import logic namespace tactic -- This is just a trick to embed the 'tactic language' as a -- Lean expression. We should view (tactic A) as automation -- that when execute produces a term of type A. -- tactic_value is just a "dummy" for creating the "fake" inductive tactic (A : Type) : Type := | tactic_value {} : tactic A -- Remark the following names are not arbitrary, the tactic module -- uses them when converting Lean expressions into actual tactic objects. -- The bultin 'by' construct triggers the process of converting a -- a term of type (tactic A) into a tactic that sythesizes a term -- of type A definition then_tac {A : Type} (t1 t2 : tactic A) : tactic A := tactic_value definition orelse_tac {A : Type} (t1 t2 : tactic A) : tactic A := tactic_value definition repeat_tac {A : Type} (t : tactic A) : tactic A := tactic_value definition now {A : Type} : tactic A := tactic_value definition state {A : Type} : tactic A := tactic_value definition fail {A : Type} : tactic A := tactic_value definition id {A : Type} : tactic A := tactic_value definition beta {A : Type} : tactic A := tactic_value definition apply {A : Type} {B : Type} (b : B) : tactic A := tactic_value infixl `;`:200 := then_tac infixl `|`:100 := orelse_tac notation `!`:max t:max := repeat_tac t end