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refactor: abbrev open'/close #815

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refactor: abbrev open'/close #815

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14 changes: 6 additions & 8 deletions Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/Basic.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -27,7 +27,7 @@ namespace Cslib

universe u

variable {Var : Type u} [HasFresh Var] [DecidableEq Var]
variable {Var : Type u}

namespace LambdaCalculus.LocallyNameless.Untyped

Expand Down Expand Up @@ -65,11 +65,13 @@ lemma openRec_abs : M.abs⟦i ↝ s⟧ = M⟦i + 1 ↝ s⟧.abs := by rfl

/-- Variable opening of the closest binding. -/
@[scoped grind =]
def open' {X} (e u):= @Term.openRec X 0 u e
abbrev open' {X} (e u):= @Term.openRec X 0 u e

@[inherit_doc]
scoped infixr:80 " ^ " => Term.open'

variable [DecidableEq Var]

/-- Variable closing, replacing a free `fvar x` with `bvar k` -/
@[scoped grind =]
def closeRec (k : ℕ) (x : Var) : Term Var → Term Var
Expand All @@ -81,11 +83,9 @@ def closeRec (k : ℕ) (x : Var) : Term Var → Term Var
@[inherit_doc]
scoped notation:68 e "⟦" k " ↜ " x "⟧"=> Term.closeRec k x e

variable {x : Var}

/-- Variable closing of the closest binding. -/
@[scoped grind =]
def close {Var} [DecidableEq Var] (e u):= @Term.closeRec Var _ 0 u e
abbrev close (e : Term Var) (u : Var) := Term.closeRec 0 u e

@[inherit_doc]
scoped infixr:80 " ^* " => Term.close
Expand Down Expand Up @@ -113,7 +113,7 @@ def fv : Term Var → Finset Var

section

omit [HasFresh Var]
variable {x : Var} {n : Term Var}

lemma closeRec_bvar : (bvar i)⟦k ↜ x⟧ = bvar i := by rfl

Expand All @@ -123,8 +123,6 @@ lemma closeRec_app : (app l r)⟦k ↜ x⟧ = app (l⟦k ↜ x⟧) (r⟦k ↜ x

lemma closeRec_abs : t.abs⟦k ↜ x⟧ = t⟦k + 1 ↜ x⟧.abs := by rfl

variable {x : Var} {n : Term Var}

lemma subst_bvar : (bvar i : Term Var)[x := n] = bvar i := by rfl

lemma subst_fvar : (fvar x')[x := n] = if x = x' then n else fvar x' := by rfl
Expand Down
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