Functional programming and type systems ( MPRI 2 - 4 ) Mid - term exam 2010 - 2011

A reduction relation m −→ is defined by the following reduction rules. This relation computes the simple substitution φ that can be applied to a pattern to match a particular value, or returns the undefined substitution ⊥ if no such simple substitution exists. {(p1, p2) 7→ (v1, v2)} m −→ {p1 7→ v1} ⊗ {p2 7→ v2} {K (p1, . . . , pn) 7→ K (v1, . . . , vn)} m −→ {p1 7→ v1} ⊗ . . .⊗ {pn 7→ vn} {K (p1, . . . , pn) 7→ K ′ (v1, . . . , vm)} m −→ ⊥ if K 6= K ′ or n 6= m ⊥⊗ S m −→ ⊥ φ⊗⊥ m −→ ⊥ Es[S] m −→ Es[S] if S m −→ S′