Dimensions in Synthesis Part 3: Ambiguity (Synthesis from Examples & Keywords)

Dimensions in SynthesisPart 3: Ambiguity

(Synthesis from Examples & Keywords)

Sumit [email protected]

Microsoft Research, Redmond

May 2012

Students and Teachers

End-Users

Algorithm Designers

Software Developers

Most Transformational Target

Potential Users of Synthesis Technology

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Most Useful Target

• Vision for End-users: Enable people to have (automated) personal assistants.

• Vision for Education: Enable every student to have access to free & high-quality education.

• Examples– Bitvector Algorithms (ICSE ‘10)– Spreadsheet Macros (CACM ‘12)

• Syntactic String Transformations (POPL ‘11)• Semantic String Transformations (VLDB ‘12)• Number Transformations (CAV ‘12)• Table Transformations (PLDI ‘11)

• Sketch– Drawings (CHI 2012)

• Keywords– SmartPhone Apps

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Intent Specification

• Examples Bitvector Algorithms (ICSE ‘10)– Spreadsheet Macros (CACM ‘12)




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ICSE 2010: Susmit Jha, Gulwani, Seshia, Tiwari.

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Synthesis from Logical Specification

Æ[ (I[p]=1 Æ (I[j]=0)) ) (J[p]=0 Æ(J[j] =

I[j])) ]

p=1

b

j=p+1

b

jp

Turn off rightmost 1-bit

Functional Specification:

Tool Output:

J = I & (I-1)

PLDI 2011: Gulwani, Jha, Tiwari, Venkatesan.

Turn-off rightmost contiguous string of 1’s

User: I want a program that maps 01011 -> 01000

Tool: There exist at least two programs that match the spec

Program 1: (x+1) & (x-1) Program 2: (x+1) & x But they differ on 00000 (Distinguishing Input) What should 00000 be mapped to?

User: 00000 -> 00000

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Interactive Synthesis using Examples

Turn-off rightmost contiguous string of 1’sUser: 01011 -> 01000

Tool: 00000 ?User: 00000

Tool: 01111 ? User: 00000

Tool: 00110 ?User: 00000

Tool: 01100 ?User: 00000

Tool: 01010 ?User: 01000

Tool: Your program is x & (1 + ((x-1)|x))7

Interactive Synthesis using Examples

• Examples– Bitvector Algorithms (ICSE ‘10) Spreadsheet Macros (CACM ‘12)




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Syntactic String Transformations (POPL ‘11)• Semantic String Transformations (VLDB ‘12)• Number Transformations (CAV ‘12)• Table Transformations (PLDI ‘11)



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Guarded Expression G := Switch((b1,e1), …, (bn,en))

String Expression e := Concatenate(f1, …, fn)

Base Expression f := s // Constant String | SubStr(vi, p1, p2)

Index Expression p := k // Constant Integer | Pos(r1, r2, k) // kth position in string whose left/right side matches with r1/r2

Notation: SubStr2(vi,r,k) ´ SubsStr(vi,Pos(²,r,k),Pos(r,²,k))

– Denotes kth occurrence of regular expression r in vi

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Language for Constructing Output Strings

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Example

Switch((b1, e1), (b2, e2)), whereb1 ´ Match(v1,NumTok,3), b2 ´ :Match(v1,NumTok,3),e1 ´ Concatenate(SubStr2(v1,NumTok,1), ConstStr(“-”),

SubStr2(v1,NumTok,2), ConstStr(“-”), SubStr2(v1,NumTok,3))

e2 ´ Concatenate(ConstStr(“425-”),SubStr2(v1,NumTok,1),

ConstStr(“-”),SubStr2(v1,NumTok,2))

Format phone numbers

Input v1 Output

(425)-706-7709 425-706-7709

510.220.5586 510-220-5586

235 7654 425-235-7654

745-8139 425-745-8139

• Reduction requires computing all solutions for each of the sub-problems:– This also allows to rank various solutions and select the

highest ranked solution at the top-level.– A challenge here is to efficiently represent, compute,

and manipulate huge number of such solutions.

• I will show three applications of this idea in the talk.– Read the paper for more tricks!

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Key Synthesis Idea: Divide and Conquer

Reduce the problem of synthesizing expressions into sub-problems of synthesizing sub-expressions.

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Synthesizing Guarded Expression

Goal: Given input-output pairs: (i1,o1), (i2,o2), (i3,o3), (i4,o4), find P such that P(i1)=o1, P(i2)=o2, P(i3)=o3, P(i4)=o4.

Algorithm: 1. Learn set S1 of string expressions s.t. 8e in S1, [[e]] i1 = o1. Similarly compute S2, S3, S4. Let S = S1 ÅS2 ÅS3 ÅS4.

2(a) If S ≠ ; then result is Switch((true,S)).

Application #1: We reduce the problem of learning guarded expression P to the problem of learning string expressions for each input-output pair.

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Example: Various choices for a String Expression

Input

Output

Constant

Constant

Constant

Number of all possible string expressions (that can construct a given output string o1 from a given input string i1) is exponential in size of output string.

– # of substrings is just quadratic in size of output string!

– We use a DAG based data-structure, and it supports efficient intersection operation!

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Synthesizing String Expressions

Application #2: To represent/learn all string expressions, it suffices to represent/learn all base expressions for each substring of the output.

Various ways to extract “706” from “425-706-7709”:

• Chars after 1st hyphen and before 2nd hyphen. Substr(v1, Pos(HyphenTok,²,1), Pos(²,HyphenTok,2))

• Chars from 2nd number and up to 2nd number. Substr(v1, Pos(²,NumTok,2), Pos(NumTok,²,2))

• Chars from 2nd number and before 2nd hyphen. Substr(v1, Pos(²,NumTok,2), Pos(²,HyphenTok,2))

• Chars from 1st hyphen and up to 2nd number. Substr(v1, Pos(HyphenTok,²,1), Pos(²,HyphenTok,2))

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Example: Various choices for a SubStr Expression

The number of SubStr(v,p1,p2) expressions that can extract a given substring w from a given string v can be large!

– This allows for representing and computing

O(n1*n2) choices for SubStr using size/time O(n1+n2).

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Synthesizing SubStr Expressions

Application #3: To represent/learn all SubStr expressions, we can independently represent/learn all choices for each of the two index expressions.

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Back to Synthesizing Guarded Expression

Goal: Given input-output pairs: (i1,o1), (i2,o2), (i3,o3), (i4,o4), find P such that P(i1)=o1, P(i2)=o2, P(i3)=o3, P(i4)=o4.

Algorithm: 1. Learn set S1 of string expressions s.t. 8e in S1, [[e]] i1 =

o1. Similarly compute S2, S3, S4. Let S = S1 ÅS2 ÅS3 ÅS4.

2(a). If S ≠ ; then result is Switch((true,S)).2(b). Else find a smallest partition, say {S1,S2}, {S3,S4}, s.t. S1 ÅS2 ≠ ; and S3 ÅS4 ≠ ;.

3. Learn boolean formulas b1, b2 s.t.

b1 maps i1, i2 to true and i3, i4 to false.

b2 maps i3, i4 to true and i1, i2 to false.

4. Result is: Switch((b1,S1 ÅS2), (b2,S3 ÅS4))

• Prefer shorter programs.– Fewer number of conditionals.– Shorter string expression, regular expressions.

• Prefer programs with less number of constants.

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Ranking Strategy


• Syntactic String Transformations (POPL ‘11)Semantic String Transformations (VLDB ‘12)Number Transformations (CAV ‘12)• Table Transformations (PLDI ‘11)



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VLDB 2012/CAV 2012: Rishabh Singh, Gulwani


• Syntactic String Transformations (POPL ‘11)• Semantic String Transformations (VLDB ‘12)• Number Transformations (CAV ‘12)Table Transformations (PLDI ‘11)



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PLDI 2011: Bill Harris, Gulwani



• Sketch Drawings (CHI 2012)


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CHI 2012: Salman Cheema, Gulwani, LaViola

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Architecture

Sketch Recognition Engine [HCI]

Model Synthesis/Beautification Engine [Theorem Proving]

Pattern Synthesis Engine [Program Synthesis]

(Partial) Sketch/Ink Strokes

Circle/Line Objects

Constraints between Objects

(Partial) Drawing

Suggestions for Drawing Completion

Constraint Inference Engine [Machine Learning]




• Keywords SmartPhone Apps

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Joint work with: Vu Le, Zhendong Su (UC-Davis)

Students and Teachers

End-Users

Algorithm Designers

Software Developers

Most Transformational Target

Potential Users of Synthesis Technology

25

Most Useful Target

• Vision for End-users: Enable people to have (automated) personal assistants.

• Vision for Education: Enable every student to have access to free & high-quality education.

• Concept Language– Programs

• Straight-line programs– Automata– Queries– Sequences

• User Intent– Logic, Natural Language– Examples, Demonstrations/Traces

• Search Technique– SAT/SMT solvers (Formal Methods)– A*-style goal-directed search (AI)– Version space algebras (Machine Learning)

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Dimensions in Synthesis

PPDP 2010: “Dimensions in Program Synthesis”, Gulwani.

(Application)

(Ambiguity)

(Algorithm)

Documents

Dimensions in Synthesis Part 3: Ambiguity (Synthesis from Examples & Keywords)