diff --git a/src/builtins/mod.rs b/src/builtins/mod.rs
index 0402004..f5bee3a 100644
--- a/src/builtins/mod.rs
+++ b/src/builtins/mod.rs
@@ -10,5 +10,18 @@ pub fn initialise_globals() -> GlobalNamespace {
     ns.register_type("integer").unwrap().add_trait(&numeric);
     ns.register_type("float").unwrap().add_trait(&numeric);
 
+    ns.register_type("string").unwrap();
+
+    // def math add [ Numeric Numeric ] -> Numeric
+    ns.register_command(
+        "add",
+        Some(TypeDef::List(vec![
+            TypeDef::Trait(numeric),
+            TypeDef::Trait(numeric),
+        ])),
+        Some(TypeDef::Trait(numeric)),
+    )
+    .unwrap();
+
     ns
 }
diff --git a/src/builtins/namespace.rs b/src/builtins/namespace.rs
index 1249cf9..26a6af3 100644
--- a/src/builtins/namespace.rs
+++ b/src/builtins/namespace.rs
@@ -101,6 +101,28 @@ impl GlobalNamespace {
         }
     }
 
+    pub fn get_type(&self, id: usize) -> Option<Type> {
+        if self.types.borrow().len() > id {
+            Some(Type {
+                id,
+                namespace: self,
+            })
+        } else {
+            None
+        }
+    }
+
+    pub fn get_trait(&self, id: usize) -> Option<Trait> {
+        if self.traits.borrow().len() > id {
+            Some(Trait {
+                id,
+                namespace: self,
+            })
+        } else {
+            None
+        }
+    }
+
     pub fn get_type_by_name(&self, name: &str) -> Option<Type> {
         if let Some(TypeNamespaceId::Types(id)) = self.type_namespace.borrow().get(name) {
             Some(Type {
@@ -129,6 +151,7 @@ pub enum TypeRegistrationError {
     NameAlreadyExists,
 }
 
+#[derive(Clone, Copy)]
 pub struct Type<'a> {
     id: usize,
     namespace: &'a GlobalNamespace,
@@ -158,6 +181,7 @@ struct InternalType {
     name: String,
 }
 
+#[derive(Clone, Copy)]
 pub struct Trait<'a> {
     id: usize,
     namespace: &'a GlobalNamespace,
@@ -169,11 +193,29 @@ struct InternalTrait {
     name: String,
 }
 
-struct Command<'a> {
+#[derive(Clone, Copy)]
+pub struct Command<'a> {
     id: usize,
     namespace: &'a GlobalNamespace,
 }
 
+impl<'a> Command<'a> {
+    pub fn get_input_types(&self) -> Option<TypeDef<'a>> {
+        self.namespace
+            .commands
+            .borrow()
+            .get(self.id)
+            .unwrap()
+            .input
+            .map(|def| TypeDef::from_internal(self.namespace, &def))
+    }
+    pub fn get_output_types(&self) -> Option<TypeDef> {
+        self.namespace.commands.borrow()[self.id]
+            .output
+            .map(|def| TypeDef::from_internal(self.namespace, &def))
+    }
+}
+
 struct InternalCommand {
     name: String,
     // gosh this is hacky
@@ -193,6 +235,28 @@ pub enum TypeDef<'a> {
     Record(Vec<(String, TypeDef<'a>)>),
 }
 
+impl<'a> TypeDef<'a> {
+    fn from_internal(ns: &'a GlobalNamespace, def: &'a InternalTypeDef) -> TypeDef<'a> {
+        match def {
+            InternalTypeDef::Single(id) => match id {
+                // safe to unwrap because this is only used with internal representations
+                TypeNamespaceId::Types(id) => TypeDef::Type(ns.get_type(*id).unwrap()),
+                TypeNamespaceId::Traits(id) => TypeDef::Trait(ns.get_trait(*id).unwrap()),
+            },
+            InternalTypeDef::List(list) => TypeDef::List(
+                list.into_iter()
+                    .map(|def| Self::from_internal(ns, def))
+                    .collect(),
+            ),
+            InternalTypeDef::Record(rec) => TypeDef::Record(
+                rec.into_iter()
+                    .map(|(name, def)| (name.clone(), Self::from_internal(ns, def)))
+                    .collect(),
+            ),
+        }
+    }
+}
+
 enum InternalTypeDef {
     Single(TypeNamespaceId),
     List(Vec<InternalTypeDef>),
diff --git a/src/lexer.rs b/src/lexer.rs
index 831a1c4..9db137c 100644
--- a/src/lexer.rs
+++ b/src/lexer.rs
@@ -7,7 +7,7 @@ pub enum Token<'a> {
     Word(&'a str),
     #[regex("[\\d]+", priority = 2, callback = |lex| lex.slice().parse::<i64>().unwrap())]
     IntLiteral(i64),
-    #[regex("[\\d]+.[\\d]+", |lex| lex.slice().parse::<f64>().unwrap())]
+    #[regex("[\\d]+\\.[\\d]+", |lex| lex.slice().parse::<f64>().unwrap())]
     FloatLiteral(f64),
     #[regex(r#""([^"\\]|\\["\\bnfrt]|u[a-fA-F0-9]{4})*""#, |lex| lex.slice().to_owned())]
     StringLiteral(String),
diff --git a/src/main.rs b/src/main.rs
index 7955b8f..467130e 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -1,16 +1,19 @@
 use builtins::initialise_globals;
-use codespan_reporting::files::SimpleFiles;
-use codespan_reporting::term;
-use codespan_reporting::term::termcolor::ColorChoice;
-use codespan_reporting::term::termcolor::StandardStream;
+use codespan_reporting::{
+    files::SimpleFiles,
+    term::{
+        self,
+        termcolor::{ColorChoice, StandardStream},
+    },
+};
 use syntax::parse_syntax;
 
 use crate::syntax::check::check;
 
 mod builtins;
-mod hir;
 mod lexer;
 mod syntax;
+mod type_repr;
 
 fn main() {
     let mut files = SimpleFiles::new();
@@ -57,7 +60,24 @@ fn main() {
         out_errs.append(&mut errs)
     }
 
-    // invalid
+    let valid_add_input_pipe = "1 | add 2";
+    let valid_add_input_pipe_id = files.add("valid_add_input_pipe", valid_add_input_pipe);
+    let syntax = dbg!(check(
+        parse_syntax(valid_add_input_pipe, valid_add_input_pipe_id).unwrap(),
+        valid_add_input_pipe,
+        valid_add_input_pipe_id,
+    )
+    .unwrap());
+
+    let valid_add_input_args = "add 1 2";
+    let valid_add_input_args_id = files.add("valid_add_input_args", valid_add_input_args);
+    let syntax = dbg!(check(
+        parse_syntax(valid_add_input_args, valid_add_input_args_id).unwrap(),
+        valid_add_input_args,
+        valid_add_input_args_id,
+    )
+    .unwrap());
+
     let writer = StandardStream::stderr(ColorChoice::Always);
     let config = term::Config::default();
 
diff --git a/src/syntax/mod.rs b/src/syntax/mod.rs
index df3c971..eec82fc 100644
--- a/src/syntax/mod.rs
+++ b/src/syntax/mod.rs
@@ -13,8 +13,8 @@ mod error;
 
 #[derive(Debug, Clone, PartialEq)]
 pub struct PipelineElement {
-    kind: PipelineElementKind,
-    span: Span,
+    pub kind: PipelineElementKind,
+    pub span: Span,
 }
 
 #[derive(Debug, Clone, PartialEq)]
@@ -25,8 +25,8 @@ pub enum PipelineElementKind {
 
 #[derive(Debug, Clone, PartialEq)]
 pub struct CommandPart {
-    kind: CommandPartKind,
-    span: Span,
+    pub kind: CommandPartKind,
+    pub span: Span,
 }
 
 #[derive(Debug, Clone, PartialEq)]