]
},
{
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {},
- "outputs": [],
- "source": [
- "from notebook_preamble import J, V, define"
- ]
- },
- {
"cell_type": "markdown",
"metadata": {},
"source": [
},
{
"cell_type": "code",
- "execution_count": 2,
+ "execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
- "[1 [2 [3 4 25 6] 7] 8]\n"
+ "[1 [2 [3 4 25 6] 7] 8]"
]
}
],
"source": [
- "J('[1 [2 [3 4 25 6] 7] 8]')"
+ "[1 [2 [3 4 25 6] 7] 8]"
]
},
{
},
{
"cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[1 [2 [3 4 25 6] 7] 8]"
+ ]
+ }
+ ],
+ "source": [
+ "[z-down [] swap uncons swap] inscribe\n",
+ "[z-up swons swap shunt] inscribe\n",
+ "[z-right roll< cons swap uncons swap] inscribe\n",
+ "[z-left swons [uncons swap] dip swap] inscribe"
+ ]
+ },
+ {
+ "cell_type": "code",
"execution_count": 3,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " [1 [2 [3 4 25 6] 7] 8] • z-down\n",
+ " [1 [2 [3 4 25 6] 7] 8] • [] swap uncons swap\n",
+ "[1 [2 [3 4 25 6] 7] 8] [] • swap uncons swap\n",
+ "[] [1 [2 [3 4 25 6] 7] 8] • uncons swap\n",
+ "[] 1 [[2 [3 4 25 6] 7] 8] • swap\n",
+ "[] [[2 [3 4 25 6] 7] 8] 1 • \n",
+ "\n",
+ "[] [[2 [3 4 25 6] 7] 8] 1"
+ ]
+ }
+ ],
"source": [
- "define('z-down == [] swap uncons swap')\n",
- "define('z-up == swons swap shunt')\n",
- "define('z-right == [swons] cons dip uncons swap')\n",
- "define('z-left == swons [uncons swap] dip swap')"
+ "[z-down] trace"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
- " . [1 [2 [3 4 25 6] 7] 8] z-down\n",
- " [1 [2 [3 4 25 6] 7] 8] . z-down\n",
- " [1 [2 [3 4 25 6] 7] 8] . [] swap uncons swap\n",
- "[1 [2 [3 4 25 6] 7] 8] [] . swap uncons swap\n",
- "[] [1 [2 [3 4 25 6] 7] 8] . uncons swap\n",
- "[] 1 [[2 [3 4 25 6] 7] 8] . swap\n",
- "[] [[2 [3 4 25 6] 7] 8] 1 . \n"
+ "[] [[2 [3 4 25 6] 7] 8] 1 • z-right\n",
+ "[] [[2 [3 4 25 6] 7] 8] 1 • roll< cons swap uncons swap\n",
+ "[[2 [3 4 25 6] 7] 8] 1 [] • cons swap uncons swap\n",
+ " [[2 [3 4 25 6] 7] 8] [1] • swap uncons swap\n",
+ " [1] [[2 [3 4 25 6] 7] 8] • uncons swap\n",
+ " [1] [2 [3 4 25 6] 7] [8] • swap\n",
+ " [1] [8] [2 [3 4 25 6] 7] • \n",
+ "\n",
+ "[1] [8] [2 [3 4 25 6] 7]"
]
}
],
"source": [
- "V('[1 [2 [3 4 25 6] 7] 8] z-down')"
+ "[z-right] trace"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
- " . [] [[2 [3 4 25 6] 7] 8] 1 z-right\n",
- " [] . [[2 [3 4 25 6] 7] 8] 1 z-right\n",
- " [] [[2 [3 4 25 6] 7] 8] . 1 z-right\n",
- " [] [[2 [3 4 25 6] 7] 8] 1 . z-right\n",
- " [] [[2 [3 4 25 6] 7] 8] 1 . [swons] cons dip uncons swap\n",
- "[] [[2 [3 4 25 6] 7] 8] 1 [swons] . cons dip uncons swap\n",
- "[] [[2 [3 4 25 6] 7] 8] [1 swons] . dip uncons swap\n",
- " [] . 1 swons [[2 [3 4 25 6] 7] 8] uncons swap\n",
- " [] 1 . swons [[2 [3 4 25 6] 7] 8] uncons swap\n",
- " [] 1 . swap cons [[2 [3 4 25 6] 7] 8] uncons swap\n",
- " 1 [] . cons [[2 [3 4 25 6] 7] 8] uncons swap\n",
- " [1] . [[2 [3 4 25 6] 7] 8] uncons swap\n",
- " [1] [[2 [3 4 25 6] 7] 8] . uncons swap\n",
- " [1] [2 [3 4 25 6] 7] [8] . swap\n",
- " [1] [8] [2 [3 4 25 6] 7] . \n"
+ "[1] [8] [] [[3 4 25 6] 7] 2"
]
}
],
"source": [
- "V('[] [[2 [3 4 25 6] 7] 8] 1 z-right')"
+ "z-down"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
- "[1] [8] [] [[3 4 25 6] 7] 2\n"
+ "[1] [8] [2] [7] [3 4 25 6]"
]
}
],
"source": [
- "J('[1] [8] [2 [3 4 25 6] 7] z-down')"
+ "z-right"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
- "[1] [8] [2] [7] [3 4 25 6]\n"
+ "[1] [8] [2] [7] [] [4 25 6] 3"
]
}
],
"source": [
- "J('[1] [8] [] [[3 4 25 6] 7] 2 z-right')"
+ "z-down"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
- "[1] [8] [2] [7] [] [4 25 6] 3\n"
+ "[1] [8] [2] [7] [3] [25 6] 4"
]
}
],
"source": [
- "J('[1] [8] [2] [7] [3 4 25 6] z-down')"
+ "z-right"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
- "[1] [8] [2] [7] [3] [25 6] 4\n"
+ "[1] [8] [2] [7] [4 3] [6] 25"
]
}
],
"source": [
- "J('[1] [8] [2] [7] [] [4 25 6] 3 z-right')"
+ "z-right"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
- "[1] [8] [2] [7] [4 3] [6] 25\n"
+ "[1] [8] [2] [7] [4 3] [6] 625"
]
}
],
"source": [
- "J('[1] [8] [2] [7] [3] [25 6] 4 z-right')"
+ "sqr"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
- "[1] [8] [2] [7] [4 3] [6] 625\n"
+ "[1] [8] [2] [7] [4 3] [6] 625 • z-up\n",
+ "[1] [8] [2] [7] [4 3] [6] 625 • swons swap shunt\n",
+ "[1] [8] [2] [7] [4 3] [625 6] • swap shunt\n",
+ "[1] [8] [2] [7] [625 6] [4 3] • shunt\n",
+ " [1] [8] [2] [7] [3 4 625 6] • \n",
+ "\n",
+ "[1] [8] [2] [7] [3 4 625 6]"
]
}
],
"source": [
- "J('[1] [8] [2] [7] [4 3] [6] 25 sqr')"
+ "[z-up] trace"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
- " . [1] [8] [2] [7] [4 3] [6] 625 z-up\n",
- " [1] . [8] [2] [7] [4 3] [6] 625 z-up\n",
- " [1] [8] . [2] [7] [4 3] [6] 625 z-up\n",
- " [1] [8] [2] . [7] [4 3] [6] 625 z-up\n",
- " [1] [8] [2] [7] . [4 3] [6] 625 z-up\n",
- " [1] [8] [2] [7] [4 3] . [6] 625 z-up\n",
- " [1] [8] [2] [7] [4 3] [6] . 625 z-up\n",
- "[1] [8] [2] [7] [4 3] [6] 625 . z-up\n",
- "[1] [8] [2] [7] [4 3] [6] 625 . swons swap shunt\n",
- "[1] [8] [2] [7] [4 3] [6] 625 . swap cons swap shunt\n",
- "[1] [8] [2] [7] [4 3] 625 [6] . cons swap shunt\n",
- "[1] [8] [2] [7] [4 3] [625 6] . swap shunt\n",
- "[1] [8] [2] [7] [625 6] [4 3] . shunt\n",
- " [1] [8] [2] [7] [3 4 625 6] . \n"
+ "[1] [8] [2 [3 4 625 6] 7]"
]
}
],
"source": [
- "V('[1] [8] [2] [7] [4 3] [6] 625 z-up')"
+ "z-up"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
- "[1] [8] [2 [3 4 625 6] 7]\n"
+ "[1 [2 [3 4 625 6] 7] 8]"
]
}
],
"source": [
- "J('[1] [8] [2] [7] [3 4 625 6] z-up')"
+ "z-up"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## `dip` and `infra`\n",
+ "In Joy we have the `dip` and `infra` combinators which can \"target\" or \"address\" any particular item in a Joy tree structure."
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
- "[1 [2 [3 4 625 6] 7] 8]\n"
+ "[1 [2 [3 4 390625 6] 7] 8]"
]
}
],
"source": [
- "J('[1] [8] [2 [3 4 625 6] 7] z-up')"
+ "[[[[[[sqr] dipd] infra] dip] infra] dip] infra"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "## `dip` and `infra`\n",
- "In Joy we have the `dip` and `infra` combinators which can \"target\" or \"address\" any particular item in a Joy tree structure."
+ "If you were to trace the program you would see that about half of it is the `dip` and `infra` combinators de-quoting programs and \"digging\" into the subject datastructure. Instead of maintaining temporary results on the stack they are pushed into the pending expression (continuation). When `sqr` has run the rest of the pending expression rebuilds the datastructure.\n",
+ "\n",
+ "## `Z`\n",
+ "Imagine a function `Z` that accepts a sequence of `dip` and `infra` combinators, a quoted program `[Q]`, and a datastructure to work on. It would effectively execute the quoted program as if it had been embedded in a nested series of quoted programs, e.g.:\n",
+ "\n",
+ " [...] [Q] [[dip] [dip] [infra] [dip] [infra] [dip] [infra]] Z\n",
+ " -------------------------------------------------------------------\n",
+ " [...] [[[[[[[Q] dip] dip] infra] dip] infra] dip] infra\n",
+ " \n",
+ "The `Z` function isn't hard to make."
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
- " . [1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra\n",
- " [1 [2 [3 4 25 6] 7] 8] . [[[[[[sqr] dipd] infra] dip] infra] dip] infra\n",
- "[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] . infra\n",
- " 8 [2 [3 4 25 6] 7] 1 . [[[[[sqr] dipd] infra] dip] infra] dip [] swaack\n",
- " 8 [2 [3 4 25 6] 7] 1 [[[[[sqr] dipd] infra] dip] infra] . dip [] swaack\n",
- " 8 [2 [3 4 25 6] 7] . [[[[sqr] dipd] infra] dip] infra 1 [] swaack\n",
- " 8 [2 [3 4 25 6] 7] [[[[sqr] dipd] infra] dip] . infra 1 [] swaack\n",
- " 7 [3 4 25 6] 2 . [[[sqr] dipd] infra] dip [8] swaack 1 [] swaack\n",
- " 7 [3 4 25 6] 2 [[[sqr] dipd] infra] . dip [8] swaack 1 [] swaack\n",
- " 7 [3 4 25 6] . [[sqr] dipd] infra 2 [8] swaack 1 [] swaack\n",
- " 7 [3 4 25 6] [[sqr] dipd] . infra 2 [8] swaack 1 [] swaack\n",
- " 6 25 4 3 . [sqr] dipd [7] swaack 2 [8] swaack 1 [] swaack\n",
- " 6 25 4 3 [sqr] . dipd [7] swaack 2 [8] swaack 1 [] swaack\n",
- " 6 25 . sqr 4 3 [7] swaack 2 [8] swaack 1 [] swaack\n",
- " 6 25 . dup mul 4 3 [7] swaack 2 [8] swaack 1 [] swaack\n",
- " 6 25 25 . mul 4 3 [7] swaack 2 [8] swaack 1 [] swaack\n",
- " 6 625 . 4 3 [7] swaack 2 [8] swaack 1 [] swaack\n",
- " 6 625 4 . 3 [7] swaack 2 [8] swaack 1 [] swaack\n",
- " 6 625 4 3 . [7] swaack 2 [8] swaack 1 [] swaack\n",
- " 6 625 4 3 [7] . swaack 2 [8] swaack 1 [] swaack\n",
- " 7 [3 4 625 6] . 2 [8] swaack 1 [] swaack\n",
- " 7 [3 4 625 6] 2 . [8] swaack 1 [] swaack\n",
- " 7 [3 4 625 6] 2 [8] . swaack 1 [] swaack\n",
- " 8 [2 [3 4 625 6] 7] . 1 [] swaack\n",
- " 8 [2 [3 4 625 6] 7] 1 . [] swaack\n",
- " 8 [2 [3 4 625 6] 7] 1 [] . swaack\n",
- " [1 [2 [3 4 625 6] 7] 8] . \n"
+ "[sqr] [[dip] [dip] [infra] [dip] [infra] [dip] [infra]]"
]
}
],
"source": [
- "V('[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra')"
+ "clear\n",
+ "[sqr]\n",
+ "[[dip][dip][infra][dip][infra][dip][infra]]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[[[[[[[sqr] dip] dip] infra] dip] infra] dip] infra]"
+ ]
+ }
+ ],
+ "source": [
+ "[cons] step"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "If you read the trace carefully you'll see that about half of it is the `dip` and `infra` combinators de-quoting programs and \"digging\" into the subject datastructure. Instead of maintaining temporary results on the stack they are pushed into the pending expression (continuation). When `sqr` has run the rest of the pending expression rebuilds the datastructure.\n",
- "\n",
- "## `Z`\n",
- "Imagine a function `Z` that accepts a sequence of `dip` and `infra` combinators, a quoted program `[Q]`, and a datastructure to work on. It would effectively execute the quoted program as if it had been embedded in a nested series of quoted programs, e.g.:\n",
- "\n",
- " [...] [Q] [dip dip infra dip infra dip infra] Z\n",
- " -------------------------------------------------------------\n",
- " [...] [[[[[[[Q] dip] dip] infra] dip] infra] dip] infra\n",
- " \n",
- "The `Z` function isn't hard to make."
+ "To use it you need to run the resulting program with the `i` combinator."
]
},
{
"cell_type": "code",
- "execution_count": 16,
+ "execution_count": 17,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[1 [2 [3 4 25 6] 7] 8] [[[[[[[[sqr] dip] dip] infra] dip] infra] dip] infra]"
+ ]
+ }
+ ],
"source": [
- "define('Z == [[] cons cons] step i')"
+ "[1 [2 [3 4 25 6] 7] 8] swap"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[1 [2 [3 4 625 6] 7] 8]"
+ ]
+ }
+ ],
+ "source": [
+ "i"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "Here it is in action in a simplified scenario."
+ "So let's define `Z` as:\n",
+ "\n",
+ " Z == [cons] step i"
]
},
{
"cell_type": "code",
- "execution_count": 17,
+ "execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
- " . 1 [2 3 4] Z\n",
- " 1 . [2 3 4] Z\n",
- " 1 [2 3 4] . Z\n",
- " 1 [2 3 4] . [[] cons cons] step i\n",
- " 1 [2 3 4] [[] cons cons] . step i\n",
- " 1 2 [[] cons cons] . i [3 4] [[] cons cons] step i\n",
- " 1 2 . [] cons cons [3 4] [[] cons cons] step i\n",
- " 1 2 [] . cons cons [3 4] [[] cons cons] step i\n",
- " 1 [2] . cons [3 4] [[] cons cons] step i\n",
- " [1 2] . [3 4] [[] cons cons] step i\n",
- " [1 2] [3 4] . [[] cons cons] step i\n",
- " [1 2] [3 4] [[] cons cons] . step i\n",
- " [1 2] 3 [[] cons cons] . i [4] [[] cons cons] step i\n",
- " [1 2] 3 . [] cons cons [4] [[] cons cons] step i\n",
- " [1 2] 3 [] . cons cons [4] [[] cons cons] step i\n",
- " [1 2] [3] . cons [4] [[] cons cons] step i\n",
- " [[1 2] 3] . [4] [[] cons cons] step i\n",
- " [[1 2] 3] [4] . [[] cons cons] step i\n",
- "[[1 2] 3] [4] [[] cons cons] . step i\n",
- " [[1 2] 3] 4 [[] cons cons] . i i\n",
- " [[1 2] 3] 4 . [] cons cons i\n",
- " [[1 2] 3] 4 [] . cons cons i\n",
- " [[1 2] 3] [4] . cons i\n",
- " [[[1 2] 3] 4] . i\n",
- " . [[1 2] 3] 4\n",
- " [[1 2] 3] . 4\n",
- " [[1 2] 3] 4 . \n"
+ "[1 [2 [3 4 625 6] 7] 8]"
]
}
],
"source": [
- "V('1 [2 3 4] Z')"
+ "[Z [cons] step i] inscribe"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "And here it is doing the main thing."
+ "And here it is doing the thing."
]
},
{
"cell_type": "code",
- "execution_count": 18,
+ "execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
- "[1 [2 [3 4 625 6] 7] 8]\n"
+ "[1 [2 [3 4 25 6] 7] 8] [sqr] [[dip] [dip] [infra] [dip] [infra] [dip] [infra]]"
]
}
],
"source": [
- "J('[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z')"
+ "clear\n",
+ "[1 [2 [3 4 25 6] 7] 8]\n",
+ "[sqr]\n",
+ "[[dip][dip][infra][dip][infra][dip][infra]]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[1 [2 [3 4 625 6] 7] 8]"
+ ]
+ }
+ ],
+ "source": [
+ "Z"
]
},
{
" [ n [ n [ n n x ...\n",
" i d i d i d d Bingo!"
]
- },
- {
- "cell_type": "code",
- "execution_count": 19,
- "metadata": {},
- "outputs": [],
- "source": []
}
],
"metadata": {
"kernelspec": {
- "display_name": "Python 2",
- "language": "python",
- "name": "python2"
+ "display_name": "Joypy",
+ "language": "",
+ "name": "thun"
},
"language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 2
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython2",
- "version": "2.7.12"
+ "file_extension": ".joy",
+ "mimetype": "text/plain",
+ "name": "Joy"
}
},
"nbformat": 4,
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