diff --git a/grammar.md b/grammar.md
index 47bbfca..41d72fb 100644
--- a/grammar.md
+++ b/grammar.md
@@ -29,9 +29,9 @@ init -- "otherwise" --> error[[error]]
 
 ```
 S -> A
-A -> A + A | A - A | M
-M -> M * M | M / M | G
-G -> ( A ) | P ^ G | ID
+A -> M + A | M - A | M
+M -> G * M | G / M | G
+G -> P ^ G | P
 P -> ( A ) | ID
 ```
 
@@ -82,16 +82,14 @@ s1("[S->.A]") --> s2(["[S->A.]"])
 
 ```mermaid
 graph LR;
-a1("[A->.A+A] | [A->.A-A] | [A->.M]")
-a2(["[A->M.]"])
-a3("[A->A.+A] | [A->A.-A]")
-a4("[A->A+.A]")
-a5(["[A->A+A.]"])
-a6("[A->A-.A]")
-a7(["[A->A-A.]"])
+a1("[A->.M+A] | [A->.M-A] | [A->.M]")
+a3(["[A->M.+A] | [A->M.-A] | [A->M.]"])
+a4("[A->M+.A]")
+a5(["[A->M+A.]"])
+a6("[A->M-.A]")
+a7(["[A->M-A.]"])
 
-a1 -- M --> a2
-a1 -- A --> a3
+a1 -- M --> a3
 a3 -- + --> a4
 a4 -- A --> a5
 a3 -- - --> a6
@@ -100,16 +98,14 @@ a6 -- A --> a7
 
 ```mermaid
 graph LR;
-m1("[M->.M*M] | [M->.M/M] | [M->.G]")
-m2(["[M->G.]"])
-m3("[M->M.*M] | [M->M./M]")
-m4("[M->M*.M]")
-m5(["[M->M*M.]"])
-m6("[M->M/.M]")
-m7(["[M->M/M.]"])
+m1("[M->.G*M] | [M->.G/M] | [M->.G]")
+m3(["[M->G.*M] | [M->G./M] | [M->G.]"])
+m4("[M->G*.M]")
+m5(["[M->G*M.]"])
+m6("[M->G/.M]")
+m7(["[M->G/M.]"])
 
-m1 -- G --> m2
-m1 -- M --> m3
+m1 -- G --> m3
 m3 -- * --> m4
 m4 -- M --> m5
 m3 -- / --> m6
@@ -118,22 +114,14 @@ m6 -- M --> m7
 
 ```mermaid
 graph LR;
-g1("[G->.(A)] | [G->.P^G] | [G->.ID]")
-g2("[G->(.A)]")
-g3("[G->(A.)]")
-g4(["[G->(A).]"])
-g5("[G->P.^G]")
+g1("[G->.P^G] | [G->.P]")
+g5(["[G->P.^G] | [G->P.]"])
 g6("[G->P^.G]")
 g7(["[G->P^G.]"])
-g8(["[G->ID.]"])
 
-g1 -- "(" --> g2
-g2 -- A --> g3
-g3 -- ")" --> g4
 g1 -- P --> g5
 g5 -- ^ --> g6
 g6 -- G --> g7
-g1 -- ID --> g8
 ```
 
 ```mermaid
diff --git a/src/lexer/mod.rs b/src/lexer/mod.rs
index b238760..b54a144 100644
--- a/src/lexer/mod.rs
+++ b/src/lexer/mod.rs
@@ -10,8 +10,8 @@ use crate::lexer::errors::LexerErrors::EmptyTextSequenceError;
 use crate::lexer::fsm::{FSM, get_token};
 use crate::lexer::tokens::{OpType, TokenMeta};
 
-mod errors;
-mod tokens;
+pub mod errors;
+pub mod tokens;
 mod fsm;
 
 pub type Result<T> = std::result::Result<T, errors::LexerErrors>;
diff --git a/src/lexer/tokens.rs b/src/lexer/tokens.rs
index a9b064e..f20370c 100644
--- a/src/lexer/tokens.rs
+++ b/src/lexer/tokens.rs
@@ -4,12 +4,12 @@
 /// * File that the token was parsed in
 /// * Line that the token was parsed in
 /// * Position of the *first character making up the token* in said line
-#[derive(Debug)]
+#[derive(Debug, Clone)]
 pub struct TokenMeta {
     pub pos: usize,
 }
 
-#[derive(Debug)]
+#[derive(Debug, Clone)]
 pub enum OpType {
     MUL,
     DIV,
@@ -45,7 +45,7 @@ pub enum BrType {
 /// 1. `OBR`: An opening bracket (`(`).
 /// 1. `CBR`: A closing bracket (`)`).
 /// 1. `OP`: An operation. Containing an [Operation Type](OpType).
-#[derive(Debug)]
+#[derive(Debug, Clone)]
 pub enum Token {
     ID (TokenMeta, f64),
     OBR (TokenMeta),
diff --git a/src/lib.rs b/src/lib.rs
index 0e5d4cb..b0a77fc 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1,5 +1,6 @@
 pub mod lexer;
 pub mod errors;
+mod parser;
 
 pub fn test() {
     println!("{}", "hi there");
diff --git a/src/parser/errors.rs b/src/parser/errors.rs
new file mode 100644
index 0000000..342643d
--- /dev/null
+++ b/src/parser/errors.rs
@@ -0,0 +1,13 @@
+use thiserror::Error;
+use crate::lexer::errors::LexerErrors;
+use crate::lexer::tokens::Token;
+
+#[derive(Debug, Error)]
+pub enum ParserErrors {
+    #[error("unexpected token: {0:?} in procedure {1}")]
+    UnexpectedTokenError(Token, String),
+    #[error("input ended prematurely")]
+    MissingTokenError,
+    #[error("lexer error")]
+    LexerError(#[from] LexerErrors),
+}
diff --git a/src/parser/mod.rs b/src/parser/mod.rs
new file mode 100644
index 0000000..7ba9655
--- /dev/null
+++ b/src/parser/mod.rs
@@ -0,0 +1,111 @@
+use std::result;
+
+use tokens::{OpType, Token};
+
+use crate::lexer;
+use crate::lexer::tokens;
+use crate::parser::errors::ParserErrors;
+use crate::parser::errors::ParserErrors::UnexpectedTokenError;
+
+mod errors;
+
+type Result<T> = result::Result<T, errors::ParserErrors>;
+
+pub struct TokenBox {
+    lexer: lexer::Lexer,
+    cur_token: Option<Token>,
+    regress: bool, // whether the last token should be outputted when reading a new token
+}
+
+impl TokenBox {
+    fn read_token(&mut self) -> Result<&Option<Token>> {
+        if self.regress {
+            // if 'regressing' as in going back in time once, just set it to false (as in done)
+            self.regress = false;
+        } else {
+            // if not, read the next token from the lexer
+            self.cur_token = self.lexer.next()?;
+        }
+        Ok(&self.cur_token)
+    }
+
+    fn regress(&mut self) {
+        self.regress = true;
+    }
+}
+
+fn expect_token(maybe_token: &Option<Token>) -> Result<&Token> {
+    match &maybe_token {
+        &Some(token) => Ok(token),
+        &None => Err(ParserErrors::MissingTokenError),
+    }
+}
+
+pub fn parse(mut lexer: lexer::Lexer) -> Result<f64> {
+    let mut tbox = TokenBox { lexer, cur_token: None, regress: false };
+    s_proc(&mut tbox)
+}
+
+pub fn s_proc(tbox: &mut TokenBox) -> Result<f64> {
+    let mut result = a_proc(tbox)?;
+    match tbox.read_token()? {
+        None => Ok(result),
+        Some(token) => Err(ParserErrors::UnexpectedTokenError(token.clone(), String::from("S"))),
+    }
+}
+
+fn a_proc(tbox: &mut TokenBox) -> Result<f64> {
+    let mut result = m_proc(tbox)?;
+    match &tbox.read_token()? {
+        Some(Token::OP(_, OpType::ADD)) => Ok(result + a_proc(tbox)?),
+        Some(Token::OP(_, OpType::SUB)) => Ok(result - a_proc(tbox)?),
+        None => Ok(result),
+        Some(token) => Err(ParserErrors::UnexpectedTokenError(token.clone(), String::from("A")))
+    }
+}
+
+fn m_proc(tbox: &mut TokenBox) -> Result<f64> {
+    let mut result = g_proc(tbox)?;
+    match &tbox.read_token()? {
+        Some(Token::OP(_, OpType::MUL)) => Ok(result * m_proc(tbox)?),
+        Some(Token::OP(_, OpType::DIV)) => Ok(result / m_proc(tbox)?),
+        None => Ok(result),
+        Some(token) => Err(UnexpectedTokenError(token.clone(), String::from("M"))),
+    }
+}
+
+fn g_proc(tbox: &mut TokenBox) -> Result<f64> {
+    let mut result = p_proc(tbox)?;
+    match tbox.read_token()? {
+        Some(Token::OP(_, OpType::POW)) => Ok(result.powf(g_proc(tbox)?)),
+        None => Ok(result),
+        Some(token) => Err(UnexpectedTokenError(token.clone(), String::from("G"))),
+    }
+}
+
+fn p_proc(tbox: &mut TokenBox) -> Result<f64> {
+    match expect_token(tbox.read_token()?)? {
+        Token::OBR(_) => {
+            let result = a_proc(tbox)?;
+            match expect_token(tbox.read_token()?)? {
+                Token::CBR(_) => Ok(result),
+                token => Err(UnexpectedTokenError(token.clone(), String::from("P"))),
+            }
+        },
+        Token::ID(_, val) => Ok(*val),
+        token => Err(ParserErrors::UnexpectedTokenError(token.clone(), String::from("P"))),
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    #[test]
+    fn simple_formula() -> Result<()> {
+        let res = parse(lexer::Lexer::new("15+3"))?;
+        println!("res: {}", res);
+        assert_eq!(res, 18.0);
+        Ok(())
+    }
+}