split bidirectional checking and conversion + defaults out of simple.rs

1 files changed, 120 insertions, 0 deletions

diff --git a/src/bidirectional.rs b/src/bidirectional.rs
new file mode 100644
index 0000000..493ae2f
--- /dev/null
+++ b/src/bidirectional.rs
@@ -0,0 +1,120 @@
+// Simple bidirectional type checking
+
+use crate::ast::*;
+
+/// Checking judgement: takes an expression and a type to check against and calls out to `infer` as needed.
+pub fn check(context: &Context, expression: Expression, target: &Type) -> Result<(), String> {
+    match expression {
+        // fall through to inference mode
+        Expression::Annotation { expr, kind } => {
+            let result = infer(context, Expression::Annotation { expr, kind })?;
+            return match subtype(&result, &target) {
+                true => Ok(()),
+                false => Err(format!("inferred type {result} does not match target {target}"))
+            }
+        },
+        // Bt-CheckInfer
+        Expression::Constant { term } => match subtype(&convert(&term)?, &target) {
+            true => Ok(()),
+            false => Err(format!("constant is of wrong type, expected {target}"))
+            // false => Ok(()) // all our constants are Empty for now
+        },
+        // Bt-CheckInfer
+        Expression::Variable { id } => match context.get(&id) {
+            Some(term) if subtype(&convert(term)?, &target) => Ok(()),
+            Some(_) => Err(format!("variable {id} is of wrong type")),
+            None => Err(format!("failed to find variable {id} in context"))
+        },
+        // Bt-Abs
+        Expression::Abstraction { param, func } => match target {
+            Type::Function { from, to } => {
+                let mut context = context.clone();
+                context.insert(param, default(from)?);
+                return check(&context, *func, &to);
+            },
+            _ => Err(format!("attempting to check an abstraction with a non-function type {target}"))
+        },
+        // fall through to inference mode
+        Expression::Application { func, arg } => {
+            let result = &infer(context, Expression::Application { func, arg })?;
+            return match subtype(&result, &target) {
+                true => Ok(()),
+                false => Err(format!("inferred type {result} does not match {target}"))
+            }
+        },
+        // T-If
+        Expression::Conditional { if_cond, if_then, if_else } => {
+            check(context, *if_cond, &Type::Boolean)?;
+            check(context, *if_then, &target)?;
+            check(context, *if_else, &target)?;
+            return Ok(());
+        }
+    }
+}
+
+/// Inference judgement: takes an expression and attempts to infer the associated type.
+pub fn infer(context: &Context, expression: Expression) -> Result<Type, String> {
+    match expression {
+        // Bt-Ann
+        Expression::Annotation { expr, kind } => check(context, *expr, &kind).map(|x| kind),
+        // Bt-True / Bt-False / etc
+        Expression::Constant { term } => convert(&term),
+        // Bt-Var
+        Expression::Variable { id } => match context.get(&id) {
+            Some(term) => infer(&Context::new(), Expression::Constant { term: term.clone() }),
+            None => Err(format!("failed to find variable in context {context:?}"))
+        },
+        // Bt-App
+        Expression::Application { func, arg } => match infer(context, *func)? {
+            Type::Function { from, to } => check(context, *arg, &*from).map(|x| *to),
+            _ => Err(format!("application abstraction is not a function type"))
+        },
+        // inference from an abstraction is always an error
+        // we could try and infer the func without adding the parameter to scope:
+        // but this is overwhelmingly likely to be an error, so just report it now.
+        Expression::Abstraction { param, func } =>
+            Err(format!("attempting to infer from an abstraction")),
+        // idk
+        Expression::Conditional { if_cond, if_then, if_else } => {
+            check(context, *if_cond, &Type::Boolean)?;
+            let if_then = infer(context, *if_then)?;
+            let if_else = infer(context, *if_else)?;
+            if subtype(&if_then, &if_else) && subtype(&if_else, &if_then) {
+                Ok(if_then) // fixme: should be the join
+            } else {
+                Err(format!("if clauses of different types: {if_then} and {if_else}"))
+            }
+        }
+    }
+}
+
+/// The subtyping relation between any two types.
+pub fn subtype(is: &Type, of: &Type) -> bool {
+    match (is, of) {
+        (Type::Record(is_fields), Type::Record(of_fields)) => {
+            // width, depth, and permutation
+            for (key, of_value) in of_fields {
+                match is_fields.get(key) {
+                    Some(is_value) => {
+                        if !subtype(is_value, of_value) {
+                            return false;
+                        }
+                    }
+                    None => return false
+                }
+            }
+            return true;
+        },
+        (Type::Enum(is_variants), Type::Enum(of_variants)) => false, // fixme
+        (Type::Function { from: is_from, to: is_to },
+         Type::Function { from: of_from, to: of_to }) => {
+            subtype(of_from, is_from) && subtype(is_to, of_to)
+        },
+        (Type::Natural, Type::Integer) => true, // obviously not, but let's pretend
+        (_, Type::Empty) => true,
+        (Type::Error, _) => true,
+        (_, _) if is == of => true,
+        (_, _) => false
+    }
+}
+