Optimizing Synthesis with Metasketches
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1 Optimizing Synthesis Artifact with Metasketches * POPL * Consistent * Complete * Well Documented * Easy to Reuse * Evaluated * AEC * James Bornholt Emina Torlak Dan Grossman Luis Ceze University of Washington SYNAPSE
2 Program synthesis
3 Specification Program synthesis
4 Specification Program synthesis Program
5 Specification Program synthesis Program f(x) =4x
6 Specification Program synthesis Program f(x) =4x x+x+x+x
7 Compilation [PLDI 14] Data Structures [PLDI 15] End-user Programming [POPL 11] Specification Program synthesis Program f(x) =4x x+x+x+x Executable Biology [POPL 13] Browser Layout [PPoPP 13] Cache Protocols [PLDI 13]
8 Compilation [PLDI 14] Data Structures [PLDI 15] End-user Programming [POPL 11] Often looking for an optimal solution, not just any correct program Specification Program synthesis Program Executable Biology [POPL 13] Browser Layout [PPoPP 13] Cache Protocols [PLDI 13]
9 Compilation [PLDI 14] Data Structures [PLDI 15] End-user Programming [POPL 11] Often looking for an optimal solution, not just any correct program Specification Program synthesis Program There are many programs, so tools must control search strategy Executable Biology [POPL 13] Browser Layout [PPoPP 13] Cache Protocols [PLDI 13]
10 Compilation [PLDI 14] Data Structures [PLDI 15] End-user Programming [POPL 11] Often looking for an optimal solution, not just any correct program Specification Program synthesis Program There are many programs, so tools must control search strategy Executable Biology [POPL 13] Browser Layout [PPoPP 13] Cache Protocols [PLDI 13]
11 Specification Program synthesis Program
12 Metasketches Specification Program synthesis Program
13 Metasketches A framework that makes search strategy and optimality part of the problem definition Specification Program synthesis Program
14 Metasketches Design and structure
15 Metasketches Design and structure Synapse A metasketch solver
16 Metasketches Design and structure Synapse A metasketch solver Results Better solutions, faster
17 Background Syntax-guided synthesis Metasketches Design and structure Synapse A metasketch solver Results Better solutions, faster
18 Syntax-guided synthesis Specification Program synthesis Program
19 Syntax-guided synthesis Specification Program synthesis Program Sketch
20 Syntax-guided synthesis Specification Program synthesis Program Sketch def f(x): return Expr Expr := x?? Expr op Expr op := + * - >> <<?? := integer constant
21 Syntax-guided synthesis: guess, check, learn def f(x): return Expr Expr := x?? Expr op Expr op := + * - >> <<?? := integer constant
22 Syntax-guided synthesis: guess, check, learn def f(x): return Expr Expr := x?? Expr op Expr op := + * - >> <<?? := integer constant Syntax
23 Syntax-guided synthesis: guess, check, learn Counterexample-guided inductive synthesis [Solar-Lezama et al, 2006] Semantics Syntax
24 Syntax-guided synthesis: guess, check, learn Counterexample-guided inductive synthesis [Solar-Lezama et al, 2006] f(x) =4x Semantics Syntax
25 Syntax-guided synthesis: guess, check, learn Counterexample-guided inductive synthesis [Solar-Lezama et al, 2006] 0 f(x) =4x Semantics Syntax
26 Syntax-guided synthesis: guess, check, learn Counterexample-guided inductive synthesis [Solar-Lezama et al, 2006] 0 f(x) =4x Semantics Syntax
27 Syntax-guided synthesis: guess, check, learn Counterexample-guided inductive synthesis [Solar-Lezama et al, 2006] f(x) =4x Semantics Syntax
28 Syntax-guided synthesis: guess, check, learn Counterexample-guided inductive synthesis [Solar-Lezama et al, 2006] f(x) =4x Semantics Syntax
29 Syntax-guided synthesis: guess, check, learn Counterexample-guided inductive synthesis [Solar-Lezama et al, 2006] f(x) =4x x+x+x+x Semantics Syntax
30 Syntax-guided synthesis: guess, check, learn Counterexample-guided inductive synthesis [Solar-Lezama et al, 2006] 1. Search order is critical x+x+x+x Syntax
31 Syntax-guided synthesis: guess, check, learn Counterexample-guided inductive synthesis [Solar-Lezama et al, 2006] 1. Search order is critical 2. Desire optimal solutions x+x+x+x Syntax
32 Syntax-guided synthesis: guess, check, learn Counterexample-guided inductive synthesis [Solar-Lezama et al, 2006] 1. Search order is critical 2. Desire optimal solutions x << 2 x+x+x+x Syntax
33 Background Syntax-guided synthesis Metasketches Design and structure Synapse A metasketch solver Results Better solutions, faster
34 Background Syntax-guided synthesis Metasketches Design and structure Synapse A metasketch solver Results Better solutions, faster
35 Metasketches express structure and strategy 1. Search order is critical 2. Desire optimal solutions Syntax
36 Metasketches express structure and strategy 1. Search order is critical 2. Desire optimal solutions A metasketch contains: 1. structured candidate space (S, ) S4 S6 S1 S3 S5 S7 S2 Syntax
37 Metasketches express structure and strategy 1. Search order is critical 2. Desire optimal solutions S1 A metasketch contains: 1. structured candidate space (S, ) 2. cost function (κ)s S4 S6 S3 S5 S7 S2 Syntax
38 Metasketches express structure and strategy 1. Search order is critical 2. Desire optimal solutions S1 A metasketch contains: 1. structured candidate space (S, ) 2. cost function (κ)s S4 S6 S3 S5 3. gradient function (g)s S7 S2 Syntax
39 Metasketches express structure and strategy 1. Search order is critical 2. Desire optimal solutions S1 A metasketch contains: 1. structured candidate space (S, ) 2. cost function (κ)s S4 S6 S3 S5 3. gradient function (g)s S7 S2 Syntax
40 Metasketches express structure and strategy 1. Search order is critical 2. Desire optimal solutions S1 A metasketch contains: 1. structured candidate space (S, ) 2. cost function (κ)s S4 S6 S3 S5 3. gradient function (g)s S7 S2 Syntax
41 Metasketches express structure and strategy 1. Search order is critical 2. Desire optimal solutions S1 A metasketch contains: 1. structured candidate space (S, ) 2. cost function (κ)s 3. gradient function (g)s S4 S6 Program S3 S5 S7 S2 Syntax
42 Metasketches express structure and strategy 1. Search order is critical 2. Desire optimal solutions S1 A metasketch contains: 1. structured candidate space (S, ) 2. cost function (κ)s 3. gradient function (g)s S4 S6 Program S3 S5 Superoptimizer S7 S2 Syntax
43 Metasketches express structure and strategy 1. Search order is critical 2. Desire optimal solutions S1 A metasketch contains: 1. structured candidate space (S, ) 2. cost function (κ)s 3. gradient function (g)s S4 S6 Program S3 S5 Superoptimizer S7 Optimal Program Syntax S2
44 Metasketches express structure and strategy 1. structured candidate space (S, ) 2. cost function (κ)s 3. gradient function (g)s
45 Metasketches express structure and strategy 1. structured candidate space (S, ) A fragmentation of the candidate space, and an ordering on those fragments. 2. cost function (κ)s 3. gradient function (g)s
46 Metasketches express structure and strategy 1. structured candidate space (S, ) A fragmentation of the candidate space, and an ordering on those fragments. S = set of all SSA programs def S 2. cost function (κ)s 3. gradient function (g)s
47 Metasketches express structure and strategy 1. structured candidate space (S, ) A fragmentation of the candidate space, and an ordering on those fragments. S = set of all SSA programs S1 S2 def S S3 S4 S5 2. cost function (κ)s 3. gradient function (g)s
48 Metasketches express structure and strategy 1. structured candidate space (S, ) a countable set S of sketches a total order on S A fragmentation of the candidate space, and an ordering on those fragments. S = set of all SSA programs S1 S2 def S S3 S4 S5 2. cost function (κ)s 3. gradient function (g)s
49 Metasketches express structure and strategy 1. structured candidate space (S, ) a countable set S of sketches a total order on S A fragmentation of the candidate space, and an ordering on those fragments. S = set of all SSA programs S1 S2 S3 S 3 (SSA programs of length 3) def f(x): r1 =??op(??{x}) r2 =??op(??{x,r1}) r3 =??op(??{x,r1,r2}) return r3 S4 S5 2. cost function (κ)s 3. gradient function (g)s
50 Metasketches express structure and strategy 1. structured candidate space (S, ) a countable set S of sketches a total order on S A fragmentation of the candidate space, and an ordering on those fragments. S 3 (SSA programs of length 3) +, -, <, if, def f(x): r1 =??op(??{x}) r2 =??op(??{x,r1}) r3 =??op(??{x,r1,r2}) return r3 2. cost function (κ)s S = set of all SSA programs S1 S2 S3 S4 S5 3. gradient function (g)s
51 Metasketches express structure and strategy 1. structured candidate space (S, ) a countable set S of sketches a total order on S A fragmentation of the candidate space, and an ordering on those fragments. S 3 (SSA programs of length 3) +, -, <, if, def f(x): r1 =??op(??{x}) r2 =??op(??{x,r1}) r3 =??op(??{x,r1,r2}) return r3 2. cost function (κ)s Vars & constants S = set of all SSA programs S1 S2 S3 S4 S5 3. gradient function (g)s
52 Metasketches express structure and strategy 1. structured candidate space (S, ) a countable set S of sketches a total order on S A fragmentation of the candidate space, and an ordering on those fragments. S = set of all SSA programs S1 S2 S3 S 3 (SSA programs of length 3) def f(x): r1 =??op(??{x}) r2 =??op(??{x,r1}) r3 =??op(??{x,r1,r2}) return r3 S4 S5 2. cost function (κ)s 3. gradient function (g)s
53 Metasketches express structure and strategy 1. structured candidate space (S, ) a countable set S of sketches a total order on S A fragmentation of the candidate space, and an ordering on those fragments. S 3 (SSA programs of length 3) def f(x): r1 =??op(??{x}) r2 =??op(??{x,r1}) r3 =??op(??{x,r1,r2}) return r3 2. cost function (κ)s Ordering expresses high-level search strategy. S = set of all SSA programs S1 S2 S3 S4 S5 3. gradient function (g)s
54 Metasketches express structure and strategy 1. structured candidate space (S, ) a countable set S of sketches a total order on S A fragmentation of the candidate space, and an ordering on those fragments. S 3 (SSA programs of length 3) def f(x): r1 =??op(??{x}) r2 =??op(??{x,r1}) r3 =??op(??{x,r1,r2}) return r3 2. cost function (κ)s Ordering expresses high-level search strategy. Here, expresses iterative deepening. S = set of all SSA programs S1 S2 S3 S4 S5 3. gradient function (g)s
55 Metasketches express structure and strategy 1. structured candidate space (S, ) a countable set S of sketches a total order on S A fragmentation of the candidate space, and an ordering on those fragments. S = set of all SSA programs def f(x): r1 =??op(??{x}) return r1 def f(x): r1 =??op(??{x}) r2 =??op(??{x,r1}) return r2 S 1 S 2 2. cost function (κ)s Implemented as a generator that returns the next sketch in the space def f(x): r1 =??op(??{x}) r2 =??op(??{x,r1}) r3 =??op(??{x,r1,r2}) return r3 S 3 3. gradient function (g)s
56 Metasketches express structure and strategy 1. structured candidate space (S, ) a countable set S of sketches a total order on S S = set of all SSA programs S1 S2 S3 S4 S5 Semantics 2. cost function (κ)s 3. gradient function (g)s
57 Metasketches express structure and strategy 1. structured candidate space (S, ) a countable set S of sketches a total order on S S = set of all SSA programs S1 S2 S3 S 3 S4 S5 Semantics 2. cost function (κ)s 3. gradient function (g)s
58 Metasketches express structure and strategy 1. structured candidate space (S, ) a countable set S of sketches a total order on S S = set of all SSA programs S1 S2 S3 S 2 S 3 S4 S5 Semantics 2. cost function (κ)s 3. gradient function (g)s
59 Metasketches express structure and strategy 1. structured candidate space (S, ) a countable set S of sketches a total order on S S 2 S 3 Semantics 2. cost function (κ)s Semantic redundancy in the search space. S = set of all SSA programs S1 S2 S3 S4 S5 3. gradient function (g)s
60 Metasketches express structure and strategy 1. structured candidate space (S, ) a countable set S of sketches a total order on S Semantic redundancy in the search space. S = set of all SSA programs S1 S2 S 2 S 3 Structure constraints eliminate some overlap between sketches S3 S4 Semantics 2. cost function (κ)s 3. gradient function (g)s S5
61 Metasketches express structure and strategy 1. structured candidate space (S, ) a countable set S of sketches a total order on S Semantic redundancy in the search space. S = set of all SSA programs S1 S2 S 2 S 3 Semantics 2. cost function (κ)s 3. gradient function (g)s Structure constraints eliminate some overlap between sketches S3 S4 S 3 (SSA programs of length 3) def f(x): S5 r1 =??op(??{x}) r2 =??op(??{x,r1}) r3 =??op(??{x,r1,r2}) return r3
62 Metasketches express structure and strategy 1. structured candidate space (S, ) a countable set S of sketches a total order on S Semantic redundancy in the search space. S = set of all SSA programs S1 S2 S 2 S 3 Semantics 2. cost function (κ)s 3. gradient function (g)s Structure constraints eliminate some overlap between sketches Eliminate dead-code redundancy: assert that each ri is read S3 S4 S 3 (SSA programs of length 3) def f(x): S5 r1 =??op(??{x}) r2 =??op(??{x,r1}) r3 =??op(??{x,r1,r2}) return r3
63 Cost functions rank candidate programs 1. structured candidate space (S, ) 2. cost function (κ)s κ : L R assigns a numeric cost to each program in the language L S = set of all SSA programs S1 S2 S3 S4 S5 3. gradient function (g)s
64 Cost functions rank candidate programs 1. structured candidate space (S, ) 2. cost function (κ)s κ : L R assigns a numeric cost to each program in the language L Cost functions can be based on both syntax and semantics (dynamic behavior) S = set of all SSA programs S1 S2 S3 S4 S5 3. gradient function (g)s
65 Cost functions rank candidate programs 1. structured candidate space (S, ) 2. cost function (κ)s κ : L R assigns a numeric cost to each program in the language L Cost functions can be based on both syntax and semantics (dynamic behavior) S = set of all SSA programs S1 S2 S3 S4 S5 κ(p) = i for P S i S The number of variables defined in P 3. gradient function (g)s
66 Gradient functions provide cost structure 1. structured candidate space (S, ) 2. cost function (κ)s 3. gradient function (g)s g : R 2 S g(c) is the set of sketches in S that may contain a solution P with κ(p) < c S = set of all SSA programs S1 S2 S3 S4 S5 κ(p) = i for P S i S
67 Gradient functions provide cost structure 1. structured candidate space (S, ) 2. cost function (κ)s 3. gradient function (g)s g : R 2 S g(c) is the set of sketches in S that may contain a solution P with κ(p) < c The gradient function overapproximates the behavior of κ on S S = set of all SSA programs S1 S2 S3 S4 S5 κ(p) = i for P S i S
68 Gradient functions provide cost structure 1. structured candidate space (S, ) 2. cost function (κ)s 3. gradient function (g)s g : R 2 S g(c) is the set of sketches in S that may contain a solution P with κ(p) < c The gradient function overapproximates the behavior of κ on S S = set of all SSA programs S1 S2 S3 S4 S5 κ(p) = i for P S i S g(c) = { S i S i < c }
69 Gradient functions provide cost structure 1. structured candidate space (S, ) 2. cost function (κ)s 3. gradient function (g)s g : R 2 S g(c) is the set of sketches in S that may contain a solution P with κ(p) < c The gradient function overapproximates the behavior of κ on S S = set of all SSA programs S1 S2 S3 S4 S5 κ(p) = i for P S i S g(c) = { S i S i < c } g(4) = {S 1, S 2, S 3 }
70 Gradient functions provide cost structure 1. structured candidate space (S, ) 2. cost function (κ)s 3. gradient function (g)s g : R 2 S g(c) is the set of sketches in S that may contain a solution P with κ(p) < c S = set of all SSA programs S1 S2 S3 S4 S5 g(4) = {S 1, S 2, S 3 } The gradient function overapproximates the behavior of κ on S Always sound for g to return all of S if a tighter bound is unavailable. κ(p) = i for P S i S g(c) = { S i S i < c }
71 Gradient functions provide cost structure 1. structured candidate space (S, ) 2. cost function (κ)s 3. gradient function (g)s g : R 2 S g(c) is the set of sketches in S that may contain a solution P with κ(p) < c S = set of all SSA programs S1 S2 S3 S4 S5 g(4) = {S 1, S 2, S 3 } The gradient function overapproximates the behavior of κ on S Always sound for g to return all of S if a tighter bound is unavailable. g(c) always being finite is sufficient (not necessary) to guarantee termination. κ(p) = i for P S i S g(c) = { S i S i < c }
72 Metasketches Design and structure 1. structured candidate space (S, ) 2. cost function (κ)s 3. gradient function (g)s S = set of all SSA programs S1 S2 S3 S4 S5 κ(p) = i for P S i S g(c) = { S i S i < c }
73 Background Syntax-guided synthesis Metasketches Design and structure Synapse A metasketch solver Results Better solutions, faster
74 Background Syntax-guided synthesis Metasketches Design and structure Synapse A metasketch solver Results Better solutions, faster
75 Solving with two cooperative searches S,, κ, g Global search Coordinates the search for an optimal solution, offloading work to parallel local searches Local search Local search... Local search
76 Solving with two cooperative searches S,, κ, g Global search Coordinates the search for an optimal solution, offloading work to parallel local searches Local search Local search... Local search An incremental form of CEGIS that can accept new information from the global search
77 Solving with two cooperative searches S,, κ, g Global search S1 S4 S6 S3 S5 Local search Local search Local search S7 S2
78 Solving with two cooperative searches S,, κ, g Global search S4 S6 S5 Local search Local search Local search S7 S1 S2 S3
79 Solving with two cooperative searches S,, κ, g Global search S4 S6 S5 Local search UNSAT Local search Local search S7 S1 S 2 S2 S3
80 Solving with two cooperative searches S,, κ, g Global search UNSAT S4 S6 S5 Local search Local search Local search S7 S1 S 2 S2 S3
81 Solving with two cooperative searches S,, κ, g Global search S6 S5 Local search Local search Local search S7 S1 S3 S4
82 Solving with two cooperative searches S,, κ, g Global search S6 S5 Local search Local search Local search SAT (P) S7 S1 S3 S4
83 Solving with two cooperative searches S,, κ, g Global search SAT (P) S6 S5 Local search Local search Local search S7 S1 S3 S4
84 Solving with two cooperative searches S,, κ, g Global search κ(p) κ(p) κ(p) S6 S5 Local search Local search Local search S7 S1 S3 S4
85 Solving with two cooperative searches S,, κ, g Global search κ(p) κ(p) κ(p) S6 S5 Local search Local search Local search S7 S1 S4 S3 Prune local search spaces using κ(p)
86 Solving with two cooperative searches S,, κ, g Global search κ(p) κ(p) κ(p) S6 S5 Local search Local search Local search S7 S1 S4 S3 Prune local search spaces using κ(p)
87 Solving with two cooperative searches S,, κ, g Global search κ(p) κ(p) κ(p) Prune global search space using g(κ(p)) S6 S5 Local search Local search Local search S7 S1 S4 S3 Prune local search spaces using κ(p)
88 Solving with two cooperative searches S,, κ, g Global search κ(p) κ(p) κ(p) Prune global search space using g(κ(p)) S6 S5 Local search Local search Local search S1 S4 S3 Prune local search spaces using κ(p)
89 Solving with two cooperative searches S,, κ, g Global search Continues until all search spaces exhausted, yielding an optimal solution. κ(p) κ(p) κ(p) Prune global search space using g(κ(p)) S6 S5 Local search Local search Local search S1 S4 S3 Prune local search spaces using κ(p)
90 Synapse implementation S,, κ, g Global search Implemented in Rosette, a solver-aided extension of Racket Local search Local search... Local search
91 Synapse implementation S,, κ, g Global search Implemented in Rosette, a solver-aided extension of Racket Local CEGIS searches can share counterexamples Local search Local search... Local search
92 Synapse implementation S,, κ, g Global search Implemented in Rosette, a solver-aided extension of Racket Local CEGIS searches can share counterexamples Local search Local search... Local search Local searches can time out, which weakens optimality
93 Background Syntax-guided synthesis Metasketches Design and structure Synapse A metasketch solver Results Better solutions, faster
94 Background Syntax-guided synthesis Metasketches Design and structure Synapse A metasketch solver Results Better solutions, faster
95 Evaluation questions Is Synapse a practical approach to solving different kinds of synthesis problems? Approximate computing, array programs
96 Evaluation questions Is Synapse a practical approach to solving different kinds of synthesis problems? Approximate computing, array programs Can Synapse reason about complex cost functions?
97 Evaluation questions Is Synapse a practical approach to solving different kinds of synthesis problems? Approximate computing, array programs Can Synapse reason about complex cost functions? In the paper: Parallel speedup Optimizations (structure constraints, sharing) More kinds of problems More complex cost functions
98 Synapse solves previously-intractable problems Parrot benchmarks from approximate computing [Esmaelizadeh et al., 2012] Find the most efficient approximate program within an error bound
99 Synapse solves previously-intractable problems Parrot benchmarks from approximate computing [Esmaelizadeh et al., 2012] Find the most efficient approximate program within an error bound fft cos fft sin inversek2j 1 inversek2j 2 kmeans sobel x sobel y Solving time (secs)
100 Synapse solves previously-intractable problems Parrot benchmarks from approximate computing [Esmaelizadeh et al., 2012] Find the most efficient approximate program within an error bound fft cos fft sin inversek2j 1 inversek2j 2 kmeans sobel x Solving time (secs) sobel y All intractable to Sketch and Stoke
101 Synapse solves standard benchmarks optimally Array Search benchmarks from the syntax-guided synthesis (SyGuS) competition [Alur et al., 2015] arraysearch-n: find program that searches lists of length n
102 Synapse solves standard benchmarks optimally Array Search benchmarks from the syntax-guided synthesis (SyGuS) competition [Alur et al., 2015] arraysearch-n: find program that searches lists of length n arraysearch 2 fft cos arraysearch 3 fft sin arraysearch 4 inversek2j 1 arraysearch 5 inversek2j 2 arraysearch 6 kmeans arraysearch 7 sobel x arraysearch 8 sobel y arraysearch 9 arraysearch 10 arraysearch 11 Solving time (secs) arraysearch 12 arraysearch 13 arraysearch 14 arraysearch 15
103 Synapse solves standard benchmarks optimally Array Search benchmarks from the syntax-guided synthesis (SyGuS) competition [Alur et al., 2015] arraysearch-n: find program that searches lists of length n Solving time (secs) Synapse: 349 bytes SyGuS: 7.1 MB arraysearch 2 fft cos arraysearch 3 fft sin arraysearch 4 inversek2j 1 arraysearch 5 inversek2j 2 arraysearch 6 kmeans arraysearch 7 sobel x arraysearch 8 sobel y arraysearch 9 arraysearch 10 arraysearch 11 arraysearch 12 arraysearch 13 arraysearch 14 arraysearch 15
104 Is this a cat?
105 Synapse reasons about complex costs??????????????????????????????
106 Synapse reasons about complex costs?????????????? κ(p) = i P (xi )???????? X???? yi?? Classification error executes the program for each point in the training set??
107 Metasketches Design and structure Synapse A metasketch solver Results Better solutions, faster
108 Metasketches Design and structure Synapse A metasketch solver Results Better solutions, faster synapse.uwplse.org
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