77 lines
1.7 KiB
Plaintext
77 lines
1.7 KiB
Plaintext
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# How to use exported files in lamb:
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#
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# [Syntax Highlighting]
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# Most languages' syntax highlighters will
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# highlight this code well. Set it manually
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# in your editor.
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#
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# Don't use a language for which you have a
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# linter installed, you'll get lots of errors.
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#
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# Choose a language you don't have extenstions for,
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# and a language that uses # comments.
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#
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# The following worked well in vscode:
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# - Julia
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# - Perl
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# - Coffeescript
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# - R
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# [Writing macros]
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# If you don't have a custom keyboard layout that can
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# create λs, you may use backslashes instead.
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# (As in `T = \ab.b`)
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#
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# This file must only contain macro definitons. Commands will be ignored.
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# Statements CANNOT be split among multiple lines.
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# Comments CANNOT be on the same line as macro defintions.
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# All leading whitespace is ignored.
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# Misc Combinators
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M = λx.(x x)
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W = (M M)
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Y = λf.((λx.(f (x x))) (λx.(f (x x))))
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# Booleans
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T = λab.a
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F = λab.b
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NOT = λa.(a F T)
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AND = λab.(a b F)
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OR = λab.(a T b)
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XOR = λab.((a (NOT b)) b)
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# Numbers
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# PAIR: prerequisite for H.
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# Makes a two-value tuple, indexed with T and F.
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#
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# H: shift-and-add, prerequisite for D
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#
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# S: successor (adds 1)
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#
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# D: predecessor (subtracts 1)
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#
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# Z: tests if a number is zero
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# NZ: equivalent to `NOT Z`
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#
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# ADD: adds two numbers
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#
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# MULT: multiply two numbers
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#
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# FAC:
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# Recursive factorial. Call with `Y FAC <number>`
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# Don't call this with numbers bigger than 5 unless you're very patient.
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#
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# `Y FAC 6` required 867,920 reductions and took 10 minutes to run.
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PAIR = λabi.(i a b)
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H = λp.((PAIR (p F)) (S (p F)))
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S = λnfa.(f (n f a))
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D = λn.((n H) ((PAIR 0) 0) T)
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Z = λn.(n (λa.F) T)
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NZ = λn.(n (λa.T) F)
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ADD = λmn.(m S n)
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MULT = λnmf.(n (m f))
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FAC = λyn.( (Z n)(1)((MULT n) (y (D n))) )
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