I'm looking for an introduction (book or lecture notes) to compositional semantics based on e-t type theory that would be suitable for first-year level linguistics presupposing knowledge of elementary set theory, propositional and predicate logic. I'm thinking of something that would explain the idea of type-theoretical composition of simple subject-verb-object sentences and a small subset of more advanced constructions such as adjectival modification, negation and coordination, or quantified noun phrases in object position, for a first introduction in five or so sessions.
Jacobson (2014) "Compositional Semantics" explains some ideas but doesn't really show concrete derivations.
Heim & Kratzer (1998) "Semantics in Generative Grammar" and Kearns (2011) "Semantics" use pretty much the style of presentation I'm looking for (typed and lambda-ized predicate logic expressions arranged in a tree structure), but I'm not a big fan of using formal notation without ever actually defining it; and these books put a lot of detail on the precise mapping between semantics and a particular syntactic theory that makes for as somewhat large rule system.
On the other hand, Gamut (1991) "Intensional Logic and Logical Grammar" and Cann (1993) "Formal Semantics" are good at explaining the formal methods, but perhaps a little too technical and long for a first introduction.
Is there any good middle ground that explains the basic ideas backed up by rigorous definitions, but without going into too much mathematical or syntactic detail?