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E : [K] -> [128] -> [128]
function
E
examples.param_modules.Common
examples/param_modules/Common/GCM.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
encrypt : {n} (2^^39 - 256 >= n) => { key : [K], iv : [IV], aad : [AAD], pt : [n] } -> { ct : [n], tag : [T] }
encrypt input = { ct = C, tag = T } where (C,T) = enc_dec input.key input.iv input.aad input.pt
function
encrypt
examples.param_modules.Common
examples/param_modules/Common/GCM.cry
[]
[ ">=", "enc_dec" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
decrypt : {n} (2^^39 - 256 >= n) => { key : [K], iv : [IV], aad : [AAD], ct : [n], tag : [T] } -> { valid : Bool, pt : [n] }
decrypt input = if input.tag == T then { valid = True, pt = P } else { valid = False, pt = 0 } where (P,T) = enc_dec input.key input.iv input.aad input.ct /** The basic functionality between encryption and decryption. In the case of decryption, the plain text is only valid if the ...
function
decrypt
examples.param_modules.Common
examples/param_modules/Common/GCM.cry
[]
[ "==", ">=", "enc_dec" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
enc_dec : {n} ((2^^39 - 256) >= n) => [K] -> [IV] -> [AAD] -> [n] -> ([n], [T])
enc_dec K IV A P = (C,T) where H = E K 0 Y0 = ifWidth`{96} IV (\IV96 -> IV96 # 1) (GHASH H [] IV) Ys = [Y0] # [ y+1 | y <- Ys ] Cs = [ p ^ E K y | p <- blockify P | y <- drop`{1} Ys ] C = unblockify Cs T = take (GHASH H A C ^ E K Y0) /** Section 2.3, equation (2) */
function
enc_dec
examples.param_modules.Common
examples/param_modules/Common/GCM.cry
[]
[ ">=", "GHASH", "IV", "blockify", "take", "unblockify" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
GHASH : {C,A} (64 >= width C, 64 >= width A) => [128] -> [A] -> [C] -> [128]
GHASH H A C = step (XS ! 0) (wa # wc) where wa = `A : [64] wc = `C : [64] XS = [0] # [ step X' B | X' <- XS | B <- blockify A # blockify C ] step x b = mult (x ^ b) H /** Section 2.5, multiplication in GF(2^^128) This is simple polynomial multipliation and reduction in Cryptol. Somewhat oddly, when thin...
function
GHASH
examples.param_modules.Common
examples/param_modules/Common/GCM.cry
[]
[ ">=", "blockify", "mult", "width" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
mult : [128] -> [128] -> [128]
mult X Y = reverse (pmod (pmult (reverse X) (reverse Y)) irred) where irred = <| 1 + x + x^^2 + x^^7 + x^^128 |> /** Create blocks as described in the spec, first paragraph of Section 2.3. Basically we split into 128-bit chunk and pad the last one with 0. */
function
mult
examples.param_modules.Common
examples/param_modules/Common/GCM.cry
[]
[ "pmod", "pmult", "reverse" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
blockify : {n} (fin n) => [n] -> [n /^ 128][128]
blockify msg = split (msg # 0) /** Join back the blocks, dropping any additional padding. */
function
blockify
examples.param_modules.Common
examples/param_modules/Common/GCM.cry
[]
[ "fin", "split" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
unblockify : {n} (fin n) => [n /^ 128][128] -> [n]
unblockify ms = take (join ms)
function
unblockify
examples.param_modules.Common
examples/param_modules/Common/GCM.cry
[]
[ "fin", "join", "take" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
ifWidth : {w,n,a} (fin n, fin w) => [n] -> ([w] -> a) -> a -> a
ifWidth thing yep nope = if `w == (`n : [max (width w) (width n)]) then yep (take (thing # (zero : [inf]))) else nope
function
ifWidth
examples.param_modules.Common
examples/param_modules/Common/GCM.cry
[]
[ "==", "fin", "take", "width", "zero" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
w : #
type
w
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
(fin w, w >= 1) /** The number of iterations in the hash computation (i.e. the number of words in K) */
type constraint
fin
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[ ">=", "fin" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
j : #
type
j
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
(fin j, j >= 17)
type constraint
fin
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[ ">=", "fin" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
block_size
= 16 * w
type
block_size
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
num_blocks L
= (L+1+2*w) /^ block_size
type
num_blocks
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[ "block_size" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
padded_size L
= num_blocks L * block_size /** (4.1) (w==32), (4.2) (w==32), (4.8) (w==64) */
type
padded_size
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[ "block_size", "num_blocks" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
H0 : [8][w]
function
H0
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
K : [j][w] /* FIPS 180-4 defines lowercase and uppercase (respective to the Greek alphabet) sigma functions for SHA-256 and SHA-512. (4.4)-(4.7) SHA-224, SHA-256 (w==32) (4.10)-(4.13) SHA-384, SHA-512, SHA-512/224, SHA-512/256 (w==64) */
function
K
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
SIGMA_0 : [w] -> [w]
function
SIGMA_0
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
SIGMA_1 : [w] -> [w]
function
SIGMA_1
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
sigma_0 : [w] -> [w]
function
sigma_0
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
sigma_1 : [w] -> [w]
function
sigma_1
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
sha : {L} (2 * w >= width L) => [L] -> [8 * w]
sha M = join (SHA_2_Common' [ split x | x <- parse`{num_blocks L} (pad`{L} M) ])
function
sha
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[ ">=", "SHA_2_Common'", "join", "num_blocks", "split", "width" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
Ch : [w] -> [w] -> [w] -> [w]
Ch x y z = (x && y) ^ (~x && z) /** (4.1) (w==32), (4.3) (w==32), (4.9) (w==64) */
function
Ch
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[ "&&" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
Maj : [w] -> [w] -> [w] -> [w]
Maj x y z = (x && y) ^ (x && z) ^ (y && z) /** 5.1 Padding the Message 5.1.1 SHA-1, SHA-224 and SHA-256 (w==32) 5.1.2 SHA-384, SHA-512, SHA-512/224 and SHA-512/256 (w==64) The constraint ensure that the message size, `L`, fits within a (2 * w)-bit word (consistent w/ Figure 1) */
function
Maj
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[ "&&" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
pad : {L} (2 * w >= width L) => [L] -> [padded_size L]
pad M = M # 0b1 # zero # (`L : [2*w]) /** 5.2 Parsing the Message 5.2.1 SHA-1, SHA-224 and SHA-256 (w==32) 5.2.2 SHA-384, SHA-512, SHA-512/224 and SHA-512/256 (w==64) */
function
pad
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[ ">=", "width", "zero" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
parse : {m} [m * block_size] -> [m][block_size]
parse = split /** SHA-256 and SHA-512 (and their respective derivatives) use a similar message schedule that can be expressed in the same way relative to their respective sigma functions. 6.2.2 SHA-256 Hash Computation (w==32, j=64) 6.4.2 SHA-512 Hash Computation (w==64, j=80) */
function
parse
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[ "split" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
messageSchedule_Common : [16][w] -> [j][w]
messageSchedule_Common Mi = take W where W : [inf][_] W = Mi # [ w1 + sigma_0 w2 + w3 + sigma_1 w4 | w1 <- W | w2 <- drop`{1} W | w3 <- drop`{9} W | w4 <- drop`{14} W ] /** Amazon S2N's SHA-256 specification includes a compression routin...
function
messageSchedule_Common
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[ "sigma_0", "sigma_1", "take" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
compress_Common : [8][w] -> [j][w] -> [8][w]
compress_Common H W = // XXX: This whole definitions looks like it might be simplifiable. [ (as ! 0) + (H @ 0), (bs ! 0) + (H @ 1), (cs ! 0) + (H @ 2), (ds ! 0) + (H @ 3), (es ! 0) + (H @ 4), (fs ! 0) + (H @ 5), (gs ! 0) + (H @ 6), (hs ! 0) + (H @ 7) ] where ...
function
compress_Common
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[ "Ch", "Maj", "SIGMA_0", "SIGMA_1", "t1", "t2" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
processBlock_Common : [8][w] -> [16][w] -> [8][w]
processBlock_Common H Mi = compress_Common H (messageSchedule_Common Mi)
function
processBlock_Common
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[ "compress_Common", "messageSchedule_Common" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
SHA_2_Common' : {L} (fin L) => [L][16][w] -> [8][w]
SHA_2_Common' blocks = hash ! 0 where hash = [H0] # [ processBlock_Common h b | h <- hash | b <- blocks]
function
SHA_2_Common'
examples.param_modules.Common
examples/param_modules/Common/SHA.cry
[]
[ "fin", "processBlock_Common" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
AES128
= SB::AES128 /** * Key schedule parameter setting for AES-192 */
type
AES128
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
AES192
= SB::AES192 /** * Key schedule parameter setting for AES-256 */
type
AES192
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
AES256
= SB::AES256 /** * Element of an AES key schedule for use in a particular round */
type
AES256
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
AESRoundKey
= SB::AESRoundKey /** * Expanded encryption key schedule for AES */
type
AESRoundKey
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
AESEncryptKeySchedule k
= SB::AESEncryptKeySchedule k /** * Expanded decryption key schedule for AES */
type
AESEncryptKeySchedule
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
AESDecryptKeySchedule k
= SB::AESDecryptKeySchedule k /** * Encryption key expansion for AES-128. * See FIPS 197, section 5.2. */
type
AESDecryptKeySchedule
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
aes128EncryptSchedule : [128] -> AESEncryptKeySchedule AES128
aes128EncryptSchedule = if aesniSupported then \key -> aesniExpandEncrypt128 (split key) else SB::aes128EncryptSchedule /** * Decryption key expansion for AES-128, for use in the "equivalent inverse cypher". * See FIPS 197, sections 5.2 and 5.3.5. */
function
aes128EncryptSchedule
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[ "AES128", "AESEncryptKeySchedule", "split" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
aes128DecryptSchedule : [128] -> AESDecryptKeySchedule AES128
aes128DecryptSchedule = if aesniSupported then \key -> aesniExpandDecrypt128 (split key) else SB::aes128DecryptSchedule /** * Encryption and decryption key schedules for AES-128. * If you will need both schedules, it is slightly more efficient * to call this function than to compute the two schedules sepa...
function
aes128DecryptSchedule
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[ "AES128", "AESDecryptKeySchedule", "split" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
aes128Schedules : [128] -> (AESEncryptKeySchedule AES128, AESDecryptKeySchedule AES128)
aes128Schedules = if aesniSupported then \key -> aesniExpandEncryptDecrypt128 (split key) else SB::aes128Schedules /** * Encryption key expansion for AES-192. * See FIPS 197, section 5.2. */
function
aes128Schedules
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[ "AES128", "AESDecryptKeySchedule", "AESEncryptKeySchedule", "split" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
aes192EncryptSchedule : [192] -> AESEncryptKeySchedule AES192
aes192EncryptSchedule = if aesniSupported then \key -> aesniExpandEncrypt192 (split key) else SB::aes192EncryptSchedule /** * Decryption key expansion for AES-192, for use in the "equivalent inverse cypher". * See FIPS 197, sections 5.2 and 5.3.5. */
function
aes192EncryptSchedule
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[ "AES192", "AESEncryptKeySchedule", "split" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
aes192DecryptSchedule : [192] -> AESDecryptKeySchedule AES192
aes192DecryptSchedule = if aesniSupported then \key -> aesniExpandDecrypt192 (split key) else SB::aes192DecryptSchedule /** * Encryption and decryption key schedules for AES-192. * If you will need both schedules, it is slightly more efficient * to call this function than to compute the two schedules sepa...
function
aes192DecryptSchedule
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[ "AES192", "AESDecryptKeySchedule", "split" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
aes192Schedules : [192] -> (AESEncryptKeySchedule AES192, AESDecryptKeySchedule AES192)
aes192Schedules = if aesniSupported then \key -> aesniExpandEncryptDecrypt192 (split key) else SB::aes192Schedules /** * Encryption key expansion for AES-256. * See FIPS 197, section 5.2 */
function
aes192Schedules
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[ "AES192", "AESDecryptKeySchedule", "AESEncryptKeySchedule", "split" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
aes256EncryptSchedule : [256] -> AESEncryptKeySchedule AES256
aes256EncryptSchedule = if aesniSupported then \key -> aesniExpandEncrypt256 (split key) else SB::aes256EncryptSchedule /** * Decryption key expansion for AES-256, for use in the "equivalent inverse cypher". * See FIPS 197, sections 5.2 and 5.3.5. */
function
aes256EncryptSchedule
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[ "AES256", "AESEncryptKeySchedule", "split" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
aes256DecryptSchedule : [256] -> AESDecryptKeySchedule AES256
aes256DecryptSchedule = if aesniSupported then \key -> aesniExpandDecrypt256 (split key) else SB::aes256DecryptSchedule /** * Encryption and decryption key schedules for AES-256. * If you will need both schedules, it is slightly more efficient * to call this function than to compute the two schedules sepa...
function
aes256DecryptSchedule
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[ "AES256", "AESDecryptKeySchedule", "split" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
aes256Schedules : [256] -> (AESEncryptKeySchedule AES256, AESDecryptKeySchedule AES256)
aes256Schedules = if aesniSupported then \key -> aesniExpandEncryptDecrypt256 (split key) else SB::aes256Schedules /** * AES block encryption algorithm. * See FIPS 197, section 5.1. */
function
aes256Schedules
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[ "AES256", "AESDecryptKeySchedule", "AESEncryptKeySchedule", "split" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
aesEncryptBlock : {k} (fin k) => AESEncryptKeySchedule k -> [128] -> [128]
aesEncryptBlock = if aesniSupported then \schedule plaintext -> join (aesniEncryptBlock schedule (split plaintext)) else SB::aesEncryptBlock /** * AES block decryption algorithm, via the "equivalent inverse cypher". * See FIPS 197, section 5.3.5. */
function
aesEncryptBlock
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[ "AESEncryptKeySchedule", "fin", "join", "split" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
aesDecryptBlock : {k} (fin k) => AESDecryptKeySchedule k -> [128] -> [128]
aesDecryptBlock = if aesniSupported then \schedule ciphertext -> join (aesniDecryptBlock schedule (split ciphertext)) else SB::aesDecryptBlock
function
aesDecryptBlock
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[ "AESDecryptKeySchedule", "fin", "join", "split" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
sha224
= SB::sha224 /** * The SHA-256 secure hash algorithm. See FIPS 180-4, section 6.2.2. */
function
sha224
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
sha256
= SB::sha256 /** * The SHA-384 secure hash algorithm. See FIPS 180-4, section 6.5. */
function
sha256
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
sha384
= SB::sha384 /** * The SHA-512 secure hash algorithm. See FIPS 180-4, section 6.4. */
function
sha384
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
sha512
= SB::sha512
function
sha512
examples.SuiteB_FFI
examples/SuiteB_FFI/SuiteB_FFI.cry
[ "SuiteB" ]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
Array : * -> * -> *
primitive type
Array
lib
lib/Array.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
arrayConstant : {a, b} b -> (Array a b)
primitive
arrayConstant
lib
lib/Array.cry
[]
[ "Array" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
arrayLookup : {a, b} (Array a b) -> a -> b
primitive
arrayLookup
lib
lib/Array.cry
[]
[ "Array" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
arrayUpdate : {a, b} (Array a b) -> a -> b -> (Array a b)
primitive
arrayUpdate
lib
lib/Array.cry
[]
[ "Array" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
arrayEq : {n, a} (Array [n] a) -> (Array [n] a) -> Bool /** * Copy elements from the source array to the destination array. * * 'arrayCopy dest_arr dest_idx src_arr src_idx len' copies the * elements from 'src_arr' at indices '[src_idx ..< (src_idx + len)]' into * 'dest_arr' at indices '[dest_idx ..< (dest_idx + ...
primitive
arrayEq
lib
lib/Array.cry
[]
[ "Array", "Bool" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
arrayCopy : {n, a} (fin n) => (Array [n] a) -> [n] -> (Array [n] a) -> [n] -> [n] -> (Array [n] a) /** * Set elements of the given array. * * 'arraySet' arr idx val len' sets the elements of 'arr' at indices * '[idx ..< (idx + len)]' to 'val'. * * The result is undefined if 'idx + len' wraps around. */
primitive
arrayCopy
lib
lib/Array.cry
[]
[ "Array", "fin" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
arraySet : {n, a} (fin n) => (Array [n] a) -> [n] -> a -> [n] -> (Array [n] a) /** * Check whether the lhs array and rhs array are equal at a range of * indices. * * 'arrayRangeEqual sym lhs_arr lhs_idx rhs_arr rhs_idx len' checks whether * the elements of 'lhs_arr' at indices '[lhs_idx ..< (lhs_idx + len)]' and ...
primitive
arraySet
lib
lib/Array.cry
[]
[ "Array", "fin" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
arrayRangeEqual : {n, a} (fin n) => (Array [n] a) -> [n] -> (Array [n] a) -> [n] -> [n] -> Bool
primitive
arrayRangeEqual
lib
lib/Array.cry
[]
[ "Array", "Bool", "fin" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
arrayRangeLookup : {a, b, n} (Integral a, fin n, LiteralLessThan n a) => (Array a b) -> a -> [n]b
arrayRangeLookup arr idx = res where res @ i = arrayLookup arr (idx + i)
function
arrayRangeLookup
lib
lib/Array.cry
[]
[ "Array", "Integral", "LiteralLessThan", "arrayLookup", "fin" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
arrayRangeUpdate : {a, b, n} (Integral a, fin n, LiteralLessThan n a) => (Array a b) -> a -> [n]b -> (Array a b)
arrayRangeUpdate arr idx vals = arrs ! 0 where arrs = [arr] # [ arrayUpdate acc (idx + i) val | acc <- arrs | i <- [0 ..< n] | val <- vals ]
function
arrayRangeUpdate
lib
lib/Array.cry
[]
[ "Array", "Integral", "LiteralLessThan", "arrayUpdate", "fin" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
Bit : * /** The type of unbounded integers. */
primitive type
Bit
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
Integer : * /** * 'Z n' is the type of integers, modulo 'n'. * * The values of 'Z n' may be thought of as equivalence * classes of integers according to the equivalence * 'x ~ y' iff 'n' divides 'x - y'. 'Z n' naturally * forms a ring, but does not support integral division * or indexing. * * However, you ma...
primitive type
Integer
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
n : #} (fin n, n >= 1) => Z n : * /** * 'Rational' is the type of rational numbers. * Rational numbers form a Field (and thus a Ring). * * The 'ratio' operation may be used to directly create * rational values from as a ratio of integers, or * the 'fromInteger' method and the field operations * can be used. */
primitive type
n
lib
lib/Cryptol.cry
[]
[ ">=", "fin" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
Rational : *
primitive type
Rational
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
Bool
= Bit
type
Bool
lib
lib/Cryptol.cry
[]
[ "Bit" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
Word n
= [n]
type
Word
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
Char
= [8]
type
Char
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
String n
= [n]Char // Numeric operators and constraints ---------------------------------------------- /** A numeric type representing infinity. */
type
String
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
inf : # /** Assert that two numeric types are equal. */
primitive type
inf
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
(==) : # -> # -> Prop /** Assert that two numeric types are different. */
primitive type
==
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
(!=) : # -> # -> Prop /** Assert that the first numeric type is larger than, or equal to the second.*/
primitive type
!=
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
(>=) : # -> # -> Prop /** Assert that a numeric type is a proper natural number (not 'inf'). */
primitive type
>=
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
fin : # -> Prop /** Assert that a numeric type is a prime number. */
primitive type
fin
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
prime : # -> Prop /** Add numeric types. */
primitive type
prime
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
(+) : # -> # -> # /** Multiply numeric types. */
primitive type
+
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
(*) : # -> # -> # /** Subtract numeric types. */
primitive type
*
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
m : #, n : # } (fin n, m >= n) => m - n : # /** Divide numeric types, rounding down. */
primitive type
m
lib
lib/Cryptol.cry
[]
[ ">=", "fin" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
m : #, n : # } (fin m, n >= 1) => m / n : # /** Remainder of numeric type division. */
primitive type
m
lib
lib/Cryptol.cry
[]
[ ">=", "fin" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
m : #, n : # } (fin m, n >= 1) => m % n : # /** Exponentiate numeric types. */
primitive type
m
lib
lib/Cryptol.cry
[]
[ ">=", "fin" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
(^^) : # -> # -> # /** The number of bits required to represent the value of a numeric type. */
primitive type
^^
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
width : # -> # /** * The ceiling of the base-2 logarithm of a numeric type. * We define 'lg2 n = width (n - 1)' for nonzero n, and 'lg2 0 = 0'. */
primitive type
width
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
lg2 n
= width (max n 1 - 1) /** The smaller of two numeric types. */
type
lg2
lib
lib/Cryptol.cry
[]
[ "max", "width" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
min : # -> # -> # /** The larger of two numeric types. */
primitive type
min
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
max : # -> # -> # /** Divide numeric types, rounding up. */
primitive type
max
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
m : #, n : # } (fin n, n >= 1) => m /^ n : # /** How much we need to add to make a proper multiple of the second argument. */
primitive type
m
lib
lib/Cryptol.cry
[]
[ ">=", "fin" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
m : #, n : # } (fin n, n >= 1) => m %^ n : # /** The length of an enumeration. */
primitive type
m
lib
lib/Cryptol.cry
[]
[ ">=", "fin" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
start : #, next : #, last : # } (fin start, fin next, fin last, start != next) => lengthFromThenTo start next last : # /** * Assert that the first numeric type is less than or equal to the second. */
primitive type
start
lib
lib/Cryptol.cry
[]
[ "!=", "fin", "last" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
i <= j = (j >= i) /** * Assert that the first numeric type is greater than the second. */
type constraint
i
lib
lib/Cryptol.cry
[]
[ "<=", ">=" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
i > j = i >= j + 1 /** * Assert that the first numeric type is less than the second. */
type constraint
i
lib
lib/Cryptol.cry
[]
[ ">=" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
i < j = j >= i + 1 // The Literal class ---------------------------------------------------- /** 'Literal n a' asserts that type 'a' contains the number 'n'. */
type constraint
i
lib
lib/Cryptol.cry
[]
[ ">=" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
Literal : # -> * -> Prop /** * 'LiteralLessThan n a' asserts that the type 'a' contains all the * natural numbers strictly below 'n'. Note that we may have 'n = inf', * in which case the type 'a' must be unbounded. */
primitive type
Literal
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
LiteralLessThan : # -> * -> Prop /** * The value corresponding to a numeric type. */
primitive type
LiteralLessThan
lib
lib/Cryptol.cry
[]
[]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
number : {val, rep} Literal val rep => rep /** * An alternative name for 'number', present for backward compatibility. */
primitive
number
lib
lib/Cryptol.cry
[]
[ "Literal" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
fromTo : {first, last, a} (fin last, last >= first, Literal last a) => [1 + (last - first)]a /** * A possibly infinite sequence counting up from 'first' up to (but not including) 'bound'. * * '[ x ..< y ]' is syntactic sugar for 'fromToLessThan`{first=x,bound=y}'. * * Note that if 'first' = 'bound' then the s...
primitive
fromTo
lib
lib/Cryptol.cry
[]
[ ">=", "Literal", "fin", "first", "last" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
fromToLessThan : {first, bound, a} (fin first, bound >= first, LiteralLessThan bound a) => [bound - first]a /** * A finite sequence counting up from 'first' to 'last' by 'stride'. * Note that 'last' will only be an element of the enumeration if * 'stride' divides 'last - first' evenly. * * '[x .. y by n]' is ...
primitive
fromToLessThan
lib
lib/Cryptol.cry
[]
[ ">=", "LiteralLessThan", "fin" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
fromToBy : {first, last, stride, a} (fin last, fin stride, stride >= 1, last >= first, Literal last a) => [1 + (last - first)/stride]a /** * A finite sequence counting from 'first' up to (but not including) 'bound' * by 'stride'. Note that if 'first = bound' then the sequence will * be empty. If 'bound = inf'...
primitive
fromToBy
lib
lib/Cryptol.cry
[]
[ ">=", "Literal", "fin", "first", "last" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
fromToByLessThan : {first, bound, stride, a} (fin first, fin stride, stride >= 1, bound >= first, LiteralLessThan bound a) => [(bound - first)/^stride]a /** * A finite sequence counting from 'first' down to 'last' by 'stride'. * Note that 'last' will only be an element of the enumeration if * 'stride' divides '...
primitive
fromToByLessThan
lib
lib/Cryptol.cry
[]
[ ">=", "LiteralLessThan", "fin", "first" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb
fromToDownBy : {first, last, stride, a} (fin first, fin stride, stride >= 1, first >= last, Literal first a) => [1 + (first - last)/stride]a /** * A finite sequence counting from 'first' down to (but not including) * 'bound' by 'stride'. * * '[x ..> y down by n]' is syntactic sugar for * 'fromToDownByGreaterT...
primitive
fromToDownBy
lib
lib/Cryptol.cry
[]
[ ">=", "Literal", "fin", "first", "last" ]
https://github.com/GaloisInc/cryptol
a50cac6eb2c30a79503814f423f375f9476aaceb