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add remaining notations for expr_term

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This commit is contained in:
Michael Sippel 2024-09-08 15:28:44 +02:00
parent c3d1649402
commit 865ceff7d4
Signed by: senvas
GPG key ID: F96CF119C34B64A6
1 changed files with 14 additions and 5 deletions
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19
coq/terms.v
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@ -98,11 +98,20 @@ Notation "[{ e }]" := e
(e custom ladder_expr at level 80) : ladder_expr_scope.
Notation "'%' x '%'" := (expr_var x%string)
(in custom ladder_expr at level 0, x constr) : ladder_expr_scope.
Notation "'λ' x τ '↦' e" := (expr_abs x τ e) (in custom ladder_expr at level 0, x constr, τ custom ladder_type at level 99, e custom ladder_expr at level 99).
Notation "'Λ' t '↦' e" := (expr_ty_abs t e)
(in custom ladder_expr at level 0, t constr, e custom ladder_expr at level 80).
(in custom ladder_expr at level 10, t constr, e custom ladder_expr at level 80) : ladder_expr_scope.
Notation "'λ' x τ '↦' e" := (expr_abs x τ e)
(in custom ladder_expr at level 10, x constr, τ custom ladder_type at level 99, e custom ladder_expr at level 99) :ladder_expr_scope.
Notation "'λ' x τ '↦morph' e" := (expr_morph x τ e)
(in custom ladder_expr at level 10, x constr, τ custom ladder_type at level 99, e custom ladder_expr at level 99) :ladder_expr_scope.
Notation "'let' x ':=' e 'in' t" := (expr_let x e t)
(in custom ladder_expr at level 20, x constr, e custom ladder_expr at level 99, t custom ladder_expr at level 99) : ladder_expr_scope.
Notation "e 'as' τ" := (expr_ascend τ e)
(in custom ladder_expr at level 30, e custom ladder_expr, τ custom ladder_type at level 99) : ladder_expr_scope.
Notation "e1 e2" := (expr_app e1 e2)
(in custom ladder_expr at level 50) : ladder_expr_scope.
Notation "'(' e ')'" := e
(in custom ladder_expr at level 0) : ladder_expr_scope.
(* EXAMPLES *)
@ -111,7 +120,7 @@ Open Scope ladder_expr_scope.
Check [< ∀"α", (< $"Seq"$ %"α"% > ~ < $"List"$ %"α"% >) >].
Definition polymorphic_identity1 : expr_term := [{ Λ"T" ↦ λ"x"%"T"% ↦ %"x"% }].
Definition polymorphic_identity1 : expr_term := [{ Λ"T" ↦ λ"x"%"T"% ↦ (%"x"%) }].
Definition polymorphic_identity2 : expr_term := [{ Λ"T" ↦ λ"y"%"T"% ↦ %"y"% }].
Compute polymorphic_identity1.