# Reference Request – Typed First Order Book

Computer scientists interested in untyped first-order logic are numerous, such as Melvin Fitting's "First-order Logic and Automated Demonstration of Theorems" or John Harrison's "Manual of Practical Logic and Automatic Reasoning."

However, I struggled to find a solid reference that deals specifically with first-order typewritten (or "sorted out") logic.

Although many knowledge of untyped first-order logic is correctly transferred to a typed parameter, there are some interesting questions specific to the first order typed logic for which rigorous processing, possibly with implementation examples, is required. # 39; interests. Type checking is an obvious example, but it also makes it possible to determine whether, in a typed parameter, it is useful to distinguish formulas and terms syntactically, or whether the formulas should only be treated as type terms. `bool`and the consequences of such decisions on the calculation of normal forms. I am sure there are also other interesting issues.

Are there any books that you can recommend that have a purpose, or even just a long enough chapter, dealing specifically with the typical first order logic?