mirror of
https://github.com/GaloisInc/cryptol.git
synced 2024-11-28 17:33:13 +03:00
7e34c25e4d
"x /^ y" is x/y rounded up, i.e. the least n such that x <= y*n. "x %^ y" is the least k such that x+k is a multiple of y. For comparison, "x / y" is x/y rounded down, i.e. the greatest n such that x >= y*n. "x % y" is the least k such that x-k is a multiple of y. The new syntax is much more suggestive of the relation to "/" and "%".
306 lines
7.5 KiB
Plaintext
306 lines
7.5 KiB
Plaintext
; ------------------------------------------------------------------------------
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; Basic datatypes
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(declare-datatypes ()
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( (InfNat (mk-infnat (value Int) (isFin Bool) (isErr Bool)))
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)
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)
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(declare-datatypes ()
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( (MaybeBool (mk-mb (prop Bool) (isErrorProp Bool)))
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)
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)
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(define-fun cryBool ((x Bool)) MaybeBool
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(mk-mb x false)
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)
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(define-fun cryErrProp () MaybeBool
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(mk-mb false true)
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)
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(define-fun cryInf () InfNat
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(mk-infnat 0 false false)
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)
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(define-fun cryNat ((x Int)) InfNat
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(mk-infnat x true false)
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)
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(define-fun cryErr () InfNat
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(mk-infnat 0 false true)
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)
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; ------------------------------------------------------------------------------
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; Cryptol version of logic
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(define-fun cryEq ((x InfNat) (y InfNat)) MaybeBool
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(ite (or (isErr x) (isErr y)) cryErrProp (cryBool
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(ite (isFin x)
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(ite (isFin y) (= (value x) (value y)) false)
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(not (isFin y))
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)))
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)
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(define-fun cryFin ((x InfNat)) MaybeBool
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(ite (isErr x) cryErrProp (cryBool
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(isFin x)))
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)
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(define-fun cryGeq ((x InfNat) (y InfNat)) MaybeBool
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(ite (or (isErr x) (isErr y)) cryErrProp (cryBool
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(ite (isFin x)
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(ite (isFin y) (>= (value x) (value y)) false)
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true
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)))
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)
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(define-fun cryAnd ((x MaybeBool) (y MaybeBool)) MaybeBool
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(ite (or (isErrorProp x) (isErrorProp y)) cryErrProp
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(cryBool (and (prop x) (prop y)))
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)
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)
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(define-fun cryTrue () MaybeBool
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(cryBool true)
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)
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; ------------------------------------------------------------------------------
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; Basic Cryptol assume/assert
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(define-fun cryVar ((x InfNat)) Bool
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(and (not (isErr x)) (>= (value x) 0))
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)
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(define-fun cryAssume ((x MaybeBool)) Bool
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(ite (isErrorProp x) true (prop x))
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)
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(declare-fun cryUnknown () Bool)
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(define-fun cryProve ((x MaybeBool)) Bool
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(ite (isErrorProp x) cryUnknown (not (prop x)))
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)
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; ------------------------------------------------------------------------------
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; Arithmetic
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(define-fun cryAdd ((x InfNat) (y InfNat)) InfNat
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(ite (or (isErr x) (isErr y)) cryErr
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(ite (isFin x)
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(ite (isFin y) (cryNat (+ (value x) (value y))) cryInf)
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cryInf
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))
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)
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(define-fun crySub ((x InfNat) (y InfNat)) InfNat
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(ite (or (isErr x) (isErr y) (not (isFin y))) cryErr
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(ite (isFin x)
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(ite (>= (value x) (value y)) (cryNat (- (value x) (value y))) cryErr)
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cryInf
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))
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)
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(define-fun cryMul ((x InfNat) (y InfNat)) InfNat
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(ite (or (isErr x) (isErr y)) cryErr
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(ite (isFin x)
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(ite (isFin y) (cryNat (* (value x) (value y)))
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(ite (= (value x) 0) (cryNat 0) cryInf))
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(ite (and (isFin y) (= (value y) 0)) (cryNat 0) cryInf)
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))
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)
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(define-fun cryDiv ((x InfNat) (y InfNat)) InfNat
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(ite (or (isErr x) (isErr y) (not (isFin x))) cryErr
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(ite (isFin y)
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(ite (= (value y) 0) cryErr (cryNat (div (value x) (value y))))
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(cryNat 0)
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))
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)
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(define-fun cryMod ((x InfNat) (y InfNat)) InfNat
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(ite (or (isErr x) (isErr y) (not (isFin x))) cryErr
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(ite (isFin y)
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(ite (= (value y) 0) cryErr (cryNat (mod (value x) (value y))))
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x
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))
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)
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(define-fun cryMin ((x InfNat) (y InfNat)) InfNat
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(ite (or (isErr x) (isErr y)) cryErr
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(ite (isFin x)
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(ite (isFin y)
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(ite (<= (value x) (value y)) x y)
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x)
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y
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))
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)
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(define-fun cryMax ((x InfNat) (y InfNat)) InfNat
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(ite (or (isErr x) (isErr y)) cryErr
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(ite (isFin x)
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(ite (isFin y)
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(ite (<= (value x) (value y)) y x)
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y)
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x
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))
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)
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(declare-fun cryWidthUnknown (Int) Int)
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; Some axioms about cryWidthUnknown
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(assert (forall ((x Int)) (> (cryWidthUnknown x) 64)))
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(assert (forall ((x Int)) (or (> x (cryWidthUnknown x))
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(< x 18446744073709551616))))
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(assert (forall ((x Int) (y Int))
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(=> (and (>= x y) (> y 64))
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(>= (cryWidthUnknown x) (cryWidthUnknown y)))))
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(define-fun cryWidthTable ((x Int)) Int
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(ite (< x 1) 0
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(ite (< x 2) 1
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(ite (< x 4) 2
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(ite (< x 8) 3
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(ite (< x 16) 4
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(ite (< x 32) 5
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(ite (< x 64) 6
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(ite (< x 128) 7
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(ite (< x 256) 8
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(ite (< x 512) 9
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(ite (< x 1024) 10
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(ite (< x 2048) 11
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(ite (< x 4096) 12
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(ite (< x 8192) 13
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(ite (< x 16384) 14
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(ite (< x 32768) 15
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(ite (< x 65536) 16
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(ite (< x 131072) 17
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(ite (< x 262144) 18
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(ite (< x 524288) 19
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(ite (< x 1048576) 20
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(ite (< x 2097152) 21
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(ite (< x 4194304) 22
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(ite (< x 8388608) 23
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(ite (< x 16777216) 24
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(ite (< x 33554432) 25
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(ite (< x 67108864) 26
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(ite (< x 134217728) 27
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(ite (< x 268435456) 28
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(ite (< x 536870912) 29
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(ite (< x 1073741824) 30
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(ite (< x 2147483648) 31
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(ite (< x 4294967296) 32
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(ite (< x 8589934592) 33
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(ite (< x 17179869184) 34
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(ite (< x 34359738368) 35
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(ite (< x 68719476736) 36
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(ite (< x 137438953472) 37
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(ite (< x 274877906944) 38
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(ite (< x 549755813888) 39
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(ite (< x 1099511627776) 40
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(ite (< x 2199023255552) 41
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(ite (< x 4398046511104) 42
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(ite (< x 8796093022208) 43
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(ite (< x 17592186044416) 44
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(ite (< x 35184372088832) 45
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(ite (< x 70368744177664) 46
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(ite (< x 140737488355328) 47
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(ite (< x 281474976710656) 48
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(ite (< x 562949953421312) 49
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(ite (< x 1125899906842624) 50
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(ite (< x 2251799813685248) 51
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(ite (< x 4503599627370496) 52
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(ite (< x 9007199254740992) 53
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(ite (< x 18014398509481984) 54
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(ite (< x 36028797018963968) 55
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(ite (< x 72057594037927936) 56
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(ite (< x 144115188075855872) 57
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(ite (< x 288230376151711744) 58
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(ite (< x 576460752303423488) 59
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(ite (< x 1152921504606846976) 60
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(ite (< x 2305843009213693952) 61
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(ite (< x 4611686018427387904) 62
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(ite (< x 9223372036854775808) 63
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(ite (< x 18446744073709551616) 64
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(cryWidthUnknown x))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
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)
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(define-fun cryWidth ((x InfNat)) InfNat
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(ite (isErr x) cryErr
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(ite (isFin x) (cryNat (cryWidthTable (value x)))
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cryInf
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))
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)
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(declare-fun cryExpUnknown (Int Int) Int)
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(define-fun cryExpTable ((x Int) (y Int)) Int
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(ite (= y 0) 1
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(ite (= y 1) x
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(ite (= x 0) 0
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(cryExpUnknown x y))))
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)
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(define-fun cryExp ((x InfNat) (y InfNat)) InfNat
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(ite (or (isErr x) (isErr y)) cryErr
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(ite (isFin x)
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(ite (isFin y)
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(cryNat (cryExpTable (value x) (value y)))
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(ite (< (value x) 2) x cryInf))
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(ite (isFin y)
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(ite (= (value y) 0) (cryNat 1) cryInf)
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cryInf)
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))
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)
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(define-fun cryCeilDiv ((x InfNat) (y InfNat)) InfNat
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(ite (or (isErr x) (isErr y) (not (isFin x)) (not (isFin y))) cryErr
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(ite (= (value y) 0) cryErr (cryNat (- (div (- (value x)) (value y)))))
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)
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)
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(define-fun cryCeilMod ((x InfNat) (y InfNat)) InfNat
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(ite (or (isErr x) (isErr y) (not (isFin x)) (not (isFin y))) cryErr
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(ite (= (value y) 0) cryErr (cryNat (mod (- (value x)) (value y))))
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)
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)
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(define-fun cryLenFromThenTo ((x InfNat) (y InfNat) (z InfNat)) InfNat
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(ite (or (isErr x) (not (isFin x))
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(isErr y) (not (isFin y))
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(isErr z) (not (isFin z))
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(= (value x) (value y))) cryErr (cryNat
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(ite (> (value x) (value y))
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(ite (> (value z) (value x)) 0 (+ (div (- (value x) (value z))
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(- (value x) (value y))) 1))
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(ite (< (value z) (value x)) 0 (+ (div (- (value z) (value x))
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(- (value y) (value x))) 1))
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)))
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)
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(define-fun cryLenFromThen ((x InfNat) (y InfNat) (z InfNat)) InfNat
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(ite (or (isErr x) (not (isFin x))
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(isErr y) (not (isFin y))
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(isErr z) (not (isFin z))
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(= (value x) (value y))) cryErr
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(ite (< (value y) (value x)) (cryLenFromThenTo x y (cryNat 0))
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(cryLenFromThenTo x y (cryNat (- (cryExpTable 2 (value z)) 1))))
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)
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)
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