleans, USA — January 2020

Federico Olmedo Tomás Díaz Éric Tanter

A mechanized formalization of GraphQL in Coq

Millennium Institute

Foundational Research on Data

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SLIDE 2

Clases de cátedra

GraphQL

2

Language for specifying the interfaces of web data services and their query mechanism

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SLIDE 3

Clases de cátedra

GraphQL

2

HTTP GET

Language for specifying the interfaces of web data services and their query mechanism

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SLIDE 4

Clases de cátedra

GraphQL

2

HTTP GET

query { artist(id:1000) { name artworks(role: ACTOR) { title } } }

Language for specifying the interfaces of web data services and their query mechanism

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SLIDE 5

Clases de cátedra

GraphQL

2

HTTP GET

query { artist(id:1000) { name artworks(role: ACTOR) { title } } }

Language for specifying the interfaces of web data services and their query mechanism

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SLIDE 6

Clases de cátedra

GraphQL

2

HTTP GET

query { artist(id:1000) { name artworks(role: ACTOR) { title } } }

Language for specifying the interfaces of web data services and their query mechanism

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SLIDE 7

Clases de cátedra

GraphQL

2

HTTP GET

query { artist(id:1000) { name artworks(role: ACTOR) { title } } }

Language for specifying the interfaces of web data services and their query mechanism

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SLIDE 8

{ “artist” : { “name” : “Tom Hanks”, “artworks” : [ { “title” : “Toy Story”, }, { “title” : “Forrest Gump”, }, … ] } }

Clases de cátedra

GraphQL

2

HTTP GET

query { artist(id:1000) { name artworks(role: ACTOR) { title } } }

Language for specifying the interfaces of web data services and their query mechanism

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SLIDE 9

{ “artist” : { “name” : “Tom Hanks”, “artworks” : [ { “title” : “Toy Story”, }, { “title” : “Forrest Gump”, }, … ] } }

Clases de cátedra

GraphQL

2

HTTP GET

query { artist(id:1000) { name artworks(role: ACTOR) { title } } }

Language for specifying the interfaces of web data services and their query mechanism

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SLIDE 10

{ “artist” : { “name” : “Tom Hanks”, “artworks” : [ { “title” : “Toy Story”, }, { “title” : “Forrest Gump”, }, … ] } }

Clases de cátedra

GraphQL

2

HTTP GET

query { artist(id:1000) { name artworks(role: ACTOR) { title } } }

Language for specifying the interfaces of web data services and their query mechanism

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Clases de cátedra

Industry involvement with GraphQL

3

2012 2015+

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Clases de cátedra

First language formalization [Hartig & Pérez, WWW’18]

4

Paper & pencil formalization to study complexity properties.

Jf[]Ku

G =

( f:(u, f[]) if (u, f[]) 2 dom() f:null else. J`:f[]Ku

G =

( `:(u, f[]) if (u, f[]) 2 dom() `:null else. Jf[]{}Ku

G =

       f:[{JK1

G } · · · {JKk G }]

if typeS(f) 2 LT and {1, ... ,k } = {i | (u, f[],i ) 2 E} f:{ JK

G }

if typeS(f) < LT and (u, f[],) 2 E f:null if typeS(f) < LT and there is no 2 N s.t. (u, f[],) 2 E J`:f[]{}Ku

G =

       `:[{JK1

G } · · · {JKk G }]

if typeS(f) 2 LT and {1, ... ,k } = {i | (u, f[],i ) 2 E} `:{ JK

G }

if typeS(f) < LT and (u, f[],) 2 E `:null if typeS(f) < LT and there is no 2 N s.t. (u, f[],) 2 E Jon t{}Ku

G =

       JKu

G

if t 2 OT and (u) = t, or t 2 IT and (u) 2 implementationS(t), or t 2 UT and (u) 2 unionS(t)

  • in other case.

J1 · · ·kKu

G = collect(J1Ku G · · · JkKu G )

Figure 5: Semantics of a GraphQL query.

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SLIDE 13

Clases de cátedra

First language formalization [Hartig & Pérez, WWW’18]

4

Paper & pencil formalization to study complexity properties.

Jf[]Ku

G =

( f:(u, f[]) if (u, f[]) 2 dom() f:null else. J`:f[]Ku

G =

( `:(u, f[]) if (u, f[]) 2 dom() `:null else. Jf[]{}Ku

G =

       f:[{JK1

G } · · · {JKk G }]

if typeS(f) 2 LT and {1, ... ,k } = {i | (u, f[],i ) 2 E} f:{ JK

G }

if typeS(f) < LT and (u, f[],) 2 E f:null if typeS(f) < LT and there is no 2 N s.t. (u, f[],) 2 E J`:f[]{}Ku

G =

       `:[{JK1

G } · · · {JKk G }]

if typeS(f) 2 LT and {1, ... ,k } = {i | (u, f[],i ) 2 E} `:{ JK

G }

if typeS(f) < LT and (u, f[],) 2 E `:null if typeS(f) < LT and there is no 2 N s.t. (u, f[],) 2 E Jon t{}Ku

G =

       JKu

G

if t 2 OT and (u) = t, or t 2 IT and (u) 2 implementationS(t), or t 2 UT and (u) 2 unionS(t)

  • in other case.

J1 · · ·kKu

G = collect(J1Ku G · · · JkKu G )

Figure 5: Semantics of a GraphQL query.

Missing proofs about fundamental properties

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Clases de cátedra

Our contribution

5

First mechanized formalization of GraphQL in the Coq proof assistant

GraphCoQL

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Clases de cátedra

Schema

6

Describes how data is structured and queried

type Artist { id: ID name: String artworks(role:Role): [Artwork] } interface Movie { id: ID title: String year: Int cast: [Artist] } type Fiction implements Movie { … } type Animation implements Movie { … style: Style } enum Role { ACTOR DIRECTOR WRITER } union Artwork = Fiction | Animation | Book type Book { … } type Query { artist(id:ID): Artist movie(id:ID): Movie }

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Clases de cátedra

Schema

6

Describes how data is structured and queried

  • bject

type

type Artist { id: ID name: String artworks(role:Role): [Artwork] } interface Movie { id: ID title: String year: Int cast: [Artist] } type Fiction implements Movie { … } type Animation implements Movie { … style: Style } enum Role { ACTOR DIRECTOR WRITER } union Artwork = Fiction | Animation | Book type Book { … } type Query { artist(id:ID): Artist movie(id:ID): Movie }

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Clases de cátedra

Schema

6

Describes how data is structured and queried

interface type

  • bject

type

type Artist { id: ID name: String artworks(role:Role): [Artwork] } interface Movie { id: ID title: String year: Int cast: [Artist] } type Fiction implements Movie { … } type Animation implements Movie { … style: Style } enum Role { ACTOR DIRECTOR WRITER } union Artwork = Fiction | Animation | Book type Book { … } type Query { artist(id:ID): Artist movie(id:ID): Movie }

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Clases de cátedra

Schema

6

Describes how data is structured and queried

interface type

  • bject

type

type Artist { id: ID name: String artworks(role:Role): [Artwork] } interface Movie { id: ID title: String year: Int cast: [Artist] } type Fiction implements Movie { … } type Animation implements Movie { … style: Style } enum Role { ACTOR DIRECTOR WRITER } union Artwork = Fiction | Animation | Book type Book { … } type Query { artist(id:ID): Artist movie(id:ID): Movie }

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Clases de cátedra

Schema

6

Describes how data is structured and queried

interface type

  • bject

type enumeration type

type Artist { id: ID name: String artworks(role:Role): [Artwork] } interface Movie { id: ID title: String year: Int cast: [Artist] } type Fiction implements Movie { … } type Animation implements Movie { … style: Style } enum Role { ACTOR DIRECTOR WRITER } union Artwork = Fiction | Animation | Book type Book { … } type Query { artist(id:ID): Artist movie(id:ID): Movie }

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Clases de cátedra

Schema

6

Describes how data is structured and queried

interface type

  • bject

type enumeration type union type

type Artist { id: ID name: String artworks(role:Role): [Artwork] } interface Movie { id: ID title: String year: Int cast: [Artist] } type Fiction implements Movie { … } type Animation implements Movie { … style: Style } enum Role { ACTOR DIRECTOR WRITER } union Artwork = Fiction | Animation | Book type Book { … } type Query { artist(id:ID): Artist movie(id:ID): Movie }

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Clases de cátedra

Schema

6

Describes how data is structured and queried

interface type

  • bject

type entry points for querying the dataset enumeration type union type

type Artist { id: ID name: String artworks(role:Role): [Artwork] } interface Movie { id: ID title: String year: Int cast: [Artist] } type Fiction implements Movie { … } type Animation implements Movie { … style: Style } enum Role { ACTOR DIRECTOR WRITER } union Artwork = Fiction | Animation | Book type Book { … } type Query { artist(id:ID): Artist movie(id:ID): Movie }

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Clases de cátedra

Schema

7

Describes how data is structured and queried

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Clases de cátedra

Graph data model

8

Datasets are modeled as directed property graphs, with labeled edges and typed nodes.

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Clases de cátedra

Graph data model

8

Datasets are modeled as directed property graphs, with labeled edges and typed nodes.

Artist

id: 1000 name: “Tom Hanks”

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Clases de cátedra

Graph data model

8

Datasets are modeled as directed property graphs, with labeled edges and typed nodes.

Artist Fiction

id: 2000 title: “Forrest Gump” year: 1994 id: 1000 name: “Tom Hanks”

Animation

id: 2001 title: “Toy Story” year: 1995 style: “3D" artworks[role:ACTOR] artworks[role:ACTOR]

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Clases de cátedra

Graph data model

8

Datasets are modeled as directed property graphs, with labeled edges and typed nodes.

Artist Fiction

id: 2000 title: “Forrest Gump” year: 1994 id: 1000 name: “Tom Hanks”

Animation

id: 2001 title: “Toy Story” year: 1995 style: “3D" artworks[role:ACTOR] artworks[role:ACTOR] cast cast

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Clases de cátedra

Graph data model

8

Datasets are modeled as directed property graphs, with labeled edges and typed nodes.

Book Artist Fiction

id: 3000 title: “Uncommon Type” year: 2017 ISBN: 1101946156 id: 2000 title: “Forrest Gump” year: 1994 id: 1000 name: “Tom Hanks”

Animation

id: 2001 title: “Toy Story” year: 1995 style: “3D" artworks[role:ACTOR] artworks[role:ACTOR] cast cast artworks[role:WRITER] author

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Clases de cátedra

Graph data model

8

Datasets are modeled as directed property graphs, with labeled edges and typed nodes.

Query Book Artist Fiction

artist[id:1000] id: 3000 title: “Uncommon Type” year: 2017 ISBN: 1101946156 id: 2000 title: “Forrest Gump” year: 1994 id: 1000 name: “Tom Hanks”

Animation

id: 2001 title: “Toy Story” year: 1995 style: “3D" movie[id:2001] movie[id:2000] artworks[role:ACTOR] artworks[role:ACTOR] cast cast artworks[role:WRITER] author

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query { artist(id:1000) { name artworks(role: ACTOR) { title } } }

Clases de cátedra

Query evaluation

9

Queries are evaluated by traversing the graph and collecting nodes’ properties

Response (à la JSON) Query Dataset

{ “artist” : { “name” : “Tom Hanks”, “artworks” : [ { … }, { … }, ] } }

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Clases de cátedra

Query evaluation

10

Queries are evaluated by traversing the graph and collecting nodes’ properties

Response (à la JSON) Query Dataset

{ “artist” : { “name” : “Tom Hanks”, “artworks” : [ { … }, { … }, ] } } query { artist(id:1000) { name artworks(role: ACTOR) { title } } }

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Clases de cátedra

Query evaluation

11

Queries are evaluated by traversing the graph and collecting nodes’ properties

Response (à la JSON) Query Dataset

{ “artist” : { “name” : “Tom Hanks”, “artworks” : [ { … }, { … }, ] } } query { artist(id:1000) { name artworks(role: ACTOR) { title } } }

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Clases de cátedra

Query evaluation

12

Queries are evaluated by traversing the graph and collecting nodes’ properties

Response (à la JSON) Query Dataset

{ “artist” : { “name” : “Tom Hanks”, “artworks” : [ { … }, { … }, ] } } query { artist(id:1000) { name artworks(role: ACTOR) { title } } }

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Clases de cátedra

Query evaluation

13

Queries are evaluated by traversing the graph and collecting nodes’ properties

Response (à la JSON) Query Dataset

{ “artist” : { “name” : “Tom Hanks”, “artworks” : [ { “title” : … }, { “title” : … }, ] } } query { artist(id:1000) { name artworks(role: ACTOR) { title } } }

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Clases de cátedra

Query evaluation - Peculiarities

14

Query evaluation is not compositional

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Clases de cátedra

Query evaluation - Peculiarities

14

Query evaluation is not compositional

query { artist(id:1000) { name } artist(id:1000) { artworks(role: ACTOR) { title } } }

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Clases de cátedra

Query evaluation - Peculiarities

14

Query evaluation is not compositional

query { artist(id:1000) { name } artist(id:1000) { artworks(role: ACTOR) { title } } }

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Clases de cátedra

Query evaluation - Peculiarities

14

Query evaluation is not compositional

query { artist(id:1000) { name } artist(id:1000) { artworks(role: ACTOR) { title } } } { “artist” : { “name” : “Tom Hanks”, }, “artist” : { “artworks” : [ { … }, { … }, ] } }

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Clases de cátedra

Query evaluation - Singularities

15

Selections are “factored-out” in between the recursive calls

Query evaluation is not compositional

{ “artist” : { “name” : “Tom Hanks”, “artworks” : [ { … }, { … }, ] } } query { artist(id:1000) { name } artist(id:1000) { artworks(role: ACTOR) { title } } }

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Clases de cátedra

Query evaluation - Singularities

15

Selections are “factored-out” in between the recursive calls

This makes reasoning significantly harder

Query evaluation is not compositional

{ “artist” : { “name” : “Tom Hanks”, “artworks” : [ { … }, { … }, ] } } query { artist(id:1000) { name } artist(id:1000) { artworks(role: ACTOR) { title } } }

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Application

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Clases de cátedra

Normalization [H&P, WWW’18]

17

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Clases de cátedra

Normalization [H&P, WWW’18]

17

Queries admit a normal form that can be evaluated purely compositionally and significantly simplifies reasoning

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Clases de cátedra

Normalization [H&P, WWW’18]

17

Queries admit a normal form that can be evaluated purely compositionally and significantly simplifies reasoning

👏

Normalization procedure not provided

👏

No correctness proof

But….

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Clases de cátedra

Query normalization

18

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Clases de cátedra

Query normalization

18

  • Certified normalization algorithm

e with

u σs. Theorem normalize_preserves_semantics : ∀ (φ : query) (s : wfGraphQLSchema) (g : conformedGraph s), eval_query (normalize s φ) g s = eval_query φ g s. Theorem normalized_query_is_in_nf : ∀ (φ : query) (s : wfGraphQLSchema), is_in_normal_form s (normalize s φ).

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Clases de cátedra

Query normalization

18

  • Certified normalization algorithm
  • Simplified evaluation for queries in normal form

e with

u σs. Theorem normalize_preserves_semantics : ∀ (φ : query) (s : wfGraphQLSchema) (g : conformedGraph s), eval_query (normalize s φ) g s = eval_query φ g s. Theorem normalized_query_is_in_nf : ∀ (φ : query) (s : wfGraphQLSchema), is_in_normal_form s (normalize s φ). Theorem simpl_eval_correctness : ∀ (φ : query) (s : wfGraphQLSchema) (g : conformedGraph s), is_in_normal_form s φ -> eval_query φ g s = simpl_eval_query φ g s.

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Formalization evaluation and details

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Clases de cátedra

Evaluation

20

Effectivity Uncovered two issues in H&P formalization:

  • Flawed definition of normal form
  • Incomplete set of equivalence rules for normalization
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Clases de cátedra

Evaluation

20

Effectivity Uncovered two issues in H&P formalization:

  • Flawed definition of normal form
  • Incomplete set of equivalence rules for normalization

Faithfulness Validated with a series of examples from different sources:

  • Examples (41) from the SPEC validation section*
  • Star Wars example from GraphQL reference implementation
  • Example used in H&P

* https://graphql.github.io/graphql-spec/June2018/#sec-Validation

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Clases de cátedra

Conclusion

21

  • First mechanized formalization of GraphQL in the Coq proof assistant
  • Certified query normalization algorithm
  • Uncover issues in initial formalization [H&P, WWW18]

Contribution

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Clases de cátedra

Conclusion

21

  • First mechanized formalization of GraphQL in the Coq proof assistant
  • Certified query normalization algorithm
  • Uncover issues in initial formalization [H&P, WWW18]
  • Further GraphQL features
  • Extraction (certified reference implementation)
  • More general data models

Contribution Future work

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Clases de cátedra

Conclusion

21

  • First mechanized formalization of GraphQL in the Coq proof assistant
  • Certified query normalization algorithm
  • Uncover issues in initial formalization [H&P, WWW18]

Thanks!

  • Further GraphQL features
  • Extraction (certified reference implementation)
  • More general data models

Contribution Future work