Use "let" instead of "var" to introduce terms

lexer.mll

@@ -22,7 +22,7 @@ rule token = parse
     | "->" { ARR }
     | "λ" { LAMBDA }
     | "type" { TYPE (Parsing.rhs_start_pos 1) }
-    | "var" { VAR (Parsing.rhs_start_pos 1) }
+    | "let" { VAR (Parsing.rhs_start_pos 1) }
     | "check" { CHECK (Parsing.rhs_start_pos 1) }
     | "norm" { NORM (Parsing.rhs_start_pos 1) }
     | [ 'a'-'z' ] ['a'-'z' 'A'-'Z' '_' '0'-'9']* as s { ID (s) }

test.sigma

@@ -3,18 +3,20 @@ type A ::= [ a : [] ].
 
 type Bool ::= [ if : A ; then : A ; else : A ].
 
-var true : Bool ::= [ if = ς(x : Bool) x.then ;
+type Arrow ::= [ arg : A ; val : A ].
+
+let true : Bool ::= [ if = ς(x : Bool) x.then ;
                       then = ς(x : Bool) x.then ;
                       else = ς(x : Bool) x.else ].
 
-var false : Bool ::= [ if = ς(x : Bool) x.else ;
+let false : Bool ::= [ if = ς(x : Bool) x.else ;
                        then = ς(x : Bool) x.then ;
                        else = ς(x : Bool) x.else ].
-var if : Bool -> A -> A -> A ::=
+let if : Bool -> A -> A -> A ::=
        λ(b : Bool) λ(t : A) λ(e : A) ((b.then := t).else := e).if.
 
 type Nat ::= [ iszero : Bool ;
                pred : A ].
 
-var 0 : Nat ::= [ iszero = ς(x : Nat) true ;
+let 0 : Nat ::= [ iszero = ς(x : Nat) true ;
                   pred = ς(x : Nat) x.pred ].