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coq notation definition for expressions

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Michael Sippel 2024-08-18 10:27:21 +02:00
parent 8da65e4d38
commit 3a84dada65
Signed by: senvas
GPG key ID: 060F22F65102F95C
2 changed files with 46 additions and 24 deletions
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68
coq/terms.v
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@ -32,40 +32,62 @@ Inductive expr_term : Type :=
| expr_descend : type_term -> expr_term -> expr_term | expr_descend : type_term -> expr_term -> expr_term
. .
Coercion type_var : string >-> type_term. (* values *)
Coercion expr_var : string >-> expr_term. Inductive is_value : expr_term -> Prop :=
| V_ValAbs : forall x τ e,
(is_value (expr_tm_abs x τ e))
(* | V_TypAbs : forall τ e,
Coercion type_var : string >-> type_term. (is_value (expr_ty_abs τ e))
Coercion expr_var : string >-> expr_term.
*) | V_Ascend : forall τ e,
(is_value e) ->
(is_value (expr_ascend τ e))
.
Declare Scope ladder_type_scope. Declare Scope ladder_type_scope.
Declare Scope ladder_expr_scope. Declare Scope ladder_expr_scope.
Declare Custom Entry ladder_type. Declare Custom Entry ladder_type.
Declare Custom Entry ladder_expr.
Notation "[ e ]" := e (e custom ladder_type at level 80) : ladder_type_scope. Notation "[ t ]" := t
(t custom ladder_type at level 80) : ladder_type_scope.
Notation "'∀' x ',' t" := (type_univ x t)
(t custom ladder_type at level 80, in custom ladder_type at level 80, x constr).
Notation "'<' σ τ '>'" := (type_spec σ τ)
(in custom ladder_type at level 80, left associativity) : ladder_type_scope.
Notation "'(' τ ')'" := τ
(in custom ladder_type at level 70) : ladder_type_scope.
Notation "σ '->' τ" := (type_fun σ τ)
(in custom ladder_type at level 75, right associativity) : ladder_type_scope.
Notation "σ '->morph' τ" := (type_morph σ τ)
(in custom ladder_type at level 75, right associativity, τ at level 80) : ladder_type_scope.
Notation "σ '~' τ" := (type_ladder σ τ)
(in custom ladder_type at level 70, right associativity) : ladder_type_scope.
Notation "'$' x '$'" := (type_id x%string)
(in custom ladder_type at level 0, x constr) : ladder_type_scope.
Notation "'%' x '%'" := (type_var x%string)
(in custom ladder_type at level 0, x constr) : ladder_type_scope.
(* TODO: allow any variable names in notation, not just α,β,γ *) Notation "[[ e ]]" := e
Notation "'∀α.' τ" := (type_univ "α" τ) (in custom ladder_type at level 80) : ladder_type_scope. (e custom ladder_expr at level 80) : ladder_expr_scope.
Notation "'∀β.' τ" := (type_univ "β" τ) (in custom ladder_type at level 80) : ladder_type_scope. Notation "'%' x '%'" := (expr_var x%string)
Notation "'∀γ.' τ" := (type_univ "γ" τ) (in custom ladder_type at level 80) : ladder_type_scope. (in custom ladder_expr at level 0, x constr) : ladder_expr_scope.
Notation "'<' σ τ '>'" := (type_spec σ τ) (in custom ladder_type at level 80, left associativity) : ladder_type_scope. Notation "'λ' x τ '↦' e" := (expr_tm_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 "'(' τ ')'" := τ (in custom ladder_type at level 70) : ladder_type_scope. Notation "'Λ' t '↦' e" := (expr_ty_abs t e)
Notation "σ '->' τ" := (type_fun σ τ) (in custom ladder_type at level 75, right associativity) : ladder_type_scope. (in custom ladder_expr at level 0, t constr, e custom ladder_expr at level 80).
Notation "σ '->morph' τ" := (type_morph σ τ) (in custom ladder_type at level 75, right associativity) : ladder_type_scope.
Notation "σ '~' τ" := (type_ladder σ τ) (in custom ladder_type at level 70, right associativity) : ladder_type_scope.
Notation "'α'" := (type_var "α") (in custom ladder_type at level 60, right associativity) : ladder_type_scope.
Notation "'β'" := (type_var "β") (in custom ladder_type at level 60, right associativity) : ladder_type_scope.
Notation "'γ'" := (type_var "γ") (in custom ladder_type at level 60, right associativity) : ladder_type_scope.
Open Scope ladder_type_scope. Open Scope ladder_type_scope.
Open Scope ladder_expr_scope.
Definition t1 : type_term := [ ∀α.∀β.(α~β~γ)->β->(α->α)->β ]. Check [ ∀"α", (< $"Seq"$ %"α"% > ~ < $"List"$ %"α"% >) ].
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.
Compute t1.
Close Scope ladder_type_scope. Close Scope ladder_type_scope.
Close Scope ladder_expr_scope.
End Terms. End Terms.

2
coq/typing.v
View file

@ -27,7 +27,7 @@ Reserved Notation "Gamma '|-' x '\compatible' X" (at level 101, x at next level
Inductive expr_type : context -> expr_term -> type_term -> Prop := Inductive expr_type : context -> expr_term -> type_term -> Prop :=
| T_Var : forall Γ x τ, | T_Var : forall Γ x τ,
(context_contains Γ x τ) -> (context_contains Γ x τ) ->
(Γ |- x \is τ) (Γ |- (expr_var x) \is τ)
| T_Let : forall Γ s (σ:type_term) t τ x, | T_Let : forall Γ s (σ:type_term) t τ x,
(Γ |- s \is σ) -> (Γ |- s \is σ) ->