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Damas and Milner state the completeness theorem for Algorithm W in a skeletal applicative language with let binding: if a type-scheme is derivable, inference succeeds and computes a principal scheme from which the others are instantiated. The inference rules distinguish outer generic quantification from free variables constrained by the environment. The result resolves the most-general-inference question left open in the1978 Milner paper and yields typeability decidability within this discipline.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
The target is the purely applicative skeletal language, its specified inference system and environment substitutions—not unrestricted higher-rank polymorphism, mutable-reference ML, termination or all program correctness. Detailed proofs are deferred to Damas's thesis and were not reconstructed here. Hindley's combinatory theorem and Milner 1978 soundness remain separate inherited contributions.
Read the original work
- Luis Damas and Robin Milner, Principal type-schemes for functional programs, POPL'82, 207–212 (1982), DOI10.1145/582153.582176
- ACM Digital Library: Principal type-schemes for functional programs
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People and systems
Luis Damas; Robin Milner
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English catalogue narrative
Damas and Milner: principal type-schemes for functional programs
Damas and Milner state the completeness theorem for Algorithm W in a skeletal applicative language with let binding: if a type-scheme is derivable, inference succeeds and computes a principal scheme from which the others are instantiated.
The inference rules distinguish outer generic quantification from free variables constrained by the environment. The result resolves the most-general-inference question left open in the1978 Milner paper and yields typeability decidability within this discipline.
Scientific scope
The target is the purely applicative skeletal language, its specified inference system and environment substitutions—not unrestricted higher-rank polymorphism, mutable-reference ML, termination or all program correctness. Detailed proofs are deferred to Damas's thesis and were not reconstructed here. Hindley's combinatory theorem and Milner 1978 soundness remain separate inherited contributions.
People and systems
Luis Damas; Robin Milner