synquid: synthesizing programs from liquid typesnpolikarpova/talks/strangeloop18.pdf ·...

type-driven program synthesis

Nadia Polikarpova

2

my goal: automate programming

example: insert into a sorted list

Input:

Output:

3

1 2 7 8

5

xs

x

1 2 7 85ys

insert in a functional language

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insert x xs =match xs with

Nil →Cons x Nil

Cons h t →if x ≤ h

then Cons x xselse Cons h (insert x t)

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875 9

5

5

insert x xs =match xs with

Nil →Cons x Nil

Cons h t →if x ≤ h

then Cons x xselse Cons h (insert x t)

void insert(node *xs, int x) {node *new;node *temp;node *prev;

new = (node *)malloc(sizeof(node));if(new == NULL) {printf("Insufficient memory.");return;

}new->val = x;new->next = NULL;if (xs == NULL) {xs = new;

} else if(x < xs->val) {new->next = xs;xs = new;

} else { prev = xs;temp = xs->next;while(temp != NULL && x > temp->val) {

prev = temp;temp = temp->next;

}if(temp == NULL) {

prev->next = new;} else {

new->next = temp;prev->next = new;

}}

}

automatespointer manipulation &memory management

C Haskell

what’s next?

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void insert(node *xs, int x) {node *new;node *temp;node *prev;

new = (node *)malloc(sizeof(node)); if(new == NULL) {printf("Insufficient memory.");return;

} new->val = x;new->next = NULL;if (xs == NULL) {xs = new;

} else if(x < xs->val) {new->next = xs;xs = new;

} else { prev = xs;temp = xs->next;while(temp != NULL && x > temp->val) {prev = temp;temp = temp->next;

}if(temp == NULL) {prev->next = new;

} else {new->next = temp;prev->next = new;

}}

}

insert x xs =match xs withNil → Cons x NilCons h t →if x ≤ hthen Cons x xselse Cons h (insert x t)

append:push ebpmov ebp, esppush eaxpush ebxpush lencall mallocmov ebx, [ebp + 12]mov [eax + info], ebxmov dword [eax + next], 0mov ebx, [ebp + 8]cmp dword [ebx], 0je null_pointermov ebx, [ebx]

next_element:cmp dword [ebx + next], 0je found_lastmov ebx, [ebx + next]jmp next_element

found_last:push eaxpush addMescall putsadd esp, 4pop eaxmov [ebx + next], eax

go_out:pop ebxpop eaxmov esp, ebppop ebpret 8

null_pointer:push eaxpush nullMescall putsadd esp, 4pop eaxmov [ebx], eaxjmp go_out

Assembly C Haskell

?future

automatesargument passing& memory access

this talk

I. specificationsare the new cool language feature

II. program synthesisis the way to make it happen

III. synthesis-aided programmingis the the future

7

this talk

I. specifications

II. program synthesis

III. synthesis-aided programming

8

this talk

I. specifications

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how do I tell the machine what I want?

specification for insert

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Input:

x

xs: sorted list

Output:

ys: sorted list

elems ys = elems xs ∪ {x}

easy to write ☺

hard to execute

specification code

program synthesis

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match xs withNil → Cons x NilCons h t →if x ≤ hthen Cons x xselse Cons h (insert x t)

in: x, sorted xsout: sorted ys

elems ys = elemsxs ∪ {x}

Synquidspecification code

program synthesis

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match xs withNil → Cons x NilCons h t →if x ≤ hthen Cons x xselse Cons h (insert x t)

in: x, sorted xsout: sorted ys

elems ys = elemsxs ∪ {x}

Synquid

Synquidspecification code

program synthesis

13

match xs withNil → Cons x NilCons h t →if x ≤ hthen Cons x xselse Cons h (insert x t)

in: x, sorted xsout: sorted ys

elems ys = elemsxs ∪ {x}

formalize this

types are specifications

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insert :: a → List a → List a

types are specifications

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insert :: a → List a → List a

ordinary types are insufficient!

refinement types

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{ v:Int | 0 ≤ v }

shape refinement

data SList a whereNil :: SList aCons :: h:a →

t:SList {v:a | h ≤ v} →SList a

from lists to sorted lists

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List aList a

List aSList a →List a →

data SList a whereNil :: SList aCons :: h:a →

t:SList {v:a | h ≤ v} →SList a

from lists to sorted lists

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7 82

all you need is one simple predicate!

insert :: x:a → xs:SList a →{v:SList a | elems v = elems xs ∪ {x}}

insert in Synquid

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Synquid generates correct code in under a second!

this talk

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I. specifications

II.program synthesis

III. synthesis-aided programming

this talk

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I. specifications

II.program synthesis

how do we get from specification to code?

type-driven program synthesis

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match xs withNil → Cons x NilCons h t →if x ≤ hthen Cons x xselse Cons h (insert x t)

? insert :: x:a →xs:SList a →{v:SList a | elems v =elems xs ∪ {x}}

specification code

synthesis as search

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...

insert :: x:a →xs:SList a →{v:SList a | elems v =elems xs ∪ {x}}

Nil, Cons, ≤, …

specification

components

code

synthesis as search

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...

too many270

insert :: x:a →xs:SList a →{v:SList a | elems v =elems xs ∪ {x}}

Nil, Cons, ≤, …

specification

components

code

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synthesis as search

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synthesis as search

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synthesis as search

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key idea: reject hopeless programs early

synthesis as search

reject hopeless programs early

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insert :: x:a →xs:SList a →{v:SList a | elems v =elems xs ∪ {x}}

specification

reject hopeless programs early

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insert :: x:a →xs:SList a →{v:SList a | elems v =elems xs ∪ {x}}

specification

reject hopeless programs early

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insert :: x:a →xs:SList a →{v:SList a | elems v =elems xs ∪ {x}}

specification

x:a → xs:SList a →{v:SList a | elems v = elems xs ∪ {x}}

insert x xs =match xs with

Nil → NilCons h t → ??

reject hopeless programs early

32

x:a → xs:SList a →{v:SList a | elems v = elems xs ∪ {x}}

insert x xs =match xs with

Nil → NilCons h t → ??

reject hopeless programs early

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250

x:a → xs:SList a →{v:SList a | elems v = elems xs ∪ {x}}

insert x xs =match xs with

Nil → NilCons h t → ??

insert x xs =match xs with

Nil → NilCons h t → ??

{v:SList a | elems v = elems xs ∪ {x}}

reject hopeless programs early

34

x:a → xs:SList a →{v:SList a | elems v = elems xs ∪ {x}}

insert x xs =match xs with

Nil → NilCons h t → ??

insert x xs =match xs with

Nil → NilCons h t → ??

insert x xs =match xs with

Nil → NilCons h t → ??

{v:SList a | elems v = elems xs ∪ {x}}{v:SList a | elems v = {x}}

reject hopeless programs early

35

x:a → xs:SList a →{v:SList a | elems v = elems xs ∪ {x}}

insert x xs =match xs with

Nil → NilCons h t → ??

insert x xs =match xs with

Nil → NilCons h t → ??

insert x xs =match xs with

Nil → NilCons h t → ??

{v:SList a | elems v = elems xs ∪ {x}}{v:SList a | elems v = {x}}

reject hopeless programs early

36

Expected {v:SList a | elems v = {x}}and got {v:SList a | elems v = {}}

synquid

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match xs withNil → Cons x NilCons h t →if x ≤ hthen Cons x xselse Cons h (insert x t)

insert :: x:a →xs:SList a →{v:SList a | elems v =elems xs ∪ {x}}

specification code

components

experiments

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lists sorting BSTAVL /

red-blackcustom

data types

¬(a ⇒ b ∨ c)¬(a ⇒ b ∨ c)¬(a ⇒ b ∨ c)

case study: negation normal form

39

1. only ¬, ∧, ∨

2. ¬ only at variables

¬(a ⇒ b ∨ c)¬(a ⇒ b ∨ c)¬(a ⇒ b ∨ c)

case study: negation normal form

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a ∧ (¬b ∨ ¬c)

1. only ¬, ∧, ∨

2. ¬ only at variables

¬(¬a ∨ (b ∨ c))

¬¬a ∧ ¬(b ∨ c)

a ∧ ¬(b ∨ c)

⇒ def.

De Morgan

double-neg

De Morgan

nnf: data types

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data Fml whereVar :: String → FmlNot :: Fml → FmlAnd :: Fml → Fml → FmlOr :: Fml → Fml → FmlImp :: Fml → Fml → Fml

data NNF whereNAtom :: String → Bool

→ NNFNAnd :: NNF → NNF → NNFNOr :: NNF → NNF → NNF

negated?

nnf: specification

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data Fml whereVar :: String → FmlNot :: Fml → FmlAnd :: Fml → Fml → FmlOr :: Fml → Fml → FmlImp :: Fml → Fml → Fml

data NNF whereNAtom :: String → Bool

→ NNFNAnd :: NNF → NNF → NNFNOr :: NNF → NNF → NNF

measure eval :: Fml → Bool whereVar v → env vNot f → !(eval f)And l r → eval l && eval rOr l r → eval l || eval rImp l r → eval l ==> eval r

measure nEval :: NNF → Bool whereNAtom neg v → if neg then env v

else !(env v)NAnd l r → nEval l && nEval rNOr l r → nEval l || nEval r

nnf: specification

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nnf :: f:Fml → {v:NNF | nEval v = eval f}

nnf: synthesized code

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nnf :: f:Fml → {v:NNF | nEval v = eval f}nnf p = match p with

BoolLiteral x2 → if x2then NOr (NAtom dummy x2) (NAtom dummy False)else NAnd (NAtom dummy x2) (NAtom dummy True)

Var x16 → NAtom x16 FalseNot x20 → match x20 withBoolLiteral x22 → if x22then nnf (BoolLiteral False)else nnf (BoolLiteral True)

Var x28 → NAtom x28 TrueNot x32 → nnf x32And x36 x37 → NOr (nnf (Not x36)) (nnf (Not x37))Or x46 x47 → NAnd (nnf (Not x46)) (nnf (Not x47))Implies x56 x57 → NAnd (nnf x56) (nnf (Not x57))

And x65 x66 → NAnd (nnf x65) (nnf x66)Or x73 x74 → NOr (nnf x73) (nnf x74)Imp x81 x82 → NOr (nnf x82) (nnf (Not x81)) ⇒ def.

double-neg

De Morgan

this talk

45

I. specifications

II. program synthesis

III. synthesis-aided programming

this talk

46

I. specifications

II. program synthesis

III. synthesis-aided programming

how can synthesis help us build software?

the future of programming

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Let there be Instagram!

the future of programming

48

Let there be Instagram!

(not)

orthogonal concerns

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functional requirements

datainvariants

security policies

resource constraints

I worry about all concerns together

synthesis-aided programming

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functional requirements

datainvariants

security policies

resource constraints

I worry about one concern at a time ☺

specification

synthesis weaves them together

synthesis-aided programming

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functional requirements

security policies

specification

information leaks

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electronic health records social networks e-commerce

information leaks

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social networks

policy checks

information leaks

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social networks

James ComeyBrian Comey

Ashley Feinberg

information security with Lifty

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program with checks

securitypolicies

program

Lifty

synthesis-aided programming

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functional requirements

resource constraints

specification

timing attacks

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password

attempt

execution time reveals length!

Compare the lengths of two strings:

resource-aware programming with ReSyn

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password

attempt

compare :: pass:List a → att:List a →{v:Bool | v = (len key = len guess)}

unit resource per element

1 1 1 11

{a || 1} →

synthesis-aided programming

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http://comcom.csail.mit.edu