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Joined 2026-09-21 Message
Incoming links: Compilation
Abstract syntax tree 2026-10-13
An abstract syntax tree is a rooted tree recording the meaningful syntactic pieces of a program and how they fit together. A program identifier such as
x, a literal value such as 2, and a node representing addition have different roles. Their arrangement answers structural questions: which program expression supplies an operand, which name is a variable assignment target, and which construct encloses another. This makes an abstract syntax tree useful to a compiler, an interpreter, and the type system that checks a program.The word "abstract" describes what is omitted. Lexical analysis first recognizes lexical tokens, such as
x, =, 2, +, 3, *, 4. A concrete parse tree can retain grammar derivation structure, including punctuation and intermediate context-free grammar categories such as expression, term and factor. An abstract syntax tree usually keeps the operation and its operands without all those grammar scaffolds. Parentheses can determine its shape without surviving as separate nodes. A parser may construct the abstract syntax tree directly; it need not first allocate a concrete parse tree.An abstract syntax tree records programming language syntax, but does not by itself supply all programming language semantics. In
a+b, the names do not reveal their current values, and + might perform addition of integers or concatenate strings. The programming language rules, name bindings, and operand types determine the meaning. In Python, successfully calling ast.parse also does not guarantee that later compilation will accept the result: parsing return 42 succeeds, but compiling that statement outside a function fails. [ref]ast — Abstract syntax trees, Python 3.14 documentation. ast.parse: parsing performs no scoping checks; the return 42 example
An abstract syntax tree is not machine code. Its nodes describe language constructs. A compiler can check and transform this structure before translating it into executable instructions; an interpreter can evaluate an appropriate tree directly. The little evaluator below demonstrates this distinction without pretending to implement an entire programming language.
Bytecode Created 2026-10-14 Updated 2026-10-31
An encoded instruction representation for a software execution mechanism. Compilation can produce bytecode that an interpreter executes.
Compilation Created 2026-10-13 Updated 2026-10-31
Compilation is the translation process performed by a compiler, which may include checking and transforming an abstract syntax tree. Translation can finish before execution, or happen during execution through just-in-time compilation. Reusing the translated representation can avoid repeated parsing and repeated constant folding when only the inputs change. This does not guarantee a speedup: translation itself costs work, and the choice of representation and execution mechanism matters.
One possible compilation pipeline for
. Details. x*(2+3)-4, with execution from an abstract syntax tree, a stack machine instruction sequence, or machine code Compilation arithmetic example 2026-10-14
Consider the program expression
x*(2+3)-4 in a deliberately small programming language. Its only program identifier is x, supplied as an integer input. Its literal values are nonnegative decimal numerals, interpreted as integers. Whitespace is ignored between lexical tokens. Its context-free grammar is:expression ::= term (("+" | "-") term)*
term ::= factor ("*" factor)*
factor ::= numeral | "x" | "(" expression ")"
numeral ::= digit digit*
digit ::= "0" | "1" | "2" | "3" | "4"
| "5" | "6" | "7" | "8" | "9"Here
* outside quotation marks means zero or more repetitions. Repeated operators are grouped to the left, specifying operator associativity; term gives multiplication higher operator precedence than addition and subtraction. Parentheses override that grouping. There is no unary minus, variable assignment, function call, or side effect in this language. Evaluation obtains each left operand before its right operand and uses exact integer arithmetic, with no fixed-width overflow.Lexical analysis recognizes
x, *, (, 2, +, 3, ), -, 4. Parsing constructs the concrete abstract syntax tree Sub(Mul(Name(x), Add(Int(2), Int(3))), Int(4)). Parentheses have done their work by making Add a child of Mul; they need not survive as nodes. Constant folding changes this to Sub(Mul(Name(x), Int(5)), Int(4)). It cannot replace Name(x) by a literal value because the input is supplied at execution. The resulting function of the input is .A compiler for our stack machine emits
LOAD x; PUSH 5; MUL; PUSH 4; SUB. LOAD x pushes the current input; PUSH n pushes the integer literal value n. Each binary instruction removes the top item as its right operand, then the next item as its left operand, and pushes the result. The instruction sequence is an intermediate representation that an interpreter can execute; no machine code has been emitted. A compact binary encoding could make it bytecode, but these printed instruction names are only a readable notation.Why does this compilation preserve the result? A structural induction supplies a short proof outline. Translating a literal value or
x appends its value to any initial stack. For a binary abstract syntax tree node, first translating the left child and then the right child appends the two operand values; the matching instruction replaces them by exactly the original operation's result. Previously present stack items remain intact. Constant folding also preserves the result because in the specified integer arithmetic. Together these facts explain agreement for every integer input, rather than merely agreement for one trial. Compiler Created 2026-10-13 Updated 2026-10-14
A compiler translates a program from one representation to another while aiming to preserve its programming language semantics. Its input might be source code or an intermediate representation; its output might be another programming language, bytecode, an intermediate representation, or machine code. Producing machine code is therefore one possible destination, rather than the definition of compilation. For example, the LLVM 20.1.0 tutorial translates an abstract syntax tree into an intermediate representation before introducing execution.[ref]
Compilation can use an abstract syntax tree for checking and transformations such as constant folding before producing machine code. These are useful possibilities, not a compulsory sequence of separate stages for every compiler. The central distinction is between translating a program and executing its operations: a compiler can translate
x*(2+3)-4 without knowing the input value of x, whereas an interpreter needs that value to produce this program expression's result.Different representations expose different questions. Source code preserves what a programmer wrote; an abstract syntax tree exposes grouping; a type system checks permitted combinations; a stack machine makes operand movement explicit. Retaining abstract syntax tree source locations across compilation helps an error message identify the original construct even after constant folding has changed its shape. A malformed
x*(2+)-4 is a programming language syntax error; an unavailable x in the valid example is instead a missing input. Locating the failing rule is more helpful than treating both as an unexplained execution failure. Constant folding 2026-10-13
Constant folding replaces a program expression whose value is known during translation by a literal value. For
x=2+3*4, first replace the multiplication subtree by Constant(value=12), then replace the addition subtree by Constant(value=14). The variable assignment and its Store target survive: the result still assigns to x. This illustrates why a bottom-up abstract syntax tree traversal is convenient: replacing one child can make its parent eligible for the next replacement.
Here is a deliberately small Python transformer. Calling
generic_visit first transforms the children; returning a node replaces the visited node. The location helpers retain or supply the metadata expected for compilation. [ref]ast — Abstract syntax trees, Python 3.14 documentation. NodeTransformer, generic_visit, copy_location and fix_missing_locations
class FoldIntegers(ast.NodeTransformer):
def visit_BinOp(self, node):
self.generic_visit(node)
if (isinstance(node.left, ast.Constant)
and isinstance(node.right, ast.Constant)
and type(node.left.value) is int
and type(node.right.value) is int
and type(node.op) in OPS):
value = OPS[type(node.op)](node.left.value, node.right.value)
return ast.copy_location(ast.Constant(value=value), node)
return node
tree = ast.parse("x=2+3*4", optimize=0)
folded = ast.fix_missing_locations(FoldIntegers().visit(tree))
namespace = {}
exec(compile(folded, "<folded example>", "exec"), namespace)
assert namespace["x"] == 14
assert ast.unparse(folded) == "x = 14"This transformer folds literal integer operands only. It leaves
a+3*4 as a+12, without inventing a value for the program identifier a. It leaves calls intact: replacing 0*f() by 0 could discard a side effect or a failure. Nor does it reassociate floating-point arithmetic, where changing parentheses can change rounding. For the supported integer arithmetic, a short structural induction explains correctness: a retained literal value has the same value; at each folded binary node, the already-correct child values are combined by exactly the original operation in the original left/right order. This claim concerns the supported fragment's values, not unrestricted equivalence of arbitrary Python programs. Interpreter arithmetic trace Created 2026-10-14 Updated 2026-10-31
Use the compilation arithmetic example with input . An abstract syntax tree interpreter first reads
x, obtains , forms , and finally computes . Interpreting the folded abstract syntax tree skips the addition but gives the same result. The compiled stack machine instructions instead produce the following trace; the top of the stack is written on the right:instruction stack after instruction
initial []
LOAD x [7]
PUSH 5 [7, 5]
MUL [35]
PUSH 4 [35, 4]
SUB [31]
Execution of
. Details. x*(2+3)-4 at : the original abstract syntax tree and the folded stack machine instructions both give 
The order in
SUB is essential: reversing its two popped operands would give . The same stored instruction sequence works for input , yielding , without repeating parsing or constant folding. An abstract syntax tree interpreter can likewise reuse its already-parsed tree. Reusing a representation is therefore useful to both approaches; it does not itself distinguish compilation from interpretation.The pleasing part is that a nested rooted tree and a flat instruction sequence express the same computation. The structural induction in the compilation arithmetic example connects them by a precise stack property. This tiny language always terminates and has no side effects; richer programming language semantics require a correctness argument that also accounts for failures, externally visible actions, and possible nontermination.
Interpreter (computing) Created 2026-10-13 Updated 2026-10-14
An interpreter executes a program's operations according to its programming language semantics. It can recursively evaluate an abstract syntax tree, or follow an instruction sequence using an execution state such as a stack and an instruction pointer. It need not repeatedly read source code characters, and it need not use an abstract syntax tree at all.
Compilation and interpretation can coexist. In CPython, Python source code is compiled into bytecode for execution by an interpreter; its bytecode is not promised to remain stable between releases.[ref]
Glossary, Python 3.14 documentation. Python 3.14 documentation; Python 3.14 glossary: bytecode and virtual machine entries; compilation, execution and release-specific bytecodes
The Python 3.14 compile function accepts text or an abstract syntax tree and can produce a code object, which eval or exec can execute.[ref]Built-in Functions, Python 3.14 documentation. Python 3.14 documentation; Python 3.14 Built-in Functions: compile, accepted source forms, code objects and execution by eval or exec
These operations make translation and execution separately accessible without requiring them to live in different applications.Just-in-time compilation gives another combination: an interactive implementation can translate a submitted program expression into machine code and then execute it immediately. The LLVM 20.1.0 tutorial demonstrates this by adding an intermediate representation module to its just-in-time compilation facility, looking up the generated function, and calling it.[ref]
4. Kaleidoscope: Adding JIT and Optimizer Support. LLVM 20.1.0 documentation; Implementing a language with LLVM, chapter 4, section 4.4: HandleTopLevelExpression, addModule, lookup and calling the generated native function
Thus calling a programming language permanently "compiled" or "interpreted" hides an implementation choice: ask which representation is translated, which is executed, and when. Just-in-time compilation 2026-10-14
Compilation performed during execution, often producing machine code for subsequent execution.
LLVM 2026-10-14
An infrastructure project providing reusable tools for compilation and intermediate representations.
Past exam of the computer science course of the University of Oxford 2015 Compilers 1 a Solution 2026-10-31
Use an abstract syntax tree with the following constructors. Here
Expr denotes the separate abstract syntax tree type for a program expression, Name identifies a variable assignment target, and the square brackets denote an ordered list.Stmt = Assign(Name, Expr)
| Seq(Stmt, Stmt)
| Case(Expr, [(Expr, Stmt)])The list in
Case must be nonempty. Its first field is the controlling program expression; each pair contains a label program expression and the corresponding body. Keep the pairs in source order and keep repeated labels: this is an ordered search, with the first successful equality test choosing the body. A label is an abstract syntax tree for a program expression, not a previously evaluated integer or a key in a map data structure. Evaluating or reordering labels during compilation would change the specified programming language semantics.Seq(s,t) executes s before t. The delimiters begin and end need no surviving constructor: the parser uses them to determine the abstract syntax tree's grouping and then returns the enclosed tree. There are no declarations in these blocks that would require a separate binding environment. A list of statements could replace binary Seq; below we choose right-associated binary trees so that the semantic actions are precise.The essential representation is an ordered, nonempty list of expression/body pairs, together with assignment and sequencing nodes. In constructor notation,
Stack invariant 2026-10-31
A property of the evaluation stack at a specified program point. For expression compilation, a useful contract is that generated code transforms any incoming stack into , leaving all pre-existing values unchanged. For a statement, a useful contract is preservation of .
Temporary variable 2026-10-31
A fresh internal name introduced during compilation to hold an intermediate result. Its lifetime and uses can be exposed to instruction selection and allocation of processor registers; it need not correspond to a variable named in the source.