feat: only compute all free variables during a-conversion

pkg/lambda/is_free_variable.go

@@ -0,0 +1,14 @@
+package lambda
+
+func IsFreeVariable(n string, e Expression) bool {
+	switch e := e.(type) {
+	case *Variable:
+		return e.Value == n
+	case *Abstraction:
+		return e.Parameter != n && IsFreeVariable(n, e.Body)
+	case *Application:
+		return IsFreeVariable(n, e.Abstraction) || IsFreeVariable(n, e.Argument)
+	default:
+		return false
+	}
+}

pkg/lambda/substitute.go

@@ -11,12 +11,12 @@ func Substitute(e *Expression, target string, replacement Expression) {
 			return
 		}
 
-		replacementFreeVars := GetFreeVariables(replacement)
-		if !replacementFreeVars.Has(typed.Parameter) {
+		if !IsFreeVariable(typed.Parameter, replacement) {
 			Substitute(&typed.Body, target, replacement)
 			return
 		}
 
+		replacementFreeVars := GetFreeVariables(replacement)
 		used := GetFreeVariables(typed.Body)
 		used.Merge(replacementFreeVars)
 		freshVar := GenerateFreshName(used)