27 lines
806 B
Text
27 lines
806 B
Text
Variable g {A : Type} (a : A) : A
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Variable a : Int
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Variable b : Int
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Axiom H1 : a = b
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(*
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The following axiom fails to be elaborated because:
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1- (g a) is actually (g _ a)
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2- > is overloaded notation for Nat::gt, Int::gt and Real::gt
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3- The current elaborator selects one of the overloads before
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the hole in (g _ a) is solved. Thus, it selects Nat::gt.
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4- During elaboration, we transform (g _ a) into (g Int a),
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and a type error is detected.
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The next elaborator should address this problem.
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*)
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Axiom H2 : (g a) > 0
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(*
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A possible workaround is to manually add the coercion in 0.
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The coercion is called nat_to_int. We define the notation
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_ i to make it easier to write
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*)
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Notation 100 _ i : nat_to_int
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Axiom H2 : (g a) > 0i
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Theorem T1 : (g b) > 0i := Subst (λ x, (g x) > 0i) H2 H1
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Show Environment 2
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