"source": [
"[z-down [] swap uncons swap] inscribe\n",
"[z-up swons swap shunt] inscribe\n",
- "[z-right [swons] cons dip uncons swap] inscribe\n",
+ "[z-right roll< cons swap uncons swap] inscribe\n",
"[z-left swons [uncons swap] dip swap] inscribe"
]
},
"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 • [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] • [[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",
+ "[] [[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]"
]
"name": "stdout",
"output_type": "stream",
"text": [
- "[1 [2 [3 4 625 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] • infra\n",
- " 8 [2 [3 4 625 6] 7] 1 • [[[[[sqr] dipd] infra] dip] infra] dip [] swaack\n",
- " 8 [2 [3 4 625 6] 7] 1 [[[[[sqr] dipd] infra] dip] infra] • dip [] swaack\n",
- " 8 [2 [3 4 625 6] 7] • [[[[sqr] dipd] infra] dip] infra 1 [] swaack\n",
- " 8 [2 [3 4 625 6] 7] [[[[sqr] dipd] infra] dip] • infra 1 [] swaack\n",
- " 7 [3 4 625 6] 2 • [[[sqr] dipd] infra] dip [8] swaack 1 [] swaack\n",
- " 7 [3 4 625 6] 2 [[[sqr] dipd] infra] • dip [8] swaack 1 [] swaack\n",
- " 7 [3 4 625 6] • [[sqr] dipd] infra 2 [8] swaack 1 [] swaack\n",
- " 7 [3 4 625 6] [[sqr] dipd] • infra 2 [8] swaack 1 [] swaack\n",
- " 6 625 4 3 • [sqr] dipd [7] swaack 2 [8] swaack 1 [] swaack\n",
- " 6 625 4 3 [sqr] • dipd [7] swaack 2 [8] swaack 1 [] swaack\n",
- " 6 625 • sqr 4 3 [7] swaack 2 [8] swaack 1 [] swaack\n",
- " 6 625 • dup * 4 3 [7] swaack 2 [8] swaack 1 [] swaack\n",
- " 6 625 625 • * 4 3 [7] swaack 2 [8] swaack 1 [] swaack\n",
- " 6 390625 • 4 3 [7] swaack 2 [8] swaack 1 [] swaack\n",
- " 6 390625 4 • 3 [7] swaack 2 [8] swaack 1 [] swaack\n",
- " 6 390625 4 3 • [7] swaack 2 [8] swaack 1 [] swaack\n",
- " 6 390625 4 3 [7] • swaack 2 [8] swaack 1 [] swaack\n",
- " 7 [3 4 390625 6] • 2 [8] swaack 1 [] swaack\n",
- " 7 [3 4 390625 6] 2 • [8] swaack 1 [] swaack\n",
- " 7 [3 4 390625 6] 2 [8] • swaack 1 [] swaack\n",
- " 8 [2 [3 4 390625 6] 7] • 1 [] swaack\n",
- " 8 [2 [3 4 390625 6] 7] 1 • [] swaack\n",
- " 8 [2 [3 4 390625 6] 7] 1 [] • swaack\n",
- " [1 [2 [3 4 390625 6] 7] 8] • \n",
- "\n",
"[1 [2 [3 4 390625 6] 7] 8]"
]
}
],
"source": [
- "[[[[[[sqr] dipd] infra] dip] infra] dip] [infra] trace"
+ "[[[[[[sqr] dipd] infra] dip] infra] dip] infra"
]
},
{
"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",
+ "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",
+ " [...] [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": []
+ "text": [
+ "[sqr] [[dip] [dip] [infra] [dip] [infra] [dip] [infra]]"
+ ]
}
],
"source": [
- "clear"
+ "clear\n",
+ "[sqr]\n",
+ "[[dip][dip][infra][dip][infra][dip][infra]]"
]
},
{
{
"name": "stdout",
"output_type": "stream",
- "text": []
+ "text": [
+ "[[[[[[[[sqr] dip] dip] infra] dip] infra] dip] infra]"
+ ]
}
],
"source": [
- "[Z [[] ccons] step i] inscribe"
+ "[cons] step"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "Here it is in action in a simplified scenario."
+ "To use it you need to run the resulting program with the `i` combinator."
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
- " 1 [2 3 4] • Z\n",
- " 1 [2 3 4] • [[] ccons] step i\n",
- " 1 [2 3 4] [[] ccons] • step i\n",
- " 1 2 [[] ccons] • i [3 4] [[] ccons] step i\n",
- " 1 2 • [] ccons [3 4] [[] ccons] step i\n",
- " 1 2 [] • ccons [3 4] [[] ccons] step i\n",
- " [1 2] • [3 4] [[] ccons] step i\n",
- " [1 2] [3 4] • [[] ccons] step i\n",
- " [1 2] [3 4] [[] ccons] • step i\n",
- " [1 2] 3 [[] ccons] • i [4] [[] ccons] step i\n",
- " [1 2] 3 • [] ccons [4] [[] ccons] step i\n",
- " [1 2] 3 [] • ccons [4] [[] ccons] step i\n",
- " [[1 2] 3] • [4] [[] ccons] step i\n",
- " [[1 2] 3] [4] • [[] ccons] step i\n",
- "[[1 2] 3] [4] [[] ccons] • step i\n",
- " [[1 2] 3] 4 [[] ccons] • i i\n",
- " [[1 2] 3] 4 • [] ccons i\n",
- " [[1 2] 3] 4 [] • ccons i\n",
- " [[[1 2] 3] 4] • i\n",
- " • [[1 2] 3] 4\n",
- " [[1 2] 3] • 4\n",
- " [[1 2] 3] 4 • \n",
- "\n",
- "[[1 2] 3] 4"
+ "[1 [2 [3 4 25 6] 7] 8] [[[[[[[[sqr] dip] dip] infra] dip] infra] dip] infra]"
]
}
],
"source": [
- "1 [2 3 4] [Z] trace"
+ "[1 [2 [3 4 25 6] 7] 8] swap"
]
},
{
{
"name": "stdout",
"output_type": "stream",
- "text": []
+ "text": [
+ "[1 [2 [3 4 625 6] 7] 8]"
+ ]
}
],
"source": [
- "clear"
+ "i"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "And here it is doing the thing."
+ "So let's define `Z` as:\n",
+ "\n",
+ " Z == [cons] step i"
]
},
{
}
],
"source": [
- "[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z"
+ "[Z [cons] step i] inscribe"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "And here it is doing the thing."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[1 [2 [3 4 25 6] 7] 8] [sqr] [[dip] [dip] [infra] [dip] [infra] [dip] [infra]]"
+ ]
+ }
+ ],
+ "source": [
+ "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"
]
},
{
OSDN Git Service
