mirror of
https://github.com/GaloisInc/cryptol.git
synced 2024-11-29 10:13:29 +03:00
121 lines
4.7 KiB
Plaintext
121 lines
4.7 KiB
Plaintext
/*
|
|
* Copyright (c) 2013-2014 Galois, Inc.
|
|
* Distributed under the terms of the BSD3 license (see LICENSE file)
|
|
*/
|
|
|
|
module FoxChickenCorn where
|
|
|
|
type OneBank = [4]
|
|
type BankState =
|
|
{left : OneBank
|
|
,right: OneBank
|
|
}
|
|
|
|
startState = { left = farmer || chicken || corn || fox, right = 0x0}
|
|
doneState = { left = 0x0, right = farmer || chicken || corn || fox}
|
|
|
|
farmer = 0x1
|
|
chicken = 0x2
|
|
corn = 0x4
|
|
fox = 0x8
|
|
|
|
// To see this work, try:
|
|
// :sat solutionInNmoves : [6]BankState -> Bit
|
|
|
|
solutionInNmoves : {n} (fin n) => [n] BankState -> Bit
|
|
property solutionInNmoves states = validMoveSequence ([startState] # states # [doneState])
|
|
|
|
validMoveSequence : {n} (fin n, n >= 1) => [n] BankState -> Bit
|
|
validMoveSequence states = all [validMove a b
|
|
| a <- states
|
|
| b <- drop`{1} states]
|
|
|
|
// Two states represent a valid move if they are both valid states (no carnage)
|
|
// and that whatever moved followed the rules
|
|
validMove : BankState -> BankState -> Bit
|
|
validMove b b' = validState b && validState b'
|
|
&& stuffOnlyMovedWithFarmer b b'
|
|
|
|
stuffOnlyMovedWithFarmer : BankState -> BankState -> Bit
|
|
stuffOnlyMovedWithFarmer b b' =
|
|
if farmerHere b.left
|
|
then farmerHere b'.right && moveFollowsRules b.left b'.right (b'.right - b.right)
|
|
else farmerHere b'.left && moveFollowsRules b.right b'.left (b'.left - b.left)
|
|
|
|
// things can't move without the farmer, and the farmer can carry at most one thing
|
|
moveFollowsRules fromBank toBank whatMoved = farmerMoved && atMostOneObjectMoved where
|
|
farmerMoved = (whatMoved && farmer) == farmer
|
|
atMostOneObjectMoved = popCount (whatMoved && ~farmer) <= 1
|
|
|
|
// "conservation of items" rule - nothing spontaneously disappears
|
|
completeState : BankState -> Bit
|
|
completeState b = (b.left ^ b.right) == 0xf
|
|
|
|
// both banks are "carnage-free"
|
|
validState : BankState -> Bit
|
|
validState bs = completeState bs && validBank bs.left
|
|
&& validBank bs.right && completeState bs
|
|
|
|
validBank : OneBank -> Bit
|
|
validBank b = farmerHere b || (~(foxWithChicken b) && ~(chickenWithCorn b))
|
|
|
|
farmerHere : OneBank -> Bit
|
|
farmerHere b = (b && farmer) > 0
|
|
|
|
chickenWithCorn : OneBank -> Bit
|
|
chickenWithCorn b = (b && (corn || chicken)) == (corn || chicken)
|
|
|
|
foxWithChicken : OneBank -> Bit
|
|
foxWithChicken b = (b && (fox || chicken)) == (fox || chicken)
|
|
|
|
// utilities
|
|
all : {n} (fin n) => [n] -> Bit
|
|
all xs = xs == ~zero
|
|
|
|
// "population count" - how many bits are on
|
|
popCount : {a,b} (fin a, b >= 1, b == (lg2 a)) => [a] -> [b]
|
|
popCount bs = ic ! 0 where
|
|
ic = [0] # [ if elt then prev + 1 else prev | elt <- bs | prev <- ic]
|
|
|
|
// pretty printing
|
|
type StringRep = [7][8]
|
|
type DirRep = [5][8]
|
|
farmerString = "farmer "
|
|
chickenString = "chicken"
|
|
cornString = "corn "
|
|
foxString = "fox "
|
|
noString = " "
|
|
|
|
ppArray = [farmerString, chickenString, cornString, foxString]
|
|
|
|
ppBits : [4] -> [4]StringRep
|
|
ppBits s = [ if b then ppArray!i else noString
|
|
| b <- s
|
|
| i <- [0 .. ]:[_][4] ]
|
|
|
|
// takes a sequence of states and derives what moved, and in which direction for each transition
|
|
extractMoves : {a} [a+1]BankState -> [a](DirRep, [4]StringRep)
|
|
extractMoves bankStates = [ getMove b b' | b <- bankStates | b' <- drop`{1} bankStates ] where
|
|
getMove start end = ( dirString, thingsString thingsMoved ) where
|
|
dirString = if farmerHere start.left then " --> " else " <-- "
|
|
thingsMoved = if farmerHere start.left
|
|
then end.right - start.right
|
|
else end.left - start.left
|
|
thingsString bits = ppBits bits
|
|
|
|
// fcc> :sat solutionInNmoves : [6]BankState -> Bit
|
|
// solutionInNmoves : [6]BankState -> Bit [{left = 12, right = 3},
|
|
// {left = 13, right = 2}, {left = 4, right = 11},
|
|
// {left = 7, right = 8}, {left = 2, right = 13},
|
|
// {left = 3, right = 12}] = True
|
|
|
|
// pretty printing: extractMoves ([startState] # [{left = 12, right = 3},{left = 13, right = 2}, {left = 4, right = 11}, {left = 7, right = 8}, {left = 2, right = 13}, {left = 3, right = 12}] # [doneState])
|
|
// [(" --> ", [" ", " ", "chicken", "farmer "]), // the farmer takes the chicken right
|
|
// (" <-- ", [" ", " ", " ", "farmer "]), // farmer goes back alone
|
|
// (" --> ", ["fox ", " ", " ", "farmer "]), // farmer takes the fox across
|
|
// (" <-- ", [" ", " ", "chicken", "farmer "]), // brings the chicken back
|
|
// (" --> ", [" ", "corn ", " ", "farmer "]), // takes the corn over
|
|
// (" <-- ", [" ", " ", " ", "farmer "]), // goes back alone
|
|
// (" --> ", [" ", " ", "chicken", "farmer "])] // brings the chicken over, all done
|
|
|