46 lines
1.2 KiB
Text
46 lines
1.2 KiB
Text
new_frontend
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abbrev Set (α : Type) := α → Prop
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axiom setOf {α : Type} : (α → Prop) → Set α
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axiom mem {α : Type} : α → Set α → Prop
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axiom univ {α : Type} : Set α
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axiom Union {α : Type} : Set (Set α) → Set α
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syntax:100 term " ∈ " term:99 : term
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macro_rules
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| `($x ∈ $s) => `(mem $x $s)
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declare_syntax_cat index
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syntax term : index
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syntax term "≤" ident "<" term : index
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syntax ident ":" term : index
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syntax "{" index " | " term "}" : term
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macro_rules
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| `({$l:term ≤ $x:ident < $u | $p}) => `(setOf (fun $x:ident => $l ≤ $x:ident ∧ $x:ident < $u ∧ $p))
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| `({$x:ident : $t | $p}) => `(setOf (fun ($x:ident : $t) => $p))
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| `({$x:term ∈ $s | $p}) => `(setOf (fun $x => $x ∈ $s ∧ $p))
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| `({$x:term ≤ $e | $p}) => `(setOf (fun $x => $x ≤ $e ∧ $p))
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| `({$b:term | $r}) => `(setOf (fun $b => $r))
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#check { 1 ≤ x < 10 | x ≠ 5 }
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#check { f : Nat → Nat | f 1 > 0 }
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syntax "⋃ " term ", " term : term
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macro_rules
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| `(⋃ $b, $r) => `(Union {$b:term | $r})
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#check ⋃ x, x = x
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#check ⋃ (x : Set Unit), x = x
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#check ⋃ x ∈ univ, x = x
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syntax "#check2" term : command
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macro_rules
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| `(#check2 $e) => `(#check $e #check $e)
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#check2 1
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