M.V. Hutz
528956b033
Add a new interpreter option (-i debruijn) that uses De Bruijn indices for variable representation, eliminating the need for variable renaming during substitution. - Add -i flag to select interpreter (lambda or debruijn) - Create debruijn package with Expression types (Variable with index, Abstraction without parameter, Application) - Implement shift and substitute operations for De Bruijn indices - Add conversion functions between lambda and De Bruijn representations - Update CLI to support switching between interpreters - Add De Bruijn tests to verify all samples pass Closes #26
35 lines
989 B
Go
35 lines
989 B
Go
package debruijn
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// Substitute replaces the variable at the given index with the replacement expression.
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// The replacement is shifted appropriately as we descend into nested abstractions.
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func Substitute(expr Expression, index int, replacement Expression) Expression {
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switch e := expr.(type) {
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case *Variable:
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if e.index == index {
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return replacement
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}
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return e
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case *Abstraction:
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// When entering an abstraction, increment the target index and shift the
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// replacement to account for the new binding context.
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shiftedReplacement := Shift(replacement, 1, 0)
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newBody := Substitute(e.body, index+1, shiftedReplacement)
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if newBody == e.body {
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return e
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}
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return NewAbstraction(newBody)
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case *Application:
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newAbs := Substitute(e.abstraction, index, replacement)
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newArg := Substitute(e.argument, index, replacement)
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if newAbs == e.abstraction && newArg == e.argument {
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return e
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}
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return NewApplication(newAbs, newArg)
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default:
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return expr
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}
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}
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