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50 lines
2.0 KiB
50 lines
2.0 KiB
From semantics.ts.stlc Require Export lang.
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Set Default Proof Using "Type".
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(* We declare two notation scopes, one for values and one for expressions.
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Afterwards, we add notations to them, which then do not interfere with
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any existing Coq notations. *)
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Declare Scope expr_scope.
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Declare Scope val_scope.
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Delimit Scope expr_scope with E.
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Delimit Scope val_scope with V.
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Bind Scope expr_scope with expr.
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Bind Scope val_scope with val.
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(* Values can be embedded into expressions with of_val
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and integers into expressions with LitInt. The following
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coercions allow us to omit the embeddings. With them
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(e1 v2 n3) desugars to (e3 (of_val v2) (LitInt n1)). *)
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Coercion of_val : val >-> expr.
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Coercion LitInt : Z >-> expr.
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Coercion LitIntV : Z >-> val.
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Coercion App : expr >-> Funclass.
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Coercion Var : string >-> expr.
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Notation "e1 + e2" := (Plus e1%E e2%E) : expr_scope.
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(* The breaking point '/ ' makes sure that the body of the λ: is indented
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by two spaces in case the whole λ: does not fit on a single line. *)
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Notation "λ: x , e" := (Lam x%binder e%E)
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(at level 200, x at level 1, e at level 200,
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format "'[' 'λ:' x , '/ ' e ']'") : expr_scope.
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Notation "λ: x y .. z , e" := (Lam x%binder (Lam y%binder .. (Lam z%binder e%E) ..))
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(at level 200, x, y, z at level 1, e at level 200,
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format "'[' 'λ:' x y .. z , '/ ' e ']'") : expr_scope.
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Notation "λ: x , e" := (LamV x%binder e%E)
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(at level 200, x at level 1, e at level 200,
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format "'[' 'λ:' x , '/ ' e ']'") : val_scope.
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Notation "λ: x y .. z , e" := (LamV x%binder (Lam y%binder .. (Lam z%binder e%E) .. ))
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(at level 200, x, y, z at level 1, e at level 200,
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format "'[' 'λ:' x y .. z , '/ ' e ']'") : val_scope.
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Notation "'let:' x := e1 'in' e2" := (Lam x%binder e2%E e1%E)
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(only parsing, at level 200, x at level 1, e1, e2 at level 200
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(*, format "'[' 'let:' x := '[' e1 ']' 'in' '/' e2 ']'" *)
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) : expr_scope.
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Notation "e1 ;; e2" := (Lam BAnon e2%E e1%E)
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(at level 100, e2 at level 200,
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format "'[' '[hv' '[' e1 ']' ;; ']' '/' e2 ']'") : expr_scope.
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