2024-09-22 15:52:06 +02:00
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Require Import Metatheory.
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2024-09-21 17:26:26 +02:00
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Require Import Atom.
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Require Import Environment.
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Require Import debruijn.
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Notation env := (list (atom * type_DeBruijn)).
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2024-09-22 15:52:06 +02:00
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(* env is well-formed if each atom is bound at most once
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* and every binding is to a locally closed type
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*)
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Inductive env_wf : env -> Prop :=
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| env_wf_empty :
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env_wf []
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| env_wf_type : forall Γ x τ,
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env_wf Γ ->
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type_lc τ ->
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x `notin` (dom Γ) ->
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env_wf ((x,τ)::Γ)
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.
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Ltac gather_atoms :=
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let A := gather_atoms_with (fun x : atoms => x) in
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let B := gather_atoms_with (fun x : atom => singleton x) in
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let C := gather_atoms_with (fun x : list (atom * type_DeBruijn) => dom x) in
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let D := gather_atoms_with (fun x : expr_DeBruijn => expr_fv x) in
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constr:(A `union` B `union` C `union` D).
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Tactic Notation "pick" "fresh" ident(x) :=
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let L := gather_atoms in
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(pick fresh x for L).
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Tactic Notation
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"pick" "fresh" ident(atom_name) "and" "apply" constr(lemma) :=
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let L := gather_atoms in
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pick fresh atom_name excluding L and apply lemma.
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