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Updated Partial Application section
Rewrote last example
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‎index.ipynb

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"id": "215f5f1e",
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"metadata": {},
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"source": [
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"This feature is called **partial application**. On its surface, it's nice for adding convenient names to helper functions. In practice, it can allow you to express complexity using simple, modular pieces:"
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"This feature is called **partial application**. It can help you express complexity using simple, modular pieces:"
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]
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"Here we build `add` and `divide` from `combine` by passing `+` and `/` to it. This code doesn't do much anything useful though... "
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"<details open=\"open\" class=\"dni-treeview\"><summary><span class=\"dni-code-hint\"><code>(7, 2)</code></span></summary><div><table><thead><tr></tr></thead><tbody><tr><td>Item1</td><td><div class=\"dni-plaintext\"><pre>7</pre></div></td></tr><tr><td>Item2</td><td><div class=\"dni-plaintext\"><pre>2</pre></div></td></tr></tbody></table></div></details><style>\r\n",
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"source": [
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"// y applied to x applied to f\n",
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"let combine f x y = f x y\n",
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"let add = combine (+) // a way to pass the + function\n",
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"let divide = combine (/)\n",
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"\n",
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"add 3 4, divide 9 4"
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]
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"We can pass a `check` function to `combine` that can perform a check and decide whether we want to continue the computation or not."
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"`f` comes first in the parameter list because we probably want will want to bind it first then later decide what type of check behavior we want."
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"source": [
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"let combine f check x y =\n",
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" check f x y"
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"We can build all different kinds of \"adders\" from `combine`:"
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]
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"text": [
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"8\n",
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"NaN\n"
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"9\n",
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"Adding 5 + 6...\n",
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"11\n",
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"8\n"
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}
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],
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"source": [
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"let combine f check x y =\n",
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" f <|| check x y\n",
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"let normalize f x y = f (abs x) (abs y)\n",
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"\n",
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"let id2 x y = x, y\n",
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"let normalizeThenAdd = combine (+) normalize\n",
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"normalizeThenAdd -4 5 |> printfn \"%d\"\n",
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"\n",
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"let add = combine (+) id2\n",
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"add 3 5 |> printfn \"%d\"\n",
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"let printThenAdd = combine (+) (fun f x y -> printfn \"Adding %d + %d...\" x y; f x y)\n",
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"printThenAdd 5 6 |> printfn \"%d\"\n",
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"\n",
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"let divideThen check = combine (/) check\n",
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"let safeDivide = divideThen (fun x y -> if y = 0 then x, nan else x, y)\n",
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"let add = combine (+) id // id is a special function that means \"do nothing\" in this context\n",
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"add 3 5 |> printfn \"%d\""
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]
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"source": [
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"We can build \"safe dividers\" that checks whether the denominator = 0."
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]
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{
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"source": [
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"`safeDivide` replaces `y` with `NaN` when `y = 0`:"
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]
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},
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"NaN\n"
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}
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],
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"source": [
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"let ``convert divBy0 to NaN`` f x y =\n",
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" f x (if y = 0 then nan else y)\n",
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"\n",
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"let safeDivide = combine (/) ``convert divBy0 to NaN``\n",
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"safeDivide 4 0 |> printfn \"%f\""
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]
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"source": [
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"`safeDivide` implicitly evaluates to a `float`, though, because `NaN` is not a valid value for `int`s. Sometimes you absolutely do want integer division, which evaluates to an `int` and ignores the remainder.\n",
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"\n",
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"`tryDivide` checks if `y = 0`, and if it is, it avoids doing the division altogether (by not evaluating `cont`).\n",
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"> ℹ️ Note\n",
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"> \n",
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"> I should move this example down further to when I explain Option types, perhaps referencing this example. It is not 100% clear what is going on here without explaining option types."
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]
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"text": [
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"Some(4)\n",
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"<null>\n"
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]
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}
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],
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"source": [
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"let ``convert divBy0 to None`` cont x y =\n",
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" if y = 0 then None else Some(cont x y)\n",
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"\n",
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"// remove this example for now and reference it when teaching the Option type\n",
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"let tryDivide = combine (/) ``convert divBy0 to None``\n",
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"\n",
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"tryDivide 4 1 |> printfn \"%O\"\n",
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"tryDivide 4 0 |> printfn \"%O\""
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]
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},
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{
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"cell_type": "markdown",
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"id": "7ec9b1fa",

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