Fundamental Propertjes of the GraphQL Language Olaf Hartjg @olafiartjg Joint work with Jorge Pérez from the Universidad de Chile
Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 2
Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 3
Why study the GraphQL language formally? Highlight intrinsic limitations of all possible implementations Identify optimization opportunities Clarify possible corner cases Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 4
Our Results in a Nutshell Formal definition of the language Study of computational complexity (the language admits really efficient evaluation methods) Solution to the problem of large results Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 5
Formalizatjon of GraphQL
Why? Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 7
Why? Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 8
Why? Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 9
GraphQL Graphs (Our Formalizatjon) Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 10
GraphQL Graphs (Our Formalizatjon) Typed nodes Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 11
GraphQL Graphs (Our Formalizatjon) One special node Typed nodes Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 12
GraphQL Graphs (Our Formalizatjon) Node properties One special node Typed nodes Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 13
GraphQL Graphs (Our Formalizatjon) Edge properties Node properties One special node Typed nodes Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 14
GraphQL Graphs (Our Formalizatjon) Edge properties Node properties One special node We also formalize the notions of GraphQL schema Typed nodes and schema satisfaction based on this data model Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 15
Formalizatjon of Query Evaluatjon Functjon Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 16
Formalizatjon of Query Evaluatjon Functjon u = friends { name } ⟧ ⟦ Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 17
Formalizatjon of Query Evaluatjon Functjon u = friends { name } ⟧ friends: [ ] ⟦ Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 18
Formalizatjon of Query Evaluatjon Functjon u v } { ⟦ w } ] = friends { name } ⟧ friends: [ { ⟦ name ⟧ name ⟧ ⟦ Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 19
Formalizatjon of Query Evaluatjon Functjon u = friends { name } ⟧ friends: [ {name:R2-D2} {name:Han} ] ⟦ Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 20
Formalizatjon of Query Evaluatjon Functjon hero[episode:EMPIRE] { friends {name} } ⟧ ⟦ Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 21
Formalizatjon of Query Evaluatjon Functjon r ⟧ ⟦ hero[episode:EMPIRE] { friends {name} } Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 22
Formalizatjon of Query Evaluatjon Functjon u } r = hero: { friends {name} ⟧ ⟧ ⟦ hero[episode:EMPIRE] { friends {name} } ⟦ Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 23
Formalizatjon of Query Evaluatjon Functjon u } r = hero: { friends {name} ⟧ ⟧ ⟦ hero[episode:EMPIRE] { friends {name} } ⟦ = hero: { friends: [ {name:R2-D2} {name:Han} ] } Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 24
Complexity Analysis Evaluation Problem
Evaluatjon Problem of GraphQL GraphQL graph G GraphQL query q data value d Does d occur in the Does d occur in the result of q over G ? result of q over G ? yes no Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 26
Complexity Classes PSPACE NP P Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 27
Complexity of Evaluatjon Problems Relational Algebra SPARQL Conjunctive Queries BGPs (SPARQL) PSPACE NP P Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 28
Complexity of Evaluatjon Problems Relational Algebra SPARQL Conjunctive Queries BGPs (SPARQL) PSPACE GraphQL NP NL P Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 29
Complexity Analysis Enumeration Problem
Non-Redundancy Valid query Invalid result hero[episode: EMPIRE] { hero { name name: Luke friends { friends: [ name { name: R2-D2} } { name: Han} id ] name id: 1000 friends { name: Luke id friends: [ } { id: 2001} } { id: 1002} ] } Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 31
Non-Redundancy Valid query Correct result hero[episode: EMPIRE] { hero { name name: Luke friends { friends: [ name { name: R2-D2 } Id: 2001 } id { name: Han name Id: 1002 } friends { ] id id: 1000 } } } Fields are collected before answering Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 32
Non-Redundancy Non-redundant query Correct result hero[episode: EMPIRE] { hero { name name: Luke friends { friends: [ name { name: R2-D2 id Id: 2001 } } { name: Han id Id: 1002 } } ] id: 1000 } Fields are collected before answering Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 33
Another Complicatjon: Type Restrictjons Valid query Invalid result hero[episode: EMPIRE] { hero { name name: Luke friends { friends: [ on Droid { name } { name: R2-D2 on Human { id } name: R2-D2 } name { id: 1002 } name: Han } } ] } Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 34
Another Complicatjon: Type Restrictjons Valid query Correct result hero[episode: EMPIRE] { hero { name name: Luke friends { friends: [ on Droid { name } { name: R2-D2 } on Human { id } { id: 1002 name name: Han } } ] } } Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 35
Another Complicatjon: Type Restrictjons Valid query Correct result hero[episode: EMPIRE] { hero { name name: Luke friends { friends: [ on Droid { name } { name: R2-D2 } on Human { id name } { id: 1002 } name: Han } } ] } Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 36
Ground-Typed Normal Form Ground-typed query Correct result hero[episode: EMPIRE] { hero { name name: Luke friends { friends: [ on Droid { name } { name: R2-D2 } on Human { id name } { id: 1002 } name: Han } } ] } Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 37
Eliminatjng Redundancies Rewriting rules for queries Every GraphQL query q can be rewritten into a query q’ that is i) non-redundant and ii) in ground-typed normal form, such that q ≡ q’ Advantage: field collection is not needed for non-redundant queries in ground-typed NF Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 38
Now to the Enumeratjon Problem Let q be i) non-redundant and ii) in ground-typed normal form Result of q can be produced symbol by symbol with only constant time between symbols hero { friends: [ { name:R2-D2} ] } Time to produce the complete query result depends linearly on the size of this result Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 39
Complexity Analysis Result Size
Results of GraphQL queries can be huge start { knows { knows { … { knows { name } }… } } } 2 N times Alice appears 2 N times in the result Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 41
Huge results in practjce: Github’s GraphQL API Owners of first five repos that user “danbri” contributes to, and the owners of first five repos that they contribute to, and so on... Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 42
Result sizes can be computed effjciently!!! Let q be i) non-redundant and ii) in ground-typed normal form Time to compute the size of the result of q over a graph G depends linearly on the product (size of q ) × (size of G ) Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 43
Result-Size Computatjon start { advisor { univ { name } } friend { univ { name } } } q 2 q 3 Result: start: { … … } size( q, r ) = 4 + size( q 2 ,u ) + size( q 3 ,u ) Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 44
Result-Size Computatjon start { advisor { univ { name } } friend { univ { name } } } q 2 q 3 size( q 2 ,u ) = size( q 3 ,u ) = size( q, r ) = 4 + size( q 2 ,u ) + size( q 3 ,u ) Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 45
Result-Size Computatjon q 4 start { advisor { univ { name } } friend { univ { name } } } q 3 q 2 size( q 2 ,u ) = 4 + size( q 4 ,v ) size( q 3 ,u ) = size( q, r ) = 4 + size( q 2 ,u ) + size( q 3 ,u ) Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 46
Result-Size Computatjon q 4 start { advisor { univ { name } } friend { univ { name } } } q 5 q 3 q 2 size( q 4 ,v ) = 4 + size( q 5 ,w ) size( q 2 ,u ) = 4 + size( q 4 ,v ) size( q 3 ,u ) = size( q, r ) = 4 + size( q 2 ,u ) + size( q 3 ,u ) Olaf Hartjg – Fundamental Propertjes of the GraphQL Language 47
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