Formal Semantics of SQL (and Cypher) Paolo Guagliardo

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1 Formal Semantics of SQL (and Cypher) Paolo Guagliardo

2 SQL Standard query language for relational databases $30B/year business Implemented in all major RDBMSs (free and commercial) First standardized in 1986 (ANSI) and 1987 (ISO) Several revision afterwards (SQL-89, SQL-92, SQL:1999, SQL:2003, SQL:2006, SQL:2008, SQL:2011, SQL:2016) The nice thing about standards is that you have so many to choose from Andrew S. Tanenbaum

3 How standard is SQL? SELECT * FROM ( SELECT R.A, R.A FROM R ) S PostgreSQL outputs a table with two columns named A Oracle throws an ERROR: reference to column A is ambiguous SELECT * FROM R WHERE EXISTS ( SELECT * FROM ( SELECT R.A, R.A FROM R ) S ) Both PostgreSQL and Oracle output R

4 Who is right? Let s have a look at the standard! A. If the <select list> * is simply contained in a <subquery> that is immediately contained in an <exists predicate>, then the <select list> is equivalent to a <value expression> that is an arbitrary <literal>. B. Otherwise, the <select list> * is equivalent to a <value expression> sequence in which each <value expression> is a column reference that references a column of T and each column of T is referenced exactly once. The columns are referenced in the ascending sequence of their ordinal position within T.

5 which means SELECT * FROM ( SELECT R.A, R.A FROM R ) S SELECT S.A, S.A FROM ( SELECT R.A, R.A FROM R ) S SELECT * FROM R WHERE EXISTS ( SELECT * FROM ( SELECT R.A, R.A FROM R ) S ) SELECT R.A FROM R WHERE EXISTS ( SELECT 1 FROM ( SELECT R.A, R.A FROM R ) S )

6 The Need for a Formal Semantics Avoid ambiguity of natural language Clearly defined and not subject to interpretation Easy to understand and implement Previous attempts Many simplifying assumptions: no bags, no nulls No justification of correctness

7 A A R 1 S NULL NULL Answer SELECT R.A FROM R EXCEPT SELECT S.A FROM S A 1 SELECT R.A FROM R WHERE R.A NOT IN ( SELECT S.A FROM S) A SELECT R.A FROM R WHERE NOT EXISTS ( SELECT S.A FROM S WHERE S.A=R.A ) A 1 NULL

8 Core SQL fragment := (T 1,...,T k ), := (N 1,...,N k ), k > 0 := (A 1,...,A m ), 0 :=(N 0 1,...,N 0 m), m > 0 Queries: Q := SELECT [DISTINCT]( : 0 *) FROM : Q (UNION INTERSECT EXCEPT) [ALL ] Q Conditions: := TRUE t (= 6=) t t IS [ NOT ] NULL t [ NOT ] IN Q EXISTS Q AND OR NOT Essentially SQL without arithmetic, grouping and aggregation

9 Formal Semantics: Challenges Data model Base relations / query outputs / intermediate results Primitive data manipulation operations Attribute references Binding rules in subqueries Environment collects and propagates bindings

10 Proposed Semantics J : JRK = R D K = J(T 1,...,T k ):(N 1,...,N k )K = N 1.JT 1 K N k.jt k K s { FROM : = ā 2 J : K J K ; ā = t t SELECT s { FROM : 1 FROM : = : t SELECT : 0 s {! FROM : 0 FROM : = : t SELECT DISTINCT : 0 0t SELECT : 0 FROM : = FROM : JTRUEK = t (A) if t = A JtK = t if t 2 C or t = NULL 8 < t if Jt 1 K = Jt 2 K and Jt 1 K 6= NULL and Jt 2 K 6= NULL Jt 1 = t 2 K = f if Jt : 1 K 6= Jt 2 K and Jt 1 K 6= NULL and Jt 2 K 6= NULL u if Jt 1 K = NULL or Jt 2 K = NULL t if JtK = NULL Jt IS NULLK = f if JtK 6= NULL Jt IS NOT NULLK = Jt IS NULLK n^ J(t 1,...t n )=(t 0 1,...,t 0 n)k = Jt i = t 0 ik J(t 1,...t n ) 6= (t 0 1,...,t 0 n)k = i=1 8 < t J t IN QK = f : u J t NOT IN QK = J t IN QK t if JQK 6=? JEXISTS QK = f if JQK =? 1 A n_ Jt i 6= t 0 ik if 9 r 2 JQK : J t = ( r)k = t if 8 r 2 JQK : J t = ( r)k = f r 2 JQK : J t = ( r)k = t and 9 r 2 JQK : J t = ( r)k 6= f i=1 Fits in one page Non-ambiguous Easy to understand Easy to implement Easy to modify J 1 AND 2 K = J 1 K ^ J 2 K J 1 OR 2 K = J 1 K _ J 2 K JNOT K = J K JQ 1 UNION ALL Q 2 K = JQ 1 K [ JQ 2 K : `(JQ 1 K) JQ 1 INTERSECT ALL Q 2 K = JQ 1 K \ JQ 2 K : `(JQ 1 K) JQ 1 EXCEPT ALL Q 2 K = JQ 1 K JQ 2 K : `(JQ 1 K) JQ 1? Q 2 K = " JQ 1? ALL Q 2 K,? 2 {UNION, INTERSECT} JQ 1 EXCEPT Q 2 K = "(JQ 1 K ) JQ 2 K : `(JQ 1 K)

11 Formal Semantics: Validation Cannot prove that semantics is correct Provide sufficient experimental evidence Implemented in Python Validated on random SQL queries

12 Formal Semantics of Cypher Collaboration between Neo Technology and the University of Edinburgh Preliminary meeting in December Legal agreements finalized recently Neo Technology sponsors a researcher (Nadime Francis)

13 Challenges Getting the (abstract) data model right Intermediate representation (QUIL?) Identify core fragment Language constantly evolving Follow the footsteps of SQL? (nulls)