Difficulty of Programming

• Subroutines may not be well documented

• User must understand documentation

• Many subroutines: takes time to become familiar with the collection

• User may rewrite subroutine rather than reusing it

• User might make mistakes, e.g. wrong type of units of argument

Constructive proof: given a theorem ∀ x ∃ y P(x,y) , prove it by constructing a y that satisfies the theorem.

During program synthesis, witnesses are constructed for existential terms. The witnesses correspond to subroutines in the SPICE library ( concrete terms).

specification → theorem → proof → program