statement stringlengths 1 15.9k | proof stringlengths 0 44.6k | type stringclasses 18
values | symbolic_name stringlengths 1 61 | library stringclasses 21
values | filename stringclasses 502
values | imports listlengths 0 38 | deps listlengths 0 64 | docstring stringlengths 0 500 | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
eval_fmla (s:state) (f:fmla) | =
match f with
| Fterm e -> eval_expr s e <> 0
| Fand f1 f2 -> eval_fmla s f1 /\ eval_fmla s f2
| Fnot f -> not (eval_fmla s f)
| Fimplies f1 f2 -> eval_fmla s f1 -> eval_fmla s f2
end | predicate | eval_fmla | examples/WP_revisited | examples/WP_revisited/imp_n.why | [
"int.Int",
"map.Const",
"map.Map"
] | [
"eval_expr",
"f1",
"f2",
"fmla",
"state"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
subst_expr (e:expr) (x:ident) (t:expr) : expr | =
match e with
| Econst _ -> e
| Evar y -> if x=y then t else e
| Ebin e1 op e2 -> Ebin (subst_expr e1 x t) op (subst_expr e2 x t)
end | function | subst_expr | examples/WP_revisited | examples/WP_revisited/imp_n.why | [
"int.Int",
"map.Const",
"map.Map"
] | [
"expr",
"ident",
"op"
] | substitution | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
eval_subst_expr:
forall s:state, e [@induction]:expr, x:ident, t:expr.
eval_expr s (subst_expr e x t) =
eval_expr (IdMap.set s x (eval_expr s t)) e | lemma | eval_subst_expr | examples/WP_revisited | examples/WP_revisited/imp_n.why | [
"int.Int",
"map.Const",
"map.Map"
] | [
"eval_expr",
"expr",
"ident",
"induction",
"set",
"state",
"subst_expr"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
subst (f:fmla) (x:ident) (t:expr) : fmla | =
match f with
| Fterm e -> Fterm (subst_expr e x t)
| Fand f1 f2 -> Fand (subst f1 x t) (subst f2 x t)
| Fnot f -> Fnot (subst f x t)
| Fimplies f1 f2 -> Fimplies (subst f1 x t) (subst f2 x t)
end | function | subst | examples/WP_revisited | examples/WP_revisited/imp_n.why | [
"int.Int",
"map.Const",
"map.Map"
] | [
"expr",
"f1",
"f2",
"fmla",
"ident",
"subst_expr"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
eval_subst:
forall s:state, f:fmla, x:ident, t:expr.
eval_fmla s (subst f x t) <-> eval_fmla (IdMap.set s x (eval_expr s t)) f | lemma | eval_subst | examples/WP_revisited | examples/WP_revisited/imp_n.why | [
"int.Int",
"map.Const",
"map.Map"
] | [
"eval_expr",
"eval_fmla",
"expr",
"fmla",
"ident",
"set",
"state",
"subst"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
valid_fmla (p:fmla) | = forall s:state. eval_fmla s p | predicate | valid_fmla | examples/WP_revisited | examples/WP_revisited/imp_n.why | [
"int.Int",
"map.Const",
"map.Map"
] | [
"eval_fmla",
"fmla",
"state"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
valid_triple (p:fmla) (i:stmt) (q:fmla) | =
forall s:state. eval_fmla s p ->
forall s':state, n:int. many_steps s i s' Sskip n ->
eval_fmla s' q | predicate | valid_triple | examples/WP_revisited | examples/WP_revisited/imp_n.why | [
"int.Int",
"map.Const",
"map.Map"
] | [
"eval_fmla",
"fmla",
"int",
"many_steps",
"state",
"stmt"
] | Hoare triples | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
assign_rule:
forall q:fmla, x:ident, e:expr.
valid_triple (subst q x e) (Sassign x e) q | lemma | assign_rule | examples/WP_revisited | examples/WP_revisited/imp_n.why | [
"int.Int",
"map.Const",
"map.Map"
] | [
"expr",
"fmla",
"ident",
"subst",
"valid_triple"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
seq_rule:
forall p q r:fmla, i1 i2:stmt.
valid_triple p i1 r /\ valid_triple r i2 q ->
valid_triple p (Sseq i1 i2) q | lemma | seq_rule | examples/WP_revisited | examples/WP_revisited/imp_n.why | [
"int.Int",
"map.Const",
"map.Map"
] | [
"fmla",
"i1",
"i2",
"stmt",
"valid_triple"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
if_rule:
forall e:expr, p q:fmla, i1 i2:stmt.
valid_triple (Fand p (Fterm e)) i1 q /\
valid_triple (Fand p (Fnot (Fterm e))) i2 q ->
valid_triple p (Sif e i1 i2) q | lemma | if_rule | examples/WP_revisited | examples/WP_revisited/imp_n.why | [
"int.Int",
"map.Const",
"map.Map"
] | [
"expr",
"fmla",
"i1",
"i2",
"stmt",
"valid_triple"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
while_rule:
forall e:expr, inv:fmla, i:stmt.
valid_triple (Fand (Fterm e) inv) i inv ->
valid_triple inv (Swhile e i) (Fand (Fnot (Fterm e)) inv) | lemma | while_rule | examples/WP_revisited | examples/WP_revisited/imp_n.why | [
"int.Int",
"map.Const",
"map.Map"
] | [
"expr",
"fmla",
"inv",
"stmt",
"valid_triple"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
consequence_rule:
forall p p' q q':fmla, i:stmt.
valid_fmla (Fimplies p' p) ->
valid_triple p i q ->
valid_fmla (Fimplies q q') ->
valid_triple p' i q' | lemma | consequence_rule | examples/WP_revisited | examples/WP_revisited/imp_n.why | [
"int.Int",
"map.Const",
"map.Map"
] | [
"fmla",
"p'",
"stmt",
"valid_fmla",
"valid_triple"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
datatype | = Tint | Tbool | type | datatype | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [] | terms and formulas | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
ident | = int | type | ident | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
term | =
| Tconst int
| Tvar ident
| Tderef ident
| Tbin term operator term | type | term | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"ident",
"int",
"operator"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
fmla | =
| Fterm term
| Fand fmla fmla
| Fnot fmla
| Fimplies fmla fmla
| Flet ident term fmla
| Fforall ident datatype fmla | type | fmla | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"datatype",
"ident",
"term"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
value | =
| Vint int
| Vbool bool | type | value | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
env | = IdMap.map ident value | type | env | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"ident",
"map",
"value"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
eval_bin (x:value) (op:operator) (y:value) : value | =
match x,y with
| Vint x,Vint y ->
match op with
| Oplus -> Vint (x+y)
| Ominus -> Vint (x-y)
| Omult -> Vint (x*y)
| Ole -> Vbool (if x <= y then True else False)
end
| _,_ -> Vbool False
end | function | eval_bin | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"op",
"operator",
"value"
] | semantics of formulas | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
get_env (i:ident) (e:env) : value | = IdMap.get e i | function | get_env | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"get",
"ident",
"value"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
eval_term (sigma:env) (pi:env) (t:term) : value | =
match t with
| Tconst n -> Vint n
| Tvar id -> get_env id pi
| Tderef id -> get_env id sigma
| Tbin t1 op t2 ->
eval_bin (eval_term sigma pi t1) op (eval_term sigma pi t2)
end | function | eval_term | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"eval_bin",
"get_env",
"id",
"op",
"pi",
"t1",
"t2",
"term",
"value"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
eval_fmla (sigma:env) (pi:env) (f:fmla) | =
match f with
| Fterm t -> eval_term sigma pi t = Vbool True
| Fand f1 f2 -> eval_fmla sigma pi f1 /\ eval_fmla sigma pi f2
| Fnot f -> not (eval_fmla sigma pi f)
| Fimplies f1 f2 -> eval_fmla sigma pi f1 -> eval_fmla sigma pi f2
| Flet x t f ->
eval_fmla sigma (IdMap.set pi x (eval_term sigma pi t))... | predicate | eval_fmla | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"eval_term",
"f1",
"f2",
"fmla",
"int",
"pi",
"set"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
subst_term (e:term) (r:ident) (v:ident) : term | =
match e with
| Tconst _ -> e
| Tvar _ -> e
| Tderef x -> if r=x then Tvar v else e
| Tbin e1 op e2 -> Tbin (subst_term e1 r v) op (subst_term e2 r v)
end | let function | subst_term | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"ident",
"op",
"term"
] | substitution of a reference `r` by a logic variable `v` warning: proper behavior only guaranted if `v` is fresh | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
fresh_in_term (id:ident) (t:term) | =
match t with
| Tconst _ -> true
| Tvar v -> id <> v
| Tderef _ -> true
| Tbin t1 _ t2 -> fresh_in_term id t1 /\ fresh_in_term id t2
end | predicate | fresh_in_term | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"id",
"ident",
"t1",
"t2",
"term"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
eval_subst_term:
forall sigma pi:env, e:term, x:ident, v:ident.
fresh_in_term v e ->
eval_term sigma pi (subst_term e x v) =
eval_term (IdMap.set sigma x (IdMap.get pi v)) pi e | lemma | eval_subst_term | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"eval_term",
"fresh_in_term",
"get",
"ident",
"pi",
"set",
"subst_term",
"term"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
eval_term_change_free :
forall t:term, sigma pi:env, id:ident, v:value.
fresh_in_term id t ->
eval_term sigma (IdMap.set pi id v) t = eval_term sigma pi t | lemma | eval_term_change_free | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"eval_term",
"fresh_in_term",
"id",
"ident",
"pi",
"set",
"term",
"value"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
subst (f:fmla) (x:ident) (v:ident) : fmla | =
match f with
| Fterm e -> Fterm (subst_term e x v)
| Fand f1 f2 -> Fand (subst f1 x v) (subst f2 x v)
| Fnot f -> Fnot (subst f x v)
| Fimplies f1 f2 -> Fimplies (subst f1 x v) (subst f2 x v)
| Flet y t f -> Flet y (subst_term t x v) (subst f x v)
| Fforall y ty f -> Fforall y ty (subst f x v)
end | let function | subst | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"f1",
"f2",
"fmla",
"ident",
"subst_term"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
eval_subst:
forall f:fmla, sigma pi:env, x:ident, v:ident.
fresh_in_fmla v f ->
(eval_fmla sigma pi (subst f x v) <->
eval_fmla (IdMap.set sigma x (IdMap.get pi v)) pi f) | lemma | eval_subst | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"eval_fmla",
"fmla",
"fresh_in_fmla",
"get",
"ident",
"pi",
"set",
"subst"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
eval_swap:
forall f:fmla, sigma pi:env, id1 id2:ident, v1 v2:value.
id1 <> id2 ->
(eval_fmla sigma (IdMap.set (IdMap.set pi id1 v1) id2 v2) f <->
eval_fmla sigma (IdMap.set (IdMap.set pi id2 v2) id1 v1) f) | lemma | eval_swap | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"eval_fmla",
"fmla",
"ident",
"pi",
"set",
"value"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
eval_change_free :
forall f:fmla, sigma pi:env, id:ident, v:value.
fresh_in_fmla id f ->
(eval_fmla sigma (IdMap.set pi id v) f <-> eval_fmla sigma pi f) | lemma | eval_change_free | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"eval_fmla",
"fmla",
"fresh_in_fmla",
"id",
"ident",
"pi",
"set",
"value"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
stmt | =
| Sskip
| Sassign ident term
| Sseq stmt stmt
| Sif term stmt stmt
| Sassert fmla
| Swhile term fmla stmt | type | stmt | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"fmla",
"ident",
"term"
] | statements | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
check_skip:
forall s:stmt. s=Sskip \/s<>Sskip | lemma | check_skip | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"stmt"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
one_step env env stmt env env stmt | =
| one_step_assign:
forall sigma pi:env, x:ident, e:term.
one_step sigma pi (Sassign x e)
(IdMap.set sigma x (eval_term sigma pi e)) pi
Sskip
| one_step_seq:
forall sigma pi sigma' pi':env, i1 i1' i2:stmt.
one_step sigma pi i1 sigma' pi' i1' ->
... | inductive | one_step | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"eval_fmla",
"eval_term",
"fmla",
"i1",
"i2",
"ident",
"inv",
"pi",
"set",
"stmt",
"term"
] | small-steps semantics for statements | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
many_steps env env stmt env env stmt int | =
| many_steps_refl:
forall sigma pi:env, i:stmt. many_steps sigma pi i sigma pi i 0
| many_steps_trans:
forall sigma1 pi1 sigma2 pi2 sigma3 pi3:env, i1 i2 i3:stmt, n:int.
one_step sigma1 pi1 i1 sigma2 pi2 i2 ->
many_steps sigma2 pi2 i2 sigma3 pi3 i3 n ->
many_steps sigma1 pi1 i1 si... | inductive | many_steps | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"i1",
"i2",
"int",
"one_step",
"pi",
"stmt"
] | many steps of execution | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
steps_non_neg:
forall sigma1 pi1 sigma2 pi2:env, i1 i2:stmt, n:int.
many_steps sigma1 pi1 i1 sigma2 pi2 i2 n -> n >= 0 | lemma | steps_non_neg | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"i1",
"i2",
"int",
"many_steps",
"stmt"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
many_steps_seq:
forall sigma1 pi1 sigma3 pi3:env, i1 i2:stmt, n:int.
many_steps sigma1 pi1 (Sseq i1 i2) sigma3 pi3 Sskip n ->
exists sigma2 pi2:env, n1 n2:int.
many_steps sigma1 pi1 i1 sigma2 pi2 Sskip n1 /\
many_steps sigma2 pi2 i2 sigma3 pi3 Sskip n2 /\
n = 1 + n1 + n2 | lemma | many_steps_seq | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"i1",
"i2",
"int",
"many_steps",
"stmt"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
valid_fmla (p:fmla) | = forall sigma pi:env. eval_fmla sigma pi p | predicate | valid_fmla | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"eval_fmla",
"fmla",
"pi"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
valid_triple (p:fmla) (i:stmt) (q:fmla) | =
forall sigma pi:env. eval_fmla sigma pi p ->
forall sigma' pi':env, n:int. many_steps sigma pi i sigma' pi' Sskip n ->
eval_fmla sigma' pi' q | predicate | valid_triple | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"eval_fmla",
"fmla",
"int",
"many_steps",
"pi",
"stmt"
] | partial correctness | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
my_pi : env | = Const.const (Vint 42) | function | my_pi | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"const",
"env"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
Test13 :
eval_term my_sigma my_pi (Tconst 13) = Vint 13 | goal | Test13 | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"eval_term",
"my_pi",
"my_sigma"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Test42 :
eval_term my_sigma my_pi (Tvar 0) = Vint 42 | goal | Test42 | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"eval_term",
"my_pi",
"my_sigma"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Test0 :
eval_term my_sigma my_pi (Tderef 0) = Vint 0 | goal | Test0 | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"eval_term",
"my_pi",
"my_sigma"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Test55 :
eval_term my_sigma my_pi (Tbin (Tvar 0) Oplus (Tconst 13)) = Vint 55 | goal | Test55 | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"eval_term",
"my_pi",
"my_sigma"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Ass42 :
let x = 0 in
forall sigma' pi':env.
one_step my_sigma my_pi (Sassign x (Tconst 42)) sigma' pi' Sskip ->
IdMap.get sigma' x = Vint 42 | goal | Ass42 | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"get",
"my_pi",
"my_sigma",
"one_step"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
If42 :
let x = 0 in
forall sigma1 pi1 sigma2 pi2:env, i:stmt.
one_step my_sigma my_pi
(Sif (Tbin (Tderef x) Ole (Tconst 10))
(Sassign x (Tconst 13))
(Sassign x (Tconst 42)))
sigma1 pi1 i ->
one_step sigma1 pi1 i sigma2 pi2 Sskip ->
IdMap.get sigma2 x... | goal | If42 | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"get",
"my_pi",
"my_sigma",
"one_step",
"stmt"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
assign_rule:
forall q:fmla, x id:ident, e:term.
fresh_in_fmla id q ->
valid_triple (Flet id e (subst q x id)) (Sassign x e) q | lemma | assign_rule | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"fmla",
"fresh_in_fmla",
"id",
"ident",
"subst",
"term",
"valid_triple"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
if_rule:
forall e:term, p q:fmla, i1 i2:stmt.
valid_triple (Fand p (Fterm e)) i1 q /\
valid_triple (Fand p (Fnot (Fterm e))) i2 q ->
valid_triple p (Sif e i1 i2) q | lemma | if_rule | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"fmla",
"i1",
"i2",
"stmt",
"term",
"valid_triple"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
while_rule_ext:
forall e:term, inv inv':fmla, i:stmt.
valid_fmla (Fimplies inv' inv) ->
valid_triple (Fand (Fterm e) inv') i inv' ->
valid_triple inv' (Swhile e inv i) (Fand (Fnot (Fterm e)) inv') | lemma | while_rule_ext | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"fmla",
"inv",
"stmt",
"term",
"valid_fmla",
"valid_triple"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
assigns (sigma:env) (a:Set.fset ident) (sigma':env) | =
forall i:ident. not (Set.mem i a) ->
IdMap.get sigma i = IdMap.get sigma' i | predicate | assigns | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"fset",
"get",
"ident",
"mem"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
assigns_refl:
forall sigma:env, a:Set.fset ident. assigns sigma a sigma | lemma | assigns_refl | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"assigns",
"env",
"fset",
"ident"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
assigns_trans:
forall sigma1 sigma2 sigma3:env, a:Set.fset ident.
assigns sigma1 a sigma2 /\ assigns sigma2 a sigma3 ->
assigns sigma1 a sigma3 | lemma | assigns_trans | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"assigns",
"env",
"fset",
"ident"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
assigns_union_left:
forall sigma sigma':env, s1 s2:Set.fset ident.
assigns sigma s1 sigma' -> assigns sigma (Set.union s1 s2) sigma' | lemma | assigns_union_left | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"assigns",
"env",
"fset",
"ident",
"union"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
assigns_union_right:
forall sigma sigma':env, s1 s2:Set.fset ident.
assigns sigma s2 sigma' -> assigns sigma (Set.union s1 s2) sigma' | lemma | assigns_union_right | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"assigns",
"env",
"fset",
"ident",
"union"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
stmt_writes (i:stmt) (w:Set.fset ident) | =
match i with
| Sskip | Sassert _ -> true
| Sassign id _ -> Set.mem id w
| Sseq s1 s2 | Sif _ s1 s2 -> stmt_writes s1 w /\ stmt_writes s2 w
| Swhile _ _ s -> stmt_writes s w
end | predicate | stmt_writes | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"fset",
"id",
"ident",
"mem",
"stmt"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
compute_writes (s:stmt) : S.set
ensures {
forall sigma pi sigma' pi':env, n:int.
many_steps sigma pi s sigma' pi' Sskip n ->
assigns sigma result sigma' }
variant { s } | = match s with
| Sskip -> S.empty ()
| Sassign i _ -> S.singleton i
| Sseq s1 s2 -> S.union (compute_writes s1) (compute_writes s2)
| Sif _ s1 s2 -> S.union (compute_writes s1) (compute_writes s2)
| Swhile _ _ s -> compute_writes s
| Sassert _ -> S.empty ()
end | let | compute_writes | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"assigns",
"empty",
"env",
"int",
"many_steps",
"pi",
"set",
"singleton",
"stmt",
"union"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
fresh_from_fmla (q:fmla) : ident
ensures { fresh_in_fmla result q } | val | fresh_from_fmla | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"fmla",
"fresh_in_fmla",
"ident"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
abstract_effects (i:stmt) (f:fmla) : fmla
ensures { forall sigma pi:env. eval_fmla sigma pi result ->
eval_fmla sigma pi f /\
(***
forall sigma':env, w:Set.set ident.
stmt_writes i w /\ assigns sigma w sigma' ->
eval_fmla sigma' pi result
*)
forall sigma' pi':env, n:int.
... | val | abstract_effects | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"env",
"eval_fmla",
"fmla",
"int",
"many_steps",
"pi",
"stmt"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
wp (i:stmt) (q:fmla)
ensures { valid_triple result i q }
variant { i } | = match i with
| Sskip -> q
| Sseq i1 i2 -> wp i1 (wp i2 q)
| Sassign x e ->
let id = fresh_from_fmla q in Flet id e (subst q x id)
| Sif e i1 i2 ->
Fand (Fimplies (Fterm e) (wp i1 q))
(Fimplies (Fnot (Fterm e)) (wp i2 q))
| Sassert f ->
Fimplies f q (* liberal wp... | let | wp | examples/WP_revisited | examples/WP_revisited/wp2.mlw | [
"HoareLogic",
"Imp",
"bool.Bool",
"int.Int",
"map.Const",
"map.Map",
"set.Fset",
"set.SetApp"
] | [
"abstract_effects",
"fmla",
"fresh_from_fmla",
"i1",
"i2",
"id",
"inv",
"stmt",
"subst",
"valid_triple"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.