[PPT] - 0 Correct Programming Compiler Compiler Hardware Language P PowerPoint Presentation

SLIDE 1

Bridging the Gap between Programming Languages and Hardware Weak Memory Models

Anton Podkopaev Ori Lahav Viktor Vafeiadis

SLIDE 2

1

Bridging the Gap between PL and Hardware Weak MMs Programming Language Hardware Compiler Correct Compiler P Syntax PL P PL compile P

HW PL HW is Memory Model

SLIDE 3

1

Bridging the Gap between PL and Hardware Weak MMs Programming Language Hardware Compiler Correct Compiler P Syntax PL P PL compile P

HW PL HW is Memory Model

SLIDE 4

1

Bridging the Gap between PL and Hardware Weak MMs Programming Language Hardware Compiler Correct Compiler P Syntax PL P PL compile P

HW PL HW is Memory Model

SLIDE 5

1

Bridging the Gap between PL and Hardware Weak MMs Programming Language Hardware Compiler Correct Compiler P Syntax PL P PL compile P

HW PL HW is Memory Model

SLIDE 6

1

Bridging the Gap between PL and Hardware Weak MMs Programming Language Hardware Compiler Correct Compiler ∀P ∈ Syntax(PL). PPL compile(P)HW

PL HW is Memory Model

SLIDE 7

1

Bridging the Gap between PL and Hardware Weak MMs Programming Language Hardware Compiler Correct Compiler ∀P ∈ Syntax(PL). PPL compile(P)HW −{PL,HW} is Memory Model

SLIDE 8

1

Bridging the Gap between PL and Hardware Weak MMs Programming Language Hardware Compiler Correct Compiler ∀P ∈ Syntax(PL). PPL compile(P)HW −{PL,HW} is Memory Model

SLIDE 9

2 Strong (SC) MM disallows a b 1

Memory ; [x] ← 0 [y] ← 0 Values ; a = ⊥ b = ⊥ a := [x]; [y] := 1; b := [y]; [x] := b; ARM and POWER weak MMs allow a b 1!

SLIDE 10

2 Strong (SC) MM disallows a b 1

Memory ; [x] ← 0 [y] ← 0 Values ; a = ⊥ b = ⊥ a := [x]; [y] := 1; b := [y]; [x] := b; ARM and POWER weak MMs allow a b 1!

SLIDE 11

2 Strong (SC) MM disallows a b 1

Memory ; [x] ← 0 [y] ← 0 Values ; a = 0 b = ⊥ a := [x]; [y] := 1; b := [y]; [x] := b; ARM and POWER weak MMs allow a b 1!

SLIDE 12

2 Strong (SC) MM disallows a b 1

Memory ; [x] ← 0 [y] ← 1 Values ; a = 0 b = ⊥ a := [x]; [y] := 1; b := [y]; [x] := b; ARM and POWER weak MMs allow a b 1!

SLIDE 13

2 Strong (SC) MM disallows a b 1

Memory ; [x] ← 0 [y] ← 1 Values ; a = 0 b = 1 a := [x]; [y] := 1; b := [y]; [x] := b; ARM and POWER weak MMs allow a b 1!

SLIDE 14

2 Strong (SC) MM disallows a b 1

Memory ; [x] ← 1 [y] ← 1 Values ; a = 0 b = 1 a := [x]; [y] := 1; b := [y]; [x] := b; ARM and POWER weak MMs allow a b 1!

SLIDE 15

2 Strong (SC) MM disallows a b 1

Memory ; [x] ← 1 [y] ← 1 Values ; a = 0 b = 1 a := [x]; [y] := 1; b := [y]; [x] := b; ARM and POWER weak MMs allow a b 1!

SLIDE 16

2 Strong (SC) MM disallows a = b = 1

Memory ; [x] ← 1 [y] ← 1 Values ; a = 0 b = 1 a := [x]; [y] := 1; b := [y]; [x] := b; ARM and POWER weak MMs allow a b 1!

SLIDE 17

2 Strong (SC) MM disallows a = b = 1

Memory ; [x] ← 1 [y] ← 1 Values ; a = 0 b = 1 a := [x]; [y] := 1; b := [y]; [x] := b; ARM and POWER weak MMs allow a = b = 1!

SLIDE 18

3

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 19

3

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 20

3

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 21

3

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 22

3

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 23

3

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 24

3

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 25

3

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 26

3

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 27

4 (Declarative) Executions in IMM

a := [x]; [y] := 1; b := [y]; [x] := b;

Rx0 Wy1 Ry0 Wx0

fr

,

Rx0 Wy1 Ry1 Wx1

data fr rf

,

Rx1 Wy1 Ry1 Wx1

data rf

Rx1 Wy1 Ry1 Wx1

po data rf

Axioms:

1. data

rf is acyclic …

SLIDE 28

4 (Declarative) Executions in IMM

a := [x]; [y] := 1; b := [y]; [x] := b;

Rx0 Wy1 Ry0 Wx0

fr

,

Rx0 Wy1 Ry1 Wx1

data fr rf

,

Rx1 Wy1 Ry1 Wx1

data rf

Rx1 Wy1 Ry1 Wx1

po data rf

Axioms:

1. data

rf is acyclic …

SLIDE 29

4 (Declarative) Executions in IMM

a := [x]; [y] := 1; b := [y]; [x] := b;

Rx0 Wy1 Ry0 Wx0

fr

,

Rx0 Wy1 Ry1 Wx1

data fr rf

,

Rx1 Wy1 Ry1 Wx1

data rf

Rx1 Wy1 Ry1 Wx1

po data rf

Axioms:

1. data

rf is acyclic …

SLIDE 30

4 (Declarative) Executions in IMM

a := [x]; [y] := 1; b := [y]; [x] := b;

Rx0 Wy1 Ry0 Wx0

fr

,

Rx0 Wy1 Ry1 Wx1

data fr rf

,

Rx1 Wy1 Ry1 Wx1

data rf

Rx1 Wy1 Ry1 Wx1

po data rf

Axioms:

1. data ∪ rf is acyclic

…

SLIDE 31

5

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 32

5

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

(deps ∪ rf is acyclic)

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 33

5

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

(deps ∪ rf is acyclic)

3. Uses C11-style coherence

(hb; eco? is irreflexive)

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 34

5

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

(deps ∪ rf is acyclic)

3. Uses C11-style coherence

(hb; eco? is irreflexive)

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 35

5

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 36

5

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 37

5

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 38

6 (Operational) Execution in Promise

Promised a := [x]; [y] := 1; b := [y]; [x] := b; Requires certification Values ; a = ⊥ b = ⊥

SLIDE 39

6 (Operational) Execution in Promise

Promised a := [x]; [y] := 1; b := [y]; [x] := b; Requires certification Values ; a = ⊥ b = ⊥

SLIDE 40

6 (Operational) Execution in Promise

Promised a := [x]; [y] := 1; b := [y]; [x] := b; Requires certification Values ; a = ⊥ b = ⊥

SLIDE 41

6 (Operational) Execution in Promise

Promised a := [x]; [y] := 1; b := [y]; [x] := b; Requires certification Values ; a = ⊥ b = ⊥

SLIDE 42

6 (Operational) Execution in Promise

Promised a := [x]; [y] := 1; b := [y]; [x] := b; Requires certification Values ; a = ⊥ b = 1

SLIDE 43

6 (Operational) Execution in Promise

Promised a := [x]; [y] := 1; b := [y]; [x] := b; Requires certification Values ; a = ⊥ b = 1

SLIDE 44

6 (Operational) Execution in Promise

Promised a := [x]; [y] := 1; b := [y]; [x] := b; Requires certification Values ; a = 1 b = 1

SLIDE 45

6 (Operational) Execution in Promise

Promised a := [x]; [y] := 1; b := [y]; [x] := b; Requires certification Values ; a = 1 b = 1

SLIDE 46

7

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 47

8 How to prove correctness of compilation? Simulation How to simulate graphs? Traverse in proper order!

SLIDE 48

8 How to prove correctness of compilation? Simulation How to simulate graphs? Traverse in proper order!

SLIDE 49

8 How to prove correctness of compilation? Simulation How to simulate graphs? Traverse in proper order!

SLIDE 50

8 How to prove correctness of compilation? Simulation How to simulate graphs? Traverse in proper order!

SLIDE 51

9 Traversal of IMM execution

a := [x]; [y] := 1; b := [y]; [x] := b; Promised Promised

Rx1 Wy1 Ry1 Wx1

Covered Issued

SLIDE 52

10

Promise → IMM compilation correctness proof

1. Operational semantics of IMM’s traversal:

G ⊢ ⟨C, I⟩ → ⟨C ′, I ′⟩

2. Completeness of traversal:

G P IMM G initTraverse G Events G Writes

3. Simulation theorems:

initTraverse initPromise

simulated by

traverse traverse promise promise

simulated by simulated by

Promise’s certification Promise’s certification via traversal of certification graph

SLIDE 53

10

Promise → IMM compilation correctness proof

1. Operational semantics of IMM’s traversal:

G ⊢ ⟨C, I⟩ → ⟨C ′, I ′⟩

2. Completeness of traversal:

∀G ∈ PIMM. G ⊢ initTraverse →∗ ⟨G.Events, G.Writes⟩

3. Simulation theorems:

initTraverse initPromise

simulated by

traverse traverse promise promise

simulated by simulated by

Promise’s certification Promise’s certification via traversal of certification graph

SLIDE 54

10

Promise → IMM compilation correctness proof

1. Operational semantics of IMM’s traversal:

G ⊢ ⟨C, I⟩ → ⟨C ′, I ′⟩

2. Completeness of traversal:

∀G ∈ PIMM. G ⊢ initTraverse →∗ ⟨G.Events, G.Writes⟩

3. Simulation theorems:

initTraverse initPromise

simulated by

traverse traverse′ promise ∃ promise′

simulated by simulated by

Promise’s certification Promise’s certification via traversal of certification graph

SLIDE 55

10

Promise → IMM compilation correctness proof

1. Operational semantics of IMM’s traversal:

G ⊢ ⟨C, I⟩ → ⟨C ′, I ′⟩

2. Completeness of traversal:

∀G ∈ PIMM. G ⊢ initTraverse →∗ ⟨G.Events, G.Writes⟩

3. Simulation theorems:

initTraverse initPromise

simulated by

traverse traverse′ promise ∃ promise′

simulated by simulated by

Promise’s certification Promise’s certification via traversal of certification graph

SLIDE 56

10

Promise → IMM compilation correctness proof

1. Operational semantics of IMM’s traversal:

G ⊢ ⟨C, I⟩ → ⟨C ′, I ′⟩

2. Completeness of traversal:

∀G ∈ PIMM. G ⊢ initTraverse →∗ ⟨G.Events, G.Writes⟩

3. Simulation theorems:

initTraverse initPromise

simulated by

traverse traverse′ promise ∃ promise′

simulated by simulated by

Promise’s certification Promise’s certification via traversal of certification graph

SLIDE 57

10

Promise → IMM compilation correctness proof

1. Operational semantics of IMM’s traversal:

G ⊢ ⟨C, I⟩ → ⟨C ′, I ′⟩

2. Completeness of traversal:

∀G ∈ PIMM. G ⊢ initTraverse →∗ ⟨G.Events, G.Writes⟩

3. Simulation theorems:

initTraverse initPromise

simulated by

traverse traverse′ promise ∃ promise′

simulated by simulated by

Promise’s certification Promise’s certification via traversal of certification graph

SLIDE 58

11 Traversal of IMM execution

a := [x]; [y] := 1; b := [y]; [x] := b; Promised Promised

Rx1 Wy1 Ry1 Wx1

Covered Issued

SLIDE 59

11 Traversal of IMM execution

a := [x]; [y] := 1; b := [y]; [x] := b; Promised Promised

Rx1 Wy1 Ry1 Wx1

Covered Issued

SLIDE 60

11 Traversal of IMM execution

a := [x]; [y] := 1; b := [y]; [x] := b; Promised Promised

Rx1 Wy1 Ry1 Wx1

Covered Issued

SLIDE 61

11 Traversal of IMM execution

a := [x]; [y] := 1; b := [y]; [x] := b; Promised Promised

Rx1 Wy1 Ry1 Wx1

Covered Issued

SLIDE 62

11 Traversal of IMM execution

a := [x]; [y] := 1; b := [y]; [x] := b; Promised Promised

Rx1 Wy1 Ry1 Wx1

Covered Issued

SLIDE 63

11 Traversal of IMM execution

a := [x]; [y] := 1; b := [y]; [x] := b; Promised Promised

Rx1 Wy1 Ry1 Wx1

Covered Issued

SLIDE 64

11 Traversal of IMM execution

a := [x]; [y] := 1; b := [y]; [x] := b; Promised Promised

Rx1 Wy1 Ry1 Wx1

Covered Issued

SLIDE 65

12

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 66

12

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 67

12

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 68

12

Bridging the Gap between PL and Hardware Weak MMs Promise (R)C11 WeakestMO

[Chakraborty and Vafeiadis, 2019]

IMM x86-TSO ARMv7 ARMv8.3 RISC-V POWER

CompCert Weak MMs

1. Declarative
1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

1. Declarative
2. Preserves syntactic dependencies

deps rf is acyclic

3. Uses C11-style coherence

hb eco is irreflexive

4. Non-multicopy-atomic

w/o mutually recursive relations

plv.mpi-sws.org/imm/ Thank you!

SLIDE 69

13

Links I

Chakraborty, S. and Vafeiadis, V. (2019). Grounding thin-air reads with event structures. In POPL 2019. ACM. Kang, J., Hur, C.-K., Lahav, O., Vafeiadis, V., and Dreyer, D. (2017). A promising semantics for relaxed-memory concurrency. In POPL 2017. ACM.

SLIDE 70

14 Backup slides

SLIDE 71

15

IMM definition

Def. G is called IMM-consistent if the following hold:
codom(G.rf) = G.R.
For every location ℓ ∈ Loc, G.co totally orders G.Wℓ.
G.rmw ∩ (G.fre ; G.coe) = ∅.
G.hb ; G.eco? is irreflexive.
G.ar is acyclic.

ar ≜ rfe ∪ bob ∪ ppo ∪ detour ∪ psc ∪ [Wstrong] ; po ; [W] bob ≜ po ; [Wrel] ∪ [Racq] ; po ∪ po ; [F] ∪ [F] ; po ∪ [Wrel] ; po|loc ; [W] ppo ≜ [R] ; (deps ∪ rfi)+ ; [W] deps ≜ data ∪ ctrl ∪ addr ; po? ∪ casdep ∪ [Rex] ; po

SLIDE 72

16

Traversal definition

a ∈ Next(G, C) ∩ Coverable(G, C, I) G ⊢ ⟨C, I⟩ → ⟨C ∪ {a}, I⟩ w ∈ Issuable(G, C, I) \ I G ⊢ ⟨C, I⟩ → ⟨C, I ∪ {w}⟩

Def. w ∈ Issuable(G, C, I) iff w ∈ G.W and the following hold:
dom(([G.Wrel] ; G.po|G.loc ∪ [G.F] ; G.po) ; [w]) ⊆ C
dom((G.detour ∪ G.rfe) ; G.ppo ; [w]) ⊆ I
dom((G.detour ∪ G.rfe) ; [G.Racq] ; G.po ; [w]) ⊆ I
dom([G.Wstrong] ; G.po ; [w]) ⊆ I
Def. e ∈ Coverable(G, C, I) iff e ∈ G.E, dom(G.po ; [e]) ⊆ C and either

(i) e ∈ G.W ∩ I; (ii) e ∈ G.R and dom(G.rf ; [e]) ⊆ I; (iii) e ∈ G.Fsc;

r (iv) e ∈ G.Fsc and dom(G.sc ; [e]) ⊆ C.

SLIDE 73

17

Mistake in Kang et al.17’s compilation to POWER correctness proof

Rrlxz1 Fsc Wrlxx1 Wrlxx2 Fsc Wrlxy1 Rrlxy1 Wrlxz1

rf co rf Consistent in Strong-POWER. Not consistent in the promise-free declarative model of [Kang et al., 2017].

SLIDE 74

18

Promise → IMM compilation of RMWs

a := [y]rlx / / 1 [z]rlx := a b := [z]rlx / / 1 c := FADDrlx,rel

strong (x, 1) /

/ 0 [y]rlx := c + 1

Rrlxy1 Wrlxz1 Rrlxz1 Rrlxx0 Wrel

strongx1