doc: fix example code & style
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Sebastian Ullrich
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3 changed files with 68 additions and 73 deletions
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@ -37,7 +37,7 @@
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- [Macro Overview](./macro_overview.md)
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- [Examples](./syntax_examples.md)
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- [Parenthesized Terms](./syntax_example.md)
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- [Arithmetic DSL](./tutorial/metaprogramming-arith.md)
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- [Arithmetic DSL](./metaprogramming-arith.md)
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- [Declaring New Types](./decltypes.md)
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- [Enumerated Types](./enum.md)
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- [Inductive Types](./inductive.md)
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59
doc/metaprogramming-arith.lean
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59
doc/metaprogramming-arith.lean
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@ -0,0 +1,59 @@
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-- example on parsing arith language via macros
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inductive Arith : Type
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| add : Arith → Arith → Arith -- e + f
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| mul : Arith → Arith → Arith -- e * f
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| int : Int → Arith -- constant
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| symbol : String → Arith -- variable
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declare_syntax_cat arith
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syntax num : arith -- int for Arith.int
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syntax str : arith -- strings for Arith.symbol
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syntax:60 arith:60 "+" arith:61 : arith -- Arith.add
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syntax:70 arith:70 "*" arith:71 : arith -- Arith.mul
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syntax "(" arith ")" : arith -- bracketed expressions
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-- auxiliary notation for translating `arith` into `term`
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syntax "`[Arith| " arith "]" : term
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macro_rules
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| `(`[Arith| $s:str]) => `(Arith.symbol $s)
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| `(`[Arith| $num:num]) => `(Arith.int $num)
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| `(`[Arith| $x:arith + $y:arith]) => `(Arith.add `[Arith| $x] `[Arith| $y])
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| `(`[Arith| $x:arith * $y:arith]) => `(Arith.mul `[Arith| $x] `[Arith| $y])
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| `(`[Arith| ($x:arith)]) => `(`[Arith| $x])
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#check `[Arith| "x" * "y"] -- mul
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-- Arith.mul (Arith.symbol "x") (Arith.symbol "y")
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#check `[Arith| "x" + "y"] -- add
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-- Arith.add (Arith.symbol "x") (Arith.symbol "y")
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#check `[Arith| "x" + 20] -- symbol + int
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-- Arith.add (Arith.symbol "x") (Arith.int 20)
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#check `[Arith| "x" + "y" * "z"] -- precedence
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-- Arith.add (Arith.symbol "x") (Arith.mul (Arith.symbol "y") (Arith.symbol "z"))
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#check `[Arith| "x" * "y" + "z"] -- precedence
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-- Arith.add (Arith.mul (Arith.symbol "x") (Arith.symbol "y")) (Arith.symbol "z")
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#check `[Arith| ("x" + "y") * "z"] -- brackets
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-- Arith.mul (Arith.add (Arith.symbol "x") (Arith.symbol "y")) (Arith.symbol "z")
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syntax ident : arith
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macro_rules
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| `(`[Arith| $x:ident]) => `(Arith.symbol $(Lean.quote (toString x.getId)))
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#check `[Arith| x] -- Arith.symbol "x"
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def xPlusY := `[Arith| x + y]
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#print xPlusY -- def xPlusY : Arith := Arith.add (Arith.symbol "x") (Arith.symbol "y")
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syntax "<[" term "]>" : arith -- escape for embedding terms into `Arith`
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macro_rules
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| `(`[Arith| <[ $e:term ]>]) => pure e
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#check `[Arith| <[ xPlusY ]> + z] -- Arith.add xPlusY (Arith.symbol "z")
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@ -139,17 +139,18 @@ Let's test and see that we can now write expressions such as `x * y` directly in
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```lean,ignore
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#check `[Arith| x ] -- Arith.symbol "x"
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#check `[Arith| x + y] -- Arith.add (Arith.symbol "x") (Arith.symbol "y")
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def xPlusY := `[Arith| x + y]
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#check xPlusY -- Arith.add (Arith.symbol "x") (Arith.symbol "y")
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```
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We now show an unfortunate consequence of the above definitions. Suppose we want to build `(x + y) + z)`.
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Since we already have defined `x_plus_y` as `x + y`, perhaps we should reuse it! Let's try:
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We now show an unfortunate consequence of the above definitions. Suppose we want to build `(x + y) + z`.
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Since we already have defined `xPlusY` as `x + y`, perhaps we should reuse it! Let's try:
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```lean,ignore
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#check `[Arith| x_plus_y + z] --Arith.add (Arith.symbol "x_plus_y") (Arith.symbol "z")
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#check `[Arith| xPlusY + z] -- Arith.add (Arith.symbol "xPlusY") (Arith.symbol "z")
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```
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Whoops, that didn't work! What happened? Lean treats `x_plus_y` _itself_ as an identifier! So we need to add some syntax
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Whoops, that didn't work! What happened? Lean treats `xPlusY` _itself_ as an identifier! So we need to add some syntax
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to be able to "escape" the `Arith|` context. Let's use the syntax `<[ $e:term ]>` to mean: evaluate `$e` as a real term,
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not an identifier. The macro looks like follows:
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@ -163,7 +164,7 @@ macro_rules
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Let's try our previous example:
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```lean,ignore
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#check `[Arith| <[ x_plus_y ]>] -- x_plus_y
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#check `[Arith| <[ xPlusY ]> + z] -- Arith.add xPlusY (Arith.symbol "z")
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```
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Perfect!
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@ -175,71 +176,6 @@ within a macro, and how to provide an escape from within the macro context.
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#### Full code listing
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```lean
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-- example on parsing arith language via macros
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inductive Arith: Type
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| add : Arith → Arith → Arith -- e + f
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| mul : Arith → Arith → Arith -- e * f
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| int : Int → Arith -- constant
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| symbol : String → Arith -- variable
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declare_syntax_cat arith
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syntax num : arith -- int for Arith.int
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syntax str : arith -- strings for Arith.symbol
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syntax:60 arith:60 "+" arith:61 : arith -- Arith.add
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syntax:70 arith:70 "*" arith:71 : arith -- Arith.mul
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syntax "(" arith ")" : arith -- bracketed expressions
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-- auxiliary notation for translating `arith` into `term`
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syntax "`[Arith| " arith "]" : term
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macro_rules
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| `(`[Arith| $s:strLit ]) => `(Arith.symbol $s )
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| `(`[Arith| $num:numLit ]) => `(Arith.int $num )
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| `(`[Arith| $x:arith + $y:arith ]) => `(Arith.add `[Arith| $x] `[Arith| $y] )
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| `(`[Arith| $x:arith * $y:arith ]) => `(Arith.mul `[Arith| $x] `[Arith| $y] )
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| `(`[Arith| ($x:arith) ]) => `(`[Arith| $x ])
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def foo :=
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#check `[Arith| "x" * "y" ] -- mul
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-- Arith.mul (Arith.symbol "x") (Arith.symbol "y")
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def bar :=
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#check `[Arith| "x" + "y"] -- add
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-- Arith.add (Arith.symbol "x") (Arith.symbol "y")
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def baz :=
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#check `[Arith| "x" + 20] -- symbol + int
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-- Arith.add (Arith.symbol "x") (Arith.int 20)
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def quux_left :=
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#check `[Arith| "x" + "y" * "z" ] -- precedence
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-- Arith.add (Arith.symbol "x") (Arith.mul (Arith.symbol "y") (Arith.symbol "z"))
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def quux_right :=
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#check `[Arith| "x" * "y" + "z"] -- precedence
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-- Arith.add (Arith.mul (Arith.symbol "x") (Arith.symbol "y")) (Arith.symbol "z")
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def quuz :=
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#check `[Arith| ("x" + "y") * "z"] -- brackets
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-- Arith.mul (Arith.add (Arith.symbol "x") (Arith.symbol "y")) (Arith.symbol "z")
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syntax ident : arith
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macro_rules
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| `(`[Arith| $x:ident]) => `(Arith.symbol $(Lean.quote (toString x.getId)))
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#check `[Arith| x ] -- Arith.symbol "x"
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#check `[Arith| x + y] -- Arith.add (Arith.symbol "x") (Arith.symbol "y")
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#check `[Arith| x_plus_y + z] -- Arith.add (Arith.symbol "x_plus_y") (Arith.symbol "z")
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syntax "<[" term "]>" : arith -- escape for embedding terms into `Arith`
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macro_rules
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| `(`[Arith| <[ $e:term ]> ]) => e
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#check `[Arith| <[ x_plus_y ]>] -- x_plus_y
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{{#include metaprogramming-arith.lean}}
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```
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