Usable Synthesis
Sumit Gulwani
(sumitg@microsoft.com)
Microsoft Research, Redmond
Usable Verification Workshop
November 2010
MSR Redmond
Automated Program Synthesis
• What is Program Synthesis?
– Synthesize an executable program from user intent expressed
in form of some constraints.
• Why today?
– Natural goal given that computing has become accessible, but:
• fundamental “how” programming models have not changed.
• most people are not expert programmers.
– Enabling technology is now available
• Better search/logical reasoning techniques (SAT/SMT solvers)
• Faster machines (good application for multi-cores)
• State of the art: We can synthesize 10-20 lines of code.
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Dimensions in Program Synthesis
• Technical Dimensions
– Search Space
– Search Technique
• Usability Dimensions
– Impact
• Who will find it useful?
• How useful would it be?
– Intent Expression Mechanism
• How will they express their intent?
2
Application 1: Bitvector Algorithms
• Search Space: Straight-line programs that use
– Arithmetic Operators: +,-,*,/
– Logical Operators: Bitwise and/or/not, Shift left/right
• Search Algorithm: SAT/SMT based techniques
Joint work with: Susmit Jha, Sanjit Seshia (UC-Berkeley),
Ashish Tiwari (SRI) and Venkie (MSR Redmond)
Paper: ICSE 2010
3
Examples of Bitvector Algorithms
Turn-off rightmost 1-bit
10101100
&
Z
10101000
Z & (Z-1)
10101100
Z
10101011
Z-1
10101000
Z & (Z-1)
4
Examples of Bitvector Algorithms
Turn-off rightmost contiguous sequence of 1-bits
10101100
10100000
Z
Z & (1 + (Z | (Z-1)))
Ceil of average of two integers without overflowing
(Y|Z) – ((Y©Z) >> 1)
5
Examples of Bitvector Algorithms
P24: Round up to next
highest power of 2
o1 := sub(x,1);
o2 := shr(o1,1);
o3 := or(o1,o2);
o4 := shr(o3,2);
o5 := or(o3,o4);
o6 := shr(o5,4);
o7 := or(o5,o6);
o8 := shr(o7,8);
o9 := or(o7,o8);
o10 := shr(o9,16);
o11 := or(o9,o10);
res := add(o10,1);
P25: Higher order half
of product of x and y
o1 := and(x,0xFFFF);
o2 := shr(x,16);
o3 := and(y,0xFFFF);
o4 := shr(y,16);
o5 := mul(o1,o3);
o6 := mul(o2,o3);
o7 := mul(o1,o4);
o8 := mul(o2,o4);
o9 := shr(o5,16);
o10 := add(o6,o9);
o11 := and(o10,0xFFFF);
o12 := shr(o10,16);
o13 := add(o7,o11);
o14 := shr(o13,16);
o15 := add(o14,o12);
res := add(o15,o8);
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Bitvector Algorithms: Usability Dimensions
• Impact: Algorithm Designers or Software Developers
• Intent Expression Mechanism: Logical Specifications
Algorithm
Designers
Software Developers
Consumers of Program Synthesis Technology
7
Application 2: String Manipulation Macros
• Search Space: Programs with conditionals/loops
– String operations: Concatenate, Substring
– Logical operations: comparison involving # of
occurrences of a regular expression
• Search Algorithm: Combination of
– Version Space Algebras
– Machine Learning
Joint work with: Bill Harris (UW, Madison), Rishabh Singh (MIT)
Paper: POPL 2011
8
String Manipulation Macros: Usability Dimensions
• Impact: End-users
• Intent Expression Mechanism: Input-output Examples
Algorithm
Designers
Software Developers
Most Useful
Target
End-Users
Consumers of Program Synthesis Technology
9
String Manipulation Macros
Excel Demo
10
Methodology: Automating end-user programming
1. Identify tasks that end-users struggle with and identify
how they can effectively communicate their intent.
– Read help-forums and blogs.
– Interview real users.
2. Design a language that satisfies the following trade-off.
–
–
Expressive enough to express a lot of tasks.
Small enough to allow efficient learning.
3. Design a learning algorithm with following features.
–
–
–
Interactive with fast convergence (with success or failure).
Provide feedback.
Noise tolerant.
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Application 3: Geometry Constructions
• Search Space: Straight-line programs
– Operations: Ruler, Compass
• Search Algorithm: Exhaustive Search
– Property Testing
– Goal-directed search
– Commonly used library of constructions
Joint work with: Kalika Bali, Monojit Chaudhuri (MSR Bangalore)
Vijay Korthikanti (UIUC), Ashish Tiwari (SRI)
Ken McMillan (MSR Redmond)
12
Geometry Constructions: Role of PL/logic/synthesis
• Programming Language for Geometry
– Objects: Point, Line, Circle
– Constructors
•
•
•
•
•
Ruler(Point, Point) -> Line
Compass(Point, Point) -> Circle
Intersect(Circle, Circle) -> Pair of Points
Intersect(Line, Circle) -> Pair of Points
Intersect(Line, Line) -> Point
• Logic for Geometry
– Inequality predicates over arithmetic expressions
• Distance(Point, Point), Angle(Line, Line), …
• Automated Problem Solving
– Given pre/postcondition, synthesize a straight-line program
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Geometry Domain: Automated Problem Solving
Automated Problem Solving
• Given pre/postcondition, synthesize a straight-line program
Example: Draw a line L’ perpendicular to a given line L.
Precondition: true
Postcondition: Angle(L’,L) = 90
Program
Step 1: P1, P2 = ChoosePoint(L);
Step 2: C1 = Circle(P1,P2);
Step 3: C2 = Circle(P2,P1);
Step 4: <P3, P4> = Intersect(C1,C2);
Step 5: L’ = Line(P3,P4);
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Constructing line L’ perpendicular to given line L
Step 1: P1, P2 = ChoosePoint(L);
Step 2: C1 = Circle(P1,P2);
Step 3: C2 = Circle(P2,P1);
Step 4: <P3, P4> = Intersect(C1,C2);
Step 5: L’ = Line(P3,P4);
L’
P3
C2
C1
P1
L
P2
P4
15
Examples of Geometry Constructions
•
•
•
•
•
•
•
Bisect a given line.
Bisect an angle.
Copy an angle.
Draw a line parallel to a given line.
Draw an equilateral triangle given two points.
Draw a regular hexagon given a side.
Given 4 points, draw a square with each of the
sides passing through a different point.
Other Applications:
• New approximate geometric constructions
• 2D/3D planning problems
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Geometry Constructions: Usability Dimensions
• Impact: Students and Teachers
• Intent Expression Mechanism: Natural Language
Algorithm
Designers
Software Developers
Most Useful
Target
Most Transformational
Target
End-Users
Students and Teachers
Consumers of Program Synthesis Technology
17
Automating Education
Make education interactive and fun
• Automated problem solving (for students)
– Provide hints
– Point out mistakes and suggest fixes
• Creation of teaching material (for teachers)
– Authoring tools
– Problem construction
• Group interaction (for teachers/students)
– Ask questions
– Share annotations
Domains: Geometry, Algebra, Probability, Mechanics,
Electrical Circuits, etc.
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Usability Dimensions
User Interface
Impact
Algorithm
Designers
Logic
Software Developers
Most Useful
Target
Most Transformational
Target
End-Users
Students and Teachers
Examples
English
Consumers of Program Synthesis Technology
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References
• Dimensions in Program Synthesis
– Invited Tutorial at FMCAD 2010
– Invited paper at PPDP 2010
• Bitvector Algorithms
– “Oracle guided component based program synthesis”,
ICSE 2010, Jha/Gulwani/Seshia/Tiwari
• String Manipulation Macros
– “Automating String Processing in Spreadsheets using InputOutput Examples”, POPL 2011, Gulwani
• Geometry Constructions
– “Synthesizing Geometry Constructions”,
Techreport 2011, Gulwani/Korthikanti/Tiwari
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