statement stringlengths 1 44.9k | proof stringlengths 0 114k | type stringclasses 26
values | symbolic_name stringlengths 1 82 | library stringclasses 153
values | filename stringlengths 13 83 | imports listlengths 0 0 | deps listlengths 0 64 | docstring stringclasses 1
value | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
'a tttree | = TEmpty | TNode 'a "'a tttree list ttree list tree"
datatype_compat tttree | datatype | tttree | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"list",
"tree",
"ttree"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
'a F | = F1 'a | F2 "'a F" | datatype | F | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"F1",
"F2"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
'a G | = G1 'a | G2 "'a G F" | datatype | G | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
H | = H1 | H2 "H G"
datatype_compat F
datatype_compat G
datatype_compat H | datatype | H | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
'a l | = N | C 'a "'a l" | datatype | l | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
('a, 'b) t = T 'a 'b "('a, 'b) t l" | datatype | t | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
f1_tl :: "(nat, 'a) t l \<Rightarrow> nat" and
f1_t :: "(nat, 'a) t \<Rightarrow> nat" | where
"f1_tl N = 0" |
"f1_tl (C t ts) = f1_t t + f1_tl ts" |
"f1_t (T n _ ts) = n + f1_tl ts" | primrec | f1_tl | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"and",
"nat",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
f2_t :: "(nat, 'b) t \<Rightarrow> nat" and
f2_tl :: "(nat, 'b) t l \<Rightarrow> nat" | where
"f2_tl N = 0" |
"f2_tl (C t ts) = f2_t t + f2_tl ts" |
"f2_t (T n _ ts) = n + f2_tl ts" | primrec | f2_t | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"and",
"nat",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
g1_t :: "('a, int) t \<Rightarrow> nat" and
g1_tl :: "('a, int) t l \<Rightarrow> nat" | where
"g1_t (T _ _ ts) = g1_tl ts" |
"g1_tl N = 0" |
"g1_tl (C _ ts) = g1_tl ts" | primrec | g1_t | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"and",
"int",
"nat",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
g2_t :: "(int, int) t \<Rightarrow> nat" and
g2_tl :: "(int, int) t l \<Rightarrow> nat" | where
"g2_t (T _ _ ts) = g2_tl ts" |
"g2_tl N = 0" |
"g2_tl (C _ ts) = g2_tl ts" | primrec | g2_t | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"and",
"int",
"nat",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
'a l1 | = N1 | C1 'a "'a l2" and
'a l2 = N2 | C2 'a "'a l1" | datatype | l1 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"and",
"l2"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
sum_l1 :: "'a::{zero,plus} l1 \<Rightarrow> 'a" and
sum_l2 :: "'a::{zero,plus} l2 \<Rightarrow> 'a" | where
"sum_l1 N1 = 0" |
"sum_l1 (C1 n ns) = n + sum_l2 ns" |
"sum_l2 N2 = 0" |
"sum_l2 (C2 n ns) = n + sum_l1 ns" | primrec | sum_l1 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"and",
"l1",
"l2",
"ns",
"plus",
"where",
"zero"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
('a, 'b) t1 = T1 'a 'b "('a, 'b) t1 l1" and
('a, 'b) t2 = T2 "('a, 'b) t1" | datatype | t1 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"T1",
"T2",
"and",
"l1",
"t2"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
h1_tl1 :: "(nat, 'a) t1 l1 \<Rightarrow> nat" and
h1_tl2 :: "(nat, 'a) t1 l2 \<Rightarrow> nat" and
h1_t1 :: "(nat, 'a) t1 \<Rightarrow> nat" | where
"h1_tl1 N1 = 0" |
"h1_tl1 (C1 t ts) = h1_t1 t + h1_tl2 ts" |
"h1_tl2 N2 = 0" |
"h1_tl2 (C2 t ts) = h1_t1 t + h1_tl1 ts" |
"h1_t1 (T1 n _ ts) = n + h1_tl1 ts" | primrec | h1_tl1 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"T1",
"and",
"l1",
"l2",
"nat",
"t1",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
h2_tl1 :: "(nat, 'a) t1 l1 \<Rightarrow> nat" and
h2_tl2 :: "(nat, 'a) t1 l2 \<Rightarrow> nat" and
h2_t1 :: "(nat, 'a) t1 \<Rightarrow> nat" | where
"h2_tl1 N1 = 0" |
"h2_tl1 (C1 t ts) = h2_t1 t + h2_tl2 ts" |
"h2_tl2 N2 = 0" |
"h2_tl2 (C2 t ts) = h2_t1 t + h2_tl1 ts" |
"h2_t1 (T1 n _ ts) = n + h2_tl1 ts" | primrec | h2_tl1 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"T1",
"and",
"l1",
"l2",
"nat",
"t1",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
h3_tl2 :: "(nat, 'a) t1 l2 \<Rightarrow> nat" and
h3_tl1 :: "(nat, 'a) t1 l1 \<Rightarrow> nat" and
h3_t1 :: "(nat, 'a) t1 \<Rightarrow> nat" | where
"h3_tl1 N1 = 0" |
"h3_tl1 (C1 t ts) = h3_t1 t + h3_tl2 ts" |
"h3_tl2 N2 = 0" |
"h3_tl2 (C2 t ts) = h3_t1 t + h3_tl1 ts" |
"h3_t1 (T1 n _ ts) = n + h3_tl1 ts" | primrec | h3_tl2 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"T1",
"and",
"l1",
"l2",
"nat",
"t1",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
i1_tl2 :: "(nat, 'a) t1 l2 \<Rightarrow> nat" and
i1_tl1 :: "(nat, 'a) t1 l1 \<Rightarrow> nat" and
i1_t1 :: "(nat, 'a) t1 \<Rightarrow> nat" and
i1_t2 :: "(nat, 'a) t2 \<Rightarrow> nat" | where
"i1_tl1 N1 = 0" |
"i1_tl1 (C1 t ts) = i1_t1 t + i1_tl2 ts" |
"i1_tl2 N2 = 0" |
"i1_tl2 (C2 t ts) = i1_t1 t + i1_tl1 ts" |
"i1_t1 (T1 n _ ts) = n + i1_tl1 ts" |
"i1_t2 (T2 t) = i1_t1 t" | primrec | i1_tl2 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"T1",
"T2",
"and",
"l1",
"l2",
"nat",
"t1",
"t2",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
j1_t2 :: "(nat, 'a) t2 \<Rightarrow> nat" and
j1_t1 :: "(nat, 'a) t1 \<Rightarrow> nat" and
j1_tl1 :: "(nat, 'a) t1 l1 \<Rightarrow> nat" and
j1_tl2 :: "(nat, 'a) t1 l2 \<Rightarrow> nat" | where
"j1_tl1 N1 = 0" |
"j1_tl1 (C1 t ts) = j1_t1 t + j1_tl2 ts" |
"j1_tl2 N2 = 0" |
"j1_tl2 (C2 t ts) = j1_t1 t + j1_tl1 ts" |
"j1_t1 (T1 n _ ts) = n + j1_tl1 ts" |
"j1_t2 (T2 t) = j1_t1 t" | primrec | j1_t2 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"T1",
"T2",
"and",
"l1",
"l2",
"nat",
"t1",
"t2",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
'a l3 | = N3 | C3 'a "'a l3" | datatype | l3 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
'a l4 | = N4 | C4 'a "'a l4" | datatype | l4 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
('a, 'b) t3 = T3 'a 'b "('a, 'b) t3 l3" "('a, 'b) t3 l4" | datatype | t3 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"T3",
"l3",
"l4"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
k1_tl3 :: "(nat, 'a) t3 l3 \<Rightarrow> nat" and
k1_tl4 :: "(nat, 'a) t3 l4 \<Rightarrow> nat" and
k1_t3 :: "(nat, 'a) t3 \<Rightarrow> nat" | where
"k1_tl3 N3 = 0" |
"k1_tl3 (C3 t ts) = k1_t3 t + k1_tl3 ts" |
"k1_tl4 N4 = 0" |
"k1_tl4 (C4 t ts) = k1_t3 t + k1_tl4 ts" |
"k1_t3 (T3 n _ ts us) = n + k1_tl3 ts + k1_tl4 us" | primrec | k1_tl3 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"T3",
"and",
"l3",
"l4",
"nat",
"t3",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
k2_tl4 :: "(nat, int) t3 l4 \<Rightarrow> nat" and
k2_tl3 :: "(nat, int) t3 l3 \<Rightarrow> nat" and
k2_t3 :: "(nat, int) t3 \<Rightarrow> nat" | where
"k2_tl4 N4 = 0" |
"k2_tl4 (C4 t ts) = k2_t3 t + k2_tl4 ts" |
"k2_tl3 N3 = 0" |
"k2_tl3 (C3 t ts) = k2_t3 t + k2_tl3 ts" |
"k2_t3 (T3 n _ ts us) = n + k2_tl3 ts + k2_tl4 us" | primrec | k2_tl4 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"T3",
"and",
"int",
"l3",
"l4",
"nat",
"t3",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
('a, 'b) l5 = N5 | C5 'a 'b "('a, 'b) l5" | datatype | l5 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
('a, 'b) l6 = N6 | C6 'a 'b "('a, 'b) l6" | datatype | l6 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
('a, 'b, 'c) t4 = T4 'a 'b "(('a, 'b, 'c) t4, 'b) l5" "(('a, 'b, 'c) t4, 'c) l6" | datatype | t4 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"l5",
"l6"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
l1_tl5 :: "((nat, 'a, 'b) t4, 'a) l5 \<Rightarrow> nat" and
l1_tl6 :: "((nat, 'a, 'b) t4, 'b) l6 \<Rightarrow> nat" and
l1_t4 :: "(nat, 'a, 'b) t4 \<Rightarrow> nat" | where
"l1_tl5 N5 = 0" |
"l1_tl5 (C5 t _ ts) = l1_t4 t + l1_tl5 ts" |
"l1_tl6 N6 = 0" |
"l1_tl6 (C6 t _ ts) = l1_t4 t + l1_tl6 ts" |
"l1_t4 (T4 n _ ts us) = n + l1_tl5 ts + l1_tl6 us" | primrec | l1_tl5 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"and",
"l5",
"l6",
"nat",
"t4",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
f1_cotcol :: "nat \<Rightarrow> (nat, 'a) cot col" and
f1_cot :: "nat \<Rightarrow> (nat, 'a) cot" | where
"n = 0 \<Longrightarrow> f1_cotcol n = N" |
"_ \<Longrightarrow> f1_cotcol n = C (f1_cot n) (f1_cotcol n)" |
"f1_cot n = T n undefined (f1_cotcol n)" | primcorec | f1_cotcol | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"and",
"cot",
"nat",
"undefined",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
f2_cotcol :: "nat \<Rightarrow> (nat, 'b) cot col" and
f2_cot :: "nat \<Rightarrow> (nat, 'b) cot" | where
"n = 0 \<Longrightarrow> f2_cotcol n = N" |
"_ \<Longrightarrow> f2_cotcol n = C (f2_cot n) (f2_cotcol n)" |
"f2_cot n = T n undefined (f2_cotcol n)" | primcorec | f2_cotcol | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"and",
"cot",
"nat",
"undefined",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
g1_cot :: "int \<Rightarrow> (int, 'a) cot" and
g1_cotcol :: "int \<Rightarrow> (int, 'a) cot col" | where
"g1_cot n = T n undefined (g1_cotcol n)" |
"n = 0 \<Longrightarrow> g1_cotcol n = N" |
"_ \<Longrightarrow> g1_cotcol n = C (g1_cot n) (g1_cotcol n)" | primcorec | g1_cot | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"and",
"cot",
"int",
"undefined",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
g2_cot :: "int \<Rightarrow> (int, int) cot" and
g2_cotcol :: "int \<Rightarrow> (int, int) cot col" | where
"g2_cot n = T n undefined (g2_cotcol n)" |
"n = 0 \<Longrightarrow> g2_cotcol n = N" |
"_ \<Longrightarrow> g2_cotcol n = C (g2_cot n) (g2_cotcol n)"
codatatype
'a col1 = N1 | C1 'a "'a col2" and
'a col2 = N2 | C2 'a "'a col1"
codatatype
('a, 'b) cot1 = T1 'a 'b "('a, 'b) cot1 col1" and
('a, 'b) ... | primcorec | g2_cot | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"T1",
"T2",
"and",
"cot",
"int",
"undefined",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
h1_cotcol1 :: "nat \<Rightarrow> (nat, 'a) cot1 col1" and
h1_cotcol2 :: "nat \<Rightarrow> (nat, 'a) cot1 col2" and
h1_cot1 :: "nat \<Rightarrow> (nat, 'a) cot1" | where
"h1_cotcol1 n = C1 (h1_cot1 n) (h1_cotcol2 n)" |
"h1_cotcol2 n = C2 (h1_cot1 n) (h1_cotcol1 n)" |
"h1_cot1 n = T1 n undefined (h1_cotcol1 n)" | primcorec | h1_cotcol1 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"T1",
"and",
"nat",
"undefined",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
h2_cotcol1 :: "nat \<Rightarrow> (nat, 'a) cot1 col1" and
h2_cotcol2 :: "nat \<Rightarrow> (nat, 'a) cot1 col2" and
h2_cot1 :: "nat \<Rightarrow> (nat, 'a) cot1" | where
"h2_cotcol1 n = C1 (h2_cot1 n) (h2_cotcol2 n)" |
"h2_cotcol2 n = C2 (h2_cot1 n) (h2_cotcol1 n)" |
"h2_cot1 n = T1 n undefined (h2_cotcol1 n)" | primcorec | h2_cotcol1 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"T1",
"and",
"nat",
"undefined",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
h3_cotcol2 :: "nat \<Rightarrow> (nat, 'a) cot1 col2" and
h3_cotcol1 :: "nat \<Rightarrow> (nat, 'a) cot1 col1" and
h3_cot1 :: "nat \<Rightarrow> (nat, 'a) cot1" | where
"h3_cotcol1 n = C1 (h3_cot1 n) (h3_cotcol2 n)" |
"h3_cotcol2 n = C2 (h3_cot1 n) (h3_cotcol1 n)" |
"h3_cot1 n = T1 n undefined (h3_cotcol1 n)" | primcorec | h3_cotcol2 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"T1",
"and",
"nat",
"undefined",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
i1_cotcol2 :: "nat \<Rightarrow> (nat, 'a) cot1 col2" and
i1_cotcol1 :: "nat \<Rightarrow> (nat, 'a) cot1 col1" and
i1_cot1 :: "nat \<Rightarrow> (nat, 'a) cot1" and
i1_cot2 :: "nat \<Rightarrow> (nat, 'a) cot2" | where
"i1_cotcol1 n = C1 (i1_cot1 n) (i1_cotcol2 n)" |
"i1_cotcol2 n = C2 (i1_cot1 n) (i1_cotcol1 n)" |
"i1_cot1 n = T1 n undefined (i1_cotcol1 n)" |
"i1_cot2 n = T2 (i1_cot1 n)" | primcorec | i1_cotcol2 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"T1",
"T2",
"and",
"nat",
"undefined",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
j1_cot2 :: "nat \<Rightarrow> (nat, 'a) cot2" and
j1_cot1 :: "nat \<Rightarrow> (nat, 'a) cot1" and
j1_cotcol1 :: "nat \<Rightarrow> (nat, 'a) cot1 col1" and
j1_cotcol2 :: "nat \<Rightarrow> (nat, 'a) cot1 col2" | where
"j1_cotcol1 n = C1 (j1_cot1 n) (j1_cotcol2 n)" |
"j1_cotcol2 n = C2 (j1_cot1 n) (j1_cotcol1 n)" |
"j1_cot1 n = T1 n undefined (j1_cotcol1 n)" |
"j1_cot2 n = T2 (j1_cot1 n)"
codatatype 'a col3 = N3 | C3 'a "'a col3"
codatatype 'a col4 = N4 | C4 'a "'a col4"
codatatype ('a, 'b) cot3 = T3 'a 'b "('a, 'b) c... | primcorec | j1_cot2 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"T1",
"T2",
"T3",
"and",
"nat",
"undefined",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
k1_cotcol3 :: "nat \<Rightarrow> (nat, 'a) cot3 col3" and
k1_cotcol4 :: "nat \<Rightarrow> (nat, 'a) cot3 col4" and
k1_cot3 :: "nat \<Rightarrow> (nat, 'a) cot3" | where
"k1_cotcol3 n = C3 (k1_cot3 n) (k1_cotcol3 n)" |
"k1_cotcol4 n = C4 (k1_cot3 n) (k1_cotcol4 n)" |
"k1_cot3 n = T3 n undefined (k1_cotcol3 n) (k1_cotcol4 n)" | primcorec | k1_cotcol3 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"T3",
"and",
"nat",
"undefined",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
k2_cotcol4 :: "nat \<Rightarrow> (nat, 'a) cot3 col4" and
k2_cotcol3 :: "nat \<Rightarrow> (nat, 'a) cot3 col3" and
k2_cot3 :: "nat \<Rightarrow> (nat, 'a) cot3" | where
"k2_cotcol4 n = C4 (k2_cot3 n) (k2_cotcol4 n)" |
"k2_cotcol3 n = C3 (k2_cot3 n) (k2_cotcol3 n)" |
"k2_cot3 n = T3 n undefined (k2_cotcol3 n) (k2_cotcol4 n)" | primcorec | k2_cotcol4 | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"T3",
"and",
"nat",
"undefined",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
('a,'b)complex =
C1 nat "'a ttree"
| C2 "('a,'b)complex list tree tree" 'b "('a,'b)complex" "('a,'b)complex2 ttree list"
and ('a,'b)complex2 = D1 "('a,'b)complex ttree"
datatype_compat complex complex2 | datatype | complex | Benchmarks.Datatype_Benchmark | src/Benchmarks/Datatype_Benchmark/Misc_N2M.thy | [] | [
"and",
"list",
"nat",
"tree",
"ttree"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
agent | = Alice | Bob | Spy | datatype | agent | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
agents :: "agent set" | where
"agents = {Spy, Alice, Bob}" | definition | agents | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"agent",
"set",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
bad :: "agent set" | where
"bad = {Spy}" | definition | bad | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"agent",
"set",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
key | = pubEK agent | priEK agent | datatype | key | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"agent",
"priEK",
"pubEK"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
invKey | where
"invKey (pubEK A) = priEK A"
| "invKey (priEK A) = pubEK A" | fun | invKey | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"priEK",
"pubEK",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
msg | = Agent agent
| Key key
| Nonce nat
| MPair msg msg
| Crypt key msg
syntax
"_MTuple" :: "['a, args] \<Rightarrow> 'a * 'b" (\<open>(\<open>indent=2 notation=\<open>mixfix message tuple\<close>\<close>\<lbrace>_,/ _\<rbrace>)\<close>)
syntax_consts
"_MTuple" \<rightleftha... | datatype | msg | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"Crypt",
"MPair",
"Nonce",
"agent",
"args",
"close",
"key",
"message",
"nat",
"open",
"syntax"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
parts :: "msg set => msg set"
for H :: "msg set" | where
Inj [intro]: "X \<in> H ==> X \<in> parts H"
| Fst: "\<lbrace>X,Y\<rbrace> \<in> parts H ==> X \<in> parts H"
| Snd: "\<lbrace>X,Y\<rbrace> \<in> parts H ==> Y \<in> parts H"
| Body: "Crypt K X \<in> parts H ==> X \<in> parts H" | inductive_set | parts | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"Crypt",
"Fst",
"Snd",
"for",
"msg",
"set",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
analz :: "msg set => msg set"
for H :: "msg set" | where
Inj [intro,simp] : "X \<in> H ==> X \<in> analz H"
| Fst: "\<lbrace>X,Y\<rbrace> \<in> analz H ==> X \<in> analz H"
| Snd: "\<lbrace>X,Y\<rbrace> \<in> analz H ==> Y \<in> analz H"
| Decrypt [dest]:
"[|Crypt K X \<in> analz H; Key(invKey K) \<in> analz H|] ==> X \<in> analz H" | inductive_set | analz | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"Crypt",
"Decrypt",
"Fst",
"Snd",
"for",
"invKey",
"msg",
"set",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
synth :: "msg set => msg set"
for H :: "msg set" | where
Inj [intro]: "X \<in> H ==> X \<in> synth H"
| Agent [intro]: "Agent agt \<in> synth H"
| MPair [intro]: "[|X \<in> synth H; Y \<in> synth H|] ==> \<lbrace>X,Y\<rbrace> \<in> synth H"
| Crypt [intro]: "[|X \<in> synth H; Key(K) \<in> H|] ==> Crypt K X \<in> synth H" | inductive_set | synth | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"Crypt",
"MPair",
"agt",
"for",
"msg",
"set",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
initState | where
initState_Alice:
"initState Alice = {Key (priEK Alice)} \<union> (Key ` pubEK ` agents)"
| initState_Bob:
"initState Bob = {Key (priEK Bob)} \<union> (Key ` pubEK ` agents)"
| initState_Spy:
"initState Spy = (Key ` priEK ` bad) \<union> (Key ` pubEK ` agents)" | primrec | initState | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"agents",
"bad",
"priEK",
"pubEK",
"union",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
event | = Says agent agent msg
| Gets agent msg
| Notes agent msg | datatype | event | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"agent",
"msg"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
knows :: "agent => event list => msg set" | where
knows_Nil: "knows A [] = initState A"
| knows_Cons:
"knows A (ev # evs) =
(if A = Spy then
(case ev of
Says A' B X => insert X (knows Spy evs)
| Gets A' X => knows Spy evs
| Notes A' X =>
if A' \<in> bad then insert X (knows Spy evs) else knows S... | primrec | knows | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"agent",
"bad",
"case",
"ev",
"event",
"if",
"initState",
"insert",
"knows_Cons",
"list",
"msg",
"set",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
(input)
spies :: "event list => msg set" | where
"spies == knows Spy" | abbreviation | spies | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"event",
"knows",
"list",
"msg",
"set",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
used :: "event list => msg set" | where
used_Nil: "used [] = \<Union>(parts ` initState ` agents)"
| used_Cons: "used (ev # evs) =
(case ev of
Says A B X => parts {X} \<union> used evs
| Gets A X => used evs
| Notes A X => parts {X} \<union> used ev... | primrec | used | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"Union",
"agents",
"case",
"ev",
"event",
"initState",
"list",
"msg",
"parts",
"set",
"union",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
find_first :: "('a => 'b option) => 'a list => 'b option" | where
"find_first f [] = None"
| "find_first f (x # xs) = (case f x of Some y => Some y | None => find_first f xs)" | fun | find_first | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"None",
"case",
"list",
"option",
"where",
"xs"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
cps_of_set :: "'a set => ('a => term list option) => term list option" | consts | cps_of_set | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"list",
"option",
"set",
"term"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
[code]: "cps_of_set (set xs) f = find_first f xs" | sorry | lemma | cps_of_set | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"cps_of_set",
"find_first",
"set",
"xs"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
pos_cps_of_set :: "'a set => ('a => (bool * term list) option) => natural => (bool * term list) option" | consts | pos_cps_of_set | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"bool",
"list",
"natural",
"option",
"set",
"term"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
neg_cps_of_set :: "'a set => ('a Quickcheck_Exhaustive.unknown => term list Quickcheck_Exhaustive.three_valued) => natural => term list Quickcheck_Exhaustive.three_valued" | consts | neg_cps_of_set | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"list",
"natural",
"set",
"term"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
[code]: "pos_cps_of_set (set xs) f i = find_first f xs" | sorry | lemma | pos_cps_of_set | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"find_first",
"pos_cps_of_set",
"set",
"xs"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
find_first' :: "('b Quickcheck_Exhaustive.unknown => 'a Quickcheck_Exhaustive.three_valued)
=> 'b list => 'a Quickcheck_Exhaustive.three_valued" | consts | find_first' | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"list"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
[code]:
"find_first' f [] = Quickcheck_Exhaustive.No_value"
"find_first' f (x # xs) = (case f (Quickcheck_Exhaustive.Known x) of Quickcheck_Exhaustive.No_value => find_first' f xs | Quickcheck_Exhaustive.Value x => Quickcheck_Exhaustive.Value x | Quickcheck_Exhaustive.Unknown_value => (case find_first' f xs of Quic... | sorry | lemma | find_first' | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"case",
"find_first'",
"xs"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
[code]: "neg_cps_of_set (set xs) f i = find_first' f xs" | sorry | lemma | neg_cps_of_set | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"find_first'",
"neg_cps_of_set",
"set",
"xs"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
[code]:
"analz H = (let
H' = H \<union> (\<Union>((%m. case m of \<lbrace>X, Y\<rbrace> => {X, Y} | Crypt K X => if Key (invKey K) \<in> H then {X} else {} | _ => {}) ` H))
in if H' = H then H else analz H')" | sorry | lemma | analz | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"Crypt",
"Union",
"analz",
"case",
"if",
"invKey",
"union"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
[code]:
"parts H = (let
H' = H \<union> (\<Union>((%m. case m of \<lbrace>X, Y\<rbrace> => {X, Y} | Crypt K X => {X} | _ => {}) ` H))
in if H' = H then H else parts H')" | sorry | lemma | parts | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"Crypt",
"Union",
"case",
"if",
"parts",
"union"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
synth' :: "msg set => msg => bool" | where
"synth' H m = (m \<in> synth H)"
lemmas [code_pred_intro] = synth.intros[folded synth'_def]
code_pred [generator_cps] synth' unfolding synth'_def by (rule synth.cases) fastforce+ | definition | synth' | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Base.thy | [] | [
"bool",
"msg",
"rule",
"set",
"synth",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
ns_public :: "event list set" | where
(*Initial trace is empty*)
Nil: "[] \<in> ns_public"
| Fake_NS1: "\<lbrakk>evs1 \<in> ns_public; Nonce NA \<in> analz (spies evs1) \<rbrakk>
\<Longrightarrow> Says Spy B (Crypt (pubEK B) \<lbrace>Nonce NA, Agent A\<rbrace>)
# evs1 \<in> ns_public"
| Fake_NS2: "\<lbrakk... | inductive_set | ns_public | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Guided_Attacker_Example.thy | [] | [
"Crypt",
"NS1",
"NS2",
"NS3",
"Nil",
"Nonce",
"analz",
"event",
"list",
"pubEK",
"set",
"spies",
"used",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
"ns_publicp evs ==> \<not> (Says Alice Bob (Crypt (pubEK Bob) (Nonce NB))) : set evs"
quickcheck[smart_exhaustive, depth = 5, timeout = 100, expect = counterexample]
(*quickcheck[narrowing, size = 6, timeout = 200, verbose, expect = no_counterexample]*) | oops | lemma | ns_publicp | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Guided_Attacker_Example.thy | [] | [
"Crypt",
"Nonce",
"depth",
"not",
"pubEK",
"set"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
"\<lbrakk>ns_publicp evs\<rbrakk>
\<Longrightarrow> Says B A (Crypt (pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) : set evs
\<Longrightarrow> A \<noteq> Spy \<Longrightarrow> B \<noteq> Spy \<Longrightarrow> A \<noteq> B
\<Longrightarrow> Nonce NB \<notin> analz (spies evs)"
(*qu... | oops | lemma | lbrakk | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Guided_Attacker_Example.thy | [] | [
"Crypt",
"Nonce",
"analz",
"noteq",
"pubEK",
"set",
"spies"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
assumes "A = Alice" "B = Bob" "C = Spy" "NA = 0" "NB = 1"
assumes "evs =
[Says Alice Spy (Crypt (pubEK Spy) (Nonce 1)),
Says Bob Alice (Crypt (pubEK Alice) \<lbrace>Nonce 0, Nonce 1\<rbrace>),
Says Spy Bob (Crypt (pubEK Bob) \<lbrace>Nonce 0, Agent Alice\<rbrace>),
Says Alice Spy (Crypt (pubEK Spy) \<lbra... | proof -
from assms show "A \<noteq> Spy" by auto
from assms show "B \<noteq> Spy" by auto
have "[] : ns_public" by (rule Nil)
then have first_step: "[?e0] : ns_public"
proof (rule NS1)
show "Nonce 0 ~: used []" by eval
qed
then have "[?e1, ?e0] : ns_public"
proof (rule Fake_NS1)
show "Nonce 0 : ... | lemma | assumes | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Guided_Attacker_Example.thy | [] | [
"Crypt",
"NS1",
"NS2",
"NS3",
"Nil",
"Nonce",
"add",
"analz",
"apply",
"auto",
"eval",
"knows",
"noteq",
"ns_public",
"pubEK",
"rule",
"set",
"shows",
"used"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
ns_public :: "event list set" | where
(*Initial trace is empty*)
Nil: "[] \<in> ns_public"
(*Alice initiates a protocol run, sending a nonce to Bob*)
| NS1: "\<lbrakk>evs1 \<in> ns_public; Nonce NA \<notin> used evs1\<rbrakk>
\<Longrightarrow> Says A B (Crypt (pubEK B) \<lbrace>Nonce NA, Agent A\<rbrace>)
... | inductive_set | ns_public | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_No_Attacker_Example.thy | [] | [
"Crypt",
"NS1",
"NS2",
"NS3",
"Nil",
"Nonce",
"event",
"list",
"pubEK",
"set",
"used",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
"ns_publicp evs ==> \<not> (Says Alice Bob (Crypt (pubEK Bob) (Nonce NB))) : set evs"
(*quickcheck[random, iterations = 1000000, size = 20, timeout = 3600, verbose]
quickcheck[exhaustive, size = 8, timeout = 3600, verbose]
quickcheck[narrowing, size = 7, timeout = 3600, verbose]*)
quickcheck[smart_exhaustive, depth = 5... | oops | lemma | ns_publicp | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_No_Attacker_Example.thy | [] | [
"Crypt",
"Nonce",
"depth",
"not",
"pubEK",
"set"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
"\<lbrakk>ns_publicp evs\<rbrakk>
\<Longrightarrow> Says B A (Crypt (pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) : set evs
\<Longrightarrow> A \<noteq> Spy \<Longrightarrow> B \<noteq> Spy \<Longrightarrow> A \<noteq> B
\<Longrightarrow> Nonce NB \<notin> analz (spies evs)"
quic... | oops | lemma | lbrakk | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_No_Attacker_Example.thy | [] | [
"Crypt",
"Nonce",
"analz",
"depth",
"narrowing",
"noteq",
"pubEK",
"set",
"size",
"spies"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
ns_public :: "event list set" | where
(*Initial trace is empty*)
Nil: "[] \<in> ns_public"
| Fake: "\<lbrakk>evs1 \<in> ns_public; X \<in> synth (analz (spies evs1)) \<rbrakk>
\<Longrightarrow> Says Spy A X # evs1 \<in> ns_public"
(*Alice initiates a protocol run, sending a nonce to Bob*)
| NS1: "\<lbrakk>evs1 \... | inductive_set | ns_public | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Unguided_Attacker_Example.thy | [] | [
"Crypt",
"Fake",
"NS1",
"NS2",
"NS3",
"Nil",
"Nonce",
"analz",
"event",
"list",
"pubEK",
"set",
"spies",
"synth",
"used",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
"ns_publicp evs ==> \<not> (Says Alice Bob (Crypt (pubEK Bob) (Nonce NB))) : set evs"
quickcheck[smart_exhaustive, depth = 5, timeout = 200, expect = counterexample]
(*quickcheck[narrowing, size = 6, timeout = 200, verbose, expect = no_counterexample]*) | oops | lemma | ns_publicp | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Unguided_Attacker_Example.thy | [] | [
"Crypt",
"Nonce",
"depth",
"not",
"pubEK",
"set"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
"\<lbrakk>ns_publicp evs\<rbrakk>
\<Longrightarrow> Says B A (Crypt (pubEK A) \<lbrace>Nonce NA, Nonce NB\<rbrace>) : set evs
\<Longrightarrow> A \<noteq> Spy \<Longrightarrow> B \<noteq> Spy \<Longrightarrow> A \<noteq> B
\<Longrightarrow> Nonce NB \<notin> analz (spies evs)"
quic... | oops | lemma | lbrakk | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Unguided_Attacker_Example.thy | [] | [
"Crypt",
"Nonce",
"analz",
"depth",
"noteq",
"pubEK",
"set",
"spies"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
assumes "A = Alice" "B = Bob" "C = Spy" "NA = 0" "NB = 1"
assumes "evs =
[Says Alice Spy (Crypt (pubEK Spy) (Nonce 1)),
Says Bob Alice (Crypt (pubEK Alice) \<lbrace>Nonce 0, Nonce 1\<rbrace>),
Says Spy Bob (Crypt (pubEK Bob) \<lbrace>Nonce 0, Agent Alice\<rbrace>),
Says Alice Spy (Crypt (pubEK Spy) \<lbra... | proof -
from assms show "A \<noteq> Spy" by auto
from assms show "B \<noteq> Spy" by auto
have "[] : ns_public" by (rule Nil)
then have first_step: "[?e0] : ns_public"
proof (rule NS1)
show "Nonce 0 ~: used []" by eval
qed
then have "[?e1, ?e0] : ns_public"
proof (rule Fake)
show "Crypt (pubEK B... | lemma | assumes | Benchmarks.Quickcheck_Benchmark | src/Benchmarks/Quickcheck_Benchmark/Needham_Schroeder_Unguided_Attacker_Example.thy | [] | [
"Crypt",
"Fake",
"NS1",
"NS2",
"NS3",
"Nil",
"Nonce",
"add",
"analz",
"apply",
"auto",
"eval",
"knows",
"noteq",
"ns_public",
"pubEK",
"rule",
"set",
"shows",
"synth",
"used"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
many_A =
A000::nat
A001::nat
A002::nat
A003::nat
A004::nat
A005::nat
A006::nat
A007::nat
A008::nat
A009::nat
A010::nat
A011::nat
A012::nat
A013::nat
A014::nat
A015::nat
A016::nat
A017::nat
A018::nat
A019::nat
A020::nat
A021::nat
A022::nat
A023::nat
A024::nat
A025::nat
A026::nat
A027::nat
A028::nat
A029::nat
A030::nat
A... | record | many_A | Benchmarks.Record_Benchmark | src/Benchmarks/Record_Benchmark/Record_Benchmark.thy | [] | [
"nat"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
many_B = many_A +
B000::nat
B001::nat
B002::nat
B003::nat
B004::nat
B005::nat
B006::nat
B007::nat
B008::nat
B009::nat
B010::nat
B011::nat
B012::nat
B013::nat
B014::nat
B015::nat
B016::nat
B017::nat
B018::nat
B019::nat
B020::nat
B021::nat
B022::nat
B023::nat
B024::nat
B025::nat
B026::nat
B027::nat
B028::nat
B029::nat
B0... | record | many_B | Benchmarks.Record_Benchmark | src/Benchmarks/Record_Benchmark/Record_Benchmark.thy | [] | [
"many_A",
"nat"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
"A155 (r\<lparr>A255:=x\<rparr>) = A155 r" | by simp | lemma | A155 | Benchmarks.Record_Benchmark | src/Benchmarks/Record_Benchmark/Record_Benchmark.thy | [] | [] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
"A155 (r\<lparr>A255:=x,A253:=y,A255:=z \<rparr>) = A155 r" | by simp | lemma | A155 | Benchmarks.Record_Benchmark | src/Benchmarks/Record_Benchmark/Record_Benchmark.thy | [] | [] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
"(r\<lparr>A255:=x,A253:=y,A255:=z \<rparr>) = r\<lparr>A253:=y,A255:=z\<rparr>" | by simp | lemma | r | Benchmarks.Record_Benchmark | src/Benchmarks/Record_Benchmark/Record_Benchmark.thy | [] | [] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
"(r\<lparr>A255:=x,A253:=y,A255:=z \<rparr>) = r\<lparr>A253:=y,A255:=z\<rparr>" | apply (tactic \<open>simp_tac
(put_simpset HOL_basic_ss \<^context> |> Simplifier.add_proc Record.upd_simproc) 1\<close>)
done | lemma | r | Benchmarks.Record_Benchmark | src/Benchmarks/Record_Benchmark/Record_Benchmark.thy | [] | [
"apply",
"close",
"open"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
"(\<forall>r. P (A155 r)) \<longrightarrow> (\<forall>x. P x)" | apply (tactic \<open>simp_tac
(put_simpset HOL_basic_ss \<^context> |> Simplifier.add_proc (Record.split_simproc (K ~1))) 1\<close>)
apply simp
done | lemma | forall | Benchmarks.Record_Benchmark | src/Benchmarks/Record_Benchmark/Record_Benchmark.thy | [] | [
"apply",
"close",
"forall",
"open"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
"(\<forall>r. P (A155 r)) \<longrightarrow> (\<forall>x. P x)" | apply (tactic \<open>Record.split_simp_tac \<^context> [] (K ~1) 1\<close>)
apply simp
done | lemma | forall | Benchmarks.Record_Benchmark | src/Benchmarks/Record_Benchmark/Record_Benchmark.thy | [] | [
"apply",
"close",
"forall",
"open"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
"(\<exists>r. P (A155 r)) \<longrightarrow> (\<exists>x. P x)" | apply (tactic \<open>simp_tac
(put_simpset HOL_basic_ss \<^context> |> Simplifier.add_proc (Record.split_simproc (K ~1))) 1\<close>)
apply simp
done | lemma | exists | Benchmarks.Record_Benchmark | src/Benchmarks/Record_Benchmark/Record_Benchmark.thy | [] | [
"apply",
"close",
"exists",
"open"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
"(\<exists>r. P (A155 r)) \<longrightarrow> (\<exists>x. P x)" | apply (tactic \<open>Record.split_simp_tac \<^context> [] (K ~1) 1\<close>)
apply simp
done | lemma | exists | Benchmarks.Record_Benchmark | src/Benchmarks/Record_Benchmark/Record_Benchmark.thy | [] | [
"apply",
"close",
"exists",
"open"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
"\<And>r. P (A155 r) \<Longrightarrow> (\<exists>x. P x)" | apply (tactic \<open>simp_tac
(put_simpset HOL_basic_ss \<^context> |> Simplifier.add_proc (Record.split_simproc (K ~1))) 1\<close>)
apply auto
done | lemma | And | Benchmarks.Record_Benchmark | src/Benchmarks/Record_Benchmark/Record_Benchmark.thy | [] | [
"And",
"apply",
"auto",
"close",
"exists",
"open"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
"\<And>r. P (A155 r) \<Longrightarrow> (\<exists>x. P x)" | apply (tactic \<open>Record.split_simp_tac \<^context> [] (K ~1) 1\<close>)
apply auto
done | lemma | And | Benchmarks.Record_Benchmark | src/Benchmarks/Record_Benchmark/Record_Benchmark.thy | [] | [
"And",
"apply",
"auto",
"close",
"exists",
"open"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
"P (A155 r) \<Longrightarrow> (\<exists>x. P x)" | apply (tactic \<open>Record.split_simp_tac \<^context> [] (K ~1) 1\<close>)
apply auto
done | lemma | P | Benchmarks.Record_Benchmark | src/Benchmarks/Record_Benchmark/Record_Benchmark.thy | [] | [
"apply",
"auto",
"close",
"exists",
"open"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
fixes r shows "P (A155 r) \<Longrightarrow> (\<exists>x. P x)" | apply (tactic \<open>Record.split_simp_tac \<^context> [] (K ~1) 1\<close>)
apply auto
done
notepad | lemma | fixes | Benchmarks.Record_Benchmark | src/Benchmarks/Record_Benchmark/Record_Benchmark.thy | [] | [
"apply",
"auto",
"close",
"exists",
"open",
"shows"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
"\<exists>r. A155 r = x" | apply (tactic \<open>simp_tac
(put_simpset HOL_basic_ss \<^context> |> Simplifier.add_proc (Record.ex_sel_eq_simproc)) 1\<close>)
done
print_record many_A
print_record many_B | lemma | exists | Benchmarks.Record_Benchmark | src/Benchmarks/Record_Benchmark/Record_Benchmark.thy | [] | [
"apply",
"close",
"exists",
"many_A",
"many_B",
"open"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | |
prog = "term"
default_sort prog | class | prog | CCL | src/CCL/CCL.thy | [] | [
"term"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
"fun" :: (prog, prog) prog ..
typedecl i | instance | fun | CCL | src/CCL/CCL.thy | [] | [
"fun",
"prog"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
i :: prog .. | instance | i | CCL | src/CCL/CCL.thy | [] | [
"prog"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
(*** Evaluation Judgement ***)
Eval :: "[i,i]\<Rightarrow>prop" (infixl \<open>\<longlongrightarrow>\<close> 20)
(*** Bisimulations for pre-order and equality ***)
po :: "['a,'a]\<Rightarrow>o" (infixl \<open>[=\<close> 50)
(*** Term Formers ***)
true :: ... | consts | Eval | CCL | src/CCL/CCL.thy | [] | [
"apply",
"bot",
"case",
"close",
"false",
"infixl",
"lam",
"lambda",
"open",
"pair",
"po",
"true"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
where
trueV: "true \<longlongrightarrow> true" and
falseV: "false \<longlongrightarrow> false" and
pairV: "<a,b> \<longlongrightarrow> <a,b>" and
lamV: "\<And>b. lam x. b(x) \<longlongrightarrow> lam x. b(x)" and
caseVtrue: "\<lbrakk>t \<longlongrightarrow> true; d \<longlongrightar... | axiomatization | where | CCL | src/CCL/CCL.thy | [] | [
"And",
"and",
"case",
"false",
"lam",
"true"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
where
canonical: "\<lbrakk>t \<longlongrightarrow> c; c==true \<Longrightarrow> u\<longlongrightarrow>v;
c==false \<Longrightarrow> u\<longlongrightarrow>v;
\<And>a b. c==<a,b> \<Longrightarrow> u\<longlongrightarrow>v;
\<And>f. c==lam x. f(x) \<Lon... | axiomatization | where | CCL | src/CCL/CCL.thy | [] | [
"And",
"false",
"lam",
"true"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
where
substitute: "\<lbrakk>a==a'; t(a)\<longlongrightarrow>c(a)\<rbrakk> \<Longrightarrow> t(a')\<longlongrightarrow>c(a')" | axiomatization | where | CCL | src/CCL/CCL.thy | [] | [
"a'"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
where
bot_def: "bot == (lam x. x`x)`(lam x. x`x)" and
apply_def: "f ` t == case(f, bot, bot, \<lambda>x y. bot, \<lambda>u. u(t))" | axiomatization | where | CCL | src/CCL/CCL.thy | [] | [
"and",
"bot",
"case",
"lam",
"lambda"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 | ||
"fix" :: "(i\<Rightarrow>i)\<Rightarrow>i" | where "fix(f) == (lam x. f(x`x))`(lam x. f(x`x))" | definition | fix | CCL | src/CCL/CCL.thy | [] | [
"lam",
"where"
] | https://github.com/isabelle-prover/mirror-isabelle | acb41fc3ab1760eee1b9ed0edd0df566941bf513 |
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