diff --git a/Makefile b/Makefile
index d12d9dd..150b04a 100644
--- a/Makefile
+++ b/Makefile
@@ -6,6 +6,7 @@ VPATH = src/
 SRC = \
     src/ast/ast.c \
     src/eval/eval.c \
+    src/parse/climbing_parse.c \
     src/parse/recursive_parse.c \
 
 BIN = evalexpr
diff --git a/src/parse/climbing_parse.c b/src/parse/climbing_parse.c
new file mode 100644
index 0000000..9080f6a
--- /dev/null
+++ b/src/parse/climbing_parse.c
@@ -0,0 +1,248 @@
+#include "parse.h"
+
+#include <ctype.h>
+#include <limits.h>
+#include <stdbool.h>
+#include <stddef.h>
+
+#include "ast/ast.h"
+
+#define UNREACHABLE() __builtin_unreachable()
+#define ARR_SIZE(Arr) (sizeof(Arr) / sizeof(*Arr))
+
+static struct ast_node *climbing_parse_internal(const char **input, int prec);
+static struct ast_node *parse_operand(const char **input);
+
+static void eat_char(const char **input)
+{
+    *input += 1; // Skip this character
+}
+
+static void skip_whitespace(const char **input)
+{
+    while (*input[0] && isspace(*input[0]))
+        eat_char(input);
+}
+
+static enum binop_kind char_to_binop(char c)
+{
+    static const struct { const char *op; const enum binop_kind kind; } ops[] = {
+#define BINOP(Op, Kind, _, __, ___) { #Op, Kind },
+#include "operators.inc"
+    };
+
+    for (size_t i = 0; i < ARR_SIZE(ops); ++i)
+        if (c == ops[i].op[0])
+            return ops[i].kind;
+
+    UNREACHABLE();
+}
+
+static enum unop_kind char_to_unop(char c)
+{
+    static const struct { const char *op; const enum unop_kind kind; } ops[] = {
+#define PREOP(Op, Kind, _, __, ___) { #Op, Kind },
+#define POSTOP(Op, Kind, _, __, ___) { #Op, Kind },
+#include "operators.inc"
+    };
+
+    for (size_t i = 0; i < ARR_SIZE(ops); ++i)
+        if (c == ops[i].op[0])
+            return ops[i].kind;
+
+    UNREACHABLE();
+}
+
+static bool is_binop(char c)
+{
+    static const char *ops[] = {
+#define BINOP(Op, _, __, ___, ____) #Op,
+#include "operators.inc"
+    };
+    for (size_t i = 0; i < ARR_SIZE(ops); ++i)
+        if (c == ops[i][0])
+            return true;
+
+    return false;
+}
+
+static bool prec_between(const char **input, int min, int max)
+{
+    static const struct { const char *op; const int prio; } ops[] = {
+#define BINOP(Op, _, Priority, __, ___) { #Op, Priority },
+#define PREOP(Op, _, Priority, __, ___) { #Op, Priority },
+#define POSTOP(Op, _, Priority, __, ___) { #Op, Priority },
+#include "operators.inc"
+    };
+
+    skip_whitespace(input);
+
+    for (size_t i = 0; i < ARR_SIZE(ops); ++i)
+        if (*input[0] == ops[i].op[0])
+            return min <= ops[i].prio && ops[i].prio <= max;
+
+    return false;
+}
+
+static const struct {
+    const char *op;
+    const int kind; // Because we store different kinds of enum...
+    const int prio;
+    const enum { ASSOC_LEFT, ASSOC_RIGHT, ASSOC_NONE } assoc;
+    const enum { OP_INFIX, OP_PREFIX, OP_POSTFIX } fix;
+} ops[] = {
+# define BINOP(Op, Kind, Prio, Assoc, Fix) { #Op, Kind, Prio, Assoc, Fix },
+#include "operators.inc"
+};
+
+static int right_prec(char c)
+{
+    for (size_t i = 0; i < ARR_SIZE(ops); ++i)
+        if (c == ops[i].op[0])
+        {
+            if (ops[i].assoc == ASSOC_RIGHT)
+                return ops[i].prio;
+            return ops[i].prio + 1;
+        }
+
+    return INT_MIN;
+}
+
+static int next_prec(char c)
+{
+    for (size_t i = 0; i < ARR_SIZE(ops); ++i)
+        if (c == ops[i].op[0])
+        {
+            if (ops[i].assoc != ASSOC_LEFT)
+                return ops[i].prio - 1;
+            return ops[i].prio;
+        }
+
+    return INT_MIN;
+}
+
+/*
+ * Simple climbing parser, see `operators.inc` for more details.
+ *
+ * Whitespace is ignored in the input string, only serving to delimit numbers.
+ *
+ * The input shall consist of a single expression, having a trailing
+ * expression in the input results in an error.
+ */
+struct ast_node *climbing_parse(const char *input)
+{
+    if (input == NULL)
+        return NULL;
+
+    struct ast_node *ast = climbing_parse_internal(&input, 0);
+
+    if (ast == NULL)
+        return NULL;
+
+    // Make sure there is no trailing character, except whitespace
+    skip_whitespace(&input);
+    if (input[0] != '\0')
+    {
+        destroy_ast(ast);
+        return NULL;
+    }
+
+    return ast;
+}
+
+static struct ast_node *climbing_parse_internal(const char **input, int prec)
+{
+    prec = prec;
+    struct ast_node *ast = parse_operand(input);
+
+    int r = INT_MAX;
+    while (/* infix_or_postfix(input) && */ prec_between(input, prec, r) && ast)
+    {
+        const char c = *input[0];
+        eat_char(input);
+        if (is_binop(c))
+        {
+            enum binop_kind op = char_to_binop(c);
+            struct ast_node *rhs = climbing_parse_internal(input, right_prec(c));
+            if (!rhs)
+            {
+                destroy_ast(ast);
+                return NULL;
+            }
+            struct ast_node *tree = make_binop(op, ast, rhs);
+
+            if (!tree)
+                destroy_ast(ast); // Error case
+            ast = tree;
+        }
+        else
+        {
+            struct ast_node *tree = make_unop(char_to_unop(c), ast);
+            if (!tree)
+                destroy_ast(ast); // Error case
+            ast = tree;
+        }
+        r = next_prec(c);
+    }
+
+    return ast;
+}
+
+static bool my_atoi(const char **input, int *val)
+{
+    if (!isdigit(*input[0]))
+        return false;
+
+    *val = 0; // Initialize its value
+    do
+    {
+        *val *= 10;
+        *val += *input[0] - '0';
+        *input += 1;
+    } while (isdigit(*input[0]));
+
+    return true;
+}
+
+static struct ast_node *parse_operand(const char **input)
+{
+    skip_whitespace(input); // Whitespace is not significant
+    struct ast_node *ast = NULL;
+
+    int val = 0;
+    if (*input[0] == '+' || *input[0] == '-')
+    {
+        enum unop_kind op = char_to_unop(*input[0]);
+        // Remove the parenthesis
+        eat_char(input);
+
+        ast = climbing_parse_internal(input, 2); // FIXME: should be from table
+
+        if (!ast)
+            return NULL;
+        struct ast_node *tree = make_unop(op, ast);
+        if (!tree)
+            destroy_ast(ast);
+        ast = tree;
+    }
+    else if (my_atoi(input, &val))
+        ast = make_num(val);
+    else if (*input[0] == '(')
+    {
+        // Remove the parenthesis
+        eat_char(input);
+        ast = climbing_parse_internal(input, 0);
+        // Check that we have our closing parenthesis
+        skip_whitespace(input);
+        if (*input[0] != ')')
+        {
+            destroy_ast(ast);
+            return NULL;
+        }
+        // Remove the parenthesis
+        eat_char(input);
+        return ast;
+    }
+
+    return ast;
+}
diff --git a/src/parse/operators.inc b/src/parse/operators.inc
new file mode 100644
index 0000000..14b6bb8
--- /dev/null
+++ b/src/parse/operators.inc
@@ -0,0 +1,34 @@
+/*
+ * Corresponds to the following grammar, with E as start:
+ *
+ * E : T [ ('+'|'-') T ]*
+ * T : F [ ('*'|'/') F ]*
+ * F : [ ('-'|'+') ]* P
+ * P : G ('^') F
+ * G : ( '(' E ')' | CONSTANT ) [ '!' ]
+ *
+ * G, the operand, is parsed by a specific function to start the process.
+ */
+
+#ifndef BINOP
+# define BINOP(_, __, ___, ____, _____)
+#endif
+#ifndef PREOP
+# define PREOP(_, __, ___, ____, _____)
+#endif
+#ifndef POSTOP
+# define POSTOP(_, __, ___, ____, _____)
+#endif
+
+BINOP(+,  BINOP_PLUS,    1, ASSOC_LEFT,  OP_INFIX)
+BINOP(-,  BINOP_MINUS,   1, ASSOC_LEFT,  OP_INFIX)
+BINOP(*,  BINOP_TIMES,   2, ASSOC_LEFT,  OP_INFIX)
+BINOP(/,  BINOP_DIVIDES, 2, ASSOC_LEFT,  OP_INFIX)
+BINOP(^,  BINOP_POW,     4, ASSOC_RIGHT, OP_INFIX)
+PREOP(-,  UNOP_NEGATE,   3, ASSOC_RIGHT, OP_PREFIX)
+PREOP(+,  UNOP_IDENTITY, 3, ASSOC_RIGHT, OP_PREFIX)
+POSTOP(!, UNOP_FACT,     5, ASSOC_NONE,  OP_POSTFIX)
+
+#undef BINOP
+#undef PREOP
+#undef POSTOP
diff --git a/src/parse/parse.h b/src/parse/parse.h
index 0dc7716..3f9f837 100644
--- a/src/parse/parse.h
+++ b/src/parse/parse.h
@@ -3,6 +3,7 @@
 
 #include "ast/ast.h"
 
+struct ast_node *climbing_parse(const char *input);
 struct ast_node *recursive_parse(const char *input);
 
 #endif /* !PARSE_H */