Compilers  consider  only  a  single  poten2al  error  source.  Therefore,  type  error  reports  are   o9en   not   useful.   Be;er:   rank   error   sources   by   some  useful   criterion   and   then  show  the  top  ranked  sources  to  the  programmer.  

Compilers   provide   a   ranking   criterion   to   prefer   type   error   sources   of   par2cular  interest.   A   ranking   criterion   assigns   weights   to   program   expressions.   A   smaller  weight   indicates   that   the   expression   more   likely   contributes   to   the   error.   For  example,   to   prefer   error   sources   that   require   fewer   correc2ons,   assign   a   weight  equal  to  the  expression’s  size.  

a  hole  expression  represen2ng  a  generic  fix  

Compiler  

Typing  Constraint  Genera2on  

Weighted  MaxSMT  Solver  

input  program  and  ranking  criterion  

constraint  

minimum  error  source  

How?   Reduce   the   problem   to   weighted   maximum   sa2sfiability   modulo   theories  (MaxSMT).   We   propose   a   general   framework   for   type   error   localiza2on   using  constraint  solving.  

A  general  framework  for  type  error  localiza2on  that  •  abstracts  from  the  par2cular  ranking  criterion  •  supports  various  type  systems  by  appropriately  instan2a2ng  the  SMT  solver  •  requires  no  substan2al  compiler  modifica2ons  due  to  use  of  SMT  solvers  

each  proposi2onal  variable  is  a  so9  clause  with  the  weight  that  the  given  ranking  criterion  assigns  to  the  corresponding  program  expression    

let x = "hi" in not x

The  constraint  genera2on  is  done  using  typing  rules.  The  constraint  for  our  running  example  is  as  follows.  

5   1   3   1   1  

weighted  MaxSMT  solu2on    

Finding  Minimum  Type  Error  Sources  Zvonimir  Pavlinovic  (New  York  University)  

OCaml:  This  expression  has  type  ‘a  list  but  an  expression  was  expected  of  type  unit  

Error  source:  a  set  of  program  expressions  that,  once  corrected,  yield  a  well-‐typed  program.    

(not  well-‐typed)  

Finding  minimum  type  error  sources  problem:  given  an  input  program  and  a  compiler-‐provided  ranking  criterion,  find  a  minimum  error  source  subject  to  the  criterion.  

 Minimum  error  source:  an  error  source  of  minimum  cumula2ve  weight.    

let x = "hi" in not x

?  

Tlet

=) ( ↵let

= ↵o

^

Tnot

=) ↵not

= ↵app

^

Tx

=) ↵x

= string ^Tapp

=) ( ↵app

= fun(↵i

,↵o

) ^

Ti

=) ↵i

= ↵x

)) ^

hard  clause  encoding  the  structure  of  the  program  

1  

A  generated  constraint  is  unsa2sfiable  iff  there  is  a  type  error  in  the  input  program.  For  instance,  the  above  constraint  is  unsa2sfiable.    

Generated  typing  constraint  is  passed  to  the  weighted  MaxSMT  solver.    

ST ^ Tlet

^ Tx

^ Tapp

^ Tnot

^ Ti

^ Tnot impl

5   1   3   1   1   1  h  

ST ^ Tlet

^ Tx

^ Tapp

^ Tnot

^ Ti

^ Tnot impl

complement  represents  a  minimum  error  source    

ST ^ Tlet

^ Tx

^ Tapp

^ Tnot

^ Ti

^ Tnot impl

let x = "hi" in not x?  

•  Framework  instan2ated  for  a  subset  of  OCaml  (Hindley-‐Milner  type  system)  •  Typing  constraint  generated  using  the  EasyOCaml  system  •  Weighted  MaxSMT  solver  implemented  using  CVC4  and  Sat4j  •  Implementa2on  evaluated  on  ~350  OCaml  scripts  from  [Lerner  et  al.,  ‘07]  

sehng  a  proposi2onal  variable  to  false  has  the  effect  of  replacing  the  corresponding  expression  with  a  hole  

0  

50  

100  

150  

200  

250  

300  

350  

0-‐50  (47)  

50-‐100  (102)  

100-‐150  (65)  

150-‐200  (57)  

200-‐250  (53)  

250-‐300  (28)  

300-‐350  (3)  

350-‐400  (1)  

max  

min  

median  

seconds  

program  size  in  loc  

(2)   (2)   (3)   (1)  

let f(lst:move list): (float*float) list =

...

let rec loop lst x y dir acc =

if lst = [] then

acc

else

print_string "foo"

in

List.rev

(loop lst 0.0 0.0 0.0 [(0.0 ,0.0)])

other  poten2al  error  sources  

Let  S   and  H  be   two  sets  of   clauses  over   some  fixed  first-‐order   theory  where  each  clause   from   S   is   assigned   a   weight.   The   weighted   MaxSMT   problem   is   to   find   a  subset  N   of  S  with  maximum  cumula2ve  weight   such   that  N∧H   is   sa2sfiable.   The  clauses  in  S  are  referred  to  as  so9  clauses,  and  the  clauses  in  H  hard  clauses.    

ST ⌘

ST ^ Tlet

^ Tx

^ Tapp

^ Tnot

^ Ti

^ Tnot impl

Tnot impl

=) ↵not

= fun(bool, bool)

h