MELT / Silver / Concepts / Reflection & Term Rewriting

Reflection & Term Rewriting


Some operations that we would like to perform on trees in Silver are not possible to express nicely with attributes, or doing so requires a large amount of boilerplate - for example, serializing and de-serializing terms, or performing template-style substitutions. The reflection library provides a solution to this, by providing an alternative uniform representation of terms with the AST nonterminal, defined as

nonterminal AST;
abstract production nonterminalAST
top::AST ::= prodName::String children::ASTs annotations::NamedASTs

abstract production terminalAST
top::AST ::= terminalName::String lexeme::String location::Location

abstract production listAST
top::AST ::= vals::ASTs

abstract production stringAST
top::AST ::= s::String

abstract production integerAST
top::AST ::= i::Integer

abstract production floatAST
top::AST ::= f::Float

abstract production booleanAST
top::AST ::= b::Boolean

abstract production anyAST
top::AST ::= x::a

nonterminal ASTs;
abstract production consAST
top::ASTs ::= h::AST t::ASTs

abstract production nilAST
top::ASTs ::=

nonterminal NamedASTs;
abstract production consNamedAST
top::NamedASTs ::= h::NamedAST t::NamedASTs

abstract production nilNamedAST
top::NamedASTs ::=

nonterminal NamedAST;
abstract production namedAST
top::NamedAST ::= n::String v::AST

Two functions allow arbitrary values to be transformed to and from the AST representation:

  • reflect :: (AST ::= a) converts an arbitrary value to an AST; values that have no such representation (e.g. functions and Decorated references) are wrapped in anyAST.
  • reify :: (Either<String a> ::= AST) converts an AST back to either an ordinary value or an error message if the AST is not well-sorted.

Users may define new attributes on the AST type, rather than on all concerned nonterminals. For example a generalized pretty-printing operation is defined (see silver:langutil:reflect) as

attribute pp occurs on AST;
aspect production nonterminalAST
top::AST ::= prodName::String children::ASTs annotations::NamedASTs
{ top.pp = cat(text(prodName),
    parens(ppImplode(pp", ", children.pps ++ annotations.pps)));
aspect production listAST
top::AST ::= vals::ASTs
{ top.pp = brackets(ppImplode(pp", ", vals.pps)); }

aspect production stringAST
top::AST ::= s::String
{ top.pp = pp"\"${text(escapeString(s))}\""; }

aspect production integerAST
top::AST ::= i::Integer
{ top.pp = text(toString(i)); }

aspect production floatAST
top::AST ::= f::Float
{ top.pp = text(toString(f)); }

attribute pps occurs on ASTs;
aspect production consAST
top::ASTs ::= h::AST t::ASTs
{ top.pps = h.pp :: t.pps; }

aspect production nilAST
top::ASTs ::=
{ top.pps = []; }


Other applications of rewriting are

Term rewriting

Another significant use of reflection is in implementing a Stratego-style strategic term rewriting library/language extension that works on undecorated terms. Note that Silver also supports a mechanism for rewriting on decorated trees (strategy attributes) that is generally preferred, as it is more efficient and better integrated with other features such as attributes and forwarding; however there are still some situations in which term rewriting is preferred, such as in implementing template instantiation.

Core library

Strategies are represented by the Strategy type, and are built by a number of combinators. The main ones are as follows:

  • id :: (Strategy ::= )
  • fail :: (Strategy ::= )
  • sequence :: (Strategy ::= Strategy Strategy)
  • choice :: (Strategy ::= Strategy Strategy)
  • all :: (Strategy ::= Strategy)
  • some :: (Strategy ::= Strategy)
  • one :: (Strategy ::= Strategy)
  • traveral :: (Strategy ::= prodName::String childStrategies::[Strategy] annoStrategies::[Pair<String Strategy>]) (congruence traversal)
  • rewriteRule :: (Strategy ::= pattern::ASTPattern result::ASTExpr)

Rewrite rule strategies are constructed by the rewriteRule constructor, parameterized by an ASTPattern and an ASTExpr - run-time representations of patterns and expressions. For example, an strategy defining an innermost optimization of x + 0 -> x could be defined as

global elimPlusZero::Strategy =
      -- addExpr(a, intExpr(0)) -> a

Extension features

The above system is implemented purely as a Silver library using the reflection mechanism; however defining strategies in this way is highly inconvenient. For this reason a corresponding collection of language extensions to Silver provide new syntax that makes using the library less painful.

One such extension provides new infix operators <* and <+ for sequence and left-choice, respectively. These are used in implementing a number of generally-useful utility strategies in the library; some of the more commonly used ones include

abstract production try
top::Strategy ::= s::Strategy
{ forwards to s <+ id(); }

abstract production repeat
top::Strategy ::= s::Strategy
{ forwards to try(s <* repeat(s)); }

abstract production bottomUp
top::Strategy ::= s::Strategy
{ forwards to all(bottomUp(s)) <* s; }

abstract production allTopDown
top::Strategy ::= s::Strategy
{ forwards to s <+ all(allTopDown(s)); }

abstract production innermost
top::Strategy ::= s::Strategy
{ forwards to bottomUp(try(s <* innermost(s))); }
  • try applies its operand strategy, and always succeeds.
  • repeat applies its operand repeatedly until failure, and succeeds with the last successful result.
  • bottomUp applies its operand to each subterm starting from the leaf terms, and fails if any applications fail.
  • allTopDown applies its operand to each subterm starting from the root term, stopping in a subterm when its argument succeeds. This is roughly analagous to a functor transformation.
  • innermost repeatedly applies its operand to the innermost, leftmost expression in a term, only moving up the tree once all sub-terms are fully reduced.

A new expression rewriteWith(strategy, term) provided by the extension applies a strategy to a term.

New syntax is provided for defining rewrite rules, based on the existing syntax for pattern matching. Using this the x + 0 -> x strategy could be specified as

global elimPlusZero::Strategy = bottomUp(try(
  rule on Expr of
  | addExpr(a, intExpr(0)) -> a

Note that rewrite rules defined using this syntax are statically to be type-preserving, meaning that no run-time errors will result from performing an invalid rewrite.

More convenient syntax for congruence traversals is also provided: traverse addExpr(id(), simplify) succeeds only when applied to the addExpr production, and applies the identity strategy to the left operand, and the simplify strategy to the right operand. The traverse syntax also checks that the production is applied to the proper number of arguments.

An example implementation of the lambda calculus using term rewriting can be found here.

Further reading

More information on reflection, term rewriting, and its applications in Silver can be found in our COLA paper Reflection of Terms in Attribute Grammars: Design and Applications.