Dependent dynamic rules

Composing Source-to-SourceData-Flow Transformations with

Dependent Dynamic Rewrite RulesProgram Transformation 2004–2005

Eelco Visser

Institute of Information & Computing SciencesUtrecht University,The Netherlands

March 3, 2005

Outline

1 Data-flow transformation strategies

2 Dependencies in data-flow transformation rules

3 Generic data-flow transformation strategies

http://www.strategoxt.org Composing Source-to-Source Data-Flow Transformations with Dependent Dynamic Rewrite Rules

http://www.strategoxt.org

Part I

Data-Flow Transformation Strategies



Flow-Sensitive Constant Propagation

(x := 3;y := x + 1;if foo(x) then

(y := 2 * x;x := y - 2)

else(x := y;y := 23);

z := x + y)

(x := 3;y := 4;if foo(3) then

(y := 6;x := 4)

else(x := 4;y := 23);

z := 4 + y)



x := 3x := 3

y := x + 1y := 4

x -> 3

if foo(x)if foo(3)

x -> 3y -> 4

y := 2 * xy := 6

x -> 3y -> 4

x := yx := 4

x -> 3y -> 4

x := y - 2x := 4

x -> 3y -> 6

x -> 4y -> 6

z := x + yz := 4 + y

x -> 4y -

y := 23y := 23

x -> 4y -> 4

x -> 4y -> 23

Strategy for Basic Constant Propagation

prop-const = PropConst <+ prop-const-assign<+ prop-const-declare <+ prop-const-let <+ prop-const-if<+ prop-const-while <+ (all(prop-const); try(EvalBinOp))

prop-const-assign =|[ x := <prop-const => e> ]|; if <is-value> ethen rules( PropConst.x : |[ x ]| -> |[ e ]| )else rules( PropConst.x :- |[ x ]| ) end

prop-const-declare =|[ var x := <prop-const => e> ]|; if <is-value> ethen rules( PropConst+x : |[ x ]| -> |[ e ]| )else rules( PropConst+x :- |[ x ]| ) end

prop-const-let =?|[ let d* in e* end ]|; {| PropConst : all(prop-const) |}



Intersection of Rule Sets

prop-const-if =|[ if <prop-const> then <id> else <id> ]|; (|[ if <id> then <prop-const> else <id> ]|

/PropConst\ |[ if <id> then <id> else <prop-const> ]|)



Intersection of Rule Sets

let var x := 1 var y := zvar z := 3 var a := 4

in x := x + z;a := 5;if y then(y := y + 5;z := 8)

else(x := a + 21;y := x + 1;z := a + z);

b := a + z;z := z + x end

x y z a b1 - - - -1 - 3 4 -4 - 3 4 -4 - 3 5 -

4 - 3 5 -4 - 8 5 -

26 - 3 5 -26 27 3 5 -26 27 8 5 -- - 8 5 -- - 8 5 13- - 8 5 13

let var x := 1 var y := zvar z := 3 var a := 4

in x := 4;a := 5;if y then

(y := y + 5;z := 8)

else(x := 26;y := 27;z := 8);

b := 13;z := 8 + x end



Fixed-Point Intersection of Rule Sets

let var w := 20 var x := 20var y := 20 var z := 10

in while SomethingUnknown() do(if x = 20 then w := 20 else w := 10;if y = 20 then x := 20 else x := 10;if z = 20 then y := 20 else y := 10);

w; x; y; z end

let var w := 20 var x := 20var y := 20 var z := 10

in while SomethingUnknown() do(if x = 20 then w := 20 else w := 10;if y = 20 then x := 20 else x := 10;y := 10);

w; x; y; 10 end

w x y z20 20 20 10

1 20 20 10 1020 20 - 10

2 20 - 10 1020 - - 10

3 - - 10 10- - - 10

4 - - 10 10- - - 10



Fixed-Point Intersection of Rule Sets

prop-const-while =?|[ while e1 do e2 ]|; (/PropConst\* |[ while <prop-const> do <prop-const> ]|)



Unreachable Code Elimination

let var x := 0 var y := 0in x := 10;

while A do(if x = 10then dosomething()else (dosomethingelse();

x := x + 1));y := x

end

let var x := 0var y := 0

in x := 10;while A dodosomething();

y := 10end



Unreachable Code Elimination

prop-const-if =|[ if <prop-const> then <id> else <id> ]|; (EvalIf; prop-const

<+ (|[ if <id> then <prop-const> else <id> ]|/PropConst\

|[ if <id> then <id> else <prop-const> ]|))

prop-const-while =?|[ while e1 do e2 ]|; (|[ while <prop-const> do <id> ]|; EvalWhile

<+ (/PropConst\*|[ while <prop-const> do <prop-const> ]|))

EvalIf : |[ if 0 then e1 else e2 ]| -> |[ e2 ]|EvalIf : |[ if i then e1 else e2 ]| -> |[ e1 ]|

where <not(eq)>(|[ i ]|, |[ 0 ]|)EvalWhile : |[ while 0 do e ]| -> |[ () ]|



Dead Code Elimination

(x := foo(b);y := bar(h);a := c + 23;if 4 > x then

(d := b + a;g := 4 + y)

else(b := 2;a := y + 3;a := 4 + x);

print(a))

{c,b}{x,c}{x,c}{x,a}{a}{a}

{x}{x}{x}{a}

(x := foo(b);

a := c + 23;if not(4> x) then

a := 4 + x;print(a))



Dead Code Elimination

dce = VarNeeded <+ ElimAssign <+ dce-assign<+ dce-seq <+ dce-if <+ dce-while <+ all(dce)

ElimAssign :|[ x := e ]| -> |[ () ]|where <not(Needed)> |[ x ]|

VarNeeded =?|[ x ]|; rules(Needed : |[ x ]|)

dce-assign =?|[ x := e ]|; rules(Needed :- |[ x ]|); |[ <id> := <dce> ]|



Dead Code Elimination – Control-Flow

dce-seq =|[ (<* reverse-filter(dce; not(?|[ () ]|)) >) ]|

dce-if =(|[ if <id> then <dce> else <id> ]|

\Needed/ |[ if <id> then <id> else <dce> ]|); |[ if <dce> then <id> else <id> ]|; try(ElimIf)

dce-while =|[ while <id> do <id> ]|; (\Needed/* |[ while <dce> do <dce> ]|)



Part II

Dependencies in Data-Flow Transformation Rules



Copy Propagation

Replace copies x produced by assignments of the form x := y byoriginal y

a := b;c := d + a

a := b;c := d + b

First attempt using dynamic rules (wrong)

copy-prop-assign =?|[ x := y ]|;if <not(eq)>(x,y) thenrules( CopyProp.x : |[ x ]| -> |[ y ]| )

elserules( CopyProp.x :- |[ x ]| )

end



Copy Propagation

Replace copies x produced by assignments of the form x := y byoriginal y

a := b;c := d + a

a := b;c := d + b

First attempt using dynamic rules (wrong)



end



Problem: Insufficient Dependencies

(a := b;b := foo();c := d + a)

(a := b;b := foo();c := d + b)

Problem: rule not undefined when variable in rhs changed

Solution: undefine rule when any of its variables is modified



end



Problem: Insufficient Dependencies

(a := b;b := foo();c := d + a)

(a := b;b := foo();c := d + b)

Problem: rule not undefined when variable in rhs changed

Solution: undefine rule when any of its variables is modified



end



Problem: Free Variable Capture

let var a := bar()var b := baz()

in a := b;let var b := foo()in print(a)end

end


in a := b;let var b := foo()in print(b) // wrong!end

end

Problem: rule not undefined when variables become shadowed

Solution: undefine rule locally when some variable shadowed



end



Problem: Free Variable Capture


in a := b;let var b := foo()in print(a)end

end


in a := b;let var b := foo()in print(b) // wrong!end

end

Problem: rule not undefined when variables become shadowed

Solution: undefine rule locally when some variable shadowed



end



Problem: Escaping Variables (1)

let var a := bar()in let var b := foo()

in a := bend;print(a)

end


in a := bend;print(b) // wrong!

end

Problem: rule not undefined when a variable goes out of scope

Solution: (re)define rule in local scope



end





in a := bend;print(a)

end


in a := bend;print(b) // wrong!

end

Problem: rule not undefined when a variable goes out of scope

Solution: (re)define rule in local scope



end




let var a := bar()var c := baz()

in let var b := foo()in a := b;

a := cend;print(a)

end



a := cend;print(c) // ok!

end

Problem: definition in local scope is too restricted

Solution: (re)define rule in innermost scope of all variablesinvolved

copy-prop-assign = ?|[ x := y ]|;if <not(eq)>(x,y) thenrules( CopyProp.x : |[ x ]| -> |[ y ]| )

else rules( CopyProp.x :- |[ x ]| ) end






a := cend;print(a)

end



a := cend;print(c) // ok!

end

Problem: definition in local scope is too restricted

Solution: (re)define rule in innermost scope of all variablesinvolved

copy-prop-assign = ?|[ x := y ]|;if <not(eq)>(x,y) thenrules( CopyProp.x : |[ x ]| -> |[ y ]| )

else rules( CopyProp.x :- |[ x ]| ) end



Common-Subexpression Elimination

(x := a + b;y := a + b;z := a + c;a := 1;z := (a + c) + (a + b))

⇒(x := a + b;y := x;z := a + c;a := 1;z := (a + c) + (a + b))

Assignment

x := e

Propagation rule

|[ e ]| -> |[ x ]|

Dependencies in common-subexpression elimination

all variables in assignment x := e




(x := a + b;y := a + b;z := a + c;a := 1;z := (a + c) + (a + b))

⇒(x := a + b;y := x;z := a + c;a := 1;z := (a + c) + (a + b))

Assignment

x := e

Propagation rule

|[ e ]| -> |[ x ]|

Dependencies in common-subexpression elimination

all variables in assignment x := e




cse = cse-assign <+ (all(cse); try(ReplaceExp))

cse-assign =|[ x := <cse => e> ]|; where(<undefine-subexpressions> |[ x ]|); if <not(is-subterm(||[ x ]|))> |[ e ]| then

rules(ReplaceExp : |[ e ]| -> |[ x ]|); where(<register-subexpressions(|e)> |[ x := e ]|)

end

register-subexpressions(|e) =get-vars; map({y : ?|[ y ]|

; rules(UsedInExp :+ |[ y ]| -> e)})

undefine-subexpressions =bagof-UsedInExp; map({?e; rules(ReplaceExp :- |[ e ]|)})

get-vars = collect({?|[ x ]|})



Dependent Dynamic Rules

Declare rule dependencies

R.lab : p1 -> p2depends on [(lab1,dep1),...,(labn,depn)]

Undefine all rules depending on dep

undefine-R(|dep)

Locally undefine all rules depending on dep

new-R(|lab, dep)

and label current scope with lab



Copy Propagation – Assignments

copy-prop =repeat1(CopyProp)<+ copy-prop-assign<+ copy-prop-declare<+ copy-prop-let <+ copy-prop-if <+ copy-prop-while<+ all(copy-prop)

copy-prop-declare =|[ var x ta := <copy-prop => e> ]|; where( new-CopyProp(|x, x) ); where( try(<copy-prop-assign-aux> |[ x := e ]|) )

copy-prop-assign =|[ x := <copy-prop => e> ]|; where( undefine-CopyProp(|x) ); where( try(copy-prop-assign-aux) )



Copy Propagation – Propagation Rule

copy-prop-assign-aux =? |[ x := y ]|; where( <not(eq)>(x,y) ); where( innermost-scope-CopyProp => z ); rules(

CopyProp.z : |[ x ]| -> |[ y ]|depends on [(x,x), (y,y)]

)

innermost-scope-CopyProp =get-var-names => vars; innermost-scope-CopyProp(elem-of(|vars))



Copy Propagation – Control-Flow

copy-prop-let =|[ let <*id> in <*id> end ]|; {| CopyProp : all(copy-prop) |}

copy-prop-if =|[ if <copy-prop> then <id> else <id> ]|; ( |[ if <id> then <copy-prop> else <id> ]|

/CopyProp\ |[ if <id> then <id> else <copy-prop> ]|)

copy-prop-while =|[ while <id> do <id> ]|; (/CopyProp\* |[ while <copy-prop> do <copy-prop> ]|)



Common-Subexpression Elimination – Assignments

cse =cse-assign <+ cse-vardec <+ cse-let <+ cse-if<+ cse-while <+ all(cse); try(CSE)

cse-vardec =|[ var x ta := <cse => e> ]|; new-CSE(|x, x); where( try(<cse-assign-aux> |[ x := e ]|) )

cse-assign =|[ x := <cse => e> ]|; undefine-CSE(|x); where(try(cse-assign-aux))



Common-Subexpression Elimination – Propagation

cse-assign-aux =? |[ x := e ]|; where( <not(oncetd(?|[ x ]|)); pure> |[ e ]| ); where( get-var-names; map(!(<id>,<id>)) => xs ); where( innermost-scope-CSE => z ); rules( CSE.z : |[ e ]| -> |[ x ]| depends on xs )

pure =?|[ i ]| + ?|[ x ]| + |[ <bo:id>(<pure>, <pure>) ]|

innermost-scope-CSE =get-var-names => vars; innermost-scope-CSE(where(<elem>(<id>, vars)))



Common-Subexpression Elimination – Control-Flow

cse-let =|[ let <*id> in <*id> end ]|; {| CSE : all(cse) |}

cse-if =|[ if <cse> then <id> else <id> ]|; ( |[ if <id> then <cse> else <id> ]|

/CSE\ |[ if <id> then <id> else <cse> ]|)

cse-while =|[ while <id> do <id> ]|; (/CSE\* |[ while <cse> do <cse> ]|)



Part III

Generic Data-Flow Transformation Strategies



Generic Data-Flow Transformation Strategies

Data-flow transformation strategies are similar

Factor out underlying strategy

Requires generalization over combinators

new-dynamic-rules(|Rs,x,x)undefine-dynamic-rules(|Rs,x)/~Rs1\~Rs2/

Allows very concise specifications for specific transformations

Combination of transformations



Generic Strategy – Framework

forward-prop(transform, before, after | Rs1, Rs2, Rs3) =<conc>(Rs1, Rs2, Rs3) => RsSc;<conc>(Rs1, Rs2) => RsDf;letfp = prop-assign <+ prop-declare <+ prop-let

<+ prop-if <+ prop-while<+ transform(fp)<+ (before; all(fp); after)

prop-assign = ...prop-declare = ...prop-let = ...prop-if = ...prop-while = ...

in fpend



Generic Strategy – Assignments

prop-assign =|[ <id> := <fp> ]|; (transform(fp)

<+ before; ?|[ x := e ]|; undefine-dynamic-rules(|RsDf,x); after)

prop-declare =|[ var <id> := <fp> ]|; (transform(fp)

<+ before; ?|[ var x := e ]|; new-dynamic-rules(|RsSc,x,x);after)

prop-let =?|[ let d* in e* end ]|; (transform(fp)

<+ {|~RsSc : before; all(fp); after |})



Generic Strategy – Control Flow

prop-if =|[ if <fp> then <id> else <id> ]|; (transform(fp)

<+ before; (|[ if <id> then <fp> else <id> ]|

/~Rs1\~Rs2/ |[ if <id> then <id> else <fp> ]|); after)

prop-while =?|[ while e1 do e2 ]|; (transform(fp)

<+ before; /~Rs1\~Rs2/* |[ while <fp> do <fp> ]|; after)



Instantation: Constant Propagation

prop-const = forward-prop(prop-const-transform, id,prop-const-after | ["PropConst"],[],[])

prop-const-transform(recur) =EvalFor <+ EvalIf; recur<+ |[ while <recur> do <id> ]|; EvalWhile

prop-const-after =try(prop-const-assign <+ prop-const-declare

<+ PropConst <+ EvalBinOp)

prop-const-assign =?|[ x := e ]|; where( <is-value> e ); rules( PropConst.x : |[ x ]| -> |[ e ]|

depends on [(x,x)] )prop-const-declare =?|[var x ta := e]|; where(<prop-const-assign>|[x := e]|)



Instantation: Copy Propagation

copy-prop =forward-prop(no-transform,id,copy-prop-after

|["CopyProp"],[],[])

copy-prop-after =try(copy-prop-assign <+ copy-prop-declare

<+ repeat1(CopyProp))

copy-prop-declare =? |[ var x ta := e ]|; where(try(<copy-prop-assign> |[ x := e ]|))

copy-prop-assign =? |[ x := y ]|; where( <not(eq)> (x, y) ); where( get-var-dependencies => xs ); where( innermost-scope-CopyProp => z ); rules( CopyProp.z : |[ x ]| -> |[ y ]| depends on xs )



Instantation: Common-Subexpression Elimination

cse =forward-prop(no-transform, id, cse-after|["CSE"],[],[])

cse-after =try(cse-assign <+ cse-declare <+ CSE)

cse-declare =?|[ var x := e ]|; where( <cse-assign> |[ x := e ]| )

cse-assign = ?|[ x := e ]|; where( <pure-and-not-trivial(|x)> |[ e ]| ); where( get-var-dependencies => xs ); where( innermost-scope-CSE => z ); rules( CSE.z : |[ e ]| -> |[ x ]| depends on xs )



Instantation: A Super Optimizer

super-opt =forward-prop(prop-const-transform, bvr-before, bvr-after; copy-prop-after; prop-const-after; cse-after

| ["PropConst", "CopyProp", "CSE"], [], ["RenameVar"])

Combination of

constant propagation

copy propagation

common-subexpression elimination

bound variable renaming



Technology

Dependent dynamic rules