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(* Title: HOL/Tools/Nitpick/kodkod.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2008-2014
ML interface for Kodkod.
*)
signature KODKOD =
sig
type n_ary_index = int * int
type setting = string * string
datatype tuple =
Tuple of int list |
TupleIndex of n_ary_index |
TupleReg of n_ary_index
datatype tuple_set =
TupleUnion of tuple_set * tuple_set |
TupleDifference of tuple_set * tuple_set |
TupleIntersect of tuple_set * tuple_set |
TupleProduct of tuple_set * tuple_set |
TupleProject of tuple_set * int |
TupleSet of tuple list |
TupleRange of tuple * tuple |
TupleArea of tuple * tuple |
TupleAtomSeq of int * int |
TupleSetReg of n_ary_index
datatype tuple_assign =
AssignTuple of n_ary_index * tuple |
AssignTupleSet of n_ary_index * tuple_set
type bound = (n_ary_index * string) list * tuple_set list
type int_bound = int option * tuple_set list
datatype formula =
All of decl list * formula |
Exist of decl list * formula |
FormulaLet of expr_assign list * formula |
FormulaIf of formula * formula * formula |
Or of formula * formula |
Iff of formula * formula |
Implies of formula * formula |
And of formula * formula |
Not of formula |
Acyclic of n_ary_index |
Function of n_ary_index * rel_expr * rel_expr |
Functional of n_ary_index * rel_expr * rel_expr |
TotalOrdering of n_ary_index * rel_expr * rel_expr * rel_expr |
Subset of rel_expr * rel_expr |
RelEq of rel_expr * rel_expr |
IntEq of int_expr * int_expr |
LT of int_expr * int_expr |
LE of int_expr * int_expr |
No of rel_expr |
Lone of rel_expr |
One of rel_expr |
Some of rel_expr |
False |
True |
FormulaReg of int
and rel_expr =
RelLet of expr_assign list * rel_expr |
RelIf of formula * rel_expr * rel_expr |
Union of rel_expr * rel_expr |
Difference of rel_expr * rel_expr |
Override of rel_expr * rel_expr |
Intersect of rel_expr * rel_expr |
Product of rel_expr * rel_expr |
IfNo of rel_expr * rel_expr |
Project of rel_expr * int_expr list |
Join of rel_expr * rel_expr |
Closure of rel_expr |
ReflexiveClosure of rel_expr |
Transpose of rel_expr |
Comprehension of decl list * formula |
Bits of int_expr |
Int of int_expr |
Iden |
Ints |
None |
Univ |
Atom of int |
AtomSeq of int * int |
Rel of n_ary_index |
Var of n_ary_index |
RelReg of n_ary_index
and int_expr =
Sum of decl list * int_expr |
IntLet of expr_assign list * int_expr |
IntIf of formula * int_expr * int_expr |
SHL of int_expr * int_expr |
SHA of int_expr * int_expr |
SHR of int_expr * int_expr |
Add of int_expr * int_expr |
Sub of int_expr * int_expr |
Mult of int_expr * int_expr |
Div of int_expr * int_expr |
Mod of int_expr * int_expr |
Cardinality of rel_expr |
SetSum of rel_expr |
BitOr of int_expr * int_expr |
BitXor of int_expr * int_expr |
BitAnd of int_expr * int_expr |
BitNot of int_expr |
Neg of int_expr |
Absolute of int_expr |
Signum of int_expr |
Num of int |
IntReg of int
and decl =
DeclNo of n_ary_index * rel_expr |
DeclLone of n_ary_index * rel_expr |
DeclOne of n_ary_index * rel_expr |
DeclSome of n_ary_index * rel_expr |
DeclSet of n_ary_index * rel_expr
and expr_assign =
AssignFormulaReg of int * formula |
AssignRelReg of n_ary_index * rel_expr |
AssignIntReg of int * int_expr
type 'a fold_expr_funcs =
{formula_func: formula -> 'a -> 'a,
rel_expr_func: rel_expr -> 'a -> 'a,
int_expr_func: int_expr -> 'a -> 'a}
val kodkodi_version : unit -> int list
val fold_formula : 'a fold_expr_funcs -> formula -> 'a -> 'a
val fold_rel_expr : 'a fold_expr_funcs -> rel_expr -> 'a -> 'a
val fold_int_expr : 'a fold_expr_funcs -> int_expr -> 'a -> 'a
val fold_decl : 'a fold_expr_funcs -> decl -> 'a -> 'a
val fold_expr_assign : 'a fold_expr_funcs -> expr_assign -> 'a -> 'a
type 'a fold_tuple_funcs =
{tuple_func: tuple -> 'a -> 'a,
tuple_set_func: tuple_set -> 'a -> 'a}
val fold_tuple : 'a fold_tuple_funcs -> tuple -> 'a -> 'a
val fold_tuple_set : 'a fold_tuple_funcs -> tuple_set -> 'a -> 'a
val fold_tuple_assign : 'a fold_tuple_funcs -> tuple_assign -> 'a -> 'a
val fold_bound :
'a fold_expr_funcs -> 'a fold_tuple_funcs -> bound -> 'a -> 'a
val fold_int_bound : 'a fold_tuple_funcs -> int_bound -> 'a -> 'a
type problem =
{comment: string,
settings: setting list,
univ_card: int,
tuple_assigns: tuple_assign list,
bounds: bound list,
int_bounds: int_bound list,
expr_assigns: expr_assign list,
formula: formula}
type raw_bound = n_ary_index * int list list
datatype outcome =
Normal of (int * raw_bound list) list * int list * string |
TimedOut of int list |
Error of string * int list
exception SYNTAX of string * string
val max_arity : int -> int
val arity_of_rel_expr : rel_expr -> int
val is_problem_trivially_false : problem -> bool
val problems_equivalent : problem * problem -> bool
val solve_any_problem :
bool -> bool -> Time.time -> int -> int -> problem list -> outcome
end;
structure Kodkod : KODKOD =
struct
type n_ary_index = int * int
type setting = string * string
datatype tuple =
Tuple of int list |
TupleIndex of n_ary_index |
TupleReg of n_ary_index
datatype tuple_set =
TupleUnion of tuple_set * tuple_set |
TupleDifference of tuple_set * tuple_set |
TupleIntersect of tuple_set * tuple_set |
TupleProduct of tuple_set * tuple_set |
TupleProject of tuple_set * int |
TupleSet of tuple list |
TupleRange of tuple * tuple |
TupleArea of tuple * tuple |
TupleAtomSeq of int * int |
TupleSetReg of n_ary_index
datatype tuple_assign =
AssignTuple of n_ary_index * tuple |
AssignTupleSet of n_ary_index * tuple_set
type bound = (n_ary_index * string) list * tuple_set list
type int_bound = int option * tuple_set list
datatype formula =
All of decl list * formula |
Exist of decl list * formula |
FormulaLet of expr_assign list * formula |
FormulaIf of formula * formula * formula |
Or of formula * formula |
Iff of formula * formula |
Implies of formula * formula |
And of formula * formula |
Not of formula |
Acyclic of n_ary_index |
Function of n_ary_index * rel_expr * rel_expr |
Functional of n_ary_index * rel_expr * rel_expr |
TotalOrdering of n_ary_index * rel_expr * rel_expr * rel_expr |
Subset of rel_expr * rel_expr |
RelEq of rel_expr * rel_expr |
IntEq of int_expr * int_expr |
LT of int_expr * int_expr |
LE of int_expr * int_expr |
No of rel_expr |
Lone of rel_expr |
One of rel_expr |
Some of rel_expr |
False |
True |
FormulaReg of int
and rel_expr =
RelLet of expr_assign list * rel_expr |
RelIf of formula * rel_expr * rel_expr |
Union of rel_expr * rel_expr |
Difference of rel_expr * rel_expr |
Override of rel_expr * rel_expr |
Intersect of rel_expr * rel_expr |
Product of rel_expr * rel_expr |
IfNo of rel_expr * rel_expr |
Project of rel_expr * int_expr list |
Join of rel_expr * rel_expr |
Closure of rel_expr |
ReflexiveClosure of rel_expr |
Transpose of rel_expr |
Comprehension of decl list * formula |
Bits of int_expr |
Int of int_expr |
Iden |
Ints |
None |
Univ |
Atom of int |
AtomSeq of int * int |
Rel of n_ary_index |
Var of n_ary_index |
RelReg of n_ary_index
and int_expr =
Sum of decl list * int_expr |
IntLet of expr_assign list * int_expr |
IntIf of formula * int_expr * int_expr |
SHL of int_expr * int_expr |
SHA of int_expr * int_expr |
SHR of int_expr * int_expr |
Add of int_expr * int_expr |
Sub of int_expr * int_expr |
Mult of int_expr * int_expr |
Div of int_expr * int_expr |
Mod of int_expr * int_expr |
Cardinality of rel_expr |
SetSum of rel_expr |
BitOr of int_expr * int_expr |
BitXor of int_expr * int_expr |
BitAnd of int_expr * int_expr |
BitNot of int_expr |
Neg of int_expr |
Absolute of int_expr |
Signum of int_expr |
Num of int |
IntReg of int
and decl =
DeclNo of n_ary_index * rel_expr |
DeclLone of n_ary_index * rel_expr |
DeclOne of n_ary_index * rel_expr |
DeclSome of n_ary_index * rel_expr |
DeclSet of n_ary_index * rel_expr
and expr_assign =
AssignFormulaReg of int * formula |
AssignRelReg of n_ary_index * rel_expr |
AssignIntReg of int * int_expr
type problem =
{comment: string,
settings: setting list,
univ_card: int,
tuple_assigns: tuple_assign list,
bounds: bound list,
int_bounds: int_bound list,
expr_assigns: expr_assign list,
formula: formula}
type raw_bound = n_ary_index * int list list
datatype outcome =
Normal of (int * raw_bound list) list * int list * string |
TimedOut of int list |
Error of string * int list
exception SYNTAX of string * string
type 'a fold_expr_funcs =
{formula_func: formula -> 'a -> 'a,
rel_expr_func: rel_expr -> 'a -> 'a,
int_expr_func: int_expr -> 'a -> 'a}
fun kodkodi_version () =
getenv "KODKODI_VERSION"
|> space_explode "."
|> map (the_default 0 o Int.fromString)
(** Auxiliary functions on Kodkod problems **)
fun fold_formula (F : 'a fold_expr_funcs) formula =
case formula of
All (ds, f) => fold (fold_decl F) ds #> fold_formula F f
| Exist (ds, f) => fold (fold_decl F) ds #> fold_formula F f
| FormulaLet (bs, f) => fold (fold_expr_assign F) bs #> fold_formula F f
| FormulaIf (f, f1, f2) =>
fold_formula F f #> fold_formula F f1 #> fold_formula F f2
| Or (f1, f2) => fold_formula F f1 #> fold_formula F f2
| Iff (f1, f2) => fold_formula F f1 #> fold_formula F f2
| Implies (f1, f2) => fold_formula F f1 #> fold_formula F f2
| And (f1, f2) => fold_formula F f1 #> fold_formula F f2
| Not f => fold_formula F f
| Acyclic x => fold_rel_expr F (Rel x)
| Function (x, r1, r2) =>
fold_rel_expr F (Rel x) #> fold_rel_expr F r1 #> fold_rel_expr F r2
| Functional (x, r1, r2) =>
fold_rel_expr F (Rel x) #> fold_rel_expr F r1 #> fold_rel_expr F r2
| TotalOrdering (x, r1, r2, r3) =>
fold_rel_expr F (Rel x) #> fold_rel_expr F r1 #> fold_rel_expr F r2
#> fold_rel_expr F r3
| Subset (r1, r2) => fold_rel_expr F r1 #> fold_rel_expr F r2
| RelEq (r1, r2) => fold_rel_expr F r1 #> fold_rel_expr F r2
| IntEq (i1, i2) => fold_int_expr F i1 #> fold_int_expr F i2
| LT (i1, i2) => fold_int_expr F i1 #> fold_int_expr F i2
| LE (i1, i2) => fold_int_expr F i1 #> fold_int_expr F i2
| No r => fold_rel_expr F r
| Lone r => fold_rel_expr F r
| One r => fold_rel_expr F r
| Some r => fold_rel_expr F r
| False => #formula_func F formula
| True => #formula_func F formula
| FormulaReg _ => #formula_func F formula
and fold_rel_expr F rel_expr =
case rel_expr of
RelLet (bs, r) => fold (fold_expr_assign F) bs #> fold_rel_expr F r
| RelIf (f, r1, r2) =>
fold_formula F f #> fold_rel_expr F r1 #> fold_rel_expr F r2
| Union (r1, r2) => fold_rel_expr F r1 #> fold_rel_expr F r2
| Difference (r1, r2) => fold_rel_expr F r1 #> fold_rel_expr F r2
| Override (r1, r2) => fold_rel_expr F r1 #> fold_rel_expr F r2
| Intersect (r1, r2) => fold_rel_expr F r1 #> fold_rel_expr F r2
| Product (r1, r2) => fold_rel_expr F r1 #> fold_rel_expr F r2
| IfNo (r1, r2) => fold_rel_expr F r1 #> fold_rel_expr F r2
| Project (r1, is) => fold_rel_expr F r1 #> fold (fold_int_expr F) is
| Join (r1, r2) => fold_rel_expr F r1 #> fold_rel_expr F r2
| Closure r => fold_rel_expr F r
| ReflexiveClosure r => fold_rel_expr F r
| Transpose r => fold_rel_expr F r
| Comprehension (ds, f) => fold (fold_decl F) ds #> fold_formula F f
| Bits i => fold_int_expr F i
| Int i => fold_int_expr F i
| Iden => #rel_expr_func F rel_expr
| Ints => #rel_expr_func F rel_expr
| None => #rel_expr_func F rel_expr
| Univ => #rel_expr_func F rel_expr
| Atom _ => #rel_expr_func F rel_expr
| AtomSeq _ => #rel_expr_func F rel_expr
| Rel _ => #rel_expr_func F rel_expr
| Var _ => #rel_expr_func F rel_expr
| RelReg _ => #rel_expr_func F rel_expr
and fold_int_expr F int_expr =
case int_expr of
Sum (ds, i) => fold (fold_decl F) ds #> fold_int_expr F i
| IntLet (bs, i) => fold (fold_expr_assign F) bs #> fold_int_expr F i
| IntIf (f, i1, i2) =>
fold_formula F f #> fold_int_expr F i1 #> fold_int_expr F i2
| SHL (i1, i2) => fold_int_expr F i1 #> fold_int_expr F i2
| SHA (i1, i2) => fold_int_expr F i1 #> fold_int_expr F i2
| SHR (i1, i2) => fold_int_expr F i1 #> fold_int_expr F i2
| Add (i1, i2) => fold_int_expr F i1 #> fold_int_expr F i2
| Sub (i1, i2) => fold_int_expr F i1 #> fold_int_expr F i2
| Mult (i1, i2) => fold_int_expr F i1 #> fold_int_expr F i2
| Div (i1, i2) => fold_int_expr F i1 #> fold_int_expr F i2
| Mod (i1, i2) => fold_int_expr F i1 #> fold_int_expr F i2
| Cardinality r => fold_rel_expr F r
| SetSum r => fold_rel_expr F r
| BitOr (i1, i2) => fold_int_expr F i1 #> fold_int_expr F i2
| BitXor (i1, i2) => fold_int_expr F i1 #> fold_int_expr F i2
| BitAnd (i1, i2) => fold_int_expr F i1 #> fold_int_expr F i2
| BitNot i => fold_int_expr F i
| Neg i => fold_int_expr F i
| Absolute i => fold_int_expr F i
| Signum i => fold_int_expr F i
| Num _ => #int_expr_func F int_expr
| IntReg _ => #int_expr_func F int_expr
and fold_decl F decl =
case decl of
DeclNo (x, r) => fold_rel_expr F (Var x) #> fold_rel_expr F r
| DeclLone (x, r) => fold_rel_expr F (Var x) #> fold_rel_expr F r
| DeclOne (x, r) => fold_rel_expr F (Var x) #> fold_rel_expr F r
| DeclSome (x, r) => fold_rel_expr F (Var x) #> fold_rel_expr F r
| DeclSet (x, r) => fold_rel_expr F (Var x) #> fold_rel_expr F r
and fold_expr_assign F assign =
case assign of
AssignFormulaReg (x, f) => fold_formula F (FormulaReg x) #> fold_formula F f
| AssignRelReg (x, r) => fold_rel_expr F (RelReg x) #> fold_rel_expr F r
| AssignIntReg (x, i) => fold_int_expr F (IntReg x) #> fold_int_expr F i
type 'a fold_tuple_funcs =
{tuple_func: tuple -> 'a -> 'a,
tuple_set_func: tuple_set -> 'a -> 'a}
fun fold_tuple (F : 'a fold_tuple_funcs) = #tuple_func F
fun fold_tuple_set F tuple_set =
case tuple_set of
TupleUnion (ts1, ts2) => fold_tuple_set F ts1 #> fold_tuple_set F ts2
| TupleDifference (ts1, ts2) => fold_tuple_set F ts1 #> fold_tuple_set F ts2
| TupleIntersect (ts1, ts2) => fold_tuple_set F ts1 #> fold_tuple_set F ts2
| TupleProduct (ts1, ts2) => fold_tuple_set F ts1 #> fold_tuple_set F ts2
| TupleProject (ts, _) => fold_tuple_set F ts
| TupleSet ts => fold (fold_tuple F) ts
| TupleRange (t1, t2) => fold_tuple F t1 #> fold_tuple F t2
| TupleArea (t1, t2) => fold_tuple F t1 #> fold_tuple F t2
| TupleAtomSeq _ => #tuple_set_func F tuple_set
| TupleSetReg _ => #tuple_set_func F tuple_set
fun fold_tuple_assign F assign =
case assign of
AssignTuple (x, t) => fold_tuple F (TupleReg x) #> fold_tuple F t
| AssignTupleSet (x, ts) =>
fold_tuple_set F (TupleSetReg x) #> fold_tuple_set F ts
fun fold_bound expr_F tuple_F (zs, tss) =
fold (fold_rel_expr expr_F) (map (Rel o fst) zs)
#> fold (fold_tuple_set tuple_F) tss
fun fold_int_bound F (_, tss) = fold (fold_tuple_set F) tss
fun max_arity univ_card = floor (Math.ln 2147483647.0
/ Math.ln (Real.fromInt univ_card))
fun arity_of_rel_expr (RelLet (_, r)) = arity_of_rel_expr r
| arity_of_rel_expr (RelIf (_, r1, _)) = arity_of_rel_expr r1
| arity_of_rel_expr (Union (r1, _)) = arity_of_rel_expr r1
| arity_of_rel_expr (Difference (r1, _)) = arity_of_rel_expr r1
| arity_of_rel_expr (Override (r1, _)) = arity_of_rel_expr r1
| arity_of_rel_expr (Intersect (r1, _)) = arity_of_rel_expr r1
| arity_of_rel_expr (Product (r1, r2)) = sum_arities_of_rel_exprs r1 r2
| arity_of_rel_expr (IfNo (r1, _)) = arity_of_rel_expr r1
| arity_of_rel_expr (Project (_, is)) = length is
| arity_of_rel_expr (Join (r1, r2)) = sum_arities_of_rel_exprs r1 r2 - 2
| arity_of_rel_expr (Closure _) = 2
| arity_of_rel_expr (ReflexiveClosure _) = 2
| arity_of_rel_expr (Transpose _) = 2
| arity_of_rel_expr (Comprehension (ds, _)) =
fold (curry op + o arity_of_decl) ds 0
| arity_of_rel_expr (Bits _) = 1
| arity_of_rel_expr (Int _) = 1
| arity_of_rel_expr Iden = 2
| arity_of_rel_expr Ints = 1
| arity_of_rel_expr None = 1
| arity_of_rel_expr Univ = 1
| arity_of_rel_expr (Atom _) = 1
| arity_of_rel_expr (AtomSeq _) = 1
| arity_of_rel_expr (Rel (n, _)) = n
| arity_of_rel_expr (Var (n, _)) = n
| arity_of_rel_expr (RelReg (n, _)) = n
and sum_arities_of_rel_exprs r1 r2 = arity_of_rel_expr r1 + arity_of_rel_expr r2
and arity_of_decl (DeclNo ((n, _), _)) = n
| arity_of_decl (DeclLone ((n, _), _)) = n
| arity_of_decl (DeclOne ((n, _), _)) = n
| arity_of_decl (DeclSome ((n, _), _)) = n
| arity_of_decl (DeclSet ((n, _), _)) = n
fun is_problem_trivially_false ({formula = False, ...} : problem) = true
| is_problem_trivially_false _ = false
val chop_solver = take 2 o space_explode ","
fun settings_equivalent ([], []) = true
| settings_equivalent ((key1, value1) :: settings1,
(key2, value2) :: settings2) =
key1 = key2 andalso
(value1 = value2 orelse key1 = "delay" orelse
(key1 = "solver" andalso chop_solver value1 = chop_solver value2)) andalso
settings_equivalent (settings1, settings2)
| settings_equivalent _ = false
fun problems_equivalent (p1 : problem, p2 : problem) =
#univ_card p1 = #univ_card p2 andalso
#formula p1 = #formula p2 andalso
#bounds p1 = #bounds p2 andalso
#expr_assigns p1 = #expr_assigns p2 andalso
#tuple_assigns p1 = #tuple_assigns p2 andalso
#int_bounds p1 = #int_bounds p2 andalso
settings_equivalent (#settings p1, #settings p2)
(** Serialization of problem **)
fun base_name j =
if j < 0 then string_of_int (~j - 1) ^ "'" else string_of_int j
fun n_ary_name (1, j) prefix _ _ = prefix ^ base_name j
| n_ary_name (2, j) _ prefix _ = prefix ^ base_name j
| n_ary_name (n, j) _ _ prefix = prefix ^ string_of_int n ^ "_" ^ base_name j
fun atom_name j = "A" ^ base_name j
fun atom_seq_name (k, 0) = "u" ^ base_name k
| atom_seq_name (k, j0) = "u" ^ base_name k ^ "@" ^ base_name j0
fun formula_reg_name j = "$f" ^ base_name j
fun rel_reg_name j = "$e" ^ base_name j
fun int_reg_name j = "$i" ^ base_name j
fun tuple_name x = n_ary_name x "A" "P" "T"
fun rel_name x = n_ary_name x "s" "r" "m"
fun var_name x = n_ary_name x "S" "R" "M"
fun tuple_reg_name x = n_ary_name x "$A" "$P" "$T"
fun tuple_set_reg_name x = n_ary_name x "$a" "$p" "$t"
fun inline_comment "" = ""
| inline_comment comment =
" /* " ^ translate_string (fn "\n" => " " | "*" => "* " | s => s) comment ^
" */"
fun block_comment "" = ""
| block_comment comment = prefix_lines "// " comment ^ "\n"
fun commented_rel_name (x, s) = rel_name x ^ inline_comment s
fun string_for_tuple (Tuple js) = "[" ^ commas (map atom_name js) ^ "]"
| string_for_tuple (TupleIndex x) = tuple_name x
| string_for_tuple (TupleReg x) = tuple_reg_name x
val no_prec = 100
val prec_TupleUnion = 1
val prec_TupleIntersect = 2
val prec_TupleProduct = 3
val prec_TupleProject = 4
fun precedence_ts (TupleUnion _) = prec_TupleUnion
| precedence_ts (TupleDifference _) = prec_TupleUnion
| precedence_ts (TupleIntersect _) = prec_TupleIntersect
| precedence_ts (TupleProduct _) = prec_TupleProduct
| precedence_ts (TupleProject _) = prec_TupleProject
| precedence_ts _ = no_prec
fun string_for_tuple_set tuple_set =
let
fun sub tuple_set outer_prec =
let
val prec = precedence_ts tuple_set
val need_parens = (prec < outer_prec)
in
(if need_parens then "(" else "") ^
(case tuple_set of
TupleUnion (ts1, ts2) => sub ts1 prec ^ " + " ^ sub ts2 (prec + 1)
| TupleDifference (ts1, ts2) =>
sub ts1 prec ^ " - " ^ sub ts2 (prec + 1)
| TupleIntersect (ts1, ts2) => sub ts1 prec ^ " & " ^ sub ts2 prec
| TupleProduct (ts1, ts2) => sub ts1 prec ^ "->" ^ sub ts2 prec
| TupleProject (ts, c) => sub ts prec ^ "[" ^ string_of_int c ^ "]"
| TupleSet ts => "{" ^ commas (map string_for_tuple ts) ^ "}"
| TupleRange (t1, t2) =>
"{" ^ string_for_tuple t1 ^
(if t1 = t2 then "" else " .. " ^ string_for_tuple t2) ^ "}"
| TupleArea (t1, t2) =>
"{" ^ string_for_tuple t1 ^ " # " ^ string_for_tuple t2 ^ "}"
| TupleAtomSeq x => atom_seq_name x
| TupleSetReg x => tuple_set_reg_name x) ^
(if need_parens then ")" else "")
end
in sub tuple_set 0 end
fun string_for_tuple_assign (AssignTuple (x, t)) =
tuple_reg_name x ^ " := " ^ string_for_tuple t ^ "\n"
| string_for_tuple_assign (AssignTupleSet (x, ts)) =
tuple_set_reg_name x ^ " := " ^ string_for_tuple_set ts ^ "\n"
fun string_for_bound (zs, tss) =
"bounds " ^ commas (map commented_rel_name zs) ^ ": " ^
(if length tss = 1 then "" else "[") ^ commas (map string_for_tuple_set tss) ^
(if length tss = 1 then "" else "]") ^ "\n"
fun int_string_for_bound (opt_n, tss) =
(case opt_n of
SOME n => signed_string_of_int n ^ ": "
| NONE => "") ^ "[" ^ commas (map string_for_tuple_set tss) ^ "]"
val prec_All = 1
val prec_Or = 2
val prec_Iff = 3
val prec_Implies = 4
val prec_And = 5
val prec_Not = 6
val prec_Eq = 7
val prec_Some = 8
val prec_SHL = 9
val prec_Add = 10
val prec_Mult = 11
val prec_Override = 12
val prec_Intersect = 13
val prec_Product = 14
val prec_IfNo = 15
val prec_Project = 17
val prec_Join = 18
val prec_BitNot = 19
fun precedence_f (All _) = prec_All
| precedence_f (Exist _) = prec_All
| precedence_f (FormulaLet _) = prec_All
| precedence_f (FormulaIf _) = prec_All
| precedence_f (Or _) = prec_Or
| precedence_f (Iff _) = prec_Iff
| precedence_f (Implies _) = prec_Implies
| precedence_f (And _) = prec_And
| precedence_f (Not _) = prec_Not
| precedence_f (Acyclic _) = no_prec
| precedence_f (Function _) = no_prec
| precedence_f (Functional _) = no_prec
| precedence_f (TotalOrdering _) = no_prec
| precedence_f (Subset _) = prec_Eq
| precedence_f (RelEq _) = prec_Eq
| precedence_f (IntEq _) = prec_Eq
| precedence_f (LT _) = prec_Eq
| precedence_f (LE _) = prec_Eq
| precedence_f (No _) = prec_Some
| precedence_f (Lone _) = prec_Some
| precedence_f (One _) = prec_Some
| precedence_f (Some _) = prec_Some
| precedence_f False = no_prec
| precedence_f True = no_prec
| precedence_f (FormulaReg _) = no_prec
and precedence_r (RelLet _) = prec_All
| precedence_r (RelIf _) = prec_All
| precedence_r (Union _) = prec_Add
| precedence_r (Difference _) = prec_Add
| precedence_r (Override _) = prec_Override
| precedence_r (Intersect _) = prec_Intersect
| precedence_r (Product _) = prec_Product
| precedence_r (IfNo _) = prec_IfNo
| precedence_r (Project _) = prec_Project
| precedence_r (Join _) = prec_Join
| precedence_r (Closure _) = prec_BitNot
| precedence_r (ReflexiveClosure _) = prec_BitNot
| precedence_r (Transpose _) = prec_BitNot
| precedence_r (Comprehension _) = no_prec
| precedence_r (Bits _) = no_prec
| precedence_r (Int _) = no_prec
| precedence_r Iden = no_prec
| precedence_r Ints = no_prec
| precedence_r None = no_prec
| precedence_r Univ = no_prec
| precedence_r (Atom _) = no_prec
| precedence_r (AtomSeq _) = no_prec
| precedence_r (Rel _) = no_prec
| precedence_r (Var _) = no_prec
| precedence_r (RelReg _) = no_prec
and precedence_i (Sum _) = prec_All
| precedence_i (IntLet _) = prec_All
| precedence_i (IntIf _) = prec_All
| precedence_i (SHL _) = prec_SHL
| precedence_i (SHA _) = prec_SHL
| precedence_i (SHR _) = prec_SHL
| precedence_i (Add _) = prec_Add
| precedence_i (Sub _) = prec_Add
| precedence_i (Mult _) = prec_Mult
| precedence_i (Div _) = prec_Mult
| precedence_i (Mod _) = prec_Mult
| precedence_i (Cardinality _) = no_prec
| precedence_i (SetSum _) = no_prec
| precedence_i (BitOr _) = prec_Intersect
| precedence_i (BitXor _) = prec_Intersect
| precedence_i (BitAnd _) = prec_Intersect
| precedence_i (BitNot _) = prec_BitNot
| precedence_i (Neg _) = prec_BitNot
| precedence_i (Absolute _) = prec_BitNot
| precedence_i (Signum _) = prec_BitNot
| precedence_i (Num _) = no_prec
| precedence_i (IntReg _) = no_prec
fun write_problem out problems =
let
fun out_outmost_f (And (f1, f2)) =
(out_outmost_f f1; out "\n && "; out_outmost_f f2)
| out_outmost_f f = out_f f prec_And
and out_f formula outer_prec =
let
val prec = precedence_f formula
val need_parens = (prec < outer_prec)
in
(if need_parens then out "(" else ());
(case formula of
All (ds, f) => (out "all ["; out_decls ds; out "] | "; out_f f prec)
| Exist (ds, f) =>
(out "some ["; out_decls ds; out "] | "; out_f f prec)
| FormulaLet (bs, f) =>
(out "let ["; out_assigns bs; out "] | "; out_f f prec)
| FormulaIf (f, f1, f2) =>
(out "if "; out_f f prec; out " then "; out_f f1 prec; out " else ";
out_f f2 prec)
| Or (f1, f2) => (out_f f1 prec; out " || "; out_f f2 prec)
| Iff (f1, f2) => (out_f f1 prec; out " <=> "; out_f f2 prec)
| Implies (f1, f2) => (out_f f1 (prec + 1); out " => "; out_f f2 prec)
| And (f1, f2) => (out_f f1 prec; out " && "; out_f f2 prec)
| Not f => (out "! "; out_f f prec)
| Acyclic x => out ("ACYCLIC(" ^ rel_name x ^ ")")
| Function (x, r1, r2) =>
(out ("FUNCTION(" ^ rel_name x ^ ", "); out_r r1 0; out " -> one ";
out_r r2 0; out ")")
| Functional (x, r1, r2) =>
(out ("FUNCTION(" ^ rel_name x ^ ", "); out_r r1 0; out " -> lone ";
out_r r2 0; out ")")
| TotalOrdering (x, r1, r2, r3) =>
(out ("TOTAL_ORDERING(" ^ rel_name x ^ ", "); out_r r1 0; out ", ";
out_r r2 0; out ", "; out_r r3 0; out ")")
| Subset (r1, r2) => (out_r r1 prec; out " in "; out_r r2 prec)
| RelEq (r1, r2) => (out_r r1 prec; out " = "; out_r r2 prec)
| IntEq (i1, i2) => (out_i i1 prec; out " = "; out_i i2 prec)
| LT (i1, i2) => (out_i i1 prec; out " < "; out_i i2 prec)
| LE (i1, i2) => (out_i i1 prec; out " <= "; out_i i2 prec)
| No r => (out "no "; out_r r prec)
| Lone r => (out "lone "; out_r r prec)
| One r => (out "one "; out_r r prec)
| Some r => (out "some "; out_r r prec)
| False => out "false"
| True => out "true"
| FormulaReg j => out (formula_reg_name j));
(if need_parens then out ")" else ())
end
and out_r rel_expr outer_prec =
let
val prec = precedence_r rel_expr
val need_parens = (prec < outer_prec)
in
(if need_parens then out "(" else ());
(case rel_expr of
RelLet (bs, r) =>
(out "let ["; out_assigns bs; out "] | "; out_r r prec)
| RelIf (f, r1, r2) =>
(out "if "; out_f f prec; out " then "; out_r r1 prec;
out " else "; out_r r2 prec)
| Union (r1, r2) => (out_r r1 prec; out " + "; out_r r2 (prec + 1))
| Difference (r1, r2) =>
(out_r r1 prec; out " - "; out_r r2 (prec + 1))
| Override (r1, r2) => (out_r r1 prec; out " ++ "; out_r r2 prec)
| Intersect (r1, r2) => (out_r r1 prec; out " & "; out_r r2 prec)
| Product (r1, r2) => (out_r r1 prec; out "->"; out_r r2 prec)
| IfNo (r1, r2) => (out_r r1 prec; out "\\"; out_r r2 prec)
| Project (r1, is) => (out_r r1 prec; out "["; out_columns is; out "]")
| Join (r1, r2) => (out_r r1 prec; out "."; out_r r2 (prec + 1))
| Closure r => (out "^"; out_r r prec)
| ReflexiveClosure r => (out "*"; out_r r prec)
| Transpose r => (out "~"; out_r r prec)
| Comprehension (ds, f) =>
(out "{["; out_decls ds; out "] | "; out_f f 0; out "}")
| Bits i => (out "Bits["; out_i i 0; out "]")
| Int i => (out "Int["; out_i i 0; out "]")
| Iden => out "iden"
| Ints => out "ints"
| None => out "none"
| Univ => out "univ"
| Atom j => out (atom_name j)
| AtomSeq x => out (atom_seq_name x)
| Rel x => out (rel_name x)
| Var x => out (var_name x)
| RelReg (_, j) => out (rel_reg_name j));
(if need_parens then out ")" else ())
end
and out_i int_expr outer_prec =
let
val prec = precedence_i int_expr
val need_parens = (prec < outer_prec)
in
(if need_parens then out "(" else ());
(case int_expr of
Sum (ds, i) => (out "sum ["; out_decls ds; out "] | "; out_i i prec)
| IntLet (bs, i) =>
(out "let ["; out_assigns bs; out "] | "; out_i i prec)
| IntIf (f, i1, i2) =>
(out "if "; out_f f prec; out " then "; out_i i1 prec;
out " else "; out_i i2 prec)
| SHL (i1, i2) => (out_i i1 prec; out " << "; out_i i2 (prec + 1))
| SHA (i1, i2) => (out_i i1 prec; out " >> "; out_i i2 (prec + 1))
| SHR (i1, i2) => (out_i i1 prec; out " >>> "; out_i i2 (prec + 1))
| Add (i1, i2) => (out_i i1 prec; out " + "; out_i i2 (prec + 1))
| Sub (i1, i2) => (out_i i1 prec; out " - "; out_i i2 (prec + 1))
| Mult (i1, i2) => (out_i i1 prec; out " * "; out_i i2 (prec + 1))
| Div (i1, i2) => (out_i i1 prec; out " / "; out_i i2 (prec + 1))
| Mod (i1, i2) => (out_i i1 prec; out " % "; out_i i2 (prec + 1))
| Cardinality r => (out "#("; out_r r 0; out ")")
| SetSum r => (out "sum("; out_r r 0; out ")")
| BitOr (i1, i2) => (out_i i1 prec; out " | "; out_i i2 prec)
| BitXor (i1, i2) => (out_i i1 prec; out " ^ "; out_i i2 prec)
| BitAnd (i1, i2) => (out_i i1 prec; out " & "; out_i i2 prec)
| BitNot i => (out "~"; out_i i prec)
| Neg i => (out "-"; out_i i prec)
| Absolute i => (out "abs "; out_i i prec)
| Signum i => (out "sgn "; out_i i prec)
| Num k => out (signed_string_of_int k)
| IntReg j => out (int_reg_name j));
(if need_parens then out ")" else ())
end
and out_decls [] = ()
| out_decls [d] = out_decl d
| out_decls (d :: ds) = (out_decl d; out ", "; out_decls ds)
and out_decl (DeclNo (x, r)) =
(out (var_name x); out " : no "; out_r r 0)
| out_decl (DeclLone (x, r)) =
(out (var_name x); out " : lone "; out_r r 0)
| out_decl (DeclOne (x, r)) =
(out (var_name x); out " : one "; out_r r 0)
| out_decl (DeclSome (x, r)) =
(out (var_name x); out " : some "; out_r r 0)
| out_decl (DeclSet (x, r)) =
(out (var_name x); out " : set "; out_r r 0)
and out_assigns [] = ()
| out_assigns [b] = out_assign b
| out_assigns (b :: bs) = (out_assign b; out ", "; out_assigns bs)
and out_assign (AssignFormulaReg (j, f)) =
(out (formula_reg_name j); out " := "; out_f f 0)
| out_assign (AssignRelReg ((_, j), r)) =
(out (rel_reg_name j); out " := "; out_r r 0)
| out_assign (AssignIntReg (j, i)) =
(out (int_reg_name j); out " := "; out_i i 0)
and out_columns [] = ()
| out_columns [i] = out_i i 0
| out_columns (i :: is) = (out_i i 0; out ", "; out_columns is)
and out_problem {comment, settings, univ_card, tuple_assigns, bounds,
int_bounds, expr_assigns, formula} =
(out ("\n" ^ block_comment comment ^
implode (map (fn (key, value) => key ^ ": " ^ value ^ "\n")
settings) ^
"univ: " ^ atom_seq_name (univ_card, 0) ^ "\n" ^
implode (map string_for_tuple_assign tuple_assigns) ^
implode (map string_for_bound bounds) ^
(if int_bounds = [] then
""
else
"int_bounds: " ^
commas (map int_string_for_bound int_bounds) ^ "\n"));
List.app (fn b => (out_assign b; out ";")) expr_assigns;
out "solve "; out_outmost_f formula; out ";\n")
in
out ("// This file was generated by Isabelle (most likely Nitpick)\n" ^
"// " ^ ATP_Util.timestamp () ^ "\n");
List.app out_problem problems
end
(** Parsing of solution **)
fun is_ident_char s =
Symbol.is_ascii_letter s orelse Symbol.is_ascii_digit s orelse
s = "_" orelse s = "'" orelse s = "$"
fun strip_blanks [] = []
| strip_blanks (" " :: ss) = strip_blanks ss
| strip_blanks [s1, " "] = [s1]
| strip_blanks (s1 :: " " :: s2 :: ss) =
if is_ident_char s1 andalso is_ident_char s2 then
s1 :: " " :: strip_blanks (s2 :: ss)
else
strip_blanks (s1 :: s2 :: ss)
| strip_blanks (s :: ss) = s :: strip_blanks ss
val scan_nat =
Scan.repeat1 (Scan.one Symbol.is_ascii_digit)
>> (the o Int.fromString o implode)
val scan_rel_name =
($$ "s" |-- scan_nat >> pair 1
|| $$ "r" |-- scan_nat >> pair 2
|| ($$ "m" |-- scan_nat --| $$ "_") -- scan_nat) -- Scan.option ($$ "'")
>> (fn ((n, j), SOME _) => (n, ~j - 1)
| ((n, j), NONE) => (n, j))
val scan_atom = $$ "A" |-- scan_nat
fun parse_non_empty_list scan = scan ::: Scan.repeat ($$ "," |-- scan)
fun parse_list scan = parse_non_empty_list scan || Scan.succeed []
val parse_tuple = $$ "[" |-- parse_list scan_atom --| $$ "]"
val parse_tuple_set = $$ "[" |-- parse_list parse_tuple --| $$ "]"
val parse_assignment = (scan_rel_name --| $$ "=") -- parse_tuple_set
val parse_instance =
Scan.this_string "relations:"
|-- $$ "{" |-- parse_list parse_assignment --| $$ "}"
val extract_instance =
fst o Scan.finite Symbol.stopper
(Scan.error (!! (fn _ =>
raise SYNTAX ("Kodkod.extract_instance",
"ill-formed Kodkodi output"))
parse_instance))
o strip_blanks o raw_explode
val problem_marker = "*** PROBLEM "
val outcome_marker = "---OUTCOME---\n"
val instance_marker = "---INSTANCE---\n"
fun read_section_body marker =
Substring.string o fst o Substring.position "\n\n"
o Substring.triml (size marker)
fun read_next_instance s =
let val s = Substring.position instance_marker s |> snd in
if Substring.isEmpty s then
raise SYNTAX ("Kodkod.read_next_instance", "expected \"INSTANCE\" marker")
else
read_section_body instance_marker s |> extract_instance
end
fun read_next_outcomes j (s, ps, js) =
let val (s1, s2) = Substring.position outcome_marker s in
if Substring.isEmpty s2 orelse
not (Substring.isEmpty (Substring.position problem_marker s1
|> snd)) then
(s, ps, js)
else
let
val outcome = read_section_body outcome_marker s2
val s = Substring.triml (size outcome_marker) s2
in
if String.isSuffix "UNSATISFIABLE" outcome then
read_next_outcomes j (s, ps, j :: js)
else if String.isSuffix "SATISFIABLE" outcome then
read_next_outcomes j (s, (j, read_next_instance s2) :: ps, js)
else
raise SYNTAX ("Kodkod.read_next_outcomes",
"unknown outcome " ^ quote outcome)
end
end
fun read_next_problems (s, ps, js) =
let val s = Substring.position problem_marker s |> snd in
if Substring.isEmpty s then
(ps, js)
else
let
val s = Substring.triml (size problem_marker) s
val j_plus_1 = s |> Substring.takel (not_equal #" ") |> Substring.string
|> Int.fromString |> the
val j = j_plus_1 - 1
in read_next_problems (read_next_outcomes j (s, ps, js)) end
end
handle Option.Option => raise SYNTAX ("Kodkod.read_next_problems",
"expected number after \"PROBLEM\"")
(** Main Kodkod entry point **)
fun serial_string_and_temporary_dir overlord =
if overlord then ("", getenv "ISABELLE_HOME_USER")
else (serial_string (), getenv "ISABELLE_TMP")
(* The fudge term below is to account for Kodkodi's slow start-up time, which
is partly due to the JVM and partly due to the ML "bash" function. *)
val fudge_ms = 250
fun uncached_solve_any_problem overlord deadline max_threads0 max_solutions problems =
let
val j = find_index (curry (op =) True o #formula) problems
val indexed_problems = if j >= 0 then
[(j, nth problems j)]
else
filter_out (is_problem_trivially_false o snd)
(0 upto length problems - 1 ~~ problems)
val triv_js = filter_out (AList.defined (op =) indexed_problems)
(0 upto length problems - 1)
val reindex = fst o nth indexed_problems
val max_threads =
if max_threads0 = 0
then Options.default_int \<^system_option>\<open>kodkod_max_threads\<close>
else max_threads0
val external_process =
not (Options.default_bool \<^system_option>\<open>kodkod_scala\<close>) orelse overlord
val timeout0 = Time.toMilliseconds (deadline - Time.now ())
val timeout = if external_process then timeout0 - fudge_ms else timeout0
val solve_all = max_solutions > 1
in
if null indexed_problems then
Normal ([], triv_js, "")
else if timeout <= 0 then TimedOut triv_js
else
let
val kki =
let
val buf = Unsynchronized.ref Buffer.empty
fun out s = Unsynchronized.change buf (Buffer.add s)
val _ = write_problem out (map snd indexed_problems)
in Buffer.content (! buf) end
val (rc, out, err) =
if external_process then
let
val (serial_str, temp_dir) = serial_string_and_temporary_dir overlord
fun path_for suf = Path.explode (temp_dir ^ "/kodkodi" ^ serial_str ^ "." ^ suf)
val kki_path = path_for "kki"
val out_path = path_for "out"
val err_path = path_for "err"
fun remove_temporary_files () =
if overlord then ()
else List.app (ignore o try File.rm) [kki_path, out_path, err_path]
in
let
val _ = File.write kki_path kki
val rc =
Isabelle_System.bash ("cd " ^ Bash.string temp_dir ^ ";\n\
\\"$KODKODI/bin/kodkodi\"" ^
(" -max-msecs " ^ string_of_int timeout) ^
(if solve_all then " -solve-all" else "") ^
" -max-solutions " ^ string_of_int max_solutions ^
(if max_threads > 0 then " -max-threads " ^ string_of_int max_threads else "") ^
" < " ^ File.bash_path kki_path ^
" > " ^ File.bash_path out_path ^
" 2> " ^ File.bash_path err_path)
val out = File.read out_path
val err = File.read err_path
val _ = remove_temporary_files ()
in (rc, out, err) end
handle exn => (remove_temporary_files (); Exn.reraise exn)
end
else
(timeout, (solve_all, (max_solutions, (max_threads, kki))))
|> let open XML.Encode in pair int (pair bool (pair int (pair int string))) end
|> YXML.string_of_body
|> \<^scala_thread>\<open>kodkod\<close>
|> YXML.parse_body
|> let open XML.Decode in triple int string string end
val (ps, nontriv_js) =
read_next_problems (Substring.full out, [], [])
|>> rev ||> rev
|> apfst (map (apfst reindex)) |> apsnd (map reindex)
val js = triv_js @ nontriv_js
val first_error =
trim_split_lines err
|> map
(perhaps (try (unsuffix ".")) #>
perhaps (try (unprefix "Solve error: ")) #>
perhaps (try (unprefix "Error: ")))
|> find_first (fn line => line <> "" andalso line <> "EXIT")
|> the_default ""
in
if not (null ps) orelse rc = 0 then Normal (ps, js, first_error)
else if rc = 2 then TimedOut js
else if rc = 130 then raise Exn.Interrupt
else Error (if first_error = "" then "Unknown error" else first_error, js)
end
end
val cached_outcome =
Synchronized.var "Kodkod.cached_outcome"
(NONE : ((int * problem list) * outcome) option)
fun solve_any_problem debug overlord deadline max_threads max_solutions
problems =
let
fun do_solve () =
uncached_solve_any_problem overlord deadline max_threads max_solutions
problems
in
if debug orelse overlord then
do_solve ()
else
case AList.lookup (fn ((max1, ps1), (max2, ps2)) =>
max1 = max2 andalso length ps1 = length ps2 andalso
forall problems_equivalent (ps1 ~~ ps2))
(the_list (Synchronized.value cached_outcome))
(max_solutions, problems) of
SOME outcome => outcome
| NONE =>
let val outcome = do_solve () in
(case outcome of
Normal (_, _, "") =>
Synchronized.change cached_outcome
(K (SOME ((max_solutions, problems), outcome)))
| _ => ());
outcome
end
end
end;
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